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Sample records for fractionation inplants final

  1. IAEA experience with authentication of in-plant NDA instrumentation

    International Nuclear Information System (INIS)

    Augustson, R.H.; Dermendjiev, E.

    1983-01-01

    The paper discusses IAEA experience with permanently installed measuring equipment, i.e. in-plant NDA instrumentation, which often has advantages over portable equipment, such as improved accuracy, automated sample handling and data collection, and capacity for higher throughput. In some cases, in-plant equipment is the only means of making a field measurement. However, the use of in-plant equipment requires an additional set of inspector procedures to ensure that the instrument is working correctly and has not been tampered with. This process of verifying instrument performance is called authentication. General guidelines for approaches to authentication have been studied and formulated by an IAEA Advisory Group Meeting held in November 1981. Procedures for specific instruments have been developed in some cases with the help of national support programmes. The field application of authentication is accomplished by incorporating specific actions into inspection procedures. Results are written down as part of the working papers and included in the final inspection report. For quantitative checks such as measurement of a working standard the results are sent along with the inspection measurements to the Agency for inclusion in the safeguards data base. The in-plant equipment may be owned by the facility, a State, a safeguards organization or the Agency. In each case, the use of the in-plant equipment will necessitate additional interactions between facility operator and inspector, in order to judge the impact on plant operation, and understand what is being measured and what can go wrong. The paper discusses the IAEA's experience gained in the field application of authentication procedures for instrument systems such as weighing and volume measuring devices, rod scanners, neutron activation systems and K-edge densitometers

  2. Authentication of nuclear-material assays made with in-plant instruments

    International Nuclear Information System (INIS)

    Hatcher, C.R.; Hsue, S.T.; Russo, P.A.

    1982-01-01

    This paper develops a general approach for International Atomic Energy Agency (IAEA) authentication of nuclear material assays made with in-plant instruments under facility operator control. The IAEA is evaluating the use of in-plant instruments as a part of international safeguards at large bulk-handling facilities, such as reprocessing plants, fuel fabrication plants, and enrichment plants. One of the major technical problems associated with IAEA use of data from in-plant instruments is the need to show that there has been no tampering with the measurements. Two fundamentally different methods are discussed that can be used by IAEA inspectors to independently verify (or authenticate) measurements made with in-plant instruments. Method 1, called external authentication, uses a protected IAEA measurement technique to compare in-plant instrument results with IAEA results. Method 2, called internal authentication, uses protected IAEA standards, known physical constants, and special test procedures to determine the performance characteristics of the in-plant instrument. The importance of measurement control programs to detect normally expected instrument failures and procedural errors is also addressed. The paper concludes with a brief discussion of factors that should be considered by the designers of new in-plant instruments in order to facilitate IAEA authentication procedures

  3. Standard guide for in-plant performance evaluation of automatic pedestrian SNM monitors

    CERN Document Server

    American Society for Testing and Materials. Philadelphia

    1997-01-01

    1.1 This guide is affiliated with Guide C1112 on special nuclear material (SNM) monitors, Guide C1169 on laboratory performance evaluation, and Guide C1189 on calibrating pedestrian SNM monitors. This guide to in-plant performance evaluation is a comparatively rapid way to verify whether a pedestrian SNM monitor performs as expected for detecting SNM or SNM-like test sources. 1.1.1 In-plant performance evaluation should not be confused with the simple daily functional test recommended in Guide C1112. In-plant performance evaluation takes place less often than daily tests, usually at intervals ranging from weekly to once every three months. In-plant evaluations are also more extensive than daily tests and may examine both a monitor's nuisance alarm record and its detection sensitivity for a particular SNM or alternative test source. 1.1.2 In-plant performance evaluation also should not be confused with laboratory performance evaluation. In-plant evaluation is comparatively rapid, takes place in the monitor...

  4. Improvements to a uranium solidification process by in-plant testing

    International Nuclear Information System (INIS)

    Rindfleisch, J.A.

    1984-01-01

    When a process is having operational or equipment problems, often there is not enough time or money available for an extensive pilot plant program. This is when in-plant testing becomes imperative. One such process at the Idaho Chemical Processing Plant (ICPP) to undergo such an in-plant testing program was the uranium product solidification (denitrator) system. The testing program took approximately six months of in-plant testing that would have required at least two years of pilot plant preparation and operation to obtain the same information. This paper describes the results of the testing program, and the equipment and procedural changes

  5. In-plant considerations for optimal offsite response to reactor accidents

    International Nuclear Information System (INIS)

    Burke, R.P.; Heising, C.D.; Aldrich, D.C.

    1982-11-01

    Offsite response decision-making methods based on in-plant conditions are developed for use during severe reactor-accident situations. Dose projections are used to eliminate all LWR plant systems except the reactor core and the spent-fuel storage pool from consideration for immediate offsite emergency response during accident situations. A simple plant information-management scheme is developed for use in offsite response decision-making. Detailed consequence calculations performed with the CRAC2 model are used to determine the appropriate timing of offsite-response implementation for a range of PWR accidents involving the reactor core. In-plant decision criteria for offsite-response implementation are defined. The definition of decision criteria is based on consideration of core-accident physical processes, in-plant accident monitoring information, and results of consequence calculations performed to determine the effectiveness of various public-protective measures. The benefits and negative aspects of the proposed response-implementation criteria are detailed

  6. In-plant logistics optimalization

    OpenAIRE

    Maroušek, Jan

    2008-01-01

    In a theoretical part of this work there is introduced a general view on logistics and its development, than a view on creating value for customer, basics of lean production, lean thinking and following methods as Six Sigma and Value Stream Mapping. At the end of the theoretical part there is mentioned outsourcing of logistics services and view on relationship between logistics provider and a client. In a practical part there is introduced a project of in-plant logistics optimalization in a f...

  7. Standard guide to In-Plant performance evaluation of Hand-Held SNM monitors

    CERN Document Server

    American Society for Testing and Materials. Philadelphia

    1999-01-01

    1.1 This guide is one of a series on the application and evaluation of special nuclear material (SNM) monitors. Other guides in the series are listed in Section 2, and the relationship of in-plant performance evaluation to other procedures described in the series is illustrated in Fig. 1. Hand-held SNM monitors are described in of Guide C1112, and performance criteria illustrating their capabilities can be found in Appendix X1. 1.2 The purpose of this guide to in-plant performance evaluation is to provide a comparatively rapid procedure to verify that a hand-held SNM monitor performs as expected for detecting SNM or alternative test sources or to disclose the need for repair. The procedure can be used as a routine operational evaluation or it can be used to verify performance after a monitor is calibrated. 1.3 In-plant performance evaluations are more comprehensive than daily functional tests. They take place less often, at intervals ranging from weekly to once every three months, and derive their result fr...

  8. Guidelines for confirmatory inplant tests of safety-relief valve discharges for BWR plants

    International Nuclear Information System (INIS)

    Su, T.M.

    1981-05-01

    Inplant tests of safety/relief valve (SRV) discharges may be required to confirm generically established specifications for SRV loads and the maximum suppression pool temperature, and to evaluate possible effects of plant-unique parameters. These tests are required in those plants which have features that differ substantially from those previously tested. Guidelines for formulating appropriate test matrices, establishing test procedures, selecting necessary instrumentation, and reporting the test results are provided in this report. Guidelines to determine if inplant tests are required on the basis of the plant unique parameters are also included in the report

  9. In-plant application of industry experience to enhance human reliability

    International Nuclear Information System (INIS)

    Hannaman, G.W.; Singh, A.

    1993-01-01

    This paper describes the way that modern data-base computer tools can enhance the ability to collect, organize, evaluate, and use industry experience. By combining the computer tools with knowledge from human reliability assessment tools, data, and frameworks, the data base can become a tool for collecting and assessing the lessons learned from past events. By integrating the data-base system with plant risk models, engineers can focus on those activities that can enhance over-all system reliability. The evaluation helps identify technology and tools to reduce human errors during operations and maintenance. Learning from both in-plant and industry experience can help enhance safety and reduce the cost of plant operations. Utility engineers currently assess events that occur in nuclear plants throughout the world for in-plant applicability. Established computer information networks, documents, bulletins, and other information sources provide a large number of event descriptions to help individual plants benefit from this industry experience. The activities for coordinating reviews of event descriptions from other plants for in-plant applications require substantial engineering time to collect, organize, evaluate, and apply. Data-base tools can help engineers efficiently handle and sort the data so that they can concentrate on understanding the importance of the event, developing cost-effective interventions, and communicating implementation plans for plant improvement. An Electric Power Research Institute human reliability project has developed a classification system with modern data-base software to help engineers efficiently process, assess, and apply information contained in the events to enhance plant operation. Plant-specific classification of industry experience provides a practical method for efficiently taking into account industry when planning maintenance activities and reviewing plant safety

  10. Industrial Electricity. In-Plant Distribution. Vocational Trade and Industrial Education.

    Science.gov (United States)

    Teague, Cash; Pewewardy, Garner

    This curriculum guide, part of a series of industrial electricity curriculum guides, consists of materials for use in teaching a course on the in-plant distribution of electricity. Discussed in the introductory lessons are the National Electrical Code, power equipment, and blueprint reading. The next section, a series of units on branch-circuit…

  11. Evaluation of seismic margins for an in-plant piping system

    International Nuclear Information System (INIS)

    Kot, C.A.; Srinivasan, M.G.; Hsieh, B.J.

    1991-01-01

    Earthquake experience as well as experiments indicate that, in general, piping systems are quite rugged in resisting seismic loadings. Therefore there is a basis to hold that the seismic margin against pipe failure is very high for systems designed according to current practice. However, there is very little data, either from tests or from earthquake experience, on the actual margin or excess capacity (against failure from seismic loading) of in-plant piping systems. Design of nuclear power plant piping systems in the US is governed by the criteria given in the ASME Boiler and Pressure Vessel (B ampersand PV) Code, which assure that pipe stresses are within specified allowable limits. Generally linear elastic analytical methods are used to determine the stresses in the pipe and forces in pipe supports. The objective of this study is to verify that piping designed according to current practice does indeed have a large margin against failure and to quantify the excess capacity for piping and dynamic pipe supports on the basis of data obtained in a series of high-level seismic experiments (designated SHAM) on an in-plant piping system at the HDR (Heissdampfreaktor) Test Facility in Germany. Note that in the present context, seismic margin refers to the deterministic excess capacities of piping or supports compared to their design capacities. The excess seismic capacities or margins of a prototypical in-plant piping system and its components are evaluated by comparing measured inputs and responses from high-level simulated seismic experiments with design loads and allowables. Large excess capacities are clearly demonstrated against pipe and overall system failure with the lower bound being about four. For snubbers the lower bound margin is estimated at two and for rigid strut supports at five. 4 refs., 2 figs., 2 tabs

  12. In-plant reliability data base for nuclear power plant components: data collection and methodology report

    International Nuclear Information System (INIS)

    Drago, J.P.; Borkowski, R.J.; Pike, D.H.; Goldberg, F.F.

    1982-07-01

    The development of a component reliability data for use in nuclear power plant probabilistic risk assessments and reliabiilty studies is presented in this report. The sources of the data are the in-plant maintenance work request records from a sample of nuclear power plants. This data base is called the In-Plant Reliability Data (IPRD) system. Features of the IPRD system are compared with other data sources such as the Licensee Event Report system, the Nuclear Plant Reliability Data system, and IEEE Standard 500. Generic descriptions of nuclear power plant systems formulated for IPRD are given

  13. Comparison of the corrosion potential for stainless steel measured in-plant and in laboratory during BWR normal water chemistry conditions

    International Nuclear Information System (INIS)

    Molander, A.; Pein, K.; Tarkpea, P.; Takagi, Junichi; Karlberg, G.; Gott, K.

    1998-01-01

    To obtain reliable crack growth rate date for stainless steel in BWR environments careful laboratory simulation of the environmental conditions is necessary. In the plant the BWR normal water chemistry environment contains hydrogen peroxide, oxygen and hydrogen. However, in crack growth rate experiments in laboratories, the environment is normally simulated by adding 200 ppb oxygen to the high temperature water. Thus, as hydrogen peroxide is a more powerful oxidant than oxygen, it is to be expected that a lower corrosion potential will be measured in the laboratory than in the plant. To resolve this issue this work has been performed. In-plant and laboratory measurements have often been performed with somewhat different equipment, due to the special requirements concerning in-plant measurements. In this work such differences have been avoided and two identical sets of equipment for electrochemical measurements were built and used for measurements in-plant in a Swedish BWR and in high purity water in the laboratory. The host plant was Barsebaeck 1. Corrosion potential monitoring in-plant was performed under both NWC (Normal Water Chemistry) and HWC (Hydrogen Water Chemistry) conditions. This paper is, however, focused on NWC conditions. This is due to the fact, that the total crack growth obtained during a reactor cycle, can be determined by NWC conditions, even for plants running with HWC due to periodic stops in the hydrogen addition for turbine inspections or failure of the dosage or hydrogen production equipment. Thus, crack growth data for NWC is of great importance both for BWRs operating with HWC and NWC. Measurements in-plant and in the laboratory were performed during additions of oxygen and hydrogen peroxide to the autoclave systems. The corrosion potentials were compared for various conditions in the autoclaves, as well as versus in-plant in-pipe corrosion potentials. (J.P.N.)

  14. Margins for an in-plant piping system under dynamic loading

    International Nuclear Information System (INIS)

    Kot, C.A.; Srinivasan, M.G.; Hsieh, B.J.

    1991-01-01

    The objective of this study is to verify that piping designed according to current practice does indeed have a large margin against failure and to quantify the excess capacity for piping and dynamic pipe supports on the basis of data obtained in a series of high-level seismic experiments (designated SHAM) on an in-plant piping system at the HDR (Heissdampfreaktor) Test Facility in Germany. 4 refs., 6 tabs

  15. Commissioning and maintenance experience of in-plant coal handling system of captive power plant at HWP, Manuguru (Paper No. 5.4)

    International Nuclear Information System (INIS)

    Murugappan, K.; Mohan Rao, A.C.; Sastry, M.S.N.

    1992-01-01

    For achieving a non-stop generation of power for a minimum period of one year can be a reality only if due importance is given to inplant coal handling system. The paper highlights the major commissioning and maintenance problem faced and corrective action taken for inplant coal handling system of the captive power plant at Heavy Water Plant, Manuguru. (author)

  16. Development of in-plant reference material for composition of chinese cabbage with certified selenium content

    Directory of Open Access Journals (Sweden)

    D. A. Chupahin

    2014-01-01

    Full Text Available In-plant reference material for composition of Chinese cabbage with certified selenium content was developed for accuracy control of the results of selenium determination and within-laboratory quality control of analytical work in the analysis of food raw material.

  17. Nondestructive assay technology and in-plant dynamic materials control: ''DYMAC''

    International Nuclear Information System (INIS)

    Keppin, G.R.; Maraman, W.J.

    1975-01-01

    An advanced system of in-plant materials control known as DYMAC, Dynamic Materials Control, is being developed. This major safeguards R and D effort merges state-of-the-art nondestructive assay instrumentation and computer technology, with the clear objective of demonstrating a workable, cost-effective system of stringent, real time control of nuclear materials in a modern plutonium processing facility. Emphasis is placed on developing practical solutions to generic problems of materials measurement and control, so that resulting safeguards techniques and instrumentation will have widespread applicability throughout the nuclear community. (auth)

  18. In-plant testing of membranes to treat electroplating wastewater

    Science.gov (United States)

    Shah, D. B.; Talu, Orhan

    1995-01-01

    This is the final report submitted for the work performed under the NASA Cooperative Agreement NCC3-301 for the project entitled 'In-Plant Testing of Membranes To Treat Electroplating Waste water'. The main objective of the research project was to determine if the crosslinked polyacrylic acid salt films developed by NASA scientists could be used for heavy metal removal from the wastewater generated by the metals-finishing or electroplating industry. A variety of tasks identified in the original proposal were completed. These included: (1) analysis of our industrial partner Aetna Plating's zinc electroplating process and its wastewater treatment needs for zinc removal; (2) design and construction of a laboratory-scale unit to continuously supply and remove the ion exchange films from the zinc wastewater; (3) performance of a series of runs on such a unit to determine its operating characteristics; and (4) design of a prototype unit for use at the industrial site. In addition, there were a number of tasks that had not been identified in the original proposal but were later judged to be necessary for the successful completion of the project. These were: (1) batch equilibrium and kinetic experiments with analysis of the experimental results to accurately determine the equilibrium and kinetic parameters for the ion exchange films; (2 ) simulation studies for proper design of the prototype unit; and (3) preliminary runs to exchange the films from H form to Calcium form.

  19. U.S. DOE’s Energy Treasure Hunt Exchange In-Plant Trainings – DOE Resources, Early Results and Lessons Learned

    Energy Technology Data Exchange (ETDEWEB)

    Nimbalkar, Sachin U. [ORNL; Brockway, Walter F. [ORNL; Lung, Bruce [U.S. Department of Energy (DOE); Thirumaran, Kiran [ORNL; Wenning, Thomas J. [ORNL

    2017-06-01

    The primary objective of the Department of Energy’s (DOE) Energy Treasure Hunt In-Plant Training (INPLT) is to train Better Plants partner employees to lead and conduct future energy efficiency Treasure Hunts within their facilities without DOE assistance. By taking a “learning-by-doing” approach, this INPLT, like other DOE INPLT trainings, has the added benefit of uncovering real energy and cost-saving opportunities. This INPLT leverages DOE and Better Plants technical staff, resources and tools and the EPA “Energy Treasure Hunt Guide: Simple Steps to Finding Energy Savings” process. While Treasure Hunts are a relatively well-known approach to identifying energy-savings in manufacturing plants, DOE is adding several additional elements in its Treasure Hunt Exchanges. The first element is technical assistance and methodology. DOE provides high-quality technical resources, such as energy efficiency calculators, fact sheets, source books etc., to facilitate the Treasure Hunt process and teaches four fundamentals: 1) how to profile equipment, 2) how to collect data, and 3), data & ROI calculation methodologies. Another element is the “train the trainer” approach wherein the training facilitator will train at least one partner employee to facilitate future treasure hunts. Another element is that DOE provides energy diagnostic equipment and teaches the participants how to use them. Finally, DOE also offers partners the opportunity to exchange teams of employees either within a partners’ enterprise or with other partners to conduct the treasure hunt in each other’s facilities. This exchange of teams is important because each team can bring different insights and uncover energy-saving opportunities that would otherwise be missed. This paper will discuss DOE methodology and the early results and lessons learned from DOE’S Energy Treasure Hunt In-Plant Trainings at Better Plants Partner facilities.

  20. Example of an in-plant near-real-time accountancy/process control system

    International Nuclear Information System (INIS)

    Anon.

    1981-01-01

    This session describes an existing computerized in-plant near-real-time accounting and process monitoring system at the Allied-General Nuclear Services (AGNS) Barnwell Nuclear Fuel Plant (BNFP). Details of the system performance, objectives, hardware, plant instrumentation, and system functions are presented. Examples of actual programs for accounting and monitoring are described and system benefits will be discussed. The purpose of this session is to enable participants to: (1) identify the major computer hardware components of functional near-real-time accounting systems; (2) identify the types of process instrumentation necessary to perform near-real-time accounting; (3) describe the major nuclear material control and accounting functions of the AGNS computer system; and (4) assess the benefits to safeguards and plant operations of a computerized near-real-time accounting system

  1. In-Plant Fission Product Behavior in SGTR Accident with Long-Term SBO

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Tae Woon; Han, Seok Jung; Ahn, Kwang Il [KAERI, Daejeon (Korea, Republic of)

    2015-05-15

    , secondary cooling and safety injection strategy of RCS. Particularly, the isolation failure provides release path of radiological source term to the environment. With the given scenarios, in-plant fission product behaviors are estimated by using MELCOR code version 1.8.6. It is necessary to study a more detailed SGTR considering its importance in the consequential effects, but there are a few of knowledge bases of radiological source term behaviors during SGTR. SGTR scenario for Surry plant treated in SOARCA project presented much reduced release amounts of source term than previous accident source term study results (TID-14844, NUREG-1465, NUREG-0956, etc.). The release of major radioactive materials (Iodine and Cesium) were estimated as about 80% of Iodine and about 21% of Cesium of total core inventories release to environment in this study. The reason of Iodine release fraction to environment (80%) is much greater than Cesium release fraction to environment (21%) is that 67% of Cesium retained in RPV while only 1.4% of Iodine retained in RPV.

  2. Critical review of gamma spectrometry detection approaches for in-plant surface deposition monitoring

    Energy Technology Data Exchange (ETDEWEB)

    Gregorich, Carola [Nuclear Fuels and Chemistry at the Electric Power Research Institute, Palo Alto, CA 94304, (United States)

    2015-07-01

    Surface deposition of activated corrosion product on oxide layers of light-water reactor primary system components is the primary source for ex-core radiation fields and personnel radiation exposure. Understanding the deposition mechanism and what factors influence the deposition and release behaviors are crucial for developing effective radiation field reduction measures. One of the available tools to assess the surface deposition is in-plant gamma spectrometry, which has been performed for several decades using either sodium iodide (NaI) or high-purity germanium (HPGe) detectors. Lately, the much more mobile cadmium-zinc-telluride (CZT) detectors are increasingly employed by stations because of their ease in use and handling. However, all of these gamma detectors face the same challenges; namely large-geometry samples of inconsistent sample compositions and sometimes gaps in the information necessary to establish proper efficiency calibrations. This paper reviews current measurements and efficiency calibration approaches taken in the industry. The validity of the measurement results and the feasibility of the data's use in understanding source term behavior is examined. Suggestions are made for the development of a more robust deposit characterization and radiation field monitoring program. (authors)

  3. The responsibilities of the in-plant environmental protection officer under civil law and under criminal law

    International Nuclear Information System (INIS)

    Salje, P.

    1993-01-01

    The scope of responsibilities of the in-plant environmental protection officer covers a wide range of tasks: Water protection, waste management, control of emissions for air pollution abatement, emergency preparedness, radiological protection. What are the consequences for the EP officer in case of neglect? This is the topic of the contribution, discussed from the viewpoint of criminal law and private law. The criminal liability of the EP officer results from the EP officer committing an offence either by wilful act or by neglect, it, in the latter case, the officer is in a warranty position. Under private law, the EP officer is subject to third party liability within the framework defined by Paragraph 823 BGB. There is no possibility for him to claim restriction of liability refering to the enhanced risks involved in his job. Hence a sound professional indemnity insurance is recommendable. (orig.) [de

  4. Fractional Vector Calculus and Fractional Special Function

    OpenAIRE

    Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao

    2010-01-01

    Fractional vector calculus is discussed in the spherical coordinate framework. A variation of the Legendre equation and fractional Bessel equation are solved by series expansion and numerically. Finally, we generalize the hypergeometric functions.

  5. Numerical Identification of Multiparameters in the Space Fractional Advection Dispersion Equation by Final Observations

    Directory of Open Access Journals (Sweden)

    Dali Zhang

    2012-01-01

    Full Text Available This paper deals with an inverse problem for identifying multiparameters in 1D space fractional advection dispersion equation (FADE on a finite domain with final observations. The parameters to be identified are the fractional order, the diffusion coefficient, and the average velocity in the FADE. The forward problem is solved by a finite difference scheme, and then an optimal perturbation regularization algorithm is introduced to determine the three parameters simultaneously. Numerical inversions are performed both with the accurate data and noisy data, and several factors having influences on realization of the algorithm are discussed. The inversion solutions are in good approximations to the exact solutions demonstrating the efficiency of the proposed algorithm.

  6. Measurement of Branching Fractions for Exclusive B Decays to Charmonium Final States

    Energy Technology Data Exchange (ETDEWEB)

    Varnes, Erich

    2002-05-13

    We report branching fraction measurements for exclusive decays of charged and neutral B mesons into two-body final states containing a charmonium meson. We use a sample of 22.72 {+-} 0.36 million B{bar B} events collected between October 1999 and October 2000 with the BABAR detector at the PEP-II storage rings at the Stanford Linear Accelerator Center. The charmonium mesons considered here are J/{psi}, {psi}(2S), {chi}{sub c1}, and the light meson in the decay is either a K, K*, or {pi}{sup 0}.

  7. Request for approval, vented container annual release fraction; FINAL

    International Nuclear Information System (INIS)

    HILL, J.S.

    1999-01-01

    In accordance with the approval conditions for Modification to the Central Waste Complex (CWC) Radioactive Air Emissions Notice of Construction (NOC). dated August 24,1998, a new release fraction has been developed for submittal to the Washington State Department of Health (WDOH). The proposed annual release fraction of 2.50 E-14 is proposed for use in future NOCs involving the storage and handling operations associated with vented containers on the Hanford Site. The proposed annual release fraction was the largest release fraction calculated from alpha measurements of the NucFil filters from 10 vented containers consisting of nine 55-gallon drums and one burial box with dimensions of 9.3 x 5.7 x 6.4 feet. An annual release fraction of 2.0 E-09 was used in the modification to the CWC radioactive air emissions NOC. This study confirmed that the release fraction used in the CWC radioactive air emissions NOC was conservative

  8. Generalized fractional Schroedinger equation with space-time fractional derivatives

    International Nuclear Information System (INIS)

    Wang Shaowei; Xu Mingyu

    2007-01-01

    In this paper the generalized fractional Schroedinger equation with space and time fractional derivatives is constructed. The equation is solved for free particle and for a square potential well by the method of integral transforms, Fourier transform and Laplace transform, and the solution can be expressed in terms of Mittag-Leffler function. The Green function for free particle is also presented in this paper. Finally, we discuss the relationship between the cases of the generalized fractional Schroedinger equation and the ones in standard quantum

  9. Theoretical Model for Volume Fraction of UC, 235U Enrichment, and Effective Density of Final U 10Mo Alloy

    Energy Technology Data Exchange (ETDEWEB)

    Devaraj, Arun [Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Environmental Molecular Sciences Lab. (EMSL); Prabhakaran, Ramprashad [Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Environmental Molecular Sciences Lab. (EMSL); Joshi, Vineet V. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Environmental Molecular Sciences Lab. (EMSL); Hu, Shenyang Y. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Environmental Molecular Sciences Lab. (EMSL); McGarrah, Eric J. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Environmental Molecular Sciences Lab. (EMSL); Lavender, Curt A. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Environmental Molecular Sciences Lab. (EMSL)

    2016-04-12

    The purpose of this document is to provide a theoretical framework for (1) estimating uranium carbide (UC) volume fraction in a final alloy of uranium with 10 weight percent molybdenum (U-10Mo) as a function of final alloy carbon concentration, and (2) estimating effective 235U enrichment in the U-10Mo matrix after accounting for loss of 235U in forming UC. This report will also serve as a theoretical baseline for effective density of as-cast low-enriched U-10Mo alloy. Therefore, this report will serve as the baseline for quality control of final alloy carbon content

  10. The responsibilities of the in-plant environmental protection officer under civil law and under criminal law. Zivilrechtliche und strafrechtliche Verantwortung des Betriebsbeauftragten fuer Umweltschutz

    Energy Technology Data Exchange (ETDEWEB)

    Salje, P.

    1993-11-20

    The scope of responsibilities of the in-plant environmental protection officer covers a wide range of tasks: Water protection, waste management, control of emissions for air pollution abatement, emergency preparedness, radiological protection. What are the consequences for the EP officer in case of neglect This is the topic of the contribution, discussed from the viewpoint of criminal law and private law. The criminal liability of the EP officer results from the EP officer committing an offence either by wilful act or by neglect, it, in the latter case, the officer is in a warranty position. Under private law, the EP officer is subject to third party liability within the framework defined by Paragraph 823 BGB. There is no possibility for him to claim restriction of liability refering to the enhanced risks involved in his job. Hence a sound professional indemnity insurance is recommendable. (orig.)

  11. Fractional bosonic strings

    Science.gov (United States)

    Diaz, Victor Alfonzo; Giusti, Andrea

    2018-03-01

    The aim of this paper is to present a simple generalization of bosonic string theory in the framework of the theory of fractional variational problems. Specifically, we present a fractional extension of the Polyakov action, for which we compute the general form of the equations of motion and discuss the connection between the new fractional action and a generalization the Nambu-Goto action. Consequently, we analyze the symmetries of the modified Polyakov action and try to fix the gauge, following the classical procedures. Then we solve the equations of motion in a simplified setting. Finally, we present a Hamiltonian description of the classical fractional bosonic string and introduce the fractional light-cone gauge. It is important to remark that, throughout the whole paper, we thoroughly discuss how to recover the known results as an "integer" limit of the presented model.

  12. Fractional Dynamics and Control

    CERN Document Server

    Machado, José; Luo, Albert

    2012-01-01

    Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science. Discusses how fractional dynamics and control can be used to solve nonlinear science and complexity issues Shows how fractional differential equations and models can be used to solve turbulence and wave equations in mechanics and gravity theories and Schrodinger’s equation  Presents factional relaxation modeling of dielectric materials and wave equations for dielectrics  Develops new methods for control and synchronization of...

  13. Robust Stabilization of Fractional-Order Systems with Interval Uncertainties via Fractional-Order Controllers

    Directory of Open Access Journals (Sweden)

    Mohammadtaghi Hamidi Beheshti

    2010-01-01

    Full Text Available We propose a fractional-order controller to stabilize unstable fractional-order open-loop systems with interval uncertainty whereas one does not need to change the poles of the closed-loop system in the proposed method. For this, we will use the robust stability theory of Fractional-Order Linear Time Invariant (FO-LTI systems. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of interval nonlinear systems and especially in fractional-order chaotic systems. Finally numerical simulations are presented to show the effectiveness of the proposed controller.

  14. Robust Stabilization of Fractional-Order Systems with Interval Uncertainties via Fractional-Order Controllers

    Directory of Open Access Journals (Sweden)

    Sayyad Delshad Saleh

    2010-01-01

    Full Text Available Abstract We propose a fractional-order controller to stabilize unstable fractional-order open-loop systems with interval uncertainty whereas one does not need to change the poles of the closed-loop system in the proposed method. For this, we will use the robust stability theory of Fractional-Order Linear Time Invariant (FO-LTI systems. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of interval nonlinear systems and especially in fractional-order chaotic systems. Finally numerical simulations are presented to show the effectiveness of the proposed controller.

  15. Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

    Directory of Open Access Journals (Sweden)

    Xiao-Li Ding

    2018-01-01

    Full Text Available In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. Finally, we give three examples to demonstrate the applicability of our obtained results.

  16. A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics

    Science.gov (United States)

    Lei, Dong; Liang, Yingjie; Xiao, Rui

    2018-01-01

    We develop a fractional model to describe the thermomechanical behavior of amorphous thermoplastics. The fractional model is composed of two parallel fractional Maxwell elements. The first fractional Maxwell model is used to describe the glass transition, while the second component is aimed at describing the viscous flow. We further derive the analytical solutions for the stress relaxation modulus and complex modulus through Laplace transform. We then demonstrate the model is able to describe the master curves of the stress relaxation modulus, storage modulus and loss modulus, which all show two distinct transition regions. The obtained parameters show that the modulus of the two fractional Maxwell elements differs in 2-3 orders of magnitude, while the relaxation time differs in 7-9 orders of magnitude. Finally, we apply the model to describe the stress response of constant strain rate tests. The model, together with the parameters obtained from fitting the master curve of stress relaxation modulus, can accurately predict the temperature and strain rate dependent stress response.

  17. Toward a minimum branching fraction for dark matter annihilation into electromagnetic final states

    International Nuclear Information System (INIS)

    Dent, James B.; Scherrer, Robert J.; Weiler, Thomas J.

    2008-01-01

    Observational limits on the high-energy neutrino background have been used to place general constraints on dark matter that annihilates only into standard model particles. Dark matter particles that annihilate into neutrinos will also inevitably branch into electromagnetic final states through higher-order tree and loop diagrams that give rise to charged leptons, and these charged particles can transfer their energy into photons via synchrotron radiation or inverse Compton scattering. In the context of effective field theory, we calculate the loop-induced branching ratio to charged leptons and show that it is generally quite large, typically > or approx. 1%, when the scale of the dark matter mass exceeds the electroweak scale, M W . For a branching fraction >or approx. 3%, the synchrotron radiation bounds on dark matter annihilation are currently stronger than the corresponding neutrino bounds in the interesting mass range from 100 GeV to 1 TeV. For dark matter masses below M W , our work provides a plausible framework for the construction of a model for 'neutrinos-only' dark matter annihilations.

  18. Finite temperature Casimir effect for a massless fractional Klein-Gordon field with fractional Neumann conditions

    International Nuclear Information System (INIS)

    Eab, C. H.; Lim, S. C.; Teo, L. P.

    2007-01-01

    This paper studies the Casimir effect due to fractional massless Klein-Gordon field confined to parallel plates. A new kind of boundary condition called fractional Neumann condition which involves vanishing fractional derivatives of the field is introduced. The fractional Neumann condition allows the interpolation of Dirichlet and Neumann conditions imposed on the two plates. There exists a transition value in the difference between the orders of the fractional Neumann conditions for which the Casimir force changes from attractive to repulsive. Low and high temperature limits of Casimir energy and pressure are obtained. For sufficiently high temperature, these quantities are dominated by terms independent of the boundary conditions. Finally, validity of the temperature inversion symmetry for various boundary conditions is discussed

  19. Final Report for Fractionation and Separation of Polydisperse Nanoparticles into Distinct Monodisperse Fractions Using CO2 Expanded Liquids

    Energy Technology Data Exchange (ETDEWEB)

    Chistopher Roberts

    2007-08-31

    The overall objective of this project was to facilitate efficient fractionation and separation of polydisperse metal nanoparticle populations into distinct monodisperse fractions using the tunable solvent properties of gas expanded liquids. Specifically, the dispersibility of ligand-stabilized nanoparticles in an organic solution was controlled by altering the ligand-solvent interaction (solvation) by the addition of carbon dioxide (CO{sub 2}) gas as an antisolvent (thereby tailoring the bulk solvent strength) in a custom high pressure apparatus developed in our lab. This was accomplished by adjusting the CO{sub 2} pressure over the liquid dispersion, resulting in a simple means of tuning the nanoparticle precipitation by size. Overall, this work utilized the highly tunable solvent properties of organic/CO{sub 2} solvent mixtures to selectively size-separate dispersions of polydisperse nanoparticles (ranging from 1 to 20 nm in size) into monodisperse fractions ({+-}1nm). Specifically, three primary tasks were performed to meet the overall objective. Task 1 involved the investigation of the effects of various operating parameters (such as temperature, pressure, ligand length and ligand type) on the efficiency of separation and fractionation of Ag nanoparticles. In addition, a thermodynamic interaction energy model was developed to predict the dispersibility of different sized nanoparticles in the gas expanded liquids at various conditions. Task 2 involved the extension of the experimental procedures identified in task 1 to the separation of other metal particles used in catalysis such as Au as well as other materials such as semiconductor particles (e.g. CdSe). Task 3 involved using the optimal conditions identified in tasks 1 and 2 to scale up the process to handle sample sizes of greater than 1 g. An experimental system was designed to allow nanoparticles of increasingly smaller sizes to be precipitated sequentially in a vertical series of high pressure vessels by

  20. Void Fraction Instrument operation and maintenance manual

    International Nuclear Information System (INIS)

    Borgonovi, G.; Stokes, T.I.; Pearce, K.L.; Martin, J.D.; Gimera, M.; Graves, D.B.

    1994-09-01

    This Operations and Maintenance Manual (O ampersand MM) addresses riser installation, equipment and personnel hazards, operating instructions, calibration, maintenance, removal, and other pertinent information necessary to safely operate and store the Void Fraction Instrument. Final decontamination and decommissioning of the Void Fraction Instrument are not covered in this document

  1. State-Space Modelling of Loudspeakers using Fractional Derivatives

    DEFF Research Database (Denmark)

    King, Alexander Weider; Agerkvist, Finn T.

    2015-01-01

    This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response of a fractio......This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response...... of a fractional harmonic oscillator, representing the mechanical part of a loudspeaker, showing the effect of the fractional derivative and its relationship to viscoelasticity. Finally, a loudspeaker model with a fractional order viscoelastic suspension and fractional order voice coil is fit to measurement data...

  2. Fractional graph theory a rational approach to the theory of graphs

    CERN Document Server

    Scheinerman, Edward R

    2013-01-01

    A unified treatment of the most important results in the study of fractional graph concepts, this volume explores the various ways in which integer-valued concepts can be modified to derive nonintegral values. It begins with the general fractional theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics. Subjects include fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, and fractional isomorphism. The final chapter examines additional topics such as fractional domination, fractional intersection numbers

  3. Non-Noether symmetries of Hamiltonian systems with conformable fractional derivatives

    International Nuclear Information System (INIS)

    Wang Lin-Li; Fu Jing-Li

    2016-01-01

    In this paper, we present the fractional Hamilton’s canonical equations and the fractional non-Noether symmetry of Hamilton systems by the conformable fractional derivative. Firstly, the exchanging relationship between isochronous variation and fractional derivatives, and the fractional Hamilton principle of the system under this fractional derivative are proposed. Secondly, the fractional Hamilton’s canonical equations of Hamilton systems based on the Hamilton principle are established. Thirdly, the fractional non-Noether symmetries, non-Noether theorem and non-Noether conserved quantities for the Hamilton systems with the conformable fractional derivatives are obtained. Finally, an example is given to illustrate the results. (paper)

  4. Density fractions versus size separates: does physical fractionation isolate functional soil compartments?

    Directory of Open Access Journals (Sweden)

    C. Moni

    2012-12-01

    Full Text Available Physical fractionation is a widely used methodology to study soil organic matter (SOM dynamics, but concerns have been raised that the available fractionation methods do not well describe functional SOM pools. In this study we explore whether physical fractionation techniques isolate soil compartments in a meaningful and functionally relevant way for the investigation of litter-derived nitrogen dynamics at the decadal timescale. We do so by performing aggregate density fractionation (ADF and particle size-density fractionation (PSDF on mineral soil samples from two European beech forests a decade after application of 15N labelled litter.

    Both density and size-based fractionation methods suggested that litter-derived nitrogen became increasingly associated with the mineral phase as decomposition progressed, within aggregates and onto mineral surfaces. However, scientists investigating specific aspects of litter-derived nitrogen dynamics are pointed towards ADF when adsorption and aggregation processes are of interest, whereas PSDF is the superior tool to research the fate of particulate organic matter (POM.

    Some methodological caveats were observed mainly for the PSDF procedure, the most important one being that fine fractions isolated after sonication can not be linked to any defined decomposition pathway or protective mechanism. This also implies that historical assumptions about the "adsorbed" state of carbon associated with fine fractions need to be re-evaluated. Finally, this work demonstrates that establishing a comprehensive picture of whole soil OM dynamics requires a combination of both methodologies and we offer a suggestion for an efficient combination of the density and size-based approaches.

  5. HANFORD MEDIUM-LOW CURIE WASTE PRETREATMENT ALTERNATIVES PROJECT FRACTIONAL CRYSTALLIZATION PILOT SCALE TESTING FINAL REPORT

    Energy Technology Data Exchange (ETDEWEB)

    HERTING DL

    2008-09-16

    The Fractional Crystallization Pilot Plant was designed and constructed to demonstrate that fractional crystallization is a viable way to separate the high-level and low-activity radioactive waste streams from retrieved Hanford single-shell tank saltcake. The focus of this report is to review the design, construction, and testing details of the fractional crystallization pilot plant not previously disseminated.

  6. HANFORD MEDIUM-LOW CURIE WASTE PRETREATMENT ALTERNATIVES PROJECT-FRACTIONAL CRYSTALLIZATION PILOT SCALE TESTING FINAL REPORT

    International Nuclear Information System (INIS)

    HERTING DL

    2008-01-01

    The Fractional Crystallization Pilot Plant was designed and constructed to demonstrate that fractional crystallization is a viable way to separate the high-level and low-activity radioactive waste streams from retrieved Hanford single-shell tank saltcake. The focus of this report is to review the design, construction, and testing details of the fractional crystallization pilot plant not previously disseminated

  7. Fractional Sobolev’s Spaces on Time Scales via Conformable Fractional Calculus and Their Application to a Fractional Differential Equation on Time Scales

    Directory of Open Access Journals (Sweden)

    Yanning Wang

    2016-01-01

    Full Text Available Using conformable fractional calculus on time scales, we first introduce fractional Sobolev spaces on time scales, characterize them, and define weak conformable fractional derivatives. Second, we prove the equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, uniform convexity, and compactness of some imbeddings, which can be regarded as a novelty item. Then, as an application, we present a recent approach via variational methods and critical point theory to obtain the existence of solutions for a p-Laplacian conformable fractional differential equation boundary value problem on time scale T:  Tα(Tαup-2Tα(u(t=∇F(σ(t,u(σ(t, Δ-a.e.  t∈a,bTκ2, u(a-u(b=0, Tα(u(a-Tα(u(b=0, where Tα(u(t denotes the conformable fractional derivative of u of order α at t, σ is the forward jump operator, a,b∈T,  01, and F:[0,T]T×RN→R. By establishing a proper variational setting, we obtain three existence results. Finally, we present two examples to illustrate the feasibility and effectiveness of the existence results.

  8. Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

    Science.gov (United States)

    Jain, Sonal

    2018-01-01

    In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

  9. A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions

    Directory of Open Access Journals (Sweden)

    Taohua Liu

    2017-01-01

    Full Text Available Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. First-order consistency, solvability, unconditional stability, and first-order convergence of the method are proven. Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of O(K and computational cost of O(Klog⁡K. Traditionally, the Gaussian elimination method requires storage of O(K2 and computational cost of O(K3. Finally, the accuracy and efficiency of the method are checked with a numerical example.

  10. Alternative Forms of Compound Fractional Poisson Processes

    Directory of Open Access Journals (Sweden)

    Luisa Beghin

    2012-01-01

    Full Text Available We study here different fractional versions of the compound Poisson process. The fractionality is introduced in the counting process representing the number of jumps as well as in the density of the jumps themselves. The corresponding distributions are obtained explicitly and proved to be solution of fractional equations of order less than one. Only in the final case treated in this paper, where the number of jumps is given by the fractional-difference Poisson process defined in Orsingher and Polito (2012, we have a fractional driving equation, with respect to the time argument, with order greater than one. Moreover, in this case, the compound Poisson process is Markovian and this is also true for the corresponding limiting process. All the processes considered here are proved to be compositions of continuous time random walks with stable processes (or inverse stable subordinators. These subordinating relationships hold, not only in the limit, but also in the finite domain. In some cases the densities satisfy master equations which are the fractional analogues of the well-known Kolmogorov one.

  11. Consensus Analysis of Fractional-Order Multiagent Systems with Double-Integrator

    Directory of Open Access Journals (Sweden)

    Chunde Yang

    2017-01-01

    Full Text Available In nature, many phenomena can be explained by coordinated behavior of agents with fractional-order dynamics. In this paper, the consensus problem of fractional-order multiagent systems with double-integrator is studied, where the fractional-order satisfies 0<α<2. Based on the fractional-order stability theory, Mittag-Leffler function, and Laplace transform, a necessary and sufficient condition is obtained under the assumption that the directed graph for the communication network contains a directed spanning tree. Finally, an example with simulation is presented to illustrate the theoretical results.

  12. Finite element method for time-space-fractional Schrodinger equation

    Directory of Open Access Journals (Sweden)

    Xiaogang Zhu

    2017-07-01

    Full Text Available In this article, we develop a fully discrete finite element method for the nonlinear Schrodinger equation (NLS with time- and space-fractional derivatives. The time-fractional derivative is described in Caputo's sense and the space-fractional derivative in Riesz's sense. Its stability is well derived; the convergent estimate is discussed by an orthogonal operator. We also extend the method to the two-dimensional time-space-fractional NLS and to avoid the iterative solvers at each time step, a linearized scheme is further conducted. Several numerical examples are implemented finally, which confirm the theoretical results as well as illustrate the accuracy of our methods.

  13. Time rescaling and Gaussian properties of the fractional Brownian motions

    International Nuclear Information System (INIS)

    Maccone, C.

    1981-01-01

    The fractional Brownian motions are proved to be a class of Gaussian (normal) stochastic processes suitably rescaled in time. Some consequences affecting their eigenfunction expansion (Karhunen-Loeve expansion) are inferred. A known formula of Cameron and Martin is generalized. The first-passage time probability density is found. The partial differential equation of the fractional Brownian diffusion is obtained. And finally the increments of the fractional Brownian motions are proved to be independent for nonoverlapping time intervals. (author)

  14. Eigenfunction expansion for fractional Brownian motions

    International Nuclear Information System (INIS)

    Maccone, C.

    1981-01-01

    The fractional Brownian motions, a class of nonstationary stochastic processes defined as the Riemann-Liouville fractional integral/derivative of the Brownian motion, are studied. It is shown that these processes can be regarded as the output of a suitable linear system of which the input is the white noise. Their autocorrelation is then derived with a study of their standard-deviation curves. Their power spectra are found by resorting to the nonstationary spectral theory. And finally their eigenfunction expansion (Karhunen-Loeve expansion) is obtained: the eigenfunctions are proved to be suitable Bessel functions and the eigenvalues zeros of the Bessel functions. (author)

  15. Current Status of Fractional Laser Resurfacing.

    Science.gov (United States)

    Carniol, Paul J; Hamilton, Mark M; Carniol, Eric T

    2015-01-01

    Fractional lasers were first developed based on observations of lasers designed for hair transplantation. In 2007, ablative fractional laser resurfacing was introduced. The fractionation allowed deeper tissue penetration, leading to greater tissue contraction, collagen production and tissue remodeling. Since then, fractional erbium:YAG resurfacing lasers have also been introduced. These lasers have yielded excellent results in treating photoaging, acne scarring, and dyschromia. With the adjustment of microspot density, pulse duration, number of passes, and fluence, the surgeon can adjust the treatment effects. These lasers have allowed surgeons to treat patients with higher Fitzpatrick skin types (types IV to VI) and greater individualize treatments to various facial subunits. Immunohistochemical analysis has demonstrated remodeling effects of the tissues for several months, producing longer lasting results. Adjuvant treatments are also under investigation, including concomitant face-lift, product deposition, and platelet-rich plasma. Finally, there is a short recovery time from treatment with these lasers, allowing patients to resume regular activities more quickly. Although there is a relatively high safety profile for ablative fractionated lasers, surgeons should be aware of the limitations of specific treatments and the associated risks and complications.

  16. Effective-field-theory model for the fractional quantum Hall effect

    International Nuclear Information System (INIS)

    Zhang, S.C.; Hansson, T.H.; Kivelson, S.

    1989-01-01

    Starting directly from the microscopic Hamiltonian, we derive a field-theory model for the fractional quantum hall effect. By considering an approximate coarse-grained version of the same model, we construct a Landau-Ginzburg theory similar to that of Girvin. The partition function of the model exhibits cusps as a function of density and the Hall conductance is quantized at filling factors ν = (2k-1)/sup -1/ with k an arbitrary integer. At these fractions the ground state is incompressible, and the quasiparticles and quasiholes have fractional charge and obey fractional statistics. Finally, we show that the collective density fluctuations are massive

  17. Generalized Combination Complex Synchronization for Fractional-Order Chaotic Complex Systems

    Directory of Open Access Journals (Sweden)

    Cuimei Jiang

    2015-07-01

    Full Text Available Based on two fractional-order chaotic complex drive systems and one fractional-order chaotic complex response system with different dimensions, we propose generalized combination complex synchronization. In this new synchronization scheme, there are two complex scaling matrices that are non-square matrices. On the basis of the stability theory of fractional-order linear systems, we design a general controller via active control. Additionally, by virtue of two complex scaling matrices, generalized combination complex synchronization between fractional-order chaotic complex systems and real systems is investigated. Finally, three typical examples are given to demonstrate the effectiveness and feasibility of the schemes.

  18. Riesz potential versus fractional Laplacian

    KAUST Repository

    Ortigueira, Manuel Duarte; Laleg-Kirati, Taous-Meriem; Machado, José Antó nio Tenreiro

    2014-01-01

    This paper starts by introducing the Grünwald-Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy-Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.

  19. Riesz potential versus fractional Laplacian

    KAUST Repository

    Ortigueira, Manuel Duarte

    2014-09-01

    This paper starts by introducing the Grünwald-Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy-Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.

  20. Isotope Fractionation by Diffusion in Liquids (Final Technical Report)

    Energy Technology Data Exchange (ETDEWEB)

    Richter, Frank [Univ. of Chicago, IL (United States)

    2016-11-09

    The overall objective of the DOE-funded research by grant DE-FG02-01ER15254 was document and quantify kinetic isotope fractionations during chemical and thermal (i.e., Soret) diffusion in liquids (silicate melts and water) and in the later years to include alloys and major minerals such as olivine and pyroxene. The research involved both laboratory experiments and applications to natural settings. The key idea is that major element zoning on natural geologic materials is common and can arise for either changes in melt composition during cooling and crystallization or from diffusion. The isotope effects associated with diffusion that we have documented are the key for determining whether or not the zoning observed in a natural system was the result of diffusion. Only in those cases were the zoning is demonstrably due to diffusion can use independently measured rates of diffusion to constrain the thermal evolution of the system.

  1. A Caputo fractional derivative of a function with respect to another function

    Science.gov (United States)

    Almeida, Ricardo

    2017-03-01

    In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor's Theorem, Fermat's Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided.

  2. Fractional Wigner Crystal in the Helical Luttinger Liquid.

    Science.gov (United States)

    Traverso Ziani, N; Crépin, F; Trauzettel, B

    2015-11-13

    The properties of the strongly interacting edge states of two dimensional topological insulators in the presence of two-particle backscattering are investigated. We find an anomalous behavior of the density-density correlation functions, which show oscillations that are neither of Friedel nor of Wigner type: they, instead, represent a Wigner crystal of fermions of fractional charge e/2, with e the electron charge. By studying the Fermi operator, we demonstrate that the state characterized by such fractional oscillations still bears the signatures of spin-momentum locking. Finally, we compare the spin-spin correlation functions and the density-density correlation functions to argue that the fractional Wigner crystal is characterized by a nontrivial spin texture.

  3. EVOLUTION OF THE BINARY FRACTION IN DENSE STELLAR SYSTEMS

    International Nuclear Information System (INIS)

    Fregeau, John M.; Ivanova, Natalia; Rasio, Frederic A.

    2009-01-01

    Using our recently improved Monte Carlo evolution code, we study the evolution of the binary fraction in globular clusters. In agreement with previous N-body simulations, we find generally that the hard binary fraction in the core tends to increase with time over a range of initial cluster central densities for initial binary fractions ∼<90%. The dominant processes driving the evolution of the core binary fraction are mass segregation of binaries into the cluster core and preferential destruction of binaries there. On a global scale, these effects and the preferential tidal stripping of single stars tend to roughly balance, leading to overall cluster binary fractions that are roughly constant with time. Our findings suggest that the current hard binary fraction near the half-mass radius is a good indicator of the hard primordial binary fraction. However, the relationship between the true binary fraction and the fraction of main-sequence stars in binaries (which is typically what observers measure) is nonlinear and rather complicated. We also consider the importance of soft binaries, which not only modify the evolution of the binary fraction, but can also drastically change the evolution of the cluster as a whole. Finally, we briefly describe the recent addition of single and binary stellar evolution to our cluster evolution code.

  4. Asymptotic behavior of solutions of linear multi-order fractional differential equation systems

    OpenAIRE

    Diethelm, Kai; Siegmund, Stefan; Tuan, H. T.

    2017-01-01

    In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of line...

  5. Identification of fractional order systems using modulating functions method

    KAUST Repository

    Liu, Dayan

    2013-06-01

    The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations.

  6. Copper and trace element fractionation in electrokinetically treated methanogenic anaerobic granular sludge

    International Nuclear Information System (INIS)

    Virkutyte, Jurate; Hullebusch, Eric van; Sillanpaeae, Mika; Lens, Piet

    2005-01-01

    The effect of electrokinetic treatment (0.15 mA cm -2 ) on the metal fractionation in anaerobic granular sludge artificially contaminated with copper (initial copper concentration 1000 mg kg -1 wet sludge) was studied. Acidification of the sludge (final pH 4.2 in the sludge bed) with the intention to desorb the copper species bound to the organic/sulfides and residual fractions did not result in an increased mobility, despite the fact that a higher quantity of copper was measured in the more mobile (i.e. exchangeable/carbonate) fractions at final pH 4.2 compared to circum-neutral pH conditions. Also addition of the chelating agent EDTA (Cu 2+ :EDTA 4- ratio 1.2:1) did not enhance the mobility of copper from the organic/sulfides and residual fractions, despite the fact that it induced a reduction of the total copper content of the sludge. The presence of sulfide precipitates likely influences the copper mobilisation from these less mobile fractions, and thus makes EDTA addition ineffective to solubilise copper from the granules. - Electrokinetic treatment of copper contaminated anaerobic granular sludge at 0.15 mA cm -2 for 14 days induces copper and trace metal mobility as well as changes in their fractionation (i.e. bonding forms)

  7. Robust fractional order differentiators using generalized modulating functions method

    KAUST Repository

    Liu, Dayan

    2015-02-01

    This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.

  8. Robust fractional order differentiators using generalized modulating functions method

    KAUST Repository

    Liu, Dayan; Laleg-Kirati, Taous-Meriem

    2015-01-01

    This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.

  9. Fractional magnetohydrodynamics Oldroyd-B fluid over an oscillating plate

    Directory of Open Access Journals (Sweden)

    Jamil Muhammad

    2013-01-01

    Full Text Available This paper presents some new exact solutions corresponding to the oscillating flows of a MHD Oldroyd-B fluid with fractional derivatives. The fractional calculus approach in the governing equations is used. The exact solutions for the oscillating motions of a fractional MHD Oldroyd-B fluid due to sine and cosine oscillations of an infinite plate are established with the help of discrete Laplace transform. The expressions for velocity field and the associated shear stress that have been obtained, presented in series form in terms of Fox H functions, satisfy all imposed initial and boundary conditions. Similar solutions for ordinary MHD Oldroyd-B, fractional and ordinary MHD Maxwell, fractional and ordinary MHD Second grade and MHD Newtonian fluid as well as those for hydrodynamic fluids are obtained as special cases of general solutions. Finally, the obtained solutions are graphically analyzed through various parameters of interest.

  10. Characterization of isolated fractions of dissolved organic matter derived from municipal solid waste compost.

    Science.gov (United States)

    Yu, Minda; He, Xiaosong; Liu, Jiaomei; Wang, Yuefeng; Xi, Beidou; Li, Dan; Zhang, Hui; Yang, Chao

    2018-04-14

    Understanding the heterogeneous evolution characteristics of dissolved organic matter fractions derived from compost is crucial to exploring the composting biodegradation process and the possible applications of compost products. Herein, two-dimensional correlation spectroscopy integrated with reversed-phase high performance liquid chromatography and size exclusion chromatography were utilized to obtain the molecular weight (MW) and polarity evolution characteristics of humic acid (HA), fulvic acid (FA), and the hydrophilic (HyI) fractions during composting. The high-MW humic substances and building blocks in the HA fraction degraded faster during composting than polymers, proteins, and organic colloids. Similarly, the low MW acid FA factions transformed faster than the low weight neutral fractions, followed by building blocks, and finally polymers, proteins, and organic colloids. The evolutions of HyI fractions during composting occurred first for building blocks, followed by low MW acids, and finally low weight neutrals. With the progress of composting, the hydrophobic properties of the HA and FA fractions were enhanced. The degradation/humification process of the hydrophilic and transphilic components was faster than that of the hydrophobic component. Compared with the FA and HyI fractions, the HA fraction exhibited a higher MW and increased hydrophobicity. Copyright © 2018 Elsevier B.V. All rights reserved.

  11. Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

    Directory of Open Access Journals (Sweden)

    Veyis Turut

    2013-01-01

    Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.

  12. Dynamical property analysis of fractionally damped van der pol oscillator and its application

    Science.gov (United States)

    Zhong, Qiuhui; Zhang, Chunrui

    2012-01-01

    In this paper, the fractionally damped van der pol equation was studied. Firstly, the fractionally damped van der pol equation was transformed into a set of integer order equations. Then the Lyapunov exponents diagram was given. Secondly, it was transformed into a set of fractional integral equations and solved by a predictor-corrector method. The time domain diagrams and phase trajectory were used to describe the dynamic behavior. Finally, the fractionally damped van der pol equation was used to detect a weak signal.

  13. In-plant demonstration of energy optimization in beck dyeing of carpet. Final report, June 1, 1979-January 1, 1980

    Energy Technology Data Exchange (ETDEWEB)

    Tincher, W.C.

    1980-01-01

    Several energy-conservative technologies have been successfully combined and transferred to a commercial carpet finishing plant to optimize beck dyeing. The technology of bump-and-run, in which the dyebath temperature was allowed to drift for the last 85% of the hold time instead of being maintained by active steam sparging, reduced the energy consumption by 38% with negligible capital investment required. Merging of dyebath reuse with bump-and-run only marginally increased the energy consumption (to 39%), but substantially lowered the plant's finishing costs further by directly recycling dyes, auxiliary chemicals, and water. Final optimization, which merged a technique whereby the carpet was pulled directly from the hot bath with bump-and-run and dyebath reuse, further improved the economics by drastically reducing water/sewer requirements by 90% and eliminating the holding tank/pumping assembly as a reuse requirement. From a carpet industry viewpoint, the demonstrated modifications have a direct energy conservation potential of 2.4 x 10/sup 5/ barrels of oil equivalent per year assuming the technology is directly transferable to similar atmospheric dyeing processes, e.g., beck dyeing of nylon and polyester fabrics, the potential to the entire textile industry is 2.6 x 10/sup 6/ BOE/year. Economically, total potential savings for the carpet industry on reuse incorporation was $1.2 x 10/sup 7//year, based on a 2.3 cents/lb. savings figure. When the allied fabric industry was included, the national potential was raised to $1.0 x 10/sup 8//year. These figures include cost savings due to materials recycled (water, auxiliary chemicals and dyes) as well as energy conservation.

  14. Geochemical importance of isotopic fractionation during respiration

    International Nuclear Information System (INIS)

    Schleser, G.; Foerstel, H.

    1975-01-01

    In 1935 it was found that atmospheric oxygen contained a relatively greater abundance of the 18 O isotope than did the oxygen bound in water (Dole effect). A major contribution to the fractionation of the stable oxygen isotopes should result from the respiration of microorganisms. In this respect our interest centers on the soil because nearly all organic material produced on land is decomposed within the soil. The oceans are less important because the primary productivity on land is twice the value for the oceans. In a first approach we measured the oxygen isotope fractionation during the respiration of E. coli K12 for different respiration rates. These results, accomplished with a chemostat, indicate that the fractionation factor α of the oxygen isotopes increases with the increasing respiratory activity, measured as Q/sub O 2 /. At low dilution rates or growth rates respectively of about 0.05 h -1 , the fractionation factor amounts to 1.006 increasing to 1.017 at dilution rates of about 1.0 h -1 . The results are interpreted as a kinetic mass fractionation due to the slightly different diffusion coefficients of 16 O 2 and 18 O 16 O. The respiration rates in conjunction with the corresponding fractionation data are compared with the respiration rates of typical soil microorganisms such as Azotobacter, in order to deduce fractionation data for these organisms. This is necessary to calculate a mean global fractionation factor. Understanding the Dole effect with these fractionation processes should finally give us the opportunity to calculate gas-exchange rates between the atmosphere and the oceans, on the basis of the behavior of the stable oxygen isotopes

  15. The Active Fractional Order Control for Maglev Suspension System

    Directory of Open Access Journals (Sweden)

    Peichang Yu

    2015-01-01

    Full Text Available Maglev suspension system is the core part of maglev train. In the practical application, the load uncertainties, inherent nonlinearity, and misalignment between sensors and actuators are the main issues that should be solved carefully. In order to design a suitable controller, the attention is paid to the fractional order controller. Firstly, the mathematical model of a single electromagnetic suspension unit is derived. Then, considering the limitation of the traditional PD controller adaptation, the fractional order controller is developed to obtain more excellent suspension specifications and robust performance. In reality, the nonlinearity affects the structure and the precision of the model after linearization, which will degrade the dynamic performance. So, a fractional order controller is addressed to eliminate the disturbance by adjusting the parameters which are added by the fractional order controller. Furthermore, the controller based on LQR is employed to compare with the fractional order controller. Finally, the performance of them is discussed by simulation. The results illustrated the validity of the fractional order controller.

  16. A Statistical Treatment of Bioassay Pour Fractions

    Science.gov (United States)

    Barengoltz, Jack; Hughes, David W.

    2014-01-01

    The binomial probability distribution is used to treat the statistics of a microbiological sample that is split into two parts, with only one part evaluated for spore count. One wishes to estimate the total number of spores in the sample based on the counts obtained from the part that is evaluated (pour fraction). Formally, the binomial distribution is recharacterized as a function of the observed counts (successes), with the total number (trials) an unknown. The pour fraction is the probability of success per spore (trial). This distribution must be renormalized in terms of the total number. Finally, the new renormalized distribution is integrated and mathematically inverted to yield the maximum estimate of the total number as a function of a desired level of confidence ( P(fraction. The extension to recovery efficiency corrections is also presented. Now the product of recovery efficiency and pour fraction may be small enough that the likely value may be much larger than the usual calculation: the number of spores divided by that product. The use of this analysis would not be limited to microbiological data.

  17. Quantum mechanics and field theory with fractional spin and statistics

    International Nuclear Information System (INIS)

    Forte, S.

    1992-01-01

    Planar systems admit quantum states that are neither bosons nor fermions, i.e., whose angular momentum is neither integer nor half-integer. After a discussion of some examples of familiar models in which fractional spin may arise, the relevant (nonrelativistic) quantum mechanics is developed from first principles. The appropriate generalization of statistics is also discussed. Some physical effects of fractional spin and statistics are worked out explicitly. The group theory underlying relativistic models with fractional spin and statistics is then introduced and applied to relativistic particle mechanics and field theory. Field-theoretical models in 2+1 dimensions are presented which admit solitons that carry fractional statistics, and are discussed in a semiclassical approach, in the functional integral approach, and in the canonical approach. Finally, fundamental field theories whose Fock states carry fractional spin and statistics are discussed

  18. Volumetric Image Guidance Using Carina vs Spine as Registration Landmarks for Conventionally Fractionated Lung Radiotherapy

    Energy Technology Data Exchange (ETDEWEB)

    Lavoie, Caroline; Higgins, Jane; Bissonnette, Jean-Pierre [Department of Radiation Oncology, Princess Margaret Hospital, University of Toronto, Toronto, Ontario, M5G 2M9 (Canada); Le, Lisa W. [Department of Biostatistics, Princess Margaret Hospital, Toronto, Ontario, M5G 2M9 (Canada); Sun, Alexander; Brade, Anthony; Hope, Andrew; Cho, John [Department of Radiation Oncology, Princess Margaret Hospital, University of Toronto, Toronto, Ontario, M5G 2M9 (Canada); Bezjak, Andrea, E-mail: andrea.bezjak@rmp.uhn.on.ca [Department of Radiation Oncology, Princess Margaret Hospital, University of Toronto, Toronto, Ontario, M5G 2M9 (Canada)

    2012-12-01

    Purpose: To compare the relative accuracy of 2 image guided radiation therapy methods using carina vs spine as landmarks and then to identify which landmark is superior relative to tumor coverage. Methods and Materials: For 98 lung patients, 2596 daily image-guidance cone-beam computed tomography scans were analyzed. Tattoos were used for initial patient alignment; then, spine and carina registrations were performed independently. A separate analysis assessed the adequacy of gross tumor volume, internal target volume, and planning target volume coverage on cone-beam computed tomography using the initial, middle, and final fractions of radiation therapy. Coverage was recorded for primary tumor (T), nodes (N), and combined target (T+N). Three scenarios were compared: tattoos alignment, spine registration, and carina registration. Results: Spine and carina registrations identified setup errors {>=}5 mm in 35% and 46% of fractions, respectively. The mean vector difference between spine and carina matching had a magnitude of 3.3 mm. Spine and carina improved combined target coverage, compared with tattoos, in 50% and 34% (spine) to 54% and 46% (carina) of the first and final fractions, respectively. Carina matching showed greater combined target coverage in 17% and 23% of fractions for the first and final fractions, respectively; with spine matching, this was only observed in 4% (first) and 6% (final) of fractions. Carina matching provided superior nodes coverage at the end of radiation compared with spine matching (P=.0006), without compromising primary tumor coverage. Conclusion: Frequent patient setup errors occur in locally advanced lung cancer patients. Spine and carina registrations improved combined target coverage throughout the treatment course, but carina matching provided superior combined target coverage.

  19. Volumetric Image Guidance Using Carina vs Spine as Registration Landmarks for Conventionally Fractionated Lung Radiotherapy

    International Nuclear Information System (INIS)

    Lavoie, Caroline; Higgins, Jane; Bissonnette, Jean-Pierre; Le, Lisa W.; Sun, Alexander; Brade, Anthony; Hope, Andrew; Cho, John; Bezjak, Andrea

    2012-01-01

    Purpose: To compare the relative accuracy of 2 image guided radiation therapy methods using carina vs spine as landmarks and then to identify which landmark is superior relative to tumor coverage. Methods and Materials: For 98 lung patients, 2596 daily image-guidance cone-beam computed tomography scans were analyzed. Tattoos were used for initial patient alignment; then, spine and carina registrations were performed independently. A separate analysis assessed the adequacy of gross tumor volume, internal target volume, and planning target volume coverage on cone-beam computed tomography using the initial, middle, and final fractions of radiation therapy. Coverage was recorded for primary tumor (T), nodes (N), and combined target (T+N). Three scenarios were compared: tattoos alignment, spine registration, and carina registration. Results: Spine and carina registrations identified setup errors ≥5 mm in 35% and 46% of fractions, respectively. The mean vector difference between spine and carina matching had a magnitude of 3.3 mm. Spine and carina improved combined target coverage, compared with tattoos, in 50% and 34% (spine) to 54% and 46% (carina) of the first and final fractions, respectively. Carina matching showed greater combined target coverage in 17% and 23% of fractions for the first and final fractions, respectively; with spine matching, this was only observed in 4% (first) and 6% (final) of fractions. Carina matching provided superior nodes coverage at the end of radiation compared with spine matching (P=.0006), without compromising primary tumor coverage. Conclusion: Frequent patient setup errors occur in locally advanced lung cancer patients. Spine and carina registrations improved combined target coverage throughout the treatment course, but carina matching provided superior combined target coverage.

  20. Microwave Pretreatments of Switchgrass Leaf and Stem Fractions to Increase Methane Production

    Directory of Open Access Journals (Sweden)

    Chunhui Wu

    2015-05-01

    Full Text Available The objective of this study was to determine the effectiveness of microwave pretreatments on methane production from two switchgrass tissues (leaf vs. stem. The methane production from the leaf fraction was significantly affected by the microwave final temperature, while production from the stem fraction was affected by the combination of the microwave final temperature and heating rate. Thus, the highest methane yield from the leaf (134.81 mL CH4/g of volatile solids (VS was obtained at 100 °C, while the highest yield from the stem (99.35 mL CH4/g VS was obtained at 150 °C, with a heating rate of 10 °C/min. Although methane production from the leaf fraction was merely enhanced by 9.1% after microwave pretreatments, the time required to reach 80% of ultimate methane production was reduced by 12 days. For the stem fraction, methane production was improved by 5.2% after microwave pretreatment, and the time to obtain 80% of ultimate methane production increased.

  1. Generalized fractional supersymmetry associated to different species of anyons

    International Nuclear Information System (INIS)

    Douari, Jamila; Abdus Salam International Centre for Theoretical Physics, Trieste; Hassouni, Yassine

    2001-01-01

    We consider multiple species of anyons characterized by different statistical parameters. First, we redefine the anyonic algebra and then generalize this definition by constructing the anyonic superalgebra. Finally, we use these tools to generalize the fractional supersymmetry already discussed. (author)

  2. Fractional vector calculus for fractional advection dispersion

    Science.gov (United States)

    Meerschaert, Mark M.; Mortensen, Jeff; Wheatcraft, Stephen W.

    2006-07-01

    We develop the basic tools of fractional vector calculus including a fractional derivative version of the gradient, divergence, and curl, and a fractional divergence theorem and Stokes theorem. These basic tools are then applied to provide a physical explanation for the fractional advection-dispersion equation for flow in heterogeneous porous media.

  3. Unsteady flow of fractional Oldroyd-B fluids through rotating annulus

    Science.gov (United States)

    Tahir, Madeeha; Naeem, Muhammad Nawaz; Javaid, Maria; Younas, Muhammad; Imran, Muhammad; Sadiq, Naeem; Safdar, Rabia

    2018-04-01

    In this paper exact solutions corresponding to the rotational flow of a fractional Oldroyd-B fluid, in an annulus, are determined by applying integral transforms. The fluid starts moving after t = 0+ when pipes start rotating about their axis. The final solutions are presented in the form of usual Bessel and hypergeometric functions, true for initial and boundary conditions. The limiting cases for the solutions for ordinary Oldroyd-B, fractional Maxwell and Maxwell and Newtonian fluids are obtained. Moreover, the solution is obtained for the fluid when one pipe is rotating and the other one is at rest. At the end of this paper some characteristics of fluid motion, the effect of the physical parameters on the flow and a correlation between different fluid models are discussed. Finally, graphical representations confirm the above affirmation.

  4. Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

    Science.gov (United States)

    Chen, Shanzhen; Jiang, Xiaoyun

    2012-08-01

    In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.

  5. Direct and inverse source problems for a space fractional advection dispersion equation

    KAUST Repository

    Aldoghaither, Abeer

    2016-05-15

    In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from final observations. We first derive the analytic solution to the direct problem which we use to prove the uniqueness and the unstability of the inverse source problem using final measurements. Finally, we illustrate the results with a numerical example.

  6. Calculation of combustible waste fraction (CWF) estimates used in organics safety issue screening

    International Nuclear Information System (INIS)

    Heasler, P.G.; Gao, F.; Toth, J.J.

    1998-08-01

    This report describes how in-tank measurements of moisture (H 2 O) and total organic carbon (TOC) are used to calculate combustible waste fractions (CWF) for 138 of the 149 Hanford single shell tanks. The combustible waste fraction of a tank is defined as that proportion of waste that is capable of burning when exposed to an ignition source. These CWF estimates are used to screen tanks for the organics complexant safety issue. Tanks with a suitably low fraction of combustible waste are classified as safe. The calculations in this report determine the combustible waste fractions in tanks under two different moisture conditions: under current moisture conditions, and after complete dry out. The first fraction is called the wet combustible waste fraction (wet CWF) and the second is called the dry combustible waste fraction (dry CWF). These two fractions are used to screen tanks into three categories: if the wet CWF is too high (above 5%), the tank is categorized as unsafe; if the wet CWF is low but the dry CWF is too high (again, above 5%), the tank is categorized as conditionally safe; finally, if both the wet and dry CWF are low, the tank is categorized as safe. Section 2 describes the data that was required for these calculations. Sections 3 and 4 describe the statistical model and resulting fit for dry combustible waste fractions. Sections 5 and 6 present the statistical model used to estimate wet CWF and the resulting fit. Section 7 describes two tests that were performed on the dry combustible waste fraction ANOVA model to validate it. Finally, Section 8 presents concluding remarks. Two Appendices present results on a tank-by-tank basis

  7. Robust Fuzzy Control for Fractional-Order Uncertain Hydroturbine Regulating System with Random Disturbances

    Directory of Open Access Journals (Sweden)

    Fengjiao Wu

    2016-01-01

    Full Text Available The robust fuzzy control for fractional-order hydroturbine regulating system is studied in this paper. First, the more practical fractional-order hydroturbine regulating system with uncertain parameters and random disturbances is presented. Then, on the basis of interval matrix theory and fractional-order stability theorem, a fuzzy control method is proposed for fractional-order hydroturbine regulating system, and the stability condition is expressed as a group of linear matrix inequalities. Furthermore, the proposed method has good robustness which can process external random disturbances and uncertain parameters. Finally, the validity and superiority are proved by the numerical simulations.

  8. Fractional vector calculus and fractional Maxwell's equations

    International Nuclear Information System (INIS)

    Tarasov, Vasily E.

    2008-01-01

    The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered

  9. Fractional Number Operator and Associated Fractional Diffusion Equations

    Science.gov (United States)

    Rguigui, Hafedh

    2018-03-01

    In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator.

  10. Optimizing mesoscopic two-band superconductors for observation of fractional vortex states

    Energy Technology Data Exchange (ETDEWEB)

    Piña, Juan C. [Departamento de Física, Universidade Federal de Pernambuco, Cidade Universitária, 50670-901 Recife, PE (Brazil); Núcleo de Tecnologia, CAA, Universidade Federal de Pernambuco, 55002-970 Caruaru, PE (Brazil); Souza Silva, Clécio C. de, E-mail: clecio@df.ufpe [Departamento de Física, Universidade Federal de Pernambuco, Cidade Universitária, 50670-901 Recife, PE (Brazil); Milošević, Milorad V. [Departamento de Física, Universidade Federal do Ceará, 60455-900 Fortaleza, Ceará (Brazil); Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen (Belgium)

    2014-08-15

    Highlights: • Observation of fractional vortices in two-band superconductors of broad size range. • There is a minimal sample size for observing each particular fractional state. • Optimal value for stability of each fractional state is determined. • A suitable magnetic dot enhances stability even further. - Abstract: Using the two-component Ginzburg–Landau model, we investigate the effect of sample size and magnitude and homogeneity of external magnetic field on the stability of fractional vortex states in a mesoscopic two-band superconducting disk. We found that each fractional state has a preferable sample size, for which the range of applied field in which the state is stable is pronouncedly large. Vice versa, there exists an optimal magnitude of applied field for which a large range of possible sample radii will support the considered fractional state. Finally, we show that the stability of fractional states can be enhanced even further by magnetic nanostructuring of the sample, i.e. by suitably chosen geometrical parameters and magnetic moment of a ferromagnetic dot placed on top of the superconducting disk.

  11. Fractional Processes and Fractional-Order Signal Processing Techniques and Applications

    CERN Document Server

    Sheng, Hu; Qiu, TianShuang

    2012-01-01

    Fractional processes are widely found in science, technology and engineering systems. In Fractional Processes and Fractional-order Signal Processing, some complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations (local and long memory), are introduced and examined from the ‘fractional’ perspective using simulation, fractional-order modeling and filtering and realization of fractional-order systems. These fractional-order signal processing (FOSP) techniques are based on fractional calculus, the fractional Fourier transform and fractional lower-order moments. Fractional Processes and Fractional-order Signal Processing: • presents fractional processes of fixed, variable and distributed order studied as the output of fractional-order differential systems; • introduces FOSP techniques and the fractional signals and fractional systems point of view; • details real-world-application examples of FOSP techniques to demonstr...

  12. Skin and lung reaction to fractionated x iradiation in mice

    International Nuclear Information System (INIS)

    Field, S.B.; Hornsey, S.; Hammersmith Hospital, London

    1980-01-01

    The dependence between the summary dose and the number of fractions for lung and skin injuries of mice, are studied. Single irradiation and irradiation consisting of a different number of fractions are applied. Results are estimated in two directions. Fractionated irradiation is compared with single irradiation. In the case of such an approach the assumption that the observed lung and skin injury results from cell death, the correlation between the initial slope of the survival curve and the final slope is about 7:1. The additional dose necessary when doubling the number of fractions is measured. In the first approximation, these results agree with the model of a single-shock multi-target curve and the 3:1 slope ratio. The conclusion is made that the double-component model gives an inadequate description of cell survival curves of both skin and lungs [ru

  13. The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method

    Directory of Open Access Journals (Sweden)

    Hasan Bulut

    2013-01-01

    Full Text Available We introduce the rudiments of fractional calculus and the consequent applications of the Sumudu transform on fractional derivatives. Once this connection is firmly established in the general setting, we turn to the application of the Sumudu transform method (STM to some interesting nonhomogeneous fractional ordinary differential equations (FODEs. Finally, we use the solutions to form two-dimensional (2D graphs, by using the symbolic algebra package Mathematica Program 7.

  14. Fractional calculus in bioengineering, part 3.

    Science.gov (United States)

    Magin, Richard L

    2004-01-01

    -threshold nerve propagation. By expanding the range of mathematical operations to include fractional calculus, we can develop new and potentially useful functional relationships for modeling complex biological systems in a direct and rigorous manner. In Part 2 of this review (Crit Rev Biomed Eng 2004; 32(1):105-193), fractional calculus was applied to problems in nerve stimulation, dielectric relaxation, and viscoelastic materials by extending the governing differential equations to include fractional order terms. In this third and final installment, we consider distributed systems that represent shear stress in fluids, heat transfer in uniform one-dimensional media, and subthreshold nerve depolarization. Classic electrochemical analysis and impedance spectroscopy are also reviewed from the perspective of fractional calculus, and selected examples from recent studies in neuroscience, bioelectricity, and tissue biomechanics are analyzed to illustrate the vitality of the field.

  15. Fractionation and Purification of Bioactive Compounds Obtained from a Brewery Waste Stream

    Directory of Open Access Journals (Sweden)

    Letricia Barbosa-Pereira

    2013-01-01

    Full Text Available The brewery industry generates waste that could be used to yield a natural extract containing bioactive phenolic compounds. We compared two methods of purifying the crude extract—solid-phase extraction (SPE and supercritical fluid extraction (SFE—with the aim of improving the quality of the final extract for potential use as safe food additive, functional food ingredient, or nutraceutical. The predominant fractions yielded by SPE were the most active, and the fraction eluted with 30% (v/v of methanol displayed the highest antioxidant activity (0.20 g L−1, similar to that of BHA. The most active fraction yielded by SFE (EC50 of 0.23 g L−1 was obtained under the following conditions: temperature 40°C, pressure 140 bar, extraction time 30 minutes, ethanol (6% as a modifier, and modifier flow 0.2 mL min−1. Finally, we found that SFE is the most suitable procedure for purifying the crude extracts and improves the organoleptic characteristics of the product: the final extract was odourless, did not contain solvent residues, and was not strongly coloured. Therefore, natural extracts obtained from the residual stream and purified by SFE can be used as natural antioxidants with potential applications in the food, cosmetic, and pharmaceutical industries.

  16. Stability analysis of fractional-order Hopfield neural networks with time delays.

    Science.gov (United States)

    Wang, Hu; Yu, Yongguang; Wen, Guoguang

    2014-07-01

    This paper investigates the stability for fractional-order Hopfield neural networks with time delays. Firstly, the fractional-order Hopfield neural networks with hub structure and time delays are studied. Some sufficient conditions for stability of the systems are obtained. Next, two fractional-order Hopfield neural networks with different ring structures and time delays are developed. By studying the developed neural networks, the corresponding sufficient conditions for stability of the systems are also derived. It is shown that the stability conditions are independent of time delays. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results obtained in this paper. Copyright © 2014 Elsevier Ltd. All rights reserved.

  17. Series expansion in fractional calculus and fractional differential equations

    OpenAIRE

    Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao

    2009-01-01

    Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this theorem, in this paper we introduce fractional series expansion method to fractional calculus. We define a kind of fractional Taylor series of an infinitely fractionally-differentiable function. Further, based on our definition we generalize hypergeometric functio...

  18. Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time

    Directory of Open Access Journals (Sweden)

    M. L. Kavvas

    2017-10-01

    Full Text Available Using fractional calculus, a dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First, a dimensionally consistent continuity equation for transient saturated groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. For the equation of water flux within a multi-fractional multidimensional confined aquifer, a dimensionally consistent equation is also developed. The governing equation of transient saturated groundwater flow in a multi-fractional, multidimensional confined aquifer in fractional time is then obtained by combining the fractional continuity and water flux equations. To illustrate the capability of the proposed governing equation of groundwater flow in a confined aquifer, a numerical application of the fractional governing equation to a confined aquifer groundwater flow problem was also performed.

  19. Algorithms for testing of fractional dynamics: a practical guide to ARFIMA modelling

    International Nuclear Information System (INIS)

    Burnecki, Krzysztof; Weron, Aleksander

    2014-01-01

    In this survey paper we present a systematic methodology which demonstrates how to identify the origins of fractional dynamics. We consider three mechanisms which lead to it, namely fractional Brownian motion, fractional Lévy stable motion and an autoregressive fractionally integrated moving average (ARFIMA) process but we concentrate on the ARFIMA modelling. The methodology is based on statistical tools for identification and validation of the fractional dynamics, in particular on an ARFIMA parameter estimator, an ergodicity test, a self-similarity index estimator based on sample p-variation and a memory parameter estimator based on sample mean-squared displacement. A complete list of algorithms needed for this is provided in appendices A–F. Finally, we illustrate the methodology on various empirical data and show that ARFIMA can be considered as a universal model for fractional dynamics. Thus, we provide a practical guide for experimentalists on how to efficiently use ARFIMA modelling for a large class of anomalous diffusion data. (paper)

  20. Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time

    OpenAIRE

    M. L. Kavvas; T. Tu; A. Ercan; J. Polsinelli

    2017-01-01

    Using fractional calculus, a dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First, a dimensionally consistent continuity equation for transient saturated groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. For the equation of water flux within a multi-fractional multidimensional confined aquifer, a dimensionally...

  1. Consensus of Fractional-Order Multiagent Systems with Double Integrator under Switching Topologies

    Directory of Open Access Journals (Sweden)

    Shiyun Shen

    2017-01-01

    Full Text Available Due to the complexity of the practical environments, many systems can only be described with the fractional-order dynamics. In this paper, the consensus of fractional-order multiagent systems with double integrator under switching topologies is investigated. By applying Mittag-Leffler function, Laplace transform, and dwell time technique, a sufficient condition on consensus is obtained. Finally, a numerical simulation is presented to illustrate the effectiveness of the theoretical result.

  2. State-Feedback Control for Fractional-Order Nonlinear Systems Subject to Input Saturation

    Directory of Open Access Journals (Sweden)

    Junhai Luo

    2014-01-01

    Full Text Available We give a state-feedback control method for fractional-order nonlinear systems subject to input saturation. First, a sufficient condition is derived for the asymptotical stability of a class of fractional-order nonlinear systems. Then based on Gronwall-Bellman lemma and a sector bounded condition of the saturation function, a linear state-feed back controller is designed. Finally, two simulation examples are presented to show the validity of the proposed method.

  3. Feasibility of fractionating Myoview cold kits for cost reduction

    International Nuclear Information System (INIS)

    Penglis, S.; Tsopelas, C.

    1999-01-01

    Full text: Myoview is a freeze-dried ethylene diphosphine ligand that upon reconstitution with 99 Tc m -pertechnetate yields a preparation containing the lipophilic cationic myocardial imaging agent 99 Tc m -tetrofosmin (Tf). The aim of this study was to determine the feasibility of fractionating Myoview kits to reduce the cost of the kit, currently A$350 per vial. Myoview vials were reconstituted with N 2 -flushed saline and split into 4 or 5 aliquots of 0.5 ml, then stored at -80 deg C in N 2 -filled vials for up to 3 months. 99 Tc m -Tf was prepared by the addition of varying volumes of 99 Tc m -pertechnetate (1.1 GBq.ml- 1 ) to give a final ligand concentration of 14.4 μg.ml- 1 , followed by a 15 min incubation at room temperature. Radiochemical purity (RCP) was examined at 0, 1, 2 and 3 months post-fractionation. At each time point, RCP was determined at 0,1, 2, 4, 6 and 24 h post-reconstitution. RCP was measured using the thin layer chromatography method according to the manufacturer's instructions. Over the 3 month evaluation period, RCP was maintained at 96.4 ± 1.7% (n = 48) over 24 h at room temperature. Animal biodistribution studies were used to validate the final product from the full cold kit to that from the fractionated kits. In conclusion, these results show that Myoview kits can be successfully fractionated and stored for up to 3 months. The subsequent 99 Tc m -Tf can be used to provide significant cost reductions, especially when only 1 patient dose is required

  4. A New Scheme on Synchronization of Commensurate Fractional-Order Chaotic Systems Based on Lyapunov Equation

    Directory of Open Access Journals (Sweden)

    Hua Wang

    2016-01-01

    Full Text Available This paper proposes a new fractional-order approach for synchronization of a class of fractional-order chaotic systems in the presence of model uncertainties and external disturbances. A simple but practical method to synchronize many familiar fractional-order chaotic systems has been put forward. A new theorem is proposed for a class of cascade fractional-order systems and it is applied in chaos synchronization. Combined with the fact that the states of the fractional chaotic systems are bounded, many coupled items can be taken as zero items. Then, the whole system can be simplified greatly and a simpler controller can be derived. Finally, the validity of the presented scheme is illustrated by numerical simulations of the fractional-order unified system.

  5. Comparing the Caputo, Caputo-Fabrizio and Atangana-Baleanu derivative with fractional order: Fractional cubic isothermal auto-catalytic chemical system

    Science.gov (United States)

    Saad, K. M.

    2018-03-01

    In this work we extend the standard model for a cubic isothermal auto-catalytic chemical system (CIACS) to a new model of a fractional cubic isothermal auto-catalytic chemical system (FCIACS) based on Caputo (C), Caputo-Fabrizio (CF) and Atangana-Baleanu in the Liouville-Caputo sense (ABC) fractional time derivatives, respectively. We present approximate solutions for these extended models using the q -homotopy analysis transform method ( q -HATM). We solve the FCIACS with the C derivative and compare our results with those obtained using the CF and ABC derivatives. The ranges of convergence of the solutions are found and the optimal values of h , the auxiliary parameter, are derived. Finally, these solutions are compared with numerical solutions of the various models obtained using finite differences and excellent agreement is found.

  6. Fractional quantum Hall states of atoms in optical lattices

    International Nuclear Information System (INIS)

    Soerensen, Anders S.; Demler, Eugene; Lukin, Mikhail D.

    2005-01-01

    We describe a method to create fractional quantum Hall states of atoms confined in optical lattices. We show that the dynamics of the atoms in the lattice is analogous to the motion of a charged particle in a magnetic field if an oscillating quadrupole potential is applied together with a periodic modulation of the tunneling between lattice sites. In a suitable parameter regime the ground state in the lattice is of the fractional quantum Hall type, and we show how these states can be reached by melting a Mott-insulator state in a superlattice potential. Finally, we discuss techniques to observe these strongly correlated states

  7. Fractional variational calculus in terms of Riesz fractional derivatives

    International Nuclear Information System (INIS)

    Agrawal, O P

    2007-01-01

    This paper presents extensions of traditional calculus of variations for systems containing Riesz fractional derivatives (RFDs). Specifically, we present generalized Euler-Lagrange equations and the transversality conditions for fractional variational problems (FVPs) defined in terms of RFDs. We consider two problems, a simple FVP and an FVP of Lagrange. Results of the first problem are extended to problems containing multiple fractional derivatives, functions and parameters, and to unspecified boundary conditions. For the second problem, we present Lagrange-type multiplier rules. For both problems, we develop the Euler-Lagrange-type necessary conditions which must be satisfied for the given functional to be extremum. Problems are considered to demonstrate applications of the formulations. Explicitly, we introduce fractional momenta, fractional Hamiltonian, fractional Hamilton equations of motion, fractional field theory and fractional optimal control. The formulations presented and the resulting equations are similar to the formulations for FVPs given in Agrawal (2002 J. Math. Anal. Appl. 272 368, 2006 J. Phys. A: Math. Gen. 39 10375) and to those that appear in the field of classical calculus of variations. These formulations are simple and can be extended to other problems in the field of fractional calculus of variations

  8. Fractional Schroedinger equation

    International Nuclear Information System (INIS)

    Laskin, Nick

    2002-01-01

    Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations

  9. Fractional thermoelasticity

    CERN Document Server

    Povstenko, Yuriy

    2015-01-01

    This book is devoted to fractional thermoelasticity, i.e. thermoelasticity based on the heat conduction equation with differential operators of fractional order. Readers will discover how time-fractional differential operators describe memory effects and space-fractional differential operators deal with the long-range interaction. Fractional calculus, generalized Fourier law, axisymmetric and central symmetric problems and many relevant equations are featured in the book. The latest developments in the field are included and the reader is brought up to date with current research.  The book contains a large number of figures, to show the characteristic features of temperature and stress distributions and to represent the whole spectrum of order of fractional operators.  This work presents a picture of the state-of-the-art of fractional thermoelasticity and is suitable for specialists in applied mathematics, physics, geophysics, elasticity, thermoelasticity and engineering sciences. Corresponding sections of ...

  10. Agribusiness geothermal energy utilization potential of Klamath and Western Snake River Basins, Oregon. Final report

    Energy Technology Data Exchange (ETDEWEB)

    Lienau, P.J.

    1978-03-01

    Resource assessment and methods of direct utilization for existing and prospective food processing plants have been determined in two geothermal resource areas in Oregon. Ore-Ida Foods, Inc. and Amalgamated Sugar Company in the Snake River Basin; Western Polymer Corporation (potato starch extraction) and three prospective industries--vegetable dehydration, alfalfa drying and greenhouses--in the Klamath Basin have been analyzed for direct utilization of geothermal fluids. Existing geologic knowledge has been integrated to indicate locations, depth, quality, and estimated productivity of the geothermal reservoirs. Energy-economic needs and balances, along with cost and energy savings associated with field development, delivery systems, in-plant applications and fluid disposal have been calculated for interested industrial representatives.

  11. Microfluidic Devices for Blood Fractionation

    Directory of Open Access Journals (Sweden)

    Chwee Teck Lim

    2011-07-01

    Full Text Available Blood, a complex biological fluid, comprises 45% cellular components suspended in protein rich plasma. These different hematologic components perform distinct functions in vivo and thus the ability to efficiently fractionate blood into its individual components has innumerable applications in both clinical diagnosis and biological research. Yet, processing blood is not trivial. In the past decade, a flurry of new microfluidic based technologies has emerged to address this compelling problem. Microfluidics is an attractive solution for this application leveraging its numerous advantages to process clinical blood samples. This paper reviews the various microfluidic approaches realized to successfully fractionate one or more blood components. Techniques to separate plasma from hematologic cellular components as well as isolating blood cells of interest including certain rare cells are discussed. Comparisons based on common separation metrics including efficiency (sensitivity, purity (selectivity, and throughput will be presented. Finally, we will provide insights into the challenges associated with blood-based separation systems towards realizing true point-of-care (POC devices and provide future perspectives.

  12. Fractional quantum mechanics

    CERN Document Server

    Laskin, Nick

    2018-01-01

    Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics. This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder. The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schrödinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Lévy flights. The fractional path integral method enhances the well-known Feynman path integral framework. Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the α-stable Lévy random process. The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique...

  13. PWR steam generator chemical cleaning. Phase I: Final report, Volume I

    International Nuclear Information System (INIS)

    1978-07-01

    Two chemical cleaning solvent systems and two application methods were developed to remove the sludge in nuclear steam generators and to remove the corrosion products in the annuli between the steam generator tubes and the support plates. Laboratory testing plus subsequent pilot testing has demonstrated that, in a reasonable length of time, both solvents are capable of dissolving significant amounts of sludge, and of dissolving tightly packed magnetite in tube/support plate crevices. Further, tests have demonstrated that surface losses of the materials of construction in steam generators can be controlled to acceptable limits for the duration of the required cleaning period. Areas requiring further study and test have been identified, and a preliminary procedure for chemical cleaning nuclear steam generators has been chosen subject to quantification based on additional tests prior to actual in-plant demonstration

  14. The response of mouse skin and lung to fractionated x-rays

    International Nuclear Information System (INIS)

    Field, S.B.; Hornsey, S.

    1975-01-01

    The relationship between total dose and number of fractions has been investigated for damage to lung and skin in mice. Single doses and various numbers of fractions have been given and the results are analysed in two ways: (i) by comparing the fractionated treatment with a single dose. With this approach, and assuming that the observed damage to lung and skin is the result of cell killing, it is estimated that the ratio of initial to final slope of the cell survival curve is about 7:1; (ii) by measuring the additional dose required when the number of fractions is doubled. These results are roughly fitted by a single-hit times multitarget survival-curve model, with the ratio of slopes about 3:1. It is concluded from this discrepancy that the two-component model is an inadequate description of the survival curve for the cells of either skin or lung. (author)

  15. Lie symmetry analysis and conservation laws for the time fractional fourth-order evolution equation

    Directory of Open Access Journals (Sweden)

    Wang Li

    2017-06-01

    Full Text Available In this paper, we study Lie symmetry analysis and conservation laws for the time fractional nonlinear fourth-order evolution equation. Using the method of Lie point symmetry, we provide the associated vector fields, and derive the similarity reductions of the equation, respectively. The method can be applied wisely and efficiently to get the reduced fractional ordinary differential equations based on the similarity reductions. Finally, by using the nonlinear self-adjointness method and Riemann-Liouville time-fractional derivative operator as well as Euler-Lagrange operator, the conservation laws of the equation are obtained.

  16. Ultrasonic flowmeters. Progress report II

    International Nuclear Information System (INIS)

    Wittekind, W.D.

    1980-01-01

    This progress report presents results of in-plant testing of the prototype ultrasonic flowmeter and describes modifications to the prototype as a result of these tests. The modified prototype, designated MOD-I, is described in detail including the principle of operation, equipment used and the results of both laboratory and in-plant demonstrations

  17. New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis.

    Science.gov (United States)

    Ingo, Carson; Magin, Richard L; Parrish, Todd B

    2014-11-01

    Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag-Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.

  18. New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis

    Directory of Open Access Journals (Sweden)

    Carson Ingo

    2014-11-01

    Full Text Available Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag–Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.

  19. Field theory of anyons and the fractional quantum Hall effect

    International Nuclear Information System (INIS)

    Viefers, S.F.

    1997-11-01

    The thesis is devoted to a theoretical study of anyons, i.e. particles with fractional statistics moving in two space dimensions, and the quantum Hall effect. The latter constitutes the only known experimental realization of anyons in that the quasiparticle excitations in the fractional quantum Hall system are believed to obey fractional statistics. First, the properties of ideal quantum gases in two dimensions and in particular the equation of state of the free anyons gas are discussed. Then, a field theory formulation of anyons in a strong magnetic field is presented and later extended to a system with several species of anyons. The relation of this model to fractional exclusion statistics, i.e. intermediate statistics introduced by a generalization of the Pauli principle, and to the low-energy excitations at the edge of the quantum Hall system is discussed. Finally, the Chern-Simons-Landau-Ginzburg theory of the fractional quantum Hall effect is studied, mainly focusing on edge effects; both the ground state and the low-energy edge excitations are examined in the simple one-component model and in an extended model which includes spin effects

  20. Effect of binary fraction on color-magnitude diagram of NGC 1904

    Science.gov (United States)

    Li, Zhongmu; Deng, Yangyang

    2018-05-01

    The age of a southern globular cluster in Milky Way, NGC 1904, was shown to be larger than the typical age of the universe, around 13.7 Gyr, by some photometric studies which assumed all stars as single stars. Besides the uncertainties in photometry, isochrone and fitting technique, the neglect of binary stars possibly distorted the result. We study the effect of binary fraction on the color-magnitude diagram (CMD) of NGC 1904, via a new tool for CMD studies, Powerful CMD, which can determine binary fraction, age, metallicity, distance modulus, color excess, rotating star fraction and star formation history simultaneously. We finally obtain the youngest age of 14.1±2.1 Gyr with a zero-age binary fraction of 60 percent for cluster NGC 1904. The result is consistent with the age of the universe. Although our result suggests that binary fraction affects the determination of age slightly, it can improve the fitting to observed CMD, in particular blue stragglers. This suggests us to consider the effect of binaries in the studies of star clusters.

  1. Design and analysis of fractional order seismic transducer for displacement and acceleration measurements

    Science.gov (United States)

    Veeraian, Parthasarathi; Gandhi, Uma; Mangalanathan, Umapathy

    2018-04-01

    Seismic transducers are widely used for measurement of displacement, velocity, and acceleration. This paper presents the design of seismic transducer in the fractional domain for the measurement of displacement and acceleration. The fractional order transfer function for seismic displacement and acceleration transducer are derived using Grünwald-Letnikov derivative. Frequency response analysis of fractional order seismic displacement transducer (FOSDT) and fractional order seismic acceleration transducer (FOSAT) are carried out for different damping ratio with the different fractional order, and the maximum dynamic measurement range is identified. The results demonstrate that fractional order seismic transducer has increased dynamic measurement range and less phase distortion as compared to the conventional seismic transducer even with a lower damping ratio. Time response of FOSDT and FOSAT are derived analytically in terms of Mittag-Leffler function, the effect of fractional behavior in the time domain is evaluated from the impulse and step response. The fractional order system is found to have significantly reduced overshoot as compared to the conventional transducer. The fractional order seismic transducer design proposed in this paper is illustrated with a design example for FOSDT and FOSAT. Finally, an electrical equivalent of FOSDT and FOSAT is considered, and its frequency response is found to be in close agreement with the proposed fractional order seismic transducer.

  2. Estimation of in-plant source term release behaviors from Fukushima daiichi reactor cores by forward method and comparison with reverse method

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Tae Won; Rhee, Bo Wook; Song, Jin Ho; Kim, Sung Il; Ha, Kwang Soon [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

    2017-06-15

    The purpose of this paper is to confirm the event timings and the magnitude of fission product aerosol release from the Fukushima accident. Over a few hundreds of technical papers have been published on the environmental impact of Fukushima Daiichi accident since the accident occurred on March 11, 2011. However, most of the research used reverse or inverse method based on the monitoring of activities in the remote places and only few papers attempted to estimate the release of fission products from individual reactor core or from individual spent fuel pool. Severe accident analysis code can be used to estimate the radioactive release from which reactor core and from which radionuclide the peaks in monitoring points can be generated. The basic material used for this study are the initial core inventory obtained from the report JAEA-Data/Code 2012–018 and the given accident scenarios provided by Japanese Government or Tokyo Electric Power Company (TEPCO) in official reports. In this research a forward method using severe accident progression code is used as it might be useful for justifying the results of reverse or inverse method or vice versa. The release timing and amounts to the environment are estimated for volatile radioactive fission products such as noble gases, cesium, iodine, and tellurium up to 184 hours (about 7.7 days) after earthquake occurs. The in-plant fission product behaviors and release characteristics to environment are estimated using the severe accident progression analysis code, MELCOR, for Fukushima Daiichi accident. These results are compared with other research results which are summarized in UNSCEAR 2013 Report and other technical papers. Also it may provide the physically based arguments for justifying or suspecting the rationale for the scenarios provided in open literature. The estimated results by MELCOR code simulation of this study indicate that the release amount of volatile fission products to environment from Units 1, 2, and 3

  3. Direct and inverse source problems for a space fractional advection dispersion equation

    KAUST Repository

    Aldoghaither, Abeer; Laleg-Kirati, Taous-Meriem; Liu, Da Yan

    2016-01-01

    In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from final observations. We first derive the analytic

  4. Fractional statistics and fractional quantized Hall effect

    International Nuclear Information System (INIS)

    Tao, R.; Wu, Y.S.

    1985-01-01

    The authors suggest that the origin of the odd-denominator rule observed in the fractional quantized Hall effect (FQHE) may lie in fractional statistics which govern quasiparticles in FQHE. A theorem concerning statistics of clusters of quasiparticles implies that fractional statistics do not allow coexistence of a large number of quasiparticles at fillings with an even denominator. Thus, no Hall plateau can be formed at these fillings, regardless of the presence of an energy gap. 15 references

  5. Exclusive B Decays to Charmonium Final States

    Energy Technology Data Exchange (ETDEWEB)

    Barrera, Barbara

    2000-10-13

    We report on exclusive decays of B mesons into final states containing charmonium using data collected with the BABAR detector at the PEP-II storage rings. The charmonium states considered here are J/{psi}, {psi}(2S), and {chi}{sub c1}. Branching fractions for several exclusive final states, a measurement of the decay amplitudes for the B{sup 0} {yields} J/{psi} K* decay, and measurements of the B{sup 0} and B{sup +} masses are presented. All of the results we present here are preliminary.

  6. Tempered fractional calculus

    Energy Technology Data Exchange (ETDEWEB)

    Sabzikar, Farzad, E-mail: sabzika2@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Meerschaert, Mark M., E-mail: mcubed@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Chen, Jinghua, E-mail: cjhdzdz@163.com [School of Sciences, Jimei University, Xiamen, Fujian, 361021 (China)

    2015-07-15

    Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

  7. Tempered fractional calculus

    Science.gov (United States)

    Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua

    2015-07-01

    Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

  8. Tempered fractional calculus

    International Nuclear Information System (INIS)

    Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua

    2015-01-01

    Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series

  9. Bio-Oil Separation and Stabilization by Supercritical Fluid Fractionation. 2014 Final Report

    Energy Technology Data Exchange (ETDEWEB)

    Agblevor, Foster [Utah State Univ., Logan, UT (United States); Petkovic, Lucia [Idaho National Lab. (INL), Idaho Falls, ID (United States); Bennion, Edward [Utah State Univ., Logan, UT (United States); Quinn, Jason [Utah State Univ., Logan, UT (United States); Moses, John [CF Technologies, Hyde Park, MA (United States); Newby, Deborah [Idaho National Lab. (INL), Idaho Falls, ID (United States); Ginosar, Daniel [Idaho National Lab. (INL), Idaho Falls, ID (United States)

    2014-03-01

    The objective of this project is to use supercritical fluids to separate and fractionate algal-based bio-oils into stable products that can be subsequently upgraded to produce drop-in renewable fuels. To accomplish this objective, algae was grown and thermochemically converted to bio-oils using hydrothermal liquefaction (HTL), pyrolysis, and catalytic pyrolysis. The bio-oils were separated into an extract and a raffinate using near-critical propane or carbon dioxide. The fractions were then subjected to thermal aging studies to determine if the extraction process had stabilized the products. It was found that the propane extract fraction was twice as stable as the parent catalytic pyrolysis bio-oils as measured by the change in viscosity after two weeks of accelerated aging at 80°C. Further, in-situ NMR aging studies found that the propane extract was chemically more stable than the parent bio-oil. Thus the milestone of stabilizing the product was met. A preliminary design of the extraction plant was prepared. The design was based on a depot scale plant processing 20,000,000 gallons per year of bio-oil. It was estimated that the capital costs for such a plant would be $8,700,000 with an operating cost of $3,500,000 per year. On a per gallon of product cost and a 10% annual rate of return, capital costs would represent $0.06 per gallon and operating costs would amount to $0.20 per gallon. Further, it was found that the energy required to run the process represented 6.2% of the energy available in the bio-oil, meeting the milestone of less than 20%. Life cycle analysis and greenhouse gas (GHG) emission analysis found that the energy for running the critical fluid separation process and the GHG emissions were minor compared to all the inputs to the overall well to pump system. For the well to pump system boundary, energetics in biofuel conversion are typically dominated by energy demands in the growth, dewater, and thermochemical process. Bio-oil stabilization by

  10. Robust fast controller design via nonlinear fractional differential equations.

    Science.gov (United States)

    Zhou, Xi; Wei, Yiheng; Liang, Shu; Wang, Yong

    2017-07-01

    A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  11. [Immune regulation activity and mechanism of Tibetan Kefir exopolysaccharide fractions].

    Science.gov (United States)

    Meng, Li; Zhang, Lanwei

    2009-12-01

    To investigate the effects and mechanism on immune regulation activity in mice of two Tibetan Kefir exoploysaccharides (EPS) with different molecular weight of 0.1 x 10(5) - 3 x 10(5) (fraction 1) and 1.8 x 10(3) (fraction 2). The immune regulation activity experiment was carried out in vitro based on the Functional Assessment Procedure and Test Methods of Health Food, which was issued by Ministry of Health of China. First, we treated mice subjects with EPS at doses of 40 mg/kg, 80 mg/kg, 120 mg/kg through ig. Then we detected the index of immune organs, the ability of antibody production (tested by HC50), activity of NK cell, delayed type hypersensitivity (DTH) and phagocytosis of macrophage in mice. Finally, we examined the expression of Erk protein in Macrophages by Western Blot assay. Fraction 1 could promote HC50, activity of NK cell and DTH in mice which low dose showed better. Fraction 2 could promote DTH, phagocytosis of macrophage which high dose showed better. The expression of Erk and COX-2 had the same trend with Phagocytic index. We verified the two fractions of Tibetan Kefir EPS could enhance immune functions in mice. Fraction 1 regulated immune function through NK cell and B cell while fraction 2 through macrophage cell and T cell. The effects to macrophage of Tibetan Kefir EPS in mice may realize through extra cellular signal-regulated kinase Erk pathway.

  12. Fractional Hopfield Neural Networks: Fractional Dynamic Associative Recurrent Neural Networks.

    Science.gov (United States)

    Pu, Yi-Fei; Yi, Zhang; Zhou, Ji-Liu

    2017-10-01

    This paper mainly discusses a novel conceptual framework: fractional Hopfield neural networks (FHNN). As is commonly known, fractional calculus has been incorporated into artificial neural networks, mainly because of its long-term memory and nonlocality. Some researchers have made interesting attempts at fractional neural networks and gained competitive advantages over integer-order neural networks. Therefore, it is naturally makes one ponder how to generalize the first-order Hopfield neural networks to the fractional-order ones, and how to implement FHNN by means of fractional calculus. We propose to introduce a novel mathematical method: fractional calculus to implement FHNN. First, we implement fractor in the form of an analog circuit. Second, we implement FHNN by utilizing fractor and the fractional steepest descent approach, construct its Lyapunov function, and further analyze its attractors. Third, we perform experiments to analyze the stability and convergence of FHNN, and further discuss its applications to the defense against chip cloning attacks for anticounterfeiting. The main contribution of our work is to propose FHNN in the form of an analog circuit by utilizing a fractor and the fractional steepest descent approach, construct its Lyapunov function, prove its Lyapunov stability, analyze its attractors, and apply FHNN to the defense against chip cloning attacks for anticounterfeiting. A significant advantage of FHNN is that its attractors essentially relate to the neuron's fractional order. FHNN possesses the fractional-order-stability and fractional-order-sensitivity characteristics.

  13. Misonidazole in fractionated radiotherapy: are many small fractions best

    International Nuclear Information System (INIS)

    Denekamp, J.; McNally, N.J.; Fowler, J.F.; Joiner, M.C.

    1980-01-01

    The largest sensitizing effect is always demonstrated with six fractions, each given with 2 g/m 2 of misonidazole. In the absence of reoxygenation a sensitizer enhancement ratio of 1.7 is predicted, but this falls to 1.1-1.2 if extensive reoxygenation occurs. Less sensitization is observed with 30 fractions, each with 0.4 g/m 2 of drug. However, for clinical use, the important question is which treatment kills the maximum number of tumour cells. Many of the simulations predict a marked disadvantage of reducing the fraction number for X rays alone. The circumstances in which this disadvantage is offset by the large Sensitizer enhancement ratio values with a six-fraction schedule are few. The model calculations suggest that many small fractions, each with a low drug dose, are safest unless the clinician has some prior knowledge that a change in fraction number is not disadvantageous. (author)

  14. Pyrolysis of tyres. Influence of the final temperature of the process on emissions and the calorific value of the products recovered

    International Nuclear Information System (INIS)

    Diez, C.; Martinez, O.; Calvo, L.F.; Cara, J.; Moran, A.

    2004-01-01

    A study was made of the pyrolysis of tyre particles, with the aim of determining the possibilities of using the products resulting from the process as fuel. Three final temperatures were used, determined from thermogravimetric data. The design of the experiment was a horizontal oven containing a reactor into which particles of the original tyre were placed. After the process, a solid fraction (char) remained in the reactor, while the gases generated went through a set of scrubbers where most of the condensable fraction (oils) was retained. Finally, once free of this fraction, the gases were collected in glass ampoules. Solid and liquids fractions were subjected to thermogravimetric analyses in order to study their combustibility. The gas fraction was analysed by means of gas chromatography to establish the content of CO, CO 2 , H 2 and hydrocarbons present in the samples (mainly components of gases produced in the pyrolysis process). A special study was made of the sulphur and chlorine content of all the fractions, as the presence of these elements could be problematic if the products are used as fuel. Tyre pyrolysis engenders a solid carbon residue that concentrates sulphur and chorine, with a relatively high calorific value, although not so high as that of the original tyre. The liquid fraction produced by the process has a high calorific value, which rises with the final temperature, up to 40 MJ/kg. The chlorine content of this fraction is negligible. Over 95% of the gas fraction, regardless of the final temperature, is composed of hydrocarbons of a low molecular weight and hydrogen, this fraction also appearing to be free of chlorine

  15. Application of Generalized Fractional Thermoelasticity Theory with Two Relaxation Times to an Electromagnetothermoelastic Thick Plate

    Directory of Open Access Journals (Sweden)

    A. M. Abd El-Latief

    2016-01-01

    Full Text Available The fractional mathematical model of Maxwell’s equations in an electromagnetic field and the fractional generalized thermoelastic theory associated with two relaxation times are applied to a 1D problem for a thick plate. Laplace transform is used. The solution in Laplace transform domain has been obtained using a direct method and its inversion is calculated numerically using a method based on Fourier series expansion technique. Finally, the effects of the two fractional parameters (thermo and magneto on variable fields distributions are made. Numerical results are represented graphically.

  16. Fractional Order Differentiation by Integration and Error Analysis in Noisy Environment

    KAUST Repository

    Liu, Dayan

    2015-03-31

    The integer order differentiation by integration method based on the Jacobi orthogonal polynomials for noisy signals was originally introduced by Mboup, Join and Fliess. We propose to extend this method from the integer order to the fractional order to estimate the fractional order derivatives of noisy signals. Firstly, two fractional order differentiators are deduced from the Jacobi orthogonal polynomial filter, using the Riemann-Liouville and the Caputo fractional order derivative definitions respectively. Exact and simple formulae for these differentiators are given by integral expressions. Hence, they can be used for both continuous-time and discrete-time models in on-line or off-line applications. Secondly, some error bounds are provided for the corresponding estimation errors. These bounds allow to study the design parameters\\' influence. The noise error contribution due to a large class of stochastic processes is studied in discrete case. The latter shows that the differentiator based on the Caputo fractional order derivative can cope with a class of noises, whose mean value and variance functions are polynomial time-varying. Thanks to the design parameters analysis, the proposed fractional order differentiators are significantly improved by admitting a time-delay. Thirdly, in order to reduce the calculation time for on-line applications, a recursive algorithm is proposed. Finally, the proposed differentiator based on the Riemann-Liouville fractional order derivative is used to estimate the state of a fractional order system and numerical simulations illustrate the accuracy and the robustness with respect to corrupting noises.

  17. Fractional dynamic calculus and fractional dynamic equations on time scales

    CERN Document Server

    Georgiev, Svetlin G

    2018-01-01

    Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations.  Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales. .

  18. Fractional gradient and its application to the fractional advection equation

    OpenAIRE

    D'Ovidio, M.; Garra, R.

    2013-01-01

    In this paper we provide a definition of fractional gradient operators, related to directional derivatives. We develop a fractional vector calculus, providing a probabilistic interpretation and mathematical tools to treat multidimensional fractional differential equations. A first application is discussed in relation to the d-dimensional fractional advection-dispersion equation. We also study the connection with multidimensional L\\'evy processes.

  19. Fractionation of Pb and Cu in the fine fraction (landfill.

    Science.gov (United States)

    Kaczala, Fabio; Orupõld, Kaja; Augustsson, Anna; Burlakovs, Juris; Hogland, Marika; Bhatnagar, Amit; Hogland, William

    2017-11-01

    The fractionation of metals in the fine fraction (landfill was carried out to evaluate the metal (Pb and Cu) contents and their potential towards not only mobility but also possibilities of recovery/extraction. The fractionation followed the BCR (Community Bureau of Reference) sequential extraction, and the exchangeable (F1), reducible (F2), oxidizable (F3) and residual fractions were determined. The results showed that Pb was highly associated with the reducible (F2) and oxidizable (F3) fractions, suggesting the potential mobility of this metal mainly when in contact with oxygen, despite the low association with the exchangeable fraction (F1). Cu has also shown the potential for mobility when in contact with oxygen, since high associations with the oxidizable fraction (F3) were observed. On the other hand, the mobility of metals in excavated waste can be seen as beneficial considering the circular economy and recovery of such valuables back into the economy. To conclude, not only the total concentration of metals but also a better understanding of fractionation and in which form metals are bound is very important to bring information on how to manage the fine fraction from excavated waste both in terms of environmental impacts and also recovery of such valuables in the economy.

  20. Fractional-Order Identification and Control of Heating Processes with Non-Continuous Materials

    Directory of Open Access Journals (Sweden)

    Riccardo Caponetto

    2016-11-01

    Full Text Available The paper presents a fractional order model of a heating process and a comparison of fractional and standard PI controllers in its closed loop system. Preliminarily, an enhanced fractional order model for the heating process on non-continuous materials has been identified through a fitting algorithm on experimental data. Experimentation has been carried out on a finite length beam filled with three non-continuous materials (air, styrofoam, metal buckshots in order to identify a model in the frequency domain and to obtain a relationship between the fractional order of the heating process and the different materials’ properties. A comparison between the experimental model and the theoretical one has been performed, proving a significant enhancement of the fitting performances. Moreover the obtained modelling results confirm the fractional nature of the heating processes when diffusion occurs in non-continuous composite materials, and they show how the model’s fractional order can be used as a characteristic parameter for non-continuous materials with different composition and structure. Finally, three different kinds of controllers have been applied and compared in order to keep constant the beam temperature constant at a fixed length.

  1. Static output feedback ℋ ∞ control for a fractional-order glucose-insulin system

    KAUST Repository

    N’Doye, Ibrahima

    2015-05-23

    This paper presents the ℋ∞ static output feedback control of nonlinear fractional-order systems. Based on the extended bounded real lemma, the ℋ∞ control is formulated and sufficient conditions are derived in terms of linear matrix inequalities (LMIs) formulation by using the fractional Lyapunov direct method where the fractional-order α belongs to 0 < α < 1. The control approach is finally applied to the regulation of the glucose level in diabetes type 1 treatment. Therefore, it is attempted to incorporate fractional-order into the mathematical minimal model of glucose-insulin system dynamics and it is still an interesting challenge to show, how the order of a fractional differential system affects the dynamics of the system in the presence of meal disturbance. Numerical simulations are carried out to illustrate our proposed results and show that the nonlinear fractional-order glucose-insulin systems are, at least, as stable as their integer-order counterpart in the presence of exogenous glucose infusion or meal disturbance. © 2015 Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg

  2. Final states in Si and GaAs via RF μSR spectroscopy

    International Nuclear Information System (INIS)

    Kreitzman, S.R.; Pfiz, T.; Riseman, T.M.; Brewer, J.H.; Williams, D.L.; Sun-Mack, S.; Estle, T.L.

    1991-01-01

    The ionization of muonium centers in Si and GaAs have been studied using radio frequency (RF) resonant techniques. In Si all three muonic centers are detectable by RF. No evidence was found for delayed Mu and Mu * states at any temperature. However, our results on the diamagnetic final state (μ f + ) show that it is composed of prompt fractions (as seen by conventional μSR) and delayed fractions arising from the ionization of Mu * and Mu. We observe a full μ f + fraction at 317 K when the Mu relaxation rate is above 10 μs -1 . GaAs differs from the situation in Si in that we observed only a partial conversion of Mu * and Mu to a μ + final state up to 310 K in spite of the fact that the transverse field relaxation rates become very high at 150 and 250 K respectively. (orig.)

  3. Final states in Si and GaAs via RF μSR spectroscopy

    Science.gov (United States)

    Kreitzman, S. R.; Pfiz, T.; Sun-Mack, S.; Riseman, T. M.; Brewer, J. H.; Williams, D. Ll.; Estle, T. L.

    1991-02-01

    The ionization of muonium centers in Si and GaAs have been studied using radio frequency (RF) resonant techniques. In Si all three muonic centers are detectable by RF. No evidence was found for delayed Mu and Mu* states at any temperature. However, our results on the diamagnetic final state (μ{f/+}) show that it is composed of prompt fractions (as seen by conventional μSR) and delayed fractions arising from the ionization of Mu* and Mu. We observe a full μ{f/+} fraction at 317 K when the Mu relaxation rate is above 10 μs-1. GaAs differs from the situation in Si in that we observed only a partial conversion of Mu* and Mu to a μ+ final state up to 310 K in spite of the fact that the transverse field relaxation rates become very high at 150 and 250 K respectively.

  4. Identification of fractional-order systems with time delays using block pulse functions

    Science.gov (United States)

    Tang, Yinggan; Li, Ning; Liu, Minmin; Lu, Yao; Wang, Weiwei

    2017-07-01

    In this paper, a novel method based on block pulse functions is proposed to identify continuous-time fractional-order systems with time delays. First, the operational matrices of block pulse functions for fractional integral operator and time delay operator are derived. Then, these operational matrices are applied to convert the continuous-time fractional-order systems with time delays to an algebraic equation. Finally, the system's parameters along with the differentiation orders and the time delays are all simultaneously estimated through minimizing a quadric error function. The proposed method reduces the computation complexity of the identification process, and also it does not require the system's differentiation orders to be commensurate. The effectiveness of the proposed method are demonstrated by several numerical examples.

  5. Bubble-Induced Color Doppler Feedback for Histotripsy Tissue Fractionation.

    Science.gov (United States)

    Miller, Ryan M; Zhang, Xi; Maxwell, Adam D; Cain, Charles A; Xu, Zhen

    2016-03-01

    Histotripsy therapy produces cavitating bubble clouds to increasingly fractionate and eventually liquefy tissue using high-intensity ultrasound pulses. Following cavitation generated by each pulse, coherent motion of the cavitation residual nuclei can be detected using metrics formed from ultrasound color Doppler acquisitions. In this paper, three experiments were performed to investigate the characteristics of this motion as real-time feedback on histotripsy tissue fractionation. In the first experiment, bubble-induced color Doppler (BCD) and particle image velocimetry (PIV) analysis monitored the residual cavitation nuclei in the treatment region in an agarose tissue phantom treated with two-cycle histotripsy pulses at [Formula: see text] using a 500-kHz transducer. Both BCD and PIV results showed brief chaotic motion of the residual nuclei followed by coherent motion first moving away from the transducer and then rebounding back. Velocity measurements from both PIV and BCD agreed well, showing a monotonic increase in rebound time up to a saturation point for increased therapy dose. In a second experiment, a thin layer of red blood cells (RBC) was added to the phantom to allow quantification of the fractionation of the RBC layer to compare with BCD metrics. A strong linear correlation was observed between the fractionation level and the time to BCD peak rebound velocity over histotripsy treatment. Finally, the correlation between BCD feedback and histotripsy tissue fractionation was validated in ex vivo porcine liver evaluated histologically. BCD metrics showed strong linear correlation with fractionation progression, suggesting that BCD provides useful quantitative real-time feedback on histotripsy treatment progression.

  6. Multiscale KF Algorithm for Strong Fractional Noise Interference Suppression in Discrete-Time UWB Systems

    Directory of Open Access Journals (Sweden)

    Liyun Su

    2011-01-01

    Full Text Available In order to suppress the interference of the strong fractional noise signal in discrete-time ultrawideband (UWB systems, this paper presents a new UWB multi-scale Kalman filter (KF algorithm for the interference suppression. This approach solves the problem of the narrowband interference (NBI as nonstationary fractional signal in UWB communication, which does not need to estimate any channel parameter. In this paper, the received sampled signal is transformed through multiscale wavelet to obtain a state transition equation and an observation equation based on the stationarity theory of wavelet coefficients in time domain. Then through the Kalman filter method, fractional signal of arbitrary scale is easily figured out. Finally, fractional noise interference is subtracted from the received signal. Performance analysis and computer simulations reveal that this algorithm is effective to reduce the strong fractional noise when the sampling rate is low.

  7. Fractional statistics and fractional quantized Hall effect. Revision

    International Nuclear Information System (INIS)

    Tao, R.; Wu, Y.S.

    1984-01-01

    We suggest that the origin of the odd denominator rule observed in the fractional quantized Hall effect (FQHE) may lie in fractional statistics which governs quasiparticles in FQHE. A theorem concerning statistics of clusters of quasiparticles implies that fractional statistics does not allow coexistence of a large number of quasiparticles at fillings with an even denominator. Thus no Hall plateau can be formed at these fillings, regardless of the presence of an energy gap. 15 references

  8. FRACTIONAL BANKING

    OpenAIRE

    Maria Klimikova

    2010-01-01

    Understanding the reasons of the present financial problems lies In understanding the substance of fractional reserve banking. The substance of fractional banking is in lending more money than the bankers have. Banking of partial reserves is an alternative form which links deposit banking and credit banking. Fractional banking is causing many unfavorable economic impacts in the worldwide system, specifically an inflation.

  9. Response analysis of a class of quasi-linear systems with fractional derivative excited by Poisson white noise

    Science.gov (United States)

    Yang, Yongge; Xu, Wei; Yang, Guidong; Jia, Wantao

    2016-08-01

    The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.

  10. Response analysis of a class of quasi-linear systems with fractional derivative excited by Poisson white noise

    International Nuclear Information System (INIS)

    Yang, Yongge; Xu, Wei; Yang, Guidong; Jia, Wantao

    2016-01-01

    The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.

  11. Response analysis of a class of quasi-linear systems with fractional derivative excited by Poisson white noise

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Yongge; Xu, Wei, E-mail: weixu@nwpu.edu.cn; Yang, Guidong; Jia, Wantao [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)

    2016-08-15

    The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.

  12. Characterization of Coconut Oil Fractions Obtained from Solvent Fractionation Using Acetone.

    Science.gov (United States)

    Sonwai, Sopark; Rungprasertphol, Poonyawee; Nantipipat, Nantinee; Tungvongcharoan, Satinee; Laiyangkoon, Nantikan

    2017-09-01

    This work was aimed to study the solvent fraction of coconut oil (CNO). The fatty acid and triacylglycerol compositions, solid fat content (SFC) and the crystallization properties of CNO and its solid and liquid fractions obtained from fractionation at different conditions were investigated using various techniques. CNO was dissolved in acetone (1:1 w/v) and left to crystallize isothermally at 10°C for 0.5, 1 and 2 h and at 12°C for 2, 3 and 6 h. The solid fractions contained significantly lower contents of saturated fatty acids of ≤ 10 carbon atoms but considerably higher contents of saturated fatty acids with > 12 carbon atoms with respect to those of CNO and the liquid fractions. They also contained higher contents of high-melting triacylglycerol species with carbon number ≥ 38. Because of this, the DSC crystallization onset temperatures and the crystallization peak temperatures of the solid fractions were higher than CNO and the liquid fractions. The SFC values of the solid fractions were significantly higher than CNO at all measuring temperatures before reaching 0% just below the body temperature with the fraction obtained at 12°C for 2 h exhibiting the highest SFC. On the contrary, the SFC values of the liquid fractions were lower than CNO. The crystallization duration exhibited strong influence on the solid fractions. There was no effect on the crystal polymorphic structure possibly because CNO has β'-2 as a stable polymorph. The enhanced SFC of the solid fractions would allow them to find use in food applications where a specific melting temperature is desired such as sophisticated confectionery fats, and the decreased SFC of the liquid fractions would provide them with a higher cold stability which would be useful during extended storage time.

  13. Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Ahmet Bekir

    2013-01-01

    Full Text Available The exp-function method is presented for finding the exact solutions of nonlinear fractional equations. New solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie's modified Riemann-Liouville sense. We apply the exp-function method to both the nonlinear time and space fractional differential equations. As a result, some new exact solutions for them are successfully established.

  14. Fractional factorial plans

    CERN Document Server

    Dey, Aloke

    2009-01-01

    A one-stop reference to fractional factorials and related orthogonal arrays.Presenting one of the most dynamic areas of statistical research, this book offers a systematic, rigorous, and up-to-date treatment of fractional factorial designs and related combinatorial mathematics. Leading statisticians Aloke Dey and Rahul Mukerjee consolidate vast amounts of material from the professional literature--expertly weaving fractional replication, orthogonal arrays, and optimality aspects. They develop the basic theory of fractional factorials using the calculus of factorial arrangements, thereby providing a unified approach to the study of fractional factorial plans. An indispensable guide for statisticians in research and industry as well as for graduate students, Fractional Factorial Plans features: * Construction procedures of symmetric and asymmetric orthogonal arrays. * Many up-to-date research results on nonexistence. * A chapter on optimal fractional factorials not based on orthogonal arrays. * Trend-free plans...

  15. Generalized characteristic ratios assignment for commensurate fractional order systems with one zero.

    Science.gov (United States)

    Tabatabaei, Mohammad

    2017-07-01

    In this paper, a new method for determination of the desired characteristic equation and zero location of commensurate fractional order systems is presented. The concept of the characteristic ratio is extended for zero-including commensurate fractional order systems. The generalized version of characteristic ratios is defined such that the time-scaling property of characteristic ratios is also preserved. The monotonicity of the magnitude frequency response is employed to assign the generalized characteristic ratios for commensurate fractional order transfer functions with one zero. A simple pattern for characteristic ratios is proposed to reach a non-overshooting step response. Then, the proposed pattern is revisited to reach a low overshoot (say for example 2%) step response. Finally, zero-including controllers such as fractional order PI or lag (lead) controllers are designed using generalized characteristic ratios assignment method. Numerical simulations are provided to show the efficiency of the so designed controllers. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  16. The Extended Fractional Subequation Method for Nonlinear Fractional Differential Equations

    OpenAIRE

    Zhao, Jianping; Tang, Bo; Kumar, Sunil; Hou, Yanren

    2012-01-01

    An extended fractional subequation method is proposed for solving fractional differential equations by introducing a new general ansätz and Bäcklund transformation of the fractional Riccati equation with known solutions. Being concise and straightforward, this method is applied to the space-time fractional coupled Burgers’ equations and coupled MKdV equations. As a result, many exact solutions are obtained. It is shown that the considered method provides a very effective, convenient, and powe...

  17. Higher fractions theory of fractional hall effect

    International Nuclear Information System (INIS)

    Kostadinov, I.Z.; Popov, V.N.

    1985-07-01

    A theory of fractional quantum Hall effect is generalized to higher fractions. N-particle model interaction is used and the gap is expressed through n-particles wave function. The excitation spectrum in general and the mean field critical behaviour are determined. The Hall conductivity is calculated from first principles. (author)

  18. Organosolv Fractionation of Softwood Biomass for Biofuel and Biorefinery Applications

    Directory of Open Access Journals (Sweden)

    Christos Nitsos

    2017-12-01

    Full Text Available Softwoods represent a significant fraction of the available lignocellulosic biomass for conversion into a variety of bio-based products. Its inherent recalcitrance, however, makes its successful utilization an ongoing challenge. In the current work the research efforts for the fractionation and utilization of softwood biomass with the organosolv process are reviewed. A short introduction into the specific challenges of softwood utilization, the development of the biorefinery concept, as well as the initial efforts for the development of organosolv as a pulping method is also provided for better understanding of the related research framework. The effect of organosolv pretreatment at various conditions, in the fractionation efficiency of wood components, enzymatic hydrolysis and bioethanol production yields is then discussed. Specific attention is given in the effect of the pretreated biomass properties such as residual lignin on enzymatic hydrolysis. Finally, the valorization of organosolv lignin via the production of biofuels, chemicals, and materials is also described.

  19. Non-probabilistic solutions of imprecisely defined fractional-order diffusion equations

    International Nuclear Information System (INIS)

    Chakraverty, S.; Tapaswini, Smita

    2014-01-01

    The fractional diffusion equation is one of the most important partial differential equations (PDEs) to model problems in mathematical physics. These PDEs are more practical when those are combined with uncertainties. Accordingly, this paper investigates the numerical solution of a non-probabilistic viz. fuzzy fractional-order diffusion equation subjected to various external forces. A fuzzy diffusion equation having fractional order 0 < α ≤ 1 with fuzzy initial condition is taken into consideration. Fuzziness appearing in the initial conditions is modelled through convex normalized triangular and Gaussian fuzzy numbers. A new computational technique is proposed based on double parametric form of fuzzy numbers to handle the fuzzy fractional diffusion equation. Using the single parametric form of fuzzy numbers, the original fuzzy diffusion equation is converted first into an interval-based fuzzy differential equation. Next, this equation is transformed into crisp form by using the proposed double parametric form of fuzzy numbers. Finally, the same is solved by Adomian decomposition method (ADM) symbolically to obtain the uncertain bounds of the solution. Computed results are depicted in terms of plots. Results obtained by the proposed method are compared with the existing results in special cases. (general)

  20. Quasi-projective synchronization of fractional-order complex-valued recurrent neural networks.

    Science.gov (United States)

    Yang, Shuai; Yu, Juan; Hu, Cheng; Jiang, Haijun

    2018-08-01

    In this paper, without separating the complex-valued neural networks into two real-valued systems, the quasi-projective synchronization of fractional-order complex-valued neural networks is investigated. First, two new fractional-order inequalities are established by using the theory of complex functions, Laplace transform and Mittag-Leffler functions, which generalize traditional inequalities with the first-order derivative in the real domain. Additionally, different from hybrid control schemes given in the previous work concerning the projective synchronization, a simple and linear control strategy is designed in this paper and several criteria are derived to ensure quasi-projective synchronization of the complex-valued neural networks with fractional-order based on the established fractional-order inequalities and the theory of complex functions. Moreover, the error bounds of quasi-projective synchronization are estimated. Especially, some conditions are also presented for the Mittag-Leffler synchronization of the addressed neural networks. Finally, some numerical examples with simulations are provided to show the effectiveness of the derived theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

  1. Initialized Fractional Calculus

    Science.gov (United States)

    Lorenzo, Carl F.; Hartley, Tom T.

    2000-01-01

    This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.

  2. Stochastic response of van der Pol oscillator with two kinds of fractional derivatives under Gaussian white noise excitation

    International Nuclear Information System (INIS)

    Yang Yong-Ge; Xu Wei; Sun Ya-Hui; Gu Xu-Dong

    2016-01-01

    This paper aims to investigate the stochastic response of the van der Pol (VDP) oscillator with two kinds of fractional derivatives under Gaussian white noise excitation. First, the fractional VDP oscillator is replaced by an equivalent VDP oscillator without fractional derivative terms by using the generalized harmonic balance technique. Then, the stochastic averaging method is applied to the equivalent VDP oscillator to obtain the analytical solution. Finally, the analytical solutions are validated by numerical results from the Monte Carlo simulation of the original fractional VDP oscillator. The numerical results not only demonstrate the accuracy of the proposed approach but also show that the fractional order, the fractional coefficient and the intensity of Gaussian white noise play important roles in the responses of the fractional VDP oscillator. An interesting phenomenon we found is that the effects of the fractional order of two kinds of fractional derivative items on the fractional stochastic systems are totally contrary. (paper)

  3. Meadow based Fraction Theory

    OpenAIRE

    Bergstra, Jan A.

    2015-01-01

    In the context of an involutive meadow a precise definition of fractions is formulated and on that basis formal definitions of various classes of fractions are given. The definitions follow the fractions as terms paradigm. That paradigm is compared with two competing paradigms for storytelling on fractions: fractions as values and fractions as pairs.

  4. Fractional corresponding operator in quantum mechanics and applications: A uniform fractional Schrödinger equation in form and fractional quantization methods

    International Nuclear Information System (INIS)

    Zhang, Xiao; Wei, Chaozhen; Liu, Yingming; Luo, Maokang

    2014-01-01

    In this paper we use Dirac function to construct a fractional operator called fractional corresponding operator, which is the general form of momentum corresponding operator. Then we give a judging theorem for this operator and with this judging theorem we prove that R–L, G–L, Caputo, Riesz fractional derivative operator and fractional derivative operator based on generalized functions, which are the most popular ones, coincide with the fractional corresponding operator. As a typical application, we use the fractional corresponding operator to construct a new fractional quantization scheme and then derive a uniform fractional Schrödinger equation in form. Additionally, we find that the five forms of fractional Schrödinger equation belong to the particular cases. As another main result of this paper, we use fractional corresponding operator to generalize fractional quantization scheme by using Lévy path integral and use it to derive the corresponding general form of fractional Schrödinger equation, which consequently proves that these two quantization schemes are equivalent. Meanwhile, relations between the theory in fractional quantum mechanics and that in classic quantum mechanics are also discussed. As a physical example, we consider a particle in an infinite potential well. We give its wave functions and energy spectrums in two ways and find that both results are the same

  5. 40 CFR 437.45 - New source performance standards (NSPS).

    Science.gov (United States)

    2010-07-01

    ... Conventional Parameters BOD 5 163 53.0 O&G 127 38.0 pH (2) (2) TSS 29.6 11.3 Metal Parameters Antimony 0.111 0... 0.216 Lead 0.350 0.160 Mercury 0.000641 0.000246 Nickel 0.794 0.309 Selenium 0.176 0.0698 Silver 0... following in-plant limitations apply to metal-bearing wastewater containing cyanide: In-Plant Limitations...

  6. Adaptative synchronization in multi-output fractional-order complex dynamical networks and secure communications

    Science.gov (United States)

    Mata-Machuca, Juan L.; Aguilar-López, Ricardo

    2018-01-01

    This work deals with the adaptative synchronization of complex dynamical networks with fractional-order nodes and its application in secure communications employing chaotic parameter modulation. The complex network is composed of multiple fractional-order systems with mismatch parameters and the coupling functions are given to realize the network synchronization. We introduce a fractional algebraic synchronizability condition (FASC) and a fractional algebraic identifiability condition (FAIC) which are used to know if the synchronization and parameters estimation problems can be solved. To overcome these problems, an adaptative synchronization methodology is designed; the strategy consists in proposing multiple receiver systems which tend to follow asymptotically the uncertain transmitters systems. The coupling functions and parameters of the receiver systems are adjusted continually according to a convenient sigmoid-like adaptative controller (SLAC), until the measurable output errors converge to zero, hence, synchronization between transmitter and receivers is achieved and message signals are recovered. Indeed, the stability analysis of the synchronization error is based on the fractional Lyapunov direct method. Finally, numerical results corroborate the satisfactory performance of the proposed scheme by means of the synchronization of a complex network consisting of several fractional-order unified chaotic systems.

  7. Morphological correlates of fractionated radiation of the mouse lung: Early and late effects

    International Nuclear Information System (INIS)

    Penney, D.P.; Siemann, D.W.; Rubin, P.; Maltby, K.

    1994-01-01

    The definition and quantitation of radiation-induced morphologic alterations in murine lungs is presented. The extent of injury to the lung, which is the dose-limiting organ in the thorax, may be reduced by fractionating the total radiation exposure to permit partial repair of radiation-induced damage between fraction administration and also to permit a larger total exposure to be administered. The authors previously reported that, following fractionated radiation exposures, as the dose/fraction decreases, the total dose to reach an isoeffect increases, with an α/β ratio of 3.2 and 3.0 for breathing rates and lethality, respectively. In the present report, they provide comparative morphologic evaluation of the effects of weekly fractionated, daily fractionated, and hyperfractionated radiation exposures. The doses administered within each group were uniform. To determine morphologic alterations, LAF1 mice were irradiated with 3, 15, and 30 fractions delivered in 19 days overall treatment time. In the hyperfractionation schedule, the two fractions per day were separated by a 6-h time interval. Total doses were as follows: 15-21 Gy for weekly fractionation, 30-41.5 Gy for daily fractionation, and 30-49.5 Gy for hyperfractionated schedules. Lung tissue, recovered either 24 or 72 weeks following the final exposure, was evaluated by transmission and scanning electron microscopy and light microscopy. Morphological damage was not uniform throughout the exposed lung and tended to be concentrated in lobes or portions of lobes. In the three fractionation regimens studied, there is progressive sparing of the lung with increased fractionation during the pnuemonitic state (24 weeks postirradiation). Both daily and twice daily fractionations provide increased sparing over weekly fractionation during the fibrotic stages (72 weeks postirradiation), but were not markedly different from each other (i.e. weekly < daily = twice daily). 41 refs., 15 figs., 2 tabs

  8. New insight on Li and B isotope fractionation during serpentinization derived from batch reaction investigations

    Science.gov (United States)

    Hansen, Christian T.; Meixner, Anette; Kasemann, Simone A.; Bach, Wolfgang

    2017-11-01

    Multiple batch experiments (100 °C, 200 °C; 40 MPa) were conducted, using Dickson-type reactors, to investigate Li and B partitioning and isotope fractionation between rock and water during serpentinization. We reacted fresh olivine (5 g; Fo90; [B] = anti-correlated with temperature, we argue for an overall attenuation of the isotopic effect through changes in B speciation in saline solutions (NaB(OH)4(aq) and B(OH)3Cl-) as well as variable B fixation and fractionation for different serpentinization product minerals (brucite, chrysotile). Breakdown of the Li-rich olivine and limited Li incorporation into product mineral phases resulted in an overall lower Li content of the final solid phase assemblage at 200 °C ([Li]final_200 °C = 0.77 μg/g; DS/FLi200 °C = 1.58). First order changes in Li isotopic compositions were defined by mixing of two isotopically distinct sources i.e. the fresh olivine and the fluid rather than by equilibrium isotope fraction. At 200 °C primary olivine is dissolved, releasing its Li budget into the fluid which shifts towards a lower δ7LiF of +38.62‰. Newly formed serpentine minerals (δ7LiS = +30.58‰) incorporate fluid derived Li with a minor preference of the 6Li isotope. At 100 °C Li enrichment of secondary phases exceeded Li release by olivine breakdown ([Li]final_100 °C = 2.10 μg/g; DS/FLi100 °C = 11.3) and it was accompanied by preferential incorporation of heavier 7Li isotope that might be due to incorporation of a 7Li enriched fluid fraction into chrysotile nanotubes.

  9. Fractional equivalent Lagrangian densities for a fractional higher-order equation

    International Nuclear Information System (INIS)

    Fujioka, J

    2014-01-01

    In this communication we show that the equivalent Lagrangian densities (ELDs) of a fractional higher-order nonlinear Schrödinger equation with stable soliton-like solutions can be related in a hitherto unknown way. This new relationship is described in terms of a new fractional operator that includes both left- and right-sided fractional derivatives. Using this operator it is possible to generate new ELDs that contain different fractional parts, in addition to the already known ELDs, which only differ by a sum of first-order partial derivatives of two arbitrary functions. (fast track communications)

  10. ψ(2S) Hadronic Decays to Vector-Tensor Final States

    International Nuclear Information System (INIS)

    Bai, J.Z.; Bian, J.G.; Chai, Z.W.; Chen, G.P.; Chen, J.C.; Chen, Y.; Chen, Y.B.; Chen, Y.Q.; Cheng, B.S.; Cui, X.Z.; Ding, H.L.; Ding, L.Y.; Dong, L.Y.; Du, Z.Z.; Feng, S.; Gao, C.S.; Gao, M.L.; Gao, S.Q.; Gu, J.H.; Gu, S.D.; Gu, W.X.; Gu, Y.F.; Guo, Y.N.; Han, S.W.; Han, Y.; He, J.; He, J.T.; Hu, G.Y.; Hu, H.M.; Hu, J.L.; Hu, Q.H.; Hu, T.; Hu, X.Q.; Huang, J.D.; Huang, Y.Z.; Jiang, C.H.; Jin, Y.; Ke, Z.J.; Lai, Y.F.; Lang, P.F.; Li, C.G.; Li, D.; Li, H.B.; Li, J.; Li, P.Q.; Li, R.B.; Li, W.; Li, W.D.; Li, W.G.; Li, X.H.; Li, X.N.; Liu, H.M.; Liu, J.; Liu, J.H.; Liu, R.G.; Liu, Y.; Lu, F.; Lu, J.G.; Lu, J.Y.; Lu, L.C.; Luo, C.H.; Ma, A.M.; Ma, E.C.; Ma, J.M.; Mao, H.S.; Mao, Z.P.; Meng, X.C.; Nie, J.; Qi, N.D.; Qi, X.R.; Qiu, J.F.; Qu, Y.H.; Que, Y.K.; Rong, G.; Shao, Y.Y.; Shen, B.W.; Shen, D.L.; Shen, H.; Shen, X.Y.; Sheng, H.Y.; Shi, H.Z.; Song, X.F.; Sun, F.; Sun, H.S.; Tang, S.Q.; Tong, G.L.; Wang, F.; Wang, L.S.; Wang, L.Z.; Wang, M.; Wang, M.; Wang, P.; Wang, P.L.; Wang, S.M.; Wang, T.J.; Wang, Y.Y.; Wei, C.L.; Wu, Y.G.; Xi, D.M.; Xia, X.M.; Xie, P.P.; Xie, Y.; Xie, Y.H.; Xiong, W.J.; Xu, C.C.; Xu, G.F.; Xue, S.T.; Yan, J.; Yan, W.G.; Yang, C.M.; Yang, C.Y.; Yang, J.; Yang, X.F.; Ye, M.H.; Yi, K.; Yu, C.S.; Yu, C.X.; Yu, Z.Q.; Yu, Z.T.; Yuan, C.Z.; Yuan, Y.; Zhang, B.Y.; Zhang, C.C.; Zhang, D.H.; Zhang, D.; Zhang, H.L.; Zhang, J.; Zhang, J.L.; Zhang, J.W.; Zhang, L.S.; Zhang, Q.J.; Zhang, S.Q.; Zhang, Y.; Zhang, Y.Y.; Zhao, D.X.; Zhao, H.W.; Zhao, J.W.; Zhao, M.; Zhao, W.R.; Zhao, Z.G.; Zheng, J.P.; Zheng, L.S.; Zheng, Z.P.; Zhou, G.P.; Zhou, H.S.; Zhou, L.; Zhu, Q.M.; Zhu, Y.C.; Zhu, Y.S.; Zhuang, B.A.; Hitlin, D.G.; Kelsey, M.H.; Oyang, J.; Panetta, J.; Porter, F.; Weaver, M.; Chen, J.; Malchow, R.; Toki, W.; Yang, W.

    1998-01-01

    The decays of the ψ(2S) into vector plus tensor meson final states have been studied for the first time using the BES detector. We determine upper limits on branching fractions for ψ(2S) decays into ωf 2 , ρa 2 , K *0 K *0 2 +c.c. , and φf ' 2 (1525) that are, in each case, significantly smaller than the corresponding branching fractions for the J/ψ meson, scaled according to the expectations of perturbative QCD. copyright 1998 The American Physical Society

  11. THE NEW SOLUTION OF TIME FRACTIONAL WAVE EQUATION WITH CONFORMABLE FRACTIONAL DERIVATIVE DEFINITION

    OpenAIRE

    Çenesiz, Yücel; Kurt, Ali

    2015-01-01

    – In this paper, we used new fractional derivative definition, the conformable fractional derivative, for solving two and three dimensional time fractional wave equation. This definition is simple and very effective in the solution procedures of the fractional differential equations that have complicated solutions with classical fractional derivative definitions like Caputo, Riemann-Liouville and etc. The results show that conformable fractional derivative definition is usable and convenient ...

  12. Development of quick-response area-averaged void fraction meter. Application to BWR condition

    Energy Technology Data Exchange (ETDEWEB)

    Iguchi, Tadashi; Watanabe, Hironori; Kimura, Mamoru; Anoda, Yoshinari [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment

    2001-05-01

    Authors have been developed a practical conductance-type void fraction meter to measure instantaneously area-averaged void fraction in rod bundle. The principle of the meter is based on the fact that the electrical conductance changes with the change of void fraction in gas-liquid two-phase flow. According to air/water two-phase flow experiment, the void fraction was approximated by {alpha}=1-I/I{sub 0}, where {alpha} and I are void fraction and current (I{sub 0} is current at {alpha}=0). Authors investigated the performance of the void fraction meter under high temperature/high pressure conditions (BWR condition; 290degC, 7MPa). The results indicated that the void fraction was approximated by {alpha}=1-I/I{sub 0} even under high temperature/high pressure condition of stem/water flow. However, it is necessary to take account of temperature dependency of water specific conductance. Therefore, authors derived a correction equation for temperature dependency. Further, for applying the void fraction meter to a large-scale facility, it was found to be necessary to reduce the capacitance of the circuit. Then, authors developed the method to reduce the capacitance effect. Finally, authors succeeded to measure the void fraction in 2 x 2 bundle flow path at the range of 0% - 70% in the error of 10% under high temperature/high pressure and mass flux of less than 133 kg/m{sup 2}s. Developed void fraction meter is theoretically not affected by flow rate. Therefore, it can be applied to the condition of oscillating flow. (author)

  13. The Fractions SNARC Revisited: Processing Fractions on a Consistent Mental Number Line.

    Science.gov (United States)

    Toomarian, Elizabeth Y; Hubbard, Edward M

    2017-07-12

    The ability to understand fractions is key to establishing a solid foundation in mathematics, yet children and adults struggle to comprehend them. Previous studies have suggested that these struggles emerge because people fail to process fraction magnitude holistically on the mental number line (MNL), focusing instead on fraction components (Bonato et al. 2007). Subsequent studies have produced evidence for default holistic processing (Meert et al., 2009; 2010), but examined only magnitude processing, not spatial representations. We explored the spatial representations of fractions on the MNL in a series of three experiments: Experiment 1 replicated Bonato et al. (2007); 30 naïve undergraduates compared unit fractions (1/1-1/9) to 1/5, resulting in a reverse SNARC effect. Experiment 2 countered potential strategic biases induced by the limited set of fractions used by Bonato et al. by expanding the stimulus set to include all irreducible, single-digit proper fractions, and asked participants to compare them against 1/2. We observed a classic SNARC effect, completely reversing the pattern from Experiment 1. Together, Experiments 1 and 2 demonstrate that stimulus properties dramatically impact spatial representations of fractions. In Experiment 3, we demonstrated within-subjects reliability of the SNARC effect across both a fractions and whole number comparison task. Our results suggest that adults can indeed process fraction magnitudes holistically, and that their spatial representations occur on a consistent MNL for both whole numbers and fractions.

  14. An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

    KAUST Repository

    Liu, Da-Yan; Tian, Yang; Boutat, Driss; Laleg-Kirati, Taous-Meriem

    2015-01-01

    This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.

  15. An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

    KAUST Repository

    Liu, Da-Yan

    2015-04-30

    This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.

  16. Linear-quadratic model underestimates sparing effect of small doses per fraction in rat spinal cord

    International Nuclear Information System (INIS)

    Shun Wong, C.; Toronto University; Minkin, S.; Hill, R.P.; Toronto University

    1993-01-01

    The application of the linear-quadratic (LQ) model to describe iso-effective fractionation schedules for dose fraction sizes less than 2 Gy has been controversial. Experiments are described in which the effect of daily fractionated irradiation given with a wide range of fraction sizes was assessed in rat cervical spine cord. The first group of rats was given doses in 1, 2, 4, 8 and 40 fractions/day. The second group received 3 initial 'top-up'doses of 9 Gy given once daily, representing 3/4 tolerance, followed by doses in 1, 2, 10, 20, 30 and 40 fractions/day. The fractionated portion of the irradiation schedule therefore constituted only the final quarter of the tolerance dose. The endpoint of the experiments was paralysis of forelimbs secondary to white matter necrosis. Direct analysis of data from experiments with full course fractionation up to 40 fractions/day (25.0-1.98 Gy/fraction) indicated consistency with the LQ model yielding an α/β value of 2.41 Gy. Analysis of data from experiments in which the 3 'top-up' doses were followed by up to 10 fractions (10.0-1.64 Gy/fraction) gave an α/β value of 3.41 Gy. However, data from 'top-up' experiments with 20, 30 and 40 fractions (1.60-0.55 Gy/fraction) were inconsistent with LQ model and gave a very small α/β of 0.48 Gy. It is concluded that LQ model based on data from large doses/fraction underestimates the sparing effect of small doses/fraction, provided sufficient time is allowed between each fraction for repair of sublethal damage. (author). 28 refs., 5 figs., 1 tab

  17. Measurement of void fraction and bubble size distribution in two-phase flow system

    International Nuclear Information System (INIS)

    Huahun, G.

    1987-01-01

    The importance of study two phase flow parameter and microstructure has appeared increasingly, with the development of two-phase flow discipline. In the paper, the measurement methods of several important microstructure parameter in a two phase flow vertical channel have been studied. Using conductance probe the two phase flow pattern and the average void fraction have been measured previously by the authors. This paper concerns microstructure of the bubble size distribution and local void fraction. The authors studied the methods of measuring bubble velocity, size distribution and local void fraction using double conductance probes and a set of apparatus. Based on our experiments and Yoshihiro work, a formula of calculated local void fraction has been deduced by using the statistical characteristics of bubbles in two phase flow and the relation between calculated bubble size and voltage has been determined. Finally the authors checked by using photograph and fast valve, which is classical but reliable. The results are the same with what has been studied before

  18. Recommended plutonium release fractions from postulated fires. Final report

    International Nuclear Information System (INIS)

    Kogan, V.; Schumacher, P.M.

    1993-12-01

    This report was written at the request of EG ampersand G Rocky Flats, Inc. in support of joint emergency planning for the Rocky Flats Plant (RFP) by EG ampersand G and the State of Colorado. The intent of the report is to provide the State of Colorado with an independent assessment of any respirable plutonium releases that might occur in the event of a severe fire at the plant. Fire releases of plutonium are of interest because they have been used by EG ampersand G to determine the RFP emergency planning zones. These zones are based on the maximum credible accident (MCA) described in the RFP Final Environmental Impact Statement (FEIS) of 1980, that MCA is assumed to be a large airplane crashing into a RFP plutonium building.The objective of this report was first, to perform a worldwide literature review of relevant release experiments from 1960 to the present and to summarize those findings, and second, to provide recommendations for application of the experimental data to fire release analyses at Rocky Flats. The latter step requires translation between experimental and expected RFP accident parameters, or ''scaling.'' The parameters of particular concern are: quantities of material, environmental parameters such as the intensity of a fire, and the physico-chemical forms of the plutonium. The latter include plutonium metal, bulk plutonium oxide powder, combustible and noncombustible wastes contaminated with plutonium oxide powder, and residues from plutonium extraction processes

  19. Reply to "Comment on 'Fractional quantum mechanics' and 'Fractional Schrödinger equation' ".

    Science.gov (United States)

    Laskin, Nick

    2016-06-01

    The fractional uncertainty relation is a mathematical formulation of Heisenberg's uncertainty principle in the framework of fractional quantum mechanics. Two mistaken statements presented in the Comment have been revealed. The origin of each mistaken statement has been clarified and corrected statements have been made. A map between standard quantum mechanics and fractional quantum mechanics has been presented to emphasize the features of fractional quantum mechanics and to avoid misinterpretations of the fractional uncertainty relation. It has been shown that the fractional probability current equation is correct in the area of its applicability. Further studies have to be done to find meaningful quantum physics problems with involvement of the fractional probability current density vector and the extra term emerging in the framework of fractional quantum mechanics.

  20. Glutamyl aminopeptidase in microvesicular and exosomal fractions of urine is related with renal dysfunction in cisplatin-treated rats.

    Directory of Open Access Journals (Sweden)

    Andrés Quesada

    Full Text Available The aim of this work was to investigate if the content of glutamyl aminopeptidase (GluAp in microvesicular and exosomal fractions of urine is related with renal dysfunction in cisplatin-treated rats.Urine samples were collected 24 hours after injection of cisplatin (7 mg/kg, n = 10 or saline serum (n = 10, and they were subjected to differential centrifugation at 1.000, 17.000 and 200.000 g to obtain microvesicular and exosomal fractions. GluAp was measured with a commercial ELISA kit in both fractions. Serum creatinine (SCr and body weight were measured 15 days after treatment. We analyzed if early excretion of GluAp in microsomal and exosomal fractions was correlated with final SCr and body weight increase. In a second experiment, enzymatic activities of GluAp and alanyl aminopeptidase (AlaAp in urine, microvesicular and exosomal fractions were measured three days after injection. We analyzed the correlation of both markers with SCr determined at this point. Finally, we studied the expression of GluAp and extracellular vesicles markers Alix and tumor susceptibility gene (TSG101 in both fractions by immunoblotting.GluAp excretion was increased in all fractions of urine after cisplatin treatment, even if data were normalized per mg of creatinine, per body weight or per total protein content of each fraction. We found significant predictive correlations with SCr concentration, and inverse correlations with body weight increase determined 15 days later. Three days after injection, aminopeptidasic activities were markedly increased in all fractions of urine in cisplatin-treated rats. The highest correlation coefficient with SCr was found for GluAp in microvesicular fraction. Increase of GluAp in microvesicular and exosomal fractions from cisplatin-treated rats was confirmed by immunoblotting. Alix and TSG101 showed different patterns of expression in each fraction.Determination of GluAp content or its enzymatic activity in microvesicular and

  1. Fractionated stereotactic radiotherapy boost for gynecologic tumors: An alternative to brachytherapy?

    International Nuclear Information System (INIS)

    Molla, Meritxell; Escude, Lluis D.; Nouet, Philippe; Popowski, Youri D.Sc.; Hidalgo, Alberto; Rouzaud, Michel; Linero, Dolores; Miralbell, Raymond

    2005-01-01

    Purpose: A brachytherapy (BT) boost to the vaginal vault is considered standard treatment for many endometrial or cervical cancers. We aimed to challenge this treatment standard by using stereotactic radiotherapy (SRT) with a linac-based micromultileaf collimator technique. Methods and Materials: Since January 2002, 16 patients with either endometrial (9) or cervical (7) cancer have been treated with a final boost to the areas at higher risk for relapse. In 14 patients, the target volume included the vaginal vault, the upper vagina, the parametria, or (if not operated) the uterus (clinical target volume [CTV]). In 2 patients with local relapse, the CTV was the tumor in the vaginal stump. Margins of 6-10 mm were added to the CTV to define the planning target volume (PTV). Hypofractionated dynamic-arc or intensity-modulated radiotherapy techniques were used. Postoperative treatment was delivered in 12 patients (2 x 7 Gy to the PTV with a 4-7-day interval between fractions). In the 4 nonoperated patients, a dose of 4 Gy/fraction in 5 fractions with 2 to 3 days' interval was delivered. Patients were immobilized in a customized vacuum body cast and optimally repositioned with an infrared-guided system developed for extracranial SRT. To further optimize daily repositioning and target immobilization, an inflated rectal balloon was used during each treatment fraction. In 10 patients, CT resimulation was performed before the last boost fraction to assess for repositioning reproducibility via CT-to-CT registration and to estimate PTV safety margins around the CTV. Finally, a comparative treatment planning study between BT and SRT was performed in 2 patients with an operated endometrial Stage I cancer. Results: No patient developed severe acute urinary or low-intestinal toxicity. No patient developed urinary late effects (>6 months). One patient with a vaginal relapse previously irradiated to the pelvic region presented with Grade 3 rectal bleeding 18 months after retreatment

  2. Search for fractional charge

    International Nuclear Information System (INIS)

    Turner, R.E.

    1984-01-01

    A search was made for fractional charges of the form Z plus two-thirds e, where Z is an integer. It was assumed that the charges exist in natural form bound with other fractional charges in neutral molecules. It was further assumed that these neutral molecules are present in air. Two concentration schemes were employed. One sample was derived from the waste gases from a xenon distillation plant. This assumes that high mass, low vapor pressure components of air are concentrated along with the xenon. The second sample involved ionizing air, allowing a brief recombination period, and then collecting residual ions on the surface of titanium discs. Both samples were analyzed at the University of Rochester in a system using a tandem Van de Graff to accelerate particles through an essentially electrostatic beam handling system. The detector system employed both a Time of Flight and an energy-sensitive gas ionization detector. In the most sensitive mode of analysis, a gas absorber was inserted in the beam path to block the intense background. The presence of an absorber limited the search to highly penetrating particles. Effectively, this limited the search to particles with low Z and masses greater than roughly fifty GeV. The final sensitivities attained were on the order of 1 x 10 -20 for the ionized air sample and 1 x 10 -21 for the gas sample. A discussion of the caveats that could reduce the actual level of sensitivity is included

  3. Thermodynamic analysis of 6xxx series Al alloys: Phase fraction diagrams

    Directory of Open Access Journals (Sweden)

    Cui S.

    2018-01-01

    Full Text Available Microstructural evolution of 6xxx Al alloys during various metallurgical processes was analyzed using accurate thermodynamic database. Phase fractions of all the possible precipitate phases which can form in the as-cast and equilibrium states of the Al-Mg-Si-Cu-Fe-Mn-Cr alloys were calculated over the technically useful composition range. The influence of minor elements such as Cu, Fe, Mn, and Cr on the amount of each type of precipitate in the as-cast and equilibrium conditions were analyzed. Phase fraction diagrams at 500 °C were mapped in the composition range of 0-1.1 wt.% Mg and 0-0.7 wt.% Si to investigate the as-homogenized microstructure. In addition, phase fraction diagram of Mg2Si at 177 °C was mapped to understand the microstructure after final annealing of 6xxx Al alloy. Based on the calculated diagrams, the design strategy of 6xxx Al alloy to produce highest strength due to Mg2Si is discussed.

  4. Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus

    International Nuclear Information System (INIS)

    He, Ji-Huan; Elagan, S.K.; Li, Z.B.

    2012-01-01

    The fractional complex transform is suggested to convert a fractional differential equation with Jumarie's modification of Riemann–Liouville derivative into its classical differential partner. Understanding the fractional complex transform and the chain rule for fractional calculus are elucidated geometrically. -- Highlights: ► The chain rule for fractional calculus is invalid, a counter example is given. ► The fractional complex transform is explained geometrically. ► Fractional equations can be converted into differential equations.

  5. Fractional order differentiation by integration: An application to fractional linear systems

    KAUST Repository

    Liu, Dayan

    2013-02-04

    In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method. © 2013 IFAC.

  6. Antioxidant activity of cod (Gadus morhua) protein hydrolysates: Fractionation and characterisation of peptide fractions

    DEFF Research Database (Denmark)

    Farvin Habebullah, Sabeena; Andersen, Lisa Lystbæk; Otte, Jeanette

    2016-01-01

    This study aimed to characterise peptide fractions (>5 kDa, 3–5 kDa and fractions were dominated by Ala, Gly, Glu and Ser. The total amino acid composition had high proportions of Lys, Ala...... and Glu. The 3–5 kDa and fractions were further fractionated by size exclusion chromatography. All sub-fractions showed high Fe2+ chelating activity. The DPPH radical-scavenging activity of the 3–5 kDa fraction was exerted mainly by one sub-fraction dominated by peptides with masses below 600 Da....... The DPPH radical-scavenging activity of the fraction was exerted by sub-fractions with low molecular weight. The highest reducing power was found in a sub-fraction containing peptides rich in Arg, Tyr and Phe. Both free amino acids and low molecular weight peptides thus seemed to contribute...

  7. Dividing Fractions: A Pedagogical Technique

    Science.gov (United States)

    Lewis, Robert

    2016-01-01

    When dividing one fraction by a second fraction, invert, that is, flip the second fraction, then multiply it by the first fraction. To multiply fractions, simply multiply across the denominators, and multiply across the numerators to get the resultant fraction. So by inverting the division of fractions it is turned into an easy multiplication of…

  8. Hyperdynamic left ventricular ejection fraction in the intensive care unit.

    Science.gov (United States)

    Paonessa, Joseph R; Brennan, Thomas; Pimentel, Marco; Steinhaus, Daniel; Feng, Mengling; Celi, Leo Anthony

    2015-08-07

    Limited information exists on the etiology, prevalence, and significance of hyperdynamic left ventricular ejection fraction (HDLVEF) in the intensive care unit (ICU). Our aim in the present study was to compare characteristics and outcomes of patients with HDLVEF with those of patients with normal left ventricular ejection fraction in the ICU using a large, public, deidentified critical care database. We conducted a longitudinal, single-center, retrospective cohort study of adult patients who underwent echocardiography during a medical or surgical ICU admission at the Beth Israel Deaconess Medical Center using the Multiparameter Intelligent Monitoring in Intensive Care II database. The final cohort had 2867 patients, of whom 324 had HDLVEF, defined as an ejection fraction >70%. Patients with an ejection fraction <55% were excluded. Compared with critically ill patients with normal left ventricular ejection fraction, the finding of HDLVEF in critically ill patients was associated with female sex, increased age, and the diagnoses of hypertension and cancer. Patients with HDLVEF had increased 28-day mortality compared with those with normal ejection fraction in multivariate logistic regression analysis adjusted for age, sex, Sequential Organ Failure Assessment score, Elixhauser score for comorbidities, vasopressor use, and mechanical ventilation use (odds ratio 1.38, 95% confidence interval 1.039-1.842, p =0.02). The presence of HDLVEF portended increased 28-day mortality, and may be helpful as a gravity marker for prognosis in patients admitted to the ICU. Further research is warranted to gain a better understanding of how these patients respond to common interventions in the ICU and to determine if pharmacologic modulation of HDLVEF improves outcomes.

  9. Measurement of void fraction distribution in two-phase flow by impedance CT with neural network

    International Nuclear Information System (INIS)

    Hayashi, Hideaki; Sumida, Isao; Sakai, Sinji; Wakai, Kazunori

    1996-01-01

    This paper describes a new method for measurement of void distribution using impedance CT with a hierarchical neural network. The present method consists of four processes. First, output electric currents are calculated by simulation of various distributions of void fraction. The relationship between distribution of void fraction and electric current is called 'teaching data'. Second, the neural network learns the teaching data by the back propagation method. Third, output electric currents are measured about actual two-phase flow. Finally, distribution of void fraction is calculated by the taught neural network using the measured electric currents. In this paper, measurement and learning parameters are adjusted, experimental results obtained using the impedance CT method are compared with data obtained by the impedance probe method. The results show that our method is effective for measurement of void fraction distribution. (author)

  10. Fractional charges

    International Nuclear Information System (INIS)

    Saminadayar, L.

    2001-01-01

    20 years ago fractional charges were imagined to explain values of conductivity in some materials. Recent experiments have proved the existence of charges whose value is the third of the electron charge. This article presents the experimental facts that have led theorists to predict the existence of fractional charges from the motion of quasi-particles in a linear chain of poly-acetylene to the quantum Hall effect. According to the latest theories, fractional charges are neither bosons nor fermions but anyons, they are submitted to an exclusive principle that is less stringent than that for fermions. (A.C.)

  11. Parrondo’s paradox for chaos control and anticontrol of fractional-order systems

    International Nuclear Information System (INIS)

    Danca, Marius-F; Tang, Wallace K S

    2016-01-01

    We present the generalized forms of Parrondo’s paradox existing in fractional-order nonlinear systems. The generalization is implemented by applying a parameter switching (PS) algorithm to the corresponding initial value problems associated with the fractional-order nonlinear systems. The PS algorithm switches a system parameter within a specific set of N ≥ 2 values when solving the system with some numerical integration method. It is proven that any attractor of the concerned system can be approximated numerically. By replacing the words “winning” and “loosing” in the classical Parrondo’s paradox with “order” and “chaos', respectively, the PS algorithm leads to the generalized Parrondo’s paradox: chaos 1 + chaos 2 + ··· + chaos N = order and order 1 + order 2 + ··· + order N = chaos. Finally, the concept is well demonstrated with the results based on the fractional-order Chen system. (paper)

  12. Pig slurry acidification and separation techniques affect soil N and C turnover and N2O emissions from solid, liquid and biochar fractions

    DEFF Research Database (Denmark)

    Gomez Muñoz, Beatriz; Case, Sean; Jensen, Lars Stoumann

    2016-01-01

    the separated solid fractions in soil, but did not affect N2O and CO2 emissions. However acidification reduced soil N and C turnover from the liquid fraction. The use of more advanced separation techniques (flocculation and drainage > decanting centrifuge > screw press) increased N mineralisation from acidified...... solid fractions, but also increased N2O and CO2 emissions in soil amended with the liquid fraction. Finally, the biochar production from the solid fraction of pig slurry resulted in a very recalcitrant material, which reduced N and C mineralisation in soil compared to the raw solid fractions....

  13. On the fractional systems fault detection: a comparison between fractional and rational residual sensitivity

    International Nuclear Information System (INIS)

    Aoun, M.; Aribi, A.; Najar, S.; Abdelkrim, M.N.

    2011-01-01

    This paper shows the interest of extending the dynamic parity space fault detection method for fractional systems. Accordingly, a comparison between fractional and rational residual generators using the later method is presented. An analysis of fractional and rational residuals sensitivity shows the merits of the fractional residual generators. A numerical example illustrating the advantage of using fractional residual generators for fractional systems diagnosis is given.

  14. A NEW FRACTIONAL MODEL OF SINGLE DEGREE OF FREEDOM SYSTEM, BY USING GENERALIZED DIFFERENTIAL TRANSFORM METHOD

    Directory of Open Access Journals (Sweden)

    HASHEM SABERI NAJAFI

    2016-07-01

    Full Text Available Generalized differential transform method (GDTM is a powerful method to solve the fractional differential equations. In this paper, a new fractional model for systems with single degree of freedom (SDOF is presented, by using the GDTM. The advantage of this method compared with some other numerical methods has been shown. The analysis of new approximations, damping and acceleration of systems are also described. Finally, by reducing damping and analysis of the errors, in one of the fractional cases, we have shown that in addition to having a suitable solution for the displacement close to the exact one, the system enjoys acceleration once crossing the equilibrium point.

  15. Exact solutions to the time-fractional differential equations via local fractional derivatives

    Science.gov (United States)

    Guner, Ozkan; Bekir, Ahmet

    2018-01-01

    This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

  16. Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

    KAUST Repository

    N'Doye, Ibrahima; Laleg-Kirati, Taous-Meriem

    2015-01-01

    This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.

  17. Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

    KAUST Repository

    N'Doye, Ibrahima

    2015-07-01

    This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.

  18. Artificial neural network based gynaecological image-guided adaptive brachytherapy treatment planning correction of intra-fractional organs at risk dose variation.

    Science.gov (United States)

    Jaberi, Ramin; Siavashpour, Zahra; Aghamiri, Mahmoud Reza; Kirisits, Christian; Ghaderi, Reza

    2017-12-01

    Intra-fractional organs at risk (OARs) deformations can lead to dose variation during image-guided adaptive brachytherapy (IGABT). The aim of this study was to modify the final accepted brachytherapy treatment plan to dosimetrically compensate for these intra-fractional organs-applicators position variations and, at the same time, fulfilling the dosimetric criteria. Thirty patients with locally advanced cervical cancer, after external beam radiotherapy (EBRT) of 45-50 Gy over five to six weeks with concomitant weekly chemotherapy, and qualified for intracavitary high-dose-rate (HDR) brachytherapy with tandem-ovoid applicators were selected for this study. Second computed tomography scan was done for each patient after finishing brachytherapy treatment with applicators in situ. Artificial neural networks (ANNs) based models were used to predict intra-fractional OARs dose-volume histogram parameters variations and propose a new final plan. A model was developed to estimate the intra-fractional organs dose variations during gynaecological intracavitary brachytherapy. Also, ANNs were used to modify the final brachytherapy treatment plan to compensate dosimetrically for changes in 'organs-applicators', while maintaining target dose at the original level. There are semi-automatic and fast responding models that can be used in the routine clinical workflow to reduce individually IGABT uncertainties. These models can be more validated by more patients' plans to be able to serve as a clinical tool.

  19. Artificial neural network based gynaecological image-guided adaptive brachytherapy treatment planning correction of intra-fractional organs at risk dose variation

    Directory of Open Access Journals (Sweden)

    Ramin Jaberi

    2017-12-01

    Full Text Available Purpose : Intra-fractional organs at risk (OARs deformations can lead to dose variation during image-guided adaptive brachytherapy (IGABT. The aim of this study was to modify the final accepted brachytherapy treatment plan to dosimetrically compensate for these intra-fractional organs-applicators position variations and, at the same time, fulfilling the dosimetric criteria. Material and methods : Thirty patients with locally advanced cervical cancer, after external beam radiotherapy (EBRT of 45-50 Gy over five to six weeks with concomitant weekly chemotherapy, and qualified for intracavitary high-dose-rate (HDR brachytherapy with tandem-ovoid applicators were selected for this study. Second computed tomography scan was done for each patient after finishing brachytherapy treatment with applicators in situ. Artificial neural networks (ANNs based models were used to predict intra-fractional OARs dose-volume histogram parameters variations and propose a new final plan. Results : A model was developed to estimate the intra-fractional organs dose variations during gynaecological intracavitary brachytherapy. Also, ANNs were used to modify the final brachytherapy treatment plan to compensate dosimetrically for changes in ‘organs-applicators’, while maintaining target dose at the original level. Conclusions : There are semi-automatic and fast responding models that can be used in the routine clinical workflow to reduce individually IGABT uncertainties. These models can be more validated by more patients’ plans to be able to serve as a clinical tool.

  20. Smarandache Continued Fractions

    OpenAIRE

    Ibstedt, H.

    2001-01-01

    The theory of general continued fractions is developed to the extent required in order to calculate Smarandache continued fractions to a given number of decimal places. Proof is given for the fact that Smarandache general continued fractions built with positive integer Smarandache sequences baving only a finite number of terms equal to 1 is convergent. A few numerical results are given.

  1. Gamma radiation-induced Impairment of hippocampal neurogenesis, comparison of single and fractionated dose regimens

    International Nuclear Information System (INIS)

    Khoshbin khoshnazar, A. R; Jahanshahi, M; Azami, N. S

    2012-01-01

    Radiation therapy of the brain is associated with many consequences, including cognitive disorders. Pathogenesis of radiation induced cognitive disorder is not clear, but reduction of neurogenesis in hippocampus may be an underlying reason. 24 adult male rats entered to study. Radiation absorbed dose to midbrain was 10 Gy, delivered by routine cobalt radiotherapy machine which its output was measured 115.24 cGy/min. The rats were divided in four groups of sixes, including groups of control, single fraction 10 Gy, fractionated 10 Gy and finally anaesthesia sham group. Number of pyramidal nerve cells was counted in two regions of hippocampus formation (CA1 and CA3). The radiation could reduce the number of cells in two regions of hippocampus significantly (p=0.000). It seems fractionated 10 Gy irradiation to more efficient than single fraction, while role of anaesthesia drug should be cautiously assessed. Moreover the rate of neurogenesis reduction was determined the same in these regions of hippocampus meaning the same radiosensitivity of cells

  2. Existence results for fractional integro-differential inclusions with state-dependent delay

    Directory of Open Access Journals (Sweden)

    Siracusa Giovana

    2017-10-01

    Full Text Available In this paper we are concerned with a class of abstract fractional integro-differential inclusions with infinite state-dependent delay. Our approach is based on the existence of a resolvent operator for the homogeneous equation.We establish the existence of mild solutions using both contractive maps and condensing maps. Finally, an application to the theory of heat conduction in materials with memory is given.

  3. Solidification microstructures in a short fiber reinforced alloy composite containing different fiber fractions

    Directory of Open Access Journals (Sweden)

    JING Qing-xiu

    2006-02-01

    Full Text Available The solidification microstructures and micro-segregation of a fiber reinforced Al-9 Cu alloy, containing different volume fractions of Al2O3 short fibers about 6 μm diameter and made by squeeze casting have been studied. The results indicate that as volume fraction of fiber Vf increases, the size of final grains becomes finer in the matrix. If λf /λ＞1, the fibers have almost no influence on the solidification behavior of the matrix, so the final grains grow coarse, where λf is the average inter-fiber spacing and λ is the secondary dendrite arm spacing. While if λf /λ＜1, the growth of crystals in the matrix is affected significantly by the fibers and the grain size is reduced to the value of the inter-fiber spacing. The fibers influence the average length of a solidification volume element L of the matrix and also influence the solidification time θt of the matrix. As a result of fibers influencing L and θt, the micro-segregation in the matrix is improved when the composite contains more fibers, although the level of the improvement is slight. The Clyne-Kurz model can be used to semi-quantitatively analyze the relationship between Vf and the volume fraction fe of the micro-segregation eutectic structure.

  4. FRACTIONS: CONCEPTUAL AND DIDACTIC ASPECTS

    Directory of Open Access Journals (Sweden)

    Sead Rešić

    2016-09-01

    Full Text Available Fractions represent the manner of writing parts of whole numbers (integers. Rules for operations with fractions differ from rules for operations with integers. Students face difficulties in understanding fractions, especially operations with fractions. These difficulties are well known in didactics of Mathematics throughout the world and there is a lot of research regarding problems in learning about fractions. Methods for facilitating understanding fractions have been discovered, which are essentially related to visualizing operations with fractions.

  5. Fractionation of human serum lipoproteins and simultaneous enzymatic determination of cholesterol and triglycerides

    International Nuclear Information System (INIS)

    Qureshi, Rashid Nazir; Kok, Wim Th.; Schoenmakers, Peter J.

    2009-01-01

    A method based on Asymmetric Flow Field-Flow Fractionation (AF4) was developed to separate different types of lipoproteins from human serum. The emphasis in the method optimization was on the possibilities to characterize the largest lipoprotein fractions (LDL and VLDL), which is usually not possible with the size-exclusion chromatography methods applied in routine analysis. Different channel geometries and flow programs were tested and compared. The use of a short fractionation channel was shown to give less sample dilution at the same fractionation power compared to a conventional, long channel. Different size selectivities were obtained with an exponential decay and a linear cross flow program. The ratio of the UV absorption signal to the light scattering signal was used to validate the relation between retention time and size of the fractionated particles. An experimental setup was developed for the simultaneous determination of the cholesterol and triglycerides distribution over the lipoprotein fractions, based on enzymatic reactions followed by UV detection at 500 nm. Coiled and knitted PTFE tubing reactors were compared. An improved peak sharpness and sensitivity were observed with the knitted tubing reactor. After optimization of the experimental conditions a satisfactory linearity and precision (2-3% rsd for cholesterol and 5-6% rsd for triglycerides) were obtained. Finally, serum samples, a pooled sample from healthy volunteers and samples of sepsis patients, were analyzed with the method developed. Lipoprotein fractionation and cholesterol and triglyceride distributions could be correlated with the clinical background of the samples.

  6. Fractionation of human serum lipoproteins and simultaneous enzymatic determination of cholesterol and triglycerides

    Energy Technology Data Exchange (ETDEWEB)

    Qureshi, Rashid Nazir [Polymer-Analysis Group, van' t Hoff Institute for Molecular Sciences, University of Amsterdam, Nieuwe Achtergracht 166, 1018WV Amsterdam (Netherlands); Kok, Wim Th., E-mail: W.Th.Kok@uva.nl [Polymer-Analysis Group, van' t Hoff Institute for Molecular Sciences, University of Amsterdam, Nieuwe Achtergracht 166, 1018WV Amsterdam (Netherlands); Schoenmakers, Peter J. [Polymer-Analysis Group, van' t Hoff Institute for Molecular Sciences, University of Amsterdam, Nieuwe Achtergracht 166, 1018WV Amsterdam (Netherlands)

    2009-11-03

    A method based on Asymmetric Flow Field-Flow Fractionation (AF4) was developed to separate different types of lipoproteins from human serum. The emphasis in the method optimization was on the possibilities to characterize the largest lipoprotein fractions (LDL and VLDL), which is usually not possible with the size-exclusion chromatography methods applied in routine analysis. Different channel geometries and flow programs were tested and compared. The use of a short fractionation channel was shown to give less sample dilution at the same fractionation power compared to a conventional, long channel. Different size selectivities were obtained with an exponential decay and a linear cross flow program. The ratio of the UV absorption signal to the light scattering signal was used to validate the relation between retention time and size of the fractionated particles. An experimental setup was developed for the simultaneous determination of the cholesterol and triglycerides distribution over the lipoprotein fractions, based on enzymatic reactions followed by UV detection at 500 nm. Coiled and knitted PTFE tubing reactors were compared. An improved peak sharpness and sensitivity were observed with the knitted tubing reactor. After optimization of the experimental conditions a satisfactory linearity and precision (2-3% rsd for cholesterol and 5-6% rsd for triglycerides) were obtained. Finally, serum samples, a pooled sample from healthy volunteers and samples of sepsis patients, were analyzed with the method developed. Lipoprotein fractionation and cholesterol and triglyceride distributions could be correlated with the clinical background of the samples.

  7. Gauge invariant fractional electromagnetic fields

    International Nuclear Information System (INIS)

    Lazo, Matheus Jatkoske

    2011-01-01

    Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators. -- Highlights: → We propose a fractional Lagrangian formulation for fractional Maxwell's fields. → We obtain gauge invariant fractional electromagnetic fields. → Our generalized fractional Maxwell's field is spatially symmetrical. → We discuss the non-causality of the theory.

  8. Integral transform method for solving time fractional systems and fractional heat equation

    Directory of Open Access Journals (Sweden)

    Arman Aghili

    2014-01-01

    Full Text Available In the present paper, time fractional partial differential equation is considered, where the fractional derivative is defined in the Caputo sense. Laplace transform method has been applied to obtain an exact solution. The authors solved certain homogeneous and nonhomogeneous time fractional heat equations using integral transform. Transform method is a powerful tool for solving fractional singular Integro - differential equations and PDEs. The result reveals that the transform method is very convenient and effective.

  9. A Fractional Micro-Macro Model for Crowds of Pedestrians Based on Fractional Mean Field Games

    Institute of Scientific and Technical Information of China (English)

    Kecai Cao; Yang Quan Chen; Daniel Stuart

    2016-01-01

    Modeling a crowd of pedestrians has been considered in this paper from different aspects. Based on fractional microscopic model that may be much more close to reality, a fractional macroscopic model has been proposed using conservation law of mass. Then in order to characterize the competitive and cooperative interactions among pedestrians, fractional mean field games are utilized in the modeling problem when the number of pedestrians goes to infinity and fractional dynamic model composed of fractional backward and fractional forward equations are constructed in macro scale. Fractional micromacro model for crowds of pedestrians are obtained in the end.Simulation results are also included to illustrate the proposed fractional microscopic model and fractional macroscopic model,respectively.

  10. Gauge invariant fractional electromagnetic fields

    Energy Technology Data Exchange (ETDEWEB)

    Lazo, Matheus Jatkoske, E-mail: matheuslazo@furg.br [Instituto de Matematica, Estatistica e Fisica - FURG, Rio Grande, RS (Brazil)

    2011-09-26

    Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators. -- Highlights: → We propose a fractional Lagrangian formulation for fractional Maxwell's fields. → We obtain gauge invariant fractional electromagnetic fields. → Our generalized fractional Maxwell's field is spatially symmetrical. → We discuss the non-causality of the theory.

  11. On matrix fractional differential equations

    Directory of Open Access Journals (Sweden)

    Adem Kılıçman

    2017-01-01

    Full Text Available The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.

  12. FRACTIONS: CONCEPTUAL AND DIDACTIC ASPECTS

    OpenAIRE

    Sead Rešić; Ismet Botonjić; Maid Omerović

    2016-01-01

    Fractions represent the manner of writing parts of whole numbers (integers). Rules for operations with fractions differ from rules for operations with integers. Students face difficulties in understanding fractions, especially operations with fractions. These difficulties are well known in didactics of Mathematics throughout the world and there is a lot of research regarding problems in learning about fractions. Methods for facilitating understanding fractions have been discovered...

  13. A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations

    International Nuclear Information System (INIS)

    Feng Qing-Hua

    2014-01-01

    In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. (general)

  14. Analytical approaches for the approximate solution of a nonlinear fractional ordinary differential equation

    International Nuclear Information System (INIS)

    Basak, K C; Ray, P C; Bera, R K

    2009-01-01

    The aim of the present analysis is to apply the Adomian decomposition method and He's variational method for the approximate analytical solution of a nonlinear ordinary fractional differential equation. The solutions obtained by the above two methods have been numerically evaluated and presented in the form of tables and also compared with the exact solution. It was found that the results obtained by the above two methods are in excellent agreement with the exact solution. Finally, a surface plot of the approximate solutions of the fractional differential equation by the above two methods is drawn for 0≤t≤2 and 1<α≤2.

  15. Novel Numerical Methods for Optimal Control Problems Involving Fractional-Order Differential Equations

    Science.gov (United States)

    2018-03-14

    UNIVERSITY OF TECHNOLOGY Final Report 03/14/2018 DISTRIBUTION A: Distribution approved for public release. AF Office Of Scientific Research (AFOSR...optimal control problems involving fractional-order differential equations Wang, Song Curtin University of Technology Kent Street, Bentley WA6102...Article history : Received 3 October 2016 Accepted 26 March 2017 Available online 29 April 2017 Keywords: Hamilton–Jacobi–Bellman equation Financial

  16. Numerical Methods for Pricing American Options with Time-Fractional PDE Models

    Directory of Open Access Journals (Sweden)

    Zhiqiang Zhou

    2016-01-01

    Full Text Available In this paper we develop a Laplace transform method and a finite difference method for solving American option pricing problem when the change of the option price with time is considered as a fractal transmission system. In this scenario, the option price is governed by a time-fractional partial differential equation (PDE with free boundary. The Laplace transform method is applied to the time-fractional PDE. It then leads to a nonlinear equation for the free boundary (i.e., optimal early exercise boundary function in Laplace space. After numerically finding the solution of the nonlinear equation, the Laplace inversion is used to transform the approximate early exercise boundary into the time space. Finally the approximate price of the American option is obtained. A boundary-searching finite difference method is also proposed to solve the free-boundary time-fractional PDEs for pricing the American options. Numerical examples are carried out to compare the Laplace approach with the finite difference method and it is confirmed that the former approach is much faster than the latter one.

  17. Permutation entropy of fractional Brownian motion and fractional Gaussian noise

    International Nuclear Information System (INIS)

    Zunino, L.; Perez, D.G.; Martin, M.T.; Garavaglia, M.; Plastino, A.; Rosso, O.A.

    2008-01-01

    We have worked out theoretical curves for the permutation entropy of the fractional Brownian motion and fractional Gaussian noise by using the Bandt and Shiha [C. Bandt, F. Shiha, J. Time Ser. Anal. 28 (2007) 646] theoretical predictions for their corresponding relative frequencies. Comparisons with numerical simulations show an excellent agreement. Furthermore, the entropy-gap in the transition between these processes, observed previously via numerical results, has been here theoretically validated. Also, we have analyzed the behaviour of the permutation entropy of the fractional Gaussian noise for different time delays

  18. Control and Synchronization of the Fractional-Order Lorenz Chaotic System via Fractional-Order Derivative

    Directory of Open Access Journals (Sweden)

    Ping Zhou

    2012-01-01

    Full Text Available The unstable equilibrium points of the fractional-order Lorenz chaotic system can be controlled via fractional-order derivative, and chaos synchronization for the fractional-order Lorenz chaotic system can be achieved via fractional-order derivative. The control and synchronization technique, based on stability theory of fractional-order systems, is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed method.

  19. Anti-diabetic and antihypertensive activities of two flaxseed protein hydrolysate fractions revealed following their simultaneous separation by electrodialysis with ultrafiltration membranes.

    Science.gov (United States)

    Doyen, Alain; Udenigwe, Chibuike C; Mitchell, Patricia L; Marette, André; Aluko, Rotimi E; Bazinet, Laurent

    2014-02-15

    Flaxseed protein hydrolysate has been fractionated by electrodialysis with two ultrafiltration membranes (20 and 50 kDa) stacked in the system for the recovery of two specific cationic peptide fractions (KCl-F1 and KCl-F2). After 360 min of treatment, peptide migration increased as a function of time in KCl compartments. Moreover, the use of two different ultrafiltration membrane allowed concentration of the 300-400 and 400-500 Da molecular weight range peptides in the KCl-F1 and KCl-F2 fractions, respectively, compared to the initial hydrolysate. After mass spectrometry analysis, higher amounts of low molecular weight peptides were recovered in the KCl-F2 compartment while relatively higher molecular weight peptides were more detected in the KCl-F1 compartment. Amino acid analysis showed that His, Lys and Arg were especially concentrated in the KCl compartments. Finally, glucose-transport assay demonstrated that the KCl-F2 fraction increased glucose uptake while oral administration of KCl-F1 and final FPH decreased systolic blood pressure. Copyright © 2013 Elsevier Ltd. All rights reserved.

  20. -Dimensional Fractional Lagrange's Inversion Theorem

    Directory of Open Access Journals (Sweden)

    F. A. Abd El-Salam

    2013-01-01

    Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.

  1. Radiation damage and waste management options for the sombrero final focus system and neutron dumps

    International Nuclear Information System (INIS)

    Reyes, S.; Latkowski, J.F.; Meier, W.R.; Reyes, S.

    2000-01-01

    Previous studies of the safety and environmental aspects of the SOMBRERO inertial fusion energy (IFE) power plant design did not completely address the issues associated with the final focus system. While past work calculated neutron fluences for a grazing incidence metal mirror (GIMM) and a final focus mirror, scattering off of the final optical component was not included, and thus, fluences in the final focus mirror were significantly underestimated. In addition, past work did not consider neutron-induced gamma-rays. Finally, power plant lifetime waste volumes may have been underestimated as neutron activation of the neutron dumps and building structure were not addressed. In the present work, a modified version of the SOMBRERO target building is presented where a significantly larger open solid-angle fraction (5%) is used to enhance beam smoothing of a diode-pumped solid-state laser (DPSSL). The GIMMs are replaced with transmissive fused silica wedges and have been included in three-dimensional neutron and photon transport calculations. This work shows that a power plant with a large open solid-angle fraction, needed for beam smoothing with a DPSSL, is acceptable from tritium breeding, and neutron activation points-of-view. (authors)

  2. A fractional spline collocation-Galerkin method for the time-fractional diffusion equation

    Directory of Open Access Journals (Sweden)

    Pezza L.

    2018-03-01

    Full Text Available The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.

  3. A generalized fractional sub-equation method for fractional differential equations with variable coefficients

    International Nuclear Information System (INIS)

    Tang, Bo; He, Yinnian; Wei, Leilei; Zhang, Xindong

    2012-01-01

    In this Letter, a generalized fractional sub-equation method is proposed for solving fractional differential equations with variable coefficients. Being concise and straightforward, this method is applied to the space–time fractional Gardner equation with variable coefficients. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the considered method provides a very effective, convenient and powerful mathematical tool for solving many other fractional differential equations in mathematical physics. -- Highlights: ► Study of fractional differential equations with variable coefficients plays a role in applied physical sciences. ► It is shown that the proposed algorithm is effective for solving fractional differential equations with variable coefficients. ► The obtained solutions may give insight into many considerable physical processes.

  4. Comment on “Maxwell's equations and electromagnetic Lagrangian density in fractional form” [J. Math. Phys. 53, 033505 (2012)

    International Nuclear Information System (INIS)

    Rabei, Eqab M.; Al-Jamel, A.; Widyan, H.; Baleanu, D.

    2014-01-01

    In a recent paper, Jaradat et al. [J. Math. Phys. 53, 033505 (2012)] have presented the fractional form of the electromagnetic Lagrangian density within the Riemann-Liouville fractional derivative. They claimed that the Agrawal procedure [O. P. Agrawal, J. Math. Anal. Appl. 272, 368 (2002)] is used to obtain Maxwell's equations in the fractional form, and the Hamilton's equations of motion together with the conserved quantities obtained from fractional Noether's theorem are reported. In this comment, we draw the attention that there are some serious steps of the procedure used in their work are not applicable even though their final results are correct. Their work should have been done based on a formulation as reported by Baleanu and Muslih [Phys. Scr. 72, 119 (2005)

  5. The distinction between chondroma and chondrosarcoma using chemical element mass fractions in tumors determined by neutron activation analysis as diagnostic markers

    International Nuclear Information System (INIS)

    Zaichick, Vladimir; Zaichick, Sofia

    2016-01-01

    The Ca, Cl, Mg, Na, and P content and Ca/P, Ca/Mg, Ca/Na, Cl/Ca, and Cl/Na ratios in tissue of intact bone, chondroma and chondrosarcoma were investigated by neutron activation analysis. It was shown that higher mass fraction of Cl and Na and also Cl/Na mass fraction ratio as well as lower Ca/Cl and Ca/Na mass fraction ratios are typical of the chondrosarcoma tissue compared to chondroma. Finally, it was proposed to use the estimation of such parameters as the Cl mass fraction and the Ca/Cl and Ca/Na mass fraction ratios as an additional test for differential diagnosis between chondroma and chondrosarcoma. (author)

  6. Altered fractionation of hemithorax irradiation for pleural mesothelioma and failure patterns after treatment

    Energy Technology Data Exchange (ETDEWEB)

    Holsti, L.R. [Dept. of Radiotherapy and Oncology, Helsinki University Central Hospital (Finland); Pyrhoenen, S. [Dept. of Radiotherapy and Oncology, Helsinki University Central Hospital (Finland); Kajanti, M. [Dept. of Radiotherapy and Oncology, Helsinki University Central Hospital (Finland); Maentylae, M. [Dept. of Radiotherapy and Oncology, Helsinki University Central Hospital (Finland); Mattson, K. [Dept. of Internal Medicine, Div. of Pulmonary Medicine, Helsinki University Central Hospital (Finland); Maasilta, P. [Dept. of Internal Medicine, Div. of Pulmonary Medicine, Helsinki University Central Hospital (Finland); Kivisaari, L. [Dept. of Diagnostic Radiology, Helsinki University Central Hospital (Finland)

    1997-09-01

    Malignant pleural mesothelioma is a rare malignancy with a bleak prognosis. The role of radiotherapy has not yet been clarified. Our aim was to study the effect of altered fractionation on mesothelioma. We have treated 57 patients, 41 males and 16 females, with hemithorax irradiation with six different fractionation schedules. All the patients have been included in a combined modality program consisting of surgery followed by chemotherapy and finally by hemithorax irradiation. The radiotherapy schedules used were: I. Conventional fractionation of 20 Gy in 10 fractions over 12 days. II, Split-course radiotherapy 55 Gy in 25 fractions of 2.2 Gy over 7 weeks (a two weeks rest halfways) followed by a boost dose of 15 Gy over 8 days to the major tumour area. III. Hyperfractionation of 70 Gy over 7 weeks, 1.25 Gy BID with a 6-h interval and a 10-day rest halfways. IV. Combined hyperfractionation and hypofractionation, 35 Gy hyperfractionation in 28 fractions (1.25 Gy BID with a 6-h interval) over three weeks followed by 36 Gy hypofractionation 9 fractions of 4 Gy given every other day over 3 weeks to the major tumour areas only. V. Hypofractionation of 38.5 Gy over 15 days (9x3.5 Gy). VI. Combined conventional radiotherapy and hypofractionation with 20 Gy given conventionally in 10 fractions followed by 10 fractions of 3 Gy over two weeks, overall time 4 weeks. The 2-year survival rate of all patients was 21% and the 5-year survival rate 9%. Two patients are still alive more than 6 and 9 years after radiotherapy. Progression occurred after surgery in four patients, during and after chemotherapy in 22 patients and after completed radiotherapy in 29 patients. The pattern of progression was similar in each treatment group. (orig.).

  7. General Output Feedback Stabilization for Fractional Order Systems: An LMI Approach

    Directory of Open Access Journals (Sweden)

    Yiheng Wei

    2014-01-01

    Full Text Available This paper is concerned with the problem of general output feedback stabilization for fractional order linear time-invariant (FO-LTI systems with the fractional commensurate order 0<α<2. The objective is to design suitable output feedback controllers that guarantee the stability of the resulting closed-loop systems. Based on the slack variable method and our previous stability criteria, some new results in the form of linear matrix inequality (LMI are developed to the static and dynamic output feedback controllers synthesis for the FO-LTI system with 0<α<1. Furthermore, the results are extended to stabilize the FO-LTI systems with 1≤α<2. Finally, robust output feedback control is discussed. Numerical examples are given to illustrate the effectiveness of the proposed design methods.

  8. TU-H-CAMPUS-TeP1-01: Variable-Beam Fractionation for SAbR

    Energy Technology Data Exchange (ETDEWEB)

    Modiri, A; Sawant, A [University of Maryland School of Medicine, Baltimore, MD (United States)

    2016-06-15

    Purpose: In current conventionally-fractionated as well as hypofractionated 3D conformal radiotherapy (CRT), the same beam arrangement is employed from fraction to fraction. We challenge this notion and postulate that by varying the beam arrangement between fractions we can achieve greater sparing of organs at risk (OARs) while maintaining PTV coverage. We use an inverse planning strategy using a swarm intelligence-based global optimization algorithm to exploit the additional degree of freedom represented by inter-fractional variation in beam angles. Methods: To evaluate our variable-beam fractionation (VBF) method, a 10-beam ITV-based conformal stereotactic ablative radiotherapy (CRT-SAbR) plan was optimized. In the clinical plan, 54 Gy was delivered to a 41cc lung tumor over 3 fractions. In VBF, each original clinically-assigned beam was multiplied to a bundle of n α-degree-spaced beams, n being number of fractions. Selection of α was a compromise between retaining similar tumor irradiation and separating inline OAR sub-regions. We optimized the beam fluence weights setting an upper limit for beam delivery duration (and implicitly, monitor units) along with clinical organ-based dose-volume constraints. Zero weights were allowed so that the optimization algorithm could remove unnecessary beams. All fractions in final plan had to deliver identical monitor units (MU) while satisfying a soft constraint on having no more than one beam from every n-beam bundle in each fraction. α was 10 degrees and the dose rate was 600 MU/min. Results: The VBF plan achieved significantly superior OAR sparing compared to the clinical internal target volume (ITV)-based plan. Setting maximum beam delivery duration to 13 seconds (well within breath-hold range), Esophagus Dmax, Heart Dmax, Spinal cord Dmax and Lung V13 were improved by 25%, 81%, 0% and 27%, respectively. Conclusion: We investigated a simple approach to inter-fractional VBF planning and demonstrated its potential in

  9. Asphalt chemical fractionation

    International Nuclear Information System (INIS)

    Obando P, Klever N.

    1998-01-01

    Asphalt fractionation were carried out in the Esmeraldas Oil Refinery using n-pentane, SiO 2 and different mixture of benzene- methane. The fractions obtained were analyzed by Fourier's Transformed Infrared Spectrophotometry (FTIR)

  10. Fractional smith chart theory

    KAUST Repository

    Shamim, Atif

    2011-03-01

    For the first time, a generalized Smith chart is introduced here to represent fractional order circuit elements. It is shown that the standard Smith chart is a special case of the generalized fractional order Smith chart. With illustrations drawn for both the conventional integer based lumped elements and the fractional elements, a graphical technique supported by the analytical method is presented to plot impedances on the fractional Smith chart. The concept is then applied towards impedance matching networks, where the fractional approach proves to be much more versatile and results in a single element matching network for a complex load as compared to the two elements in the conventional approach. © 2010 IEEE.

  11. The determination of an unknown source for a space fractional advection dispersion equation

    KAUST Repository

    Aldoghaither, Abeer

    2014-09-01

    In this paper, we are interested in the estimation of the source term for a space fractional advection dispersion equation using concentration and flux measurements at final time. An example of application is the identification of contamination source in groundwater transport. We propose to use the socalled modulating functions method which has been introduced for parameters estimation. This method allows to transfer the estimation problem into solving a system of algebraic equations. Numerical examples are given to illustrate the effectiveness and the robustness of the proposed method. Finally, a comparison between a Tikhonov-based optimization method and the modulating functions approach is presented.

  12. Adapting IMRT delivery fraction-by-fraction to cater for variable intrafraction motion

    International Nuclear Information System (INIS)

    Webb, S

    2008-01-01

    This paper presents a technique for coping with variable intrafraction organ motion when delivering intensity-modulated radiation therapy (IMRT). The strategy is an adaptive delivery in which the fluence delivered up to a particular fraction is subtracted from the required total-course planned fluence to create an adapted residual fluence for the next fraction. This requires that the fluence already delivered can be computed, knowing the intrafraction motion during each fraction. If the adaptation is unconstrained, as would be required for perfect delivery of the planned fluence, then the individual fractional fluences would become unphysical, with both negative components and spikes. Hence it is argued that constraints must be applied; first, positivity constraints and second, constraints to limit fluence spikes. Additionally, it is shown to be helpful to constrain other quantities which are explained. The power of the strategy is that it adapts to the (potentially variable) moving geometry during each fraction. It is not a perfect delivery but it is always better than making no adaptation. The fractionated nature of radiation therapy is thus exploited to advantage. The fluence adaptation method does not require re-planning at each fraction but this imposes limitations which are stated. The fuller theory of dose adaptation is also developed for intrafraction motion. The method is complementary to other adaptive strategies recently discussed with respect to interfraction motion

  13. A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors

    Science.gov (United States)

    Zou, Changfu; Zhang, Lei; Hu, Xiaosong; Wang, Zhenpo; Wik, Torsten; Pecht, Michael

    2018-06-01

    Electrochemical energy storage systems play an important role in diverse applications, such as electrified transportation and integration of renewable energy with the electrical grid. To facilitate model-based management for extracting full system potentials, proper mathematical models are imperative. Due to extra degrees of freedom brought by differentiation derivatives, fractional-order models may be able to better describe the dynamic behaviors of electrochemical systems. This paper provides a critical overview of fractional-order techniques for managing lithium-ion batteries, lead-acid batteries, and supercapacitors. Starting with the basic concepts and technical tools from fractional-order calculus, the modeling principles for these energy systems are presented by identifying disperse dynamic processes and using electrochemical impedance spectroscopy. Available battery/supercapacitor models are comprehensively reviewed, and the advantages of fractional types are discussed. Two case studies demonstrate the accuracy and computational efficiency of fractional-order models. These models offer 15-30% higher accuracy than their integer-order analogues, but have reasonable complexity. Consequently, fractional-order models can be good candidates for the development of advanced battery/supercapacitor management systems. Finally, the main technical challenges facing electrochemical energy storage system modeling, state estimation, and control in the fractional-order domain, as well as future research directions, are highlighted.

  14. Analytic solutions of Oldroyd-B fluid with fractional derivatives in a circular duct that applies a constant couple

    Directory of Open Access Journals (Sweden)

    M.B. Riaz

    2016-12-01

    Full Text Available The aim of this article was to analyze the rotational flow of an Oldroyd-B fluid with fractional derivatives, induced by an infinite circular cylinder that applies a constant couple to the fluid. Such kind of problem in the settings of fractional derivatives has not been found in the literature. The solutions are based on an important remark regarding the governing equation for the non-trivial shear stress. The solutions that have been obtained satisfy all imposed initial and boundary conditions and can easily be reduced to the similar solutions corresponding to ordinary Oldroyd-B, fractional/ordinary Maxwell, fractional/ordinary second-grade, and Newtonian fluids performing the same motion. The obtained results are expressed in terms of Newtonian and non-Newtonian contributions. Finally, the influence of fractional parameters on the velocity, shear stress and a comparison between generalized and ordinary fluids is graphically underlined.

  15. Output Feedback Fractional-Order Nonsingular Terminal Sliding Mode Control of Underwater Remotely Operated Vehicles

    Directory of Open Access Journals (Sweden)

    Yaoyao Wang

    2014-01-01

    Full Text Available For the 4-DOF (degrees of freedom trajectory tracking control problem of underwater remotely operated vehicles (ROVs in the presence of model uncertainties and external disturbances, a novel output feedback fractional-order nonsingular terminal sliding mode control (FO-NTSMC technique is introduced in light of the equivalent output injection sliding mode observer (SMO and TSMC principle and fractional calculus technology. The equivalent output injection SMO is applied to reconstruct the full states in finite time. Meanwhile, the FO-NTSMC algorithm, based on a new proposed fractional-order switching manifold, is designed to stabilize the tracking error to equilibrium points in finite time. The corresponding stability analysis of the closed-loop system is presented using the fractional-order version of the Lyapunov stability theory. Comparative numerical simulation results are presented and analyzed to demonstrate the effectiveness of the proposed method. Finally, it is noteworthy that the proposed output feedback FO-NTSMC technique can be used to control a broad range of nonlinear second-order dynamical systems in finite time.

  16. Advances in robust fractional control

    CERN Document Server

    Padula, Fabrizio

    2015-01-01

    This monograph presents design methodologies for (robust) fractional control systems. It shows the reader how to take advantage of the superior flexibility of fractional control systems compared with integer-order systems in achieving more challenging control requirements. There is a high degree of current interest in fractional systems and fractional control arising from both academia and industry and readers from both milieux are catered to in the text. Different design approaches having in common a trade-off between robustness and performance of the control system are considered explicitly. The text generalizes methodologies, techniques and theoretical results that have been successfully applied in classical (integer) control to the fractional case. The first part of Advances in Robust Fractional Control is the more industrially-oriented. It focuses on the design of fractional controllers for integer processes. In particular, it considers fractional-order proportional-integral-derivative controllers, becau...

  17. Gauge invariant fractional electromagnetic fields

    Science.gov (United States)

    Lazo, Matheus Jatkoske

    2011-09-01

    Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators.

  18. Comparative proteomics of matrix fractions between pimpled and normal chicken eggshells.

    Science.gov (United States)

    Liu, Zhangguo; Song, Lingzi; Lu, Lizhi; Zhang, Xianfu; Zhang, Fuming; Wang, Kehua; Linhardt, Robert J

    2017-09-07

    Eggshell matrix can be dissociated into three matrix fractions: acid-insoluble matrix (M1), water-insoluble matrix (M2) and acid-water facultative-soluble matrix (M3). Matrix fractions from pimpled and normal eggshells were compared using label-free proteomic method to understand the differences among three matrix fractions and the proteins involved with eggshell quality. A total of 738 and 600 proteins were identified in the pimpled and normal calcified eggshells, respectively. Both eggshells showed a combined proteomic inventory of 769 proteins. In the same type of eggshell, a high similarity was present in the proteomes of three matrix fractions. These triply overlapped common proteins formed the predominant contributor to proteomic abundance in the matrix fractions. In each matrix fraction and between both eggshell models, normal and pimpled eggshells, a majority of the proteomes of the fractions were commonly observed. Forty-two common major proteins (iBAQ-derived abundance ≥0.095% of proteomic abundance) were identified throughout the three matrix fractions and these proteins might act as backbone constituents in chicken eggshell matrix. Finally, using 1.75-fold as up-regulated and using 0.57-fold as down-regulated cutoff values, twenty-five differential major proteins were screened and they all negatively influence and none showed any effect on eggshell quality. Overall, we uncovered the characteristics of proteomics of three eggshell matrix fractions and identified candidate proteins influencing eggshell quality. The next research on differential proteins will uncover the potential mechanisms underlying how proteins affect eggshell quality. It was reported that the proteins in an eggshell can be divided into insoluble and soluble proteins. The insoluble proteins are thought to be an inter-mineral matrix and acts as a structural framework, while the soluble proteins are thought as intra-mineral matrix that are embedded within the crystal during

  19. Fractional statistics and quantum scaling properties of the integrable Penson-Kolb-Hubbard chain

    Science.gov (United States)

    Vitoriano, Carlindo; Coutinho-Filho, M. D.

    2010-09-01

    We investigate the ground-state and low-temperature properties of the integrable version of the Penson-Kolb-Hubbard chain. The model obeys fractional statistical properties, which give rise to fractional elementary excitations and manifest differently in the four regions of the phase diagram U/t versus n , where U is the Coulomb coupling, t is the correlated hopping amplitude, and n is the particle density. In fact, we can find local pair formation, fractionalization of the average occupation number per orbital k , or U - and n -dependent average electric charge per orbital k . We also study the scaling behavior near the U -driven quantum phase transitions and characterize their universality classes. Finally, it is shown that in the regime of parameters where local pair formation is energetically more favorable, the ground state exhibits power-law superconductivity; we also stress that above half filling the pair-hopping term stabilizes local Cooper pairs in the repulsive- U regime for U

  20. An improved electrical-conductance sensor for void-fraction measurement in a horizontal pipe

    International Nuclear Information System (INIS)

    Ko, Min Seok; Jemg, Dong Wook; Kim, Sin; Lee, Bo An; Won, Woo Youn; Lee, Yeon Gun

    2015-01-01

    The electrical-impedance method has been widely used for void-fraction measurement in two-phase flow due to its many favorable features. In the impedance method, the response characteristics of the electrical signal heavily depend upon flow pattern, as well as phasic volume. Thus, information on the flow pattern should be given for reliable void-fraction measurement. This study proposes an improved electrical-conductance sensor composed of a three-electrode set of adjacent and opposite electrodes. In the proposed sensor, conductance readings are directly converted into the flow pattern through a specified criterion and are consecutively used to estimate the corresponding void fraction. Since the flow pattern and the void fraction are evaluated by reading conductance measurements, complexity of data processing can be significantly reduced and real-time information provided. Before actual applications, several numerical calculations are performed to optimize electrode and insulator sizes, and optimal design is verified by static experiments. Finally, the proposed sensor is applied for air-water two-phase flow in a horizontal loop with a 40-mm inner diameter and a 5-m length, and its measurement results are compared with those of a wire-mesh sensor

  1. Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations

    International Nuclear Information System (INIS)

    Lu, Bin

    2012-01-01

    In this Letter, the fractional derivatives in the sense of modified Riemann–Liouville derivative and the Bäcklund transformation of fractional Riccati equation are employed for constructing the exact solutions of nonlinear fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. This approach can also be applied to other nonlinear fractional differential equations. -- Highlights: ► Backlund transformation of fractional Riccati equation is presented. ► A new method for solving nonlinear fractional differential equations is proposed. ► Three important fractional differential equations are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained.

  2. Finite Time Control for Fractional Order Nonlinear Hydroturbine Governing System via Frequency Distributed Model

    Directory of Open Access Journals (Sweden)

    Bin Wang

    2016-01-01

    Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.

  3. Stability and Hopf Bifurcation of Fractional-Order Complex-Valued Single Neuron Model with Time Delay

    Science.gov (United States)

    Wang, Zhen; Wang, Xiaohong; Li, Yuxia; Huang, Xia

    2017-12-01

    In this paper, the problems of stability and Hopf bifurcation in a class of fractional-order complex-valued single neuron model with time delay are addressed. With the help of the stability theory of fractional-order differential equations and Laplace transforms, several new sufficient conditions, which ensure the stability of the system are derived. Taking the time delay as the bifurcation parameter, Hopf bifurcation is investigated and the critical value of the time delay for the occurrence of Hopf bifurcation is determined. Finally, two representative numerical examples are given to show the effectiveness of the theoretical results.

  4. Exact Solutions of Fractional Burgers and Cahn-Hilliard Equations Using Extended Fractional Riccati Expansion Method

    Directory of Open Access Journals (Sweden)

    Wei Li

    2014-01-01

    Full Text Available Based on a general fractional Riccati equation and with Jumarie’s modified Riemann-Liouville derivative to an extended fractional Riccati expansion method for solving the time fractional Burgers equation and the space-time fractional Cahn-Hilliard equation, the exact solutions expressed by the hyperbolic functions and trigonometric functions are obtained. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.

  5. Improved measurements of branching fractions for eta(c) -> phi phi and omega phi

    NARCIS (Netherlands)

    Haddadi, Z.; Kalantar-Nayestanaki, N.; Kavatsyuk, M.; Löhner, H.; Messchendorp, J.; Tiemens, M.

    2017-01-01

    Using (223.7 +/- 1.4) x 10(6) J / Psi events accumulated with the BESIII detector, we study eta(c) decays to phi phi and omega phi final states. The branching fraction of n(c) -> phi phi is measured to be Br(eta(c) -> phi phi) = (2.5 +/- 0(-0.7)(+0.3) +/- 0.6) X 10(-3,) where the first uncertainty

  6. Using artificial neural networks to constrain the halo baryon fraction during reionization

    Science.gov (United States)

    Sullivan, David; Iliev, Ilian T.; Dixon, Keri L.

    2018-01-01

    Radiative feedback from stars and galaxies has been proposed as a potential solution to many of the tensions with simplistic galaxy formation models based on Λcold dark matter, such as the faint end of the ultraviolet (UV) luminosity function. The total energy budget of radiation could exceed that of galactic winds and supernovae combined, which has driven the development of sophisticated algorithms that evolve both the radiation field and the hydrodynamical response of gas simultaneously, in a cosmological context. We probe self-feedback on galactic scales using the adaptive mesh refinement, radiative transfer, hydrodynamics, and N-body code RAMSES-RT. Unlike previous studies which assume a homogeneous UV background, we self-consistently evolve both the radiation field and gas to constrain the halo baryon fraction during cosmic reionization. We demonstrate that the characteristic halo mass with mean baryon fraction half the cosmic mean, Mc(z), shows very little variation as a function of mass-weighted ionization fraction. Furthermore, we find that the inclusion of metal cooling and the ability to resolve scales small enough for self-shielding to become efficient leads to a significant drop in Mc when compared to recent studies. Finally, we develop an artificial neural network that is capable of predicting the baryon fraction of haloes based on recent tidal interactions, gas temperature, and mass-weighted ionization fraction. Such a model can be applied to any reionization history, and trivially incorporated into semi-analytical models of galaxy formation.

  7. Existence of mild solutions for nonlocal Cauchy problem for fractional neutral evolution equations with infinite delay

    Directory of Open Access Journals (Sweden)

    V. Vijayakumar

    2014-09-01

    Full Text Available In this article, we study the existence of mild solutions for nonlocal Cauchy problem for fractional neutral evolution equations with infinite delay. The results are obtained by using the Banach contraction principle. Finally, an application is given to illustrate the theory.

  8. Generalized Fractional Processes with Long Memory and Time Dependent Volatility Revisited

    Directory of Open Access Journals (Sweden)

    M. Shelton Peiris

    2016-09-01

    Full Text Available In recent years, fractionally-differenced processes have received a great deal of attention due to their flexibility in financial applications with long-memory. This paper revisits the class of generalized fractionally-differenced processes generated by Gegenbauer polynomials and the ARMA structure (GARMA with both the long-memory and time-dependent innovation variance. We establish the existence and uniqueness of second-order solutions. We also extend this family with innovations to follow GARCH and stochastic volatility (SV. Under certain regularity conditions, we give asymptotic results for the approximate maximum likelihood estimator for the GARMA-GARCH model. We discuss a Monte Carlo likelihood method for the GARMA-SV model and investigate finite sample properties via Monte Carlo experiments. Finally, we illustrate the usefulness of this approach using monthly inflation rates for France, Japan and the United States.

  9. Achieving higher productivity of UO2 fuel at NUOFP through improved in-plant quality surveillance

    International Nuclear Information System (INIS)

    Meena, R.; Pramanik, D.; Sairam, S.; Rajkumar, J.V.; Rao, R.V.R.L.V.; Sinha, T.K.; Santra, N.; Rao, G.V.S.H.; Jayaraj, R.N.

    2009-01-01

    At Nuclear Fuel Complex (NFC), in the production of UO 2 fuel for PHWRs, a standard set of process parameters are monitored regularly for every lot of powder and pellet. Quality of intermediate products in the production process like UNP, ADU(dry), U 3 O 8 , UO 2+x , UO 2 granules, green pellets, sintered pellets are also regularly analysed/monitored apart from the final finished pellet and ensured to be within specified range. This range is decided by final product specifications and sometimes also based on the feed requirement in the next process in the downstream of the flow sheet. Vast experience gained over the years, behavior of various equipment under given set of conditions, feed back from the customer plants etc; have been primary criteria hither to, for defining the process conditions and chemical/physical properties of intermediate products

  10. Clinical evaluation of the SmartSkin fractional laser for the treatment of photodamage and acne scars.

    Science.gov (United States)

    Gold, Michael H; Heath, Amanda D; Biron, Julie A

    2009-11-01

    Fractional photothermolysis with a CO2 laser shows promise in the treatment of photodamaged skin. The purpose of this study was to evaluate a fractional CO2 laser device (SmartSkin, Cynosure, Westford, MA) for the treatment of facial photodamage. Twelve subjects seeking treatment of facial hyperpigmentation, skin laxity, wrinkles and fine lines, enlarged pores and acne scars enrolled in the study. Each subject was treated twice with the SmartSkin device at three- to five-week intervals. Results were evaluated at one week, one month and three months after the final treatment. All 12 subjects completed the study. Physician and subject assessments both indicated that clinical improvements in all photodamage parameters were apparent at one month and persisted at least three months. Improvements in acne scars were noted but not graded. Eleven subjects would recommend the treatment to family and friends. The median pain scores during the initial and final treatments were 2.00 and 2.00, respectively, on a scale of 0-5. Only one adverse effect, facial edema, was judged "probably related to treatment." The SmartSkin fractional laser device improves photodamaged skin for at least three months. The treatment was well tolerated and adverse effects were limited to transient facial edema.

  11. Image Encryption Technology Based on Fractional Two-Dimensional Triangle Function Combination Discrete Chaotic Map Coupled with Menezes-Vanstone Elliptic Curve Cryptosystem

    Directory of Open Access Journals (Sweden)

    Zeyu Liu

    2018-01-01

    Full Text Available A new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM with the discrete fractional difference is proposed. We observe the bifurcation behaviors and draw the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits of the proposed map, respectively. On the application side, we apply the proposed discrete fractional map into image encryption with the secret keys ciphered by Menezes-Vanstone Elliptic Curve Cryptosystem (MVECC. Finally, the image encryption algorithm is analysed in four main aspects that indicate the proposed algorithm is better than others.

  12. Hypofractionated stereotactic radiation therapy in three to five fractions for vestibular schwannoma

    International Nuclear Information System (INIS)

    Morimoto, Masahiro; Yoshioka, Yasuo; Kotsuma, Tadayuki

    2013-01-01

    The objective of this study was to retrospectively examine the outcomes of hypofractionated stereotactic radiation therapy in three to five fractions for vestibular schwannomas. Twenty-five patients with 26 vestibular schwannomas were treated with hypofractionated stereotactic radiation therapy using a CyberKnife. The vestibular schwannomas of 5 patients were associated with type II neurofibromatosis. The median follow-up time was 80 months (range: 6-167); the median planning target volume was 2.6 cm 3 (0.3-15.4); and the median prescribed dose (≥D90) was 21 Gy in three fractions (18-25 Gy in three to five fractions). Progression was defined as ≥2 mm 3-dimensional post-treatment tumor enlargement excluding transient expansion. Progression or any death was counted as an event in progression-free survival rates, whereas only progression was counted in progression-free rates. The 7-year progression-free survival and progression-free rates were 78 and 95%, respectively. Late adverse events (≥3 months) with grades based on Common Terminology Criteria for Adverse Events, v4.03 were observed in 6 patients: Grade 3 hydrocephalus in one patient, Grade 2 facial nerve disorders in two and Grade 1-2 tinnitus in three. In total, 12 out of 25 patients maintained pure tone averages ≤50 dB before hypofractionated stereotactic radiation therapy, and 6 of these 12 patients (50%) maintained pure tone averages at this level at the final audiometric follow-up after hypofractionated stereotactic radiation therapy. However, gradient deterioration of pure tone average was observed in 11 of these 12 patients. The mean pure tone averages before hypofractionated stereotactic radiation therapy and at the final follow-up for the aforementioned 12 patients were 29.8 and 57.1 dB, respectively. Treating vestibular schwannomas with hypofractionated stereotactic radiation therapy in three to five fractions may prevent tumor progression with tolerable toxicity. However, gradient

  13. Hypofractionated stereotactic radiation therapy in three to five fractions for vestibular schwannoma

    Energy Technology Data Exchange (ETDEWEB)

    Morimoto, Masahiro; Yoshioka, Yasuo [Osaka Univ., Graduate School of Medicine, Suita, Osaka (Japan); Kotsuma, Tadayuki [Kinki-chuo Chest Medical Center, Sakai, Osaka (Japan); others, and

    2013-08-15

    The objective of this study was to retrospectively examine the outcomes of hypofractionated stereotactic radiation therapy in three to five fractions for vestibular schwannomas. Twenty-five patients with 26 vestibular schwannomas were treated with hypofractionated stereotactic radiation therapy using a CyberKnife. The vestibular schwannomas of 5 patients were associated with type II neurofibromatosis. The median follow-up time was 80 months (range: 6-167); the median planning target volume was 2.6 cm{sup 3} (0.3-15.4); and the median prescribed dose ({>=}D90) was 21 Gy in three fractions (18-25 Gy in three to five fractions). Progression was defined as {>=}2 mm 3-dimensional post-treatment tumor enlargement excluding transient expansion. Progression or any death was counted as an event in progression-free survival rates, whereas only progression was counted in progression-free rates. The 7-year progression-free survival and progression-free rates were 78 and 95%, respectively. Late adverse events ({>=}3 months) with grades based on Common Terminology Criteria for Adverse Events, v4.03 were observed in 6 patients: Grade 3 hydrocephalus in one patient, Grade 2 facial nerve disorders in two and Grade 1-2 tinnitus in three. In total, 12 out of 25 patients maintained pure tone averages {<=}50 dB before hypofractionated stereotactic radiation therapy, and 6 of these 12 patients (50%) maintained pure tone averages at this level at the final audiometric follow-up after hypofractionated stereotactic radiation therapy. However, gradient deterioration of pure tone average was observed in 11 of these 12 patients. The mean pure tone averages before hypofractionated stereotactic radiation therapy and at the final follow-up for the aforementioned 12 patients were 29.8 and 57.1 dB, respectively. Treating vestibular schwannomas with hypofractionated stereotactic radiation therapy in three to five fractions may prevent tumor progression with tolerable toxicity. However, gradient

  14. Fraction Reduction through Continued Fractions

    Science.gov (United States)

    Carley, Holly

    2011-01-01

    This article presents a method of reducing fractions without factoring. The ideas presented may be useful as a project for motivated students in an undergraduate number theory course. The discussion is related to the Euclidean Algorithm and its variations may lead to projects or early examples involving efficiency of an algorithm.

  15. Measurement of the Branching Fractions for B+ --> K*{sup 0}pi{sup +}

    Energy Technology Data Exchange (ETDEWEB)

    Aubert, B.

    2004-02-10

    We present a preliminary result of the branching fraction for the B meson decay to the final state K{sup +}{pi}{sup -}{pi}{sup +} via an intermediate K*{sup 0} resonance using the sample of approximately 23 million B{bar B} mesons produced at the {Upsilon}(4S) resonance with the BABAR detector at the PEP II e{sup +}e{sup -} collider. The K*{sup 0} was detected through the decay to the final state K{sup +}{pi}{sup -}. The result of this analysis is {Beta}(B{sup +} {yields} K*{sup 0}{pi}{sup +}) = (15.5 {+-} 3.4 {+-} 1.8) x 10{sup -6} where the first error is statistical and the second is systematic.

  16. Fractional quiver W-algebras

    Science.gov (United States)

    Kimura, Taro; Pestun, Vasily

    2018-04-01

    We introduce quiver gauge theory associated with the non-simply laced type fractional quiver and define fractional quiver W-algebras by using construction of Kimura and Pestun (Lett Math Phys, 2018. https://doi.org/10.1007/s11005-018-1072-1; Lett Math Phys, 2018. https://doi.org/10.1007/s11005-018-1073-0) with representation of fractional quivers.

  17. Intrinsic densitometry: In-plant evaluation

    International Nuclear Information System (INIS)

    Nishida, K.; Kurosawa, A.; Masui, J.; Hsue, S.T.

    1994-11-01

    A measurement of the plutonium concentration in a sample is always necessary for nuclear material control and accounting. This report describes the testing of the intrinsic densitometry (ID) technique for implant applications. The authors found that the ID method can determine the plutonium concentrations to between 2 and 3% at concentrations of 100 g/l to 200 g/l with quartz cells and a measurement time of 3600 s. The precision can be improved to 1 to 2% with a higher counting rate. The authors also found that nitric acid concentration and the impurity level of uranium in the product plutonium solution do not affect the concentration measurement. When this technique is applied to plutonium solutions in stainless steel pipes, they found that similar precision in plutonium concentration can be achieved using a high-count-rate detector. The precision, however, is reduced with aged plutonium solutions

  18. Discrete fractional calculus

    CERN Document Server

    Goodrich, Christopher

    2015-01-01

    This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...

  19. On the Approximate Solutions of Local Fractional Differential Equations with Local Fractional Operators

    Directory of Open Access Journals (Sweden)

    Hossein Jafari

    2016-04-01

    Full Text Available In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods.

  20. Comparison of some peptidic and proteic ovine pineal fractions with a bovine pineal E5 fraction

    Energy Technology Data Exchange (ETDEWEB)

    Noteborn, H P; Ebels, I; Salemink, C A [State Univ. of Utrecht, Utrecht (Netherlands). Department of Organic Chemistry; Pevet, P [The Netherlands Institute for Brain Research, Amsterdam (Netherlands).; Reinharz, A C [Hopital Cantonal, Geneva (Switzerland). Department of Medicine, Division of Endocrinology; Neacsu, C [Institute of Cellular Biology and Pathology, Bucharest (Romania).

    1982-01-01

    Using rather simple and mild extraction and separation methods, three ovine pineal fractions (XM 300R - PP 7.2, PP 7.2' and PP 7.2S) were obtained, which contain peptidic/proteic substances and which show fluorescence characteristics of indoles. The ovine fractions were compared with the bovine pineal E5-fraction. The ovine fractions are chemically sensitive to normal laboratory light and stable in red light (..lambda.. > 600 nm). Immunologically, these fractions and the bovine E5 fraction are stable. From the results of radioimmunological experiments it was concluded that the bovine pineal E5 fraction as well as the ovine pineal fraction XM 300R - PP 7.2 and PP 7.2S may contain (a) peptide(s) ending by the same carboxy terminal tripeptide Pro-Arg-Gly(NH/sub 2/).

  1. Analysis of football player's motion in view of fractional calculus

    Science.gov (United States)

    Couceiro, Micael S.; Clemente, Filipe M.; Martins, Fernando M. L.

    2013-06-01

    Accurately retrieving the position of football players over time may lay the foundations for a whole series of possible new performance metrics for coaches and assistants. Despite the recent developments of automatic tracking systems, the misclassification problem ( i.e., misleading a given player by another) still exists and requires human operators as final evaluators. This paper proposes an adaptive fractional calculus (FC) approach to improve the accuracy of tracking methods by estimating the position of players based on their trajectory so far. One half-time of an official football match was used to evaluate the accuracy of the proposed approach under different sampling periods of 250, 500 and 1000 ms. Moreover, the performance of the FC approach was compared with position-based and velocity-based methods. The experimental evaluation shows that the FC method presents a high classification accuracy for small sampling periods. Such results suggest that fractional dynamics may fit the trajectory of football players, thus being useful to increase the autonomy of tracking systems.

  2. Coefficient of restitution in fractional viscoelastic compliant impacts using fractional Chebyshev collocation

    Science.gov (United States)

    Dabiri, Arman; Butcher, Eric A.; Nazari, Morad

    2017-02-01

    Compliant impacts can be modeled using linear viscoelastic constitutive models. While such impact models for realistic viscoelastic materials using integer order derivatives of force and displacement usually require a large number of parameters, compliant impact models obtained using fractional calculus, however, can be advantageous since such models use fewer parameters and successfully capture the hereditary property. In this paper, we introduce the fractional Chebyshev collocation (FCC) method as an approximation tool for numerical simulation of several linear fractional viscoelastic compliant impact models in which the overall coefficient of restitution for the impact is studied as a function of the fractional model parameters for the first time. Other relevant impact characteristics such as hysteresis curves, impact force gradient, penetration and separation depths are also studied.

  3. Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

    KAUST Repository

    N U+02BC Doye, Ibrahima

    2018-02-13

    In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

  4. Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

    KAUST Repository

    N U+02BC Doye, Ibrahima; Salama, Khaled N.; Laleg-Kirati, Taous-Meriem

    2018-01-01

    In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

  5. Numerical analysis for trajectory controllability of a coupled multi-order fractional delay differential system via the shifted Jacobi method

    Science.gov (United States)

    Priya, B. Ganesh; Muthukumar, P.

    2018-02-01

    This paper deals with the trajectory controllability for a class of multi-order fractional linear systems subject to a constant delay in state vector. The solution for the coupled fractional delay differential equation is established by the Mittag-Leffler function. The necessary and sufficient condition for the trajectory controllability is formulated and proved by the generalized Gronwall's inequality. The approximate trajectory for the proposed system is obtained through the shifted Jacobi operational matrix method. The numerical simulation of the approximate solution shows the theoretical results. Finally, some remarks and comments on the existing results of constrained controllability for the fractional dynamical system are also presented.

  6. Fractional distillation of oil

    Energy Technology Data Exchange (ETDEWEB)

    Jones, L D

    1931-10-31

    A method of dividing oil into lubricating oil fractions without substantial cracking by introducing the oil in a heated state into a fractionating column from which oil fractions having different boiling points are withdrawn at different levels, while reflux liquid is supplied to the top of the column, and additional heat is introduced into the column by contacting with the oil therein a heated fluid of higher monlecular weight than water and less susceptible to thermal decomposition than is the highest boiling oil fraction resulting from the distillation, or of which any products produced by thermal decomposition will not occur in the highest boiling distillate withdrawn from the column.

  7. One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order 1 < q < 2

    Science.gov (United States)

    Zhou, Ping; Bai, Rongji

    2014-01-01

    Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in 1 < q < 2, one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order 1 < q < 2 is considered. Numerical simulations show the validity and feasibility of the proposed scheme. PMID:25247207

  8. Charmless Hadronic B Decays into Vector, Axial Vector and Tensor Final States at BaBar

    International Nuclear Information System (INIS)

    Gandini, Paolo

    2012-01-01

    We present experimental measurements of branching fraction and longitudinal polarization fraction in charmless hadronic B decays into vector, axial vector and tensor final states with the final dataset of BABAR. Measurements of such kind of decays are a powerful tool both to test the Standard Model and search possible sources of new physics. In this document we present a short review of the last experimental results at BABAR concerning charmless quasi two-body decays in final states containing particles with spin 1 or spin 2 and different parities. This kind of decays has received considerable theoretical interest in the last few years and this particular attention has led to interesting experimental results at the current b-factories. In fact, the study of longitudinal polarization fraction f L in charmless B decays to vector vector (VV), vector axial-vector (VA) and axial-vector axial-vector (AA) mesons provides information on the underlying helicity structure of the decay mechanism. Naive helicity conservation arguments predict a dominant longitudinal polarization fraction f L ∼ 1 for both tree and penguin dominated decays and this pattern seems to be confirmed by tree-dominated B → ρρ and B + → (Omega)ρ + decays. Other penguin dominated decays, instead, show a different behavior: the measured value of f L ∼ 0.5 in B → φK* decays is in contrast with naive Standard Model (SM) calculations. Several solutions have been proposed such as the introduction of non-factorizable terms and penguin-annihilation amplitudes, while other explanations invoke new physics. New modes have been investigated to shed more light on the problem.

  9. Toward lattice fractional vector calculus

    International Nuclear Information System (INIS)

    Tarasov, Vasily E

    2014-01-01

    An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity. (papers)

  10. Toward lattice fractional vector calculus

    Science.gov (United States)

    Tarasov, Vasily E.

    2014-09-01

    An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

  11. The fractionation of adipose tissue procedure to obtain stromal vascular fractions for regenerative purposes

    NARCIS (Netherlands)

    van Dongen, Joris A.; Stevens, Hieronymus P.; Parvizi, Mojtaba; van der Lei, Berend; Harmsen, Martin C.

    2016-01-01

    Autologous adipose tissue transplantation is clinically used to reduce dermal scarring and to restore volume loss. The therapeutic benefit on tissue damage more likely depends on the stromal vascular fraction of adipose tissue than on the adipocyte fraction. This stromal vascular fraction can be

  12. One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order 1

    Directory of Open Access Journals (Sweden)

    Ping Zhou

    2014-01-01

    Full Text Available Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in 1fractional-order Lorenz chaotic system with fractional-order 1

  13. Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Xu, Kaixuan, E-mail: kaixuanxubjtu@yeah.net; Wang, Jun

    2017-02-26

    In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model. - Highlights: • Two new entropy approaches for estimation of nonlinear complexity are proposed for the financial market. • Effectiveness analysis of proposed methods is presented and their respective features are studied. • Empirical research of proposed analysis on seven world financial market indices. • Numerical simulation of Potts financial dynamics is preformed for nonlinear complexity behaviors.

  14. Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

    International Nuclear Information System (INIS)

    Xu, Kaixuan; Wang, Jun

    2017-01-01

    In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model. - Highlights: • Two new entropy approaches for estimation of nonlinear complexity are proposed for the financial market. • Effectiveness analysis of proposed methods is presented and their respective features are studied. • Empirical research of proposed analysis on seven world financial market indices. • Numerical simulation of Potts financial dynamics is preformed for nonlinear complexity behaviors.

  15. Global Mittag-Leffler stability analysis of fractional-order impulsive neural networks with one-side Lipschitz condition.

    Science.gov (United States)

    Zhang, Xinxin; Niu, Peifeng; Ma, Yunpeng; Wei, Yanqiao; Li, Guoqiang

    2017-10-01

    This paper is concerned with the stability analysis issue of fractional-order impulsive neural networks. Under the one-side Lipschitz condition or the linear growth condition of activation function, the existence of solution is analyzed respectively. In addition, the existence, uniqueness and global Mittag-Leffler stability of equilibrium point of the fractional-order impulsive neural networks with one-side Lipschitz condition are investigated by the means of contraction mapping principle and Lyapunov direct method. Finally, an example with numerical simulation is given to illustrate the validity and feasibility of the proposed results. Copyright © 2017 Elsevier Ltd. All rights reserved.

  16. Optimization of fractional composition of the excipient in the elastomeric covering for asphalt highways

    Directory of Open Access Journals (Sweden)

    E. M. Nurullaev

    2013-04-01

    Full Text Available The computational method of optimum fractional composition of a dispersible filler of polymeric composite on the basis of three-dimensionally linked elastomer is developed according to non-linear programming. The coefficient of dynamic viscosity of polymeric suspension or the initial module of a viscoelasticity of the join solidification low-molecular rubbers with the final functional groups, filled by many fractional dioxide of silicon are considered as criteria of optimization. Influence of the limiting volume filling on energy of mechanical destruction was investigated. The elastomeric material is offered for use as a covering of asphalt highways in the form of a frost-proof waterproofing layer, which allowing multiply to increase operating properties.

  17. Intracellular Cadmium Isotope Fractionation

    Science.gov (United States)

    Horner, T. J.; Lee, R. B.; Henderson, G. M.; Rickaby, R. E.

    2011-12-01

    Recent stable isotope studies into the biological utilization of transition metals (e.g. Cu, Fe, Zn, Cd) suggest several stepwise cellular processes can fractionate isotopes in both culture and nature. However, the determination of fractionation factors is often unsatisfactory, as significant variability can exist - even between different organisms with the same cellular functions. Thus, it has not been possible to adequately understand the source and mechanisms of metal isotopic fractionation. In order to address this problem, we investigated the biological fractionation of Cd isotopes within genetically-modified bacteria (E. coli). There is currently only one known biological use or requirement of Cd, a Cd/Zn carbonic anhydrase (CdCA, from the marine diatom T. weissfloggii), which we introduce into the E. coli genome. We have also developed a cleaning procedure that allows for the treating of bacteria so as to study the isotopic composition of different cellular components. We find that whole cells always exhibit a preference for uptake of the lighter isotopes of Cd. Notably, whole cells appear to have a similar Cd isotopic composition regardless of the expression of CdCA within the E. coli. However, isotopic fractionation can occur within the genetically modified E. coli during Cd use, such that Cd bound in CdCA can display a distinct isotopic composition compared to the cell as a whole. Thus, the externally observed fractionation is independent of the internal uses of Cd, with the largest Cd isotope fractionation occurring during cross-membrane transport. A general implication of these experiments is that trace metal isotopic fractionation most likely reflects metal transport into biological cells (either actively or passively), rather than relating to expression of specific physiological function and genetic expression of different metalloenzymes.

  18. Misconception on Addition and Subtraction of Fraction at Primary School Students in Fifth-Grade

    Science.gov (United States)

    Trivena, V.; Ningsih, A. R.; Jupri, A.

    2017-09-01

    This study aims to investigate the mastery concept of the student in mathematics learning especially in addition and subtraction of fraction at primary school level. By using qualitative research method, the data were collected from 23 grade five students (10-11-year-old). Instruments included a test, that is accompanied by Certainty Response Index (CRI) and interview with students and teacher. The result of the test has been obtained, then processed by analyzing the student’s answers for each item and then grouped by the CRI categories that combined with the results of the interview with students and teacher. The results showed that student’s mastery-concept on additional and subtraction dominated by category ‘misconception’. So, we can say that mastery-concept on addition and subtraction of fraction at fifth-grade students is still low. Finally, the impact can make most of primary student think that learning addition and subtraction of fraction in mathematics is difficult.

  19. Sliding Mode Control of Fractional-Order Delayed Memristive Chaotic System with Uncertainty and Disturbance

    Science.gov (United States)

    Ding, Da-Wei; Liu, Fang-Fang; Chen, Hui; Wang, Nian; Liang, Dong

    2017-12-01

    In this paper, a simplest fractional-order delayed memristive chaotic system is proposed in order to control the chaos behaviors via sliding mode control strategy. Firstly, we design a sliding mode control strategy for the fractional-order system with time delay to make the states of the system asymptotically stable. Then, we obtain theoretical analysis results of the control method using Lyapunov stability theorem which guarantees the asymptotic stability of the non-commensurate order and commensurate order system with and without uncertainty and an external disturbance. Finally, numerical simulations are given to verify that the proposed sliding mode control method can eliminate chaos and stabilize the fractional-order delayed memristive system in a finite time. Supported by the National Nature Science Foundation of China under Grant No. 61201227, Funding of China Scholarship Council, the Natural Science Foundation of Anhui Province under Grant No. 1208085M F93, 211 Innovation Team of Anhui University under Grant Nos. KJTD007A and KJTD001B

  20. Existence and discrete approximation for optimization problems governed by fractional differential equations

    Science.gov (United States)

    Bai, Yunru; Baleanu, Dumitru; Wu, Guo-Cheng

    2018-06-01

    We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Carathe ´odory solution is proved by using Weierstrass existence theorem, fixed point theorem and Filippov implicit function lemma etc. Then a numerical approximation algorithm is introduced, and a convergence theorem is established. Finally, a nonlinear programming problem constrained by the fractional differential equation is illustrated and the results verify the validity of the algorithm.

  1. Modelling the spread of Ebola virus with Atangana-Baleanu fractional operators

    Science.gov (United States)

    Koca, Ilknur

    2018-03-01

    The model of Ebola spread within a targeted population is extended to the concept of fractional differentiation and integration with non-local and non-singular fading memory introduced by Atangana and Baleanu. It is expected that the proposed model will show better approximation than the models established before. The existence and uniqueness of solutions for the spread of Ebola disease model is given via the Picard-Lindelof method. Finally, numerical solutions for the model are given by using different parameter values.

  2. Fraction magnitude understanding and its unique role in predicting general mathematics achievement at two early stages of fraction instruction.

    Science.gov (United States)

    Liu, Yingyi

    2017-09-08

    Prior studies on fraction magnitude understanding focused mainly on students with relatively sufficient formal instruction on fractions whose fraction magnitude understanding is relatively mature. This study fills a research gap by investigating fraction magnitude understanding in the early stages of fraction instruction. It extends previous findings to children with limited and primary formal fraction instruction. Thirty-five fourth graders with limited fraction instruction and forty fourth graders with primary fraction instruction were recruited from a Chinese primary school. Children's fraction magnitude understanding was assessed with a fraction number line estimation task. Approximate number system (ANS) acuity was assessed with a dot discrimination task. Whole number knowledge was assessed with a whole number line estimation task. General reading and mathematics achievements were collected concurrently and 1 year later. In children with limited fraction instruction, fraction representation was linear and fraction magnitude understanding was concurrently related to both ANS and whole number knowledge. In children with primary fraction instruction, fraction magnitude understanding appeared to (marginally) significantly predict general mathematics achievement 1 year later. Fraction magnitude understanding emerged early during formal instruction of fractions. ANS and whole number knowledge were related to fraction magnitude understanding when children first began to learn about fractions in school. The predictive value of fraction magnitude understanding is likely constrained by its sophistication level. © 2017 The British Psychological Society.

  3. Fractional laser skin resurfacing.

    Science.gov (United States)

    Alexiades-Armenakas, Macrene R; Dover, Jeffrey S; Arndt, Kenneth A

    2012-11-01

    Laser skin resurfacing (LSR) has evolved over the past 2 decades from traditional ablative to fractional nonablative and fractional ablative resurfacing. Traditional ablative LSR was highly effective in reducing rhytides, photoaging, and acne scarring but was associated with significant side effects and complications. In contrast, nonablative LSR was very safe but failed to deliver consistent clinical improvement. Fractional LSR has achieved the middle ground; it combined the efficacy of traditional LSR with the safety of nonablative modalities. The first fractional laser was a nonablative erbium-doped yttrium aluminum garnet (Er:YAG) laser that produced microscopic columns of thermal injury in the epidermis and upper dermis. Heralding an entirely new concept of laser energy delivery, it delivered the laser beam in microarrays. It resulted in microscopic columns of treated tissue and intervening areas of untreated skin, which yielded rapid reepithelialization. Fractional delivery was quickly applied to ablative wavelengths such as carbon dioxide, Er:YAG, and yttrium scandium gallium garnet (2,790 nm), providing more significant clinical outcomes. Adjustable laser parameters, including power, pitch, dwell time, and spot density, allowed for precise determination of percent surface area, affected penetration depth, and clinical recovery time and efficacy. Fractional LSR has been a significant advance to the laser field, striking the balance between safety and efficacy.

  4. On-line vibration monitoring for submerged vertical shaft pumps: Final report

    International Nuclear Information System (INIS)

    Walter, T.J.; Marchione, M.M.

    1988-03-01

    The overall goal of this project was to extend to vertical pumps the capability that presently exists to monitor and diagnose vibration problems in horizontal pumps. Specific objectives included the development of analytical techniques to interpret vibration measurements, the verification of these techniqeus by in-plant tests, and the development of recommendations for procuring submergible vibration sensors. A concurrent analytical and experimental approach was used to accomplish these objectives. Rotordynamic analyses of selected pumps were accomplished, and each pump was instrumented and monitored for extended periods of time. The models were used to determine important frequencies and optimum sensor locations and to predict the effect that wear, imbalance, misalighment, and other mechanical changes would have on measured vibration. The predictive ability of the models was confirmed by making changes to instrumented pumps and observing actual changes in pump vibration. Simplified guidelines have been developed to assist the interested user to develop a computer model that realistically predicts the rotordynamic performance of the installed pump. Based on the work accomplished, typical sensor locations have been established. Experience gained in application of commercially available submergible sensors is also related. 11 refs., 11 figs

  5. Accessible solitons of fractional dimension

    Energy Technology Data Exchange (ETDEWEB)

    Zhong, Wei-Ping, E-mail: zhongwp6@126.com [Department of Electronic and Information Engineering, Shunde Polytechnic, Guangdong Province, Shunde 528300 (China); Texas A& M University at Qatar, P.O. Box 23874, Doha (Qatar); Belić, Milivoj [Texas A& M University at Qatar, P.O. Box 23874, Doha (Qatar); Zhang, Yiqi [Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)

    2016-05-15

    We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential. •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.

  6. Palliation of advanced pelvic malignant disease with large fraction pelvic radiation and misonidazole: final report of RTOG phase I/II study

    International Nuclear Information System (INIS)

    Spanos, W.J. Jr.; Wasserman, T.; Meoz, R.; Sala, J.; Kong, J.; Stetz, J.

    1987-01-01

    Between October 1979 and June 1982 forty-six patients were entered on a non-randomized Phase I-II protocol for the evaluation of Misonidazole combined with high dose per fraction radiation for the treatment of advanced pelvic malignancies. Pelvic radiation consisted of 1000 cGy in one fraction repeated at 4-week intervals for a total of three treatments. Oral Misonidazole at a dose of 4 gm/m2 was administered 4-6 hr prior to radiation (total dose 12 g/m2). The distribution of histology consisted of 20 gynecologic, 24 bowel, and 2 prostate malignancies. Of the thirty-seven patients completing the three treatments; there were 6 complete responses (14% CR), 10 partial responses (27% PR) 19 minimal or no response (32% NR), and 4 unevaluable. One patient remains NED 5.5 years following radiation. Toxicity directly related to Misonidazole was minimal and consisted primarily of transcient Grade 1, 2 peripheral neuropathy (20% Grade 1, 4% Grade 2) and Grade 2 ototoxicity (4%). Radiation toxicity was significant for late bowel damage. There were 4 (11%) Grade 3 and 7 (19%) Grade 4 gastro-intestinal (GI) toxicities. Kaplan-Meier plot of GI toxicity showed a progressive increase in incidence with time for projected rate of 49% Grade 3, 4 by 12-month. GI toxicity (Grade 3, 4) was also related to tumor response. The complication rate was 80% (4/6) for CR, 30% (3/10) for PR and 26% (5/19) for NR or progression. Because of the GI complication rate, this protocol for palliation of advanced pelvic malignancies has been replaced by a protocol that uses 4 fractions over 2 days (b.i.d.) of 370 cGy per fraction repeated at 3-week intervals for a total of 3 courses

  7. Fraction Reduction in Membrane Systems

    Directory of Open Access Journals (Sweden)

    Ping Guo

    2014-01-01

    Full Text Available Fraction reduction is a basic computation for rational numbers. P system is a new computing model, while the current methods for fraction reductions are not available in these systems. In this paper, we propose a method of fraction reduction and discuss how to carry it out in cell-like P systems with the membrane structure and the rules with priority designed. During the application of fraction reduction rules, synchronization is guaranteed by arranging some special objects in these rules. Our work contributes to performing the rational computation in P systems since the rational operands can be given in the form of fraction.

  8. Thermochemical transformations of anthracite fractions

    Energy Technology Data Exchange (ETDEWEB)

    Belkina, T.V.; Privalov, V.E.; Stepanenko, atM.A.

    1979-08-01

    Research on the nature of thermochemical transformations of anthracite fractions and the possibility of increasing their activity and identifying conditions for their use in the electrode pitch process is described. From research done on different anthracite fractions processed at varying temperatures it was concluded that accumulations of condensates from heating anthracite fractions occur significantly slower in comparison with pitch. As a result the electrode pitch process is prolonged. Thermal treatment of an anthracite fraction causes the formation and accumulation of condensates and promotes thermochemical transformations. Lastly, the use of thermally treated anthracite fractions apparently intensifies the electrode pitch process and improves its quality. (16 refs.) (In Russian)

  9. A fractional Dirac equation and its solution

    International Nuclear Information System (INIS)

    Muslih, Sami I; Agrawal, Om P; Baleanu, Dumitru

    2010-01-01

    This paper presents a fractional Dirac equation and its solution. The fractional Dirac equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives. By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion. We present a Lagrangian and a Hamiltonian for the fractional Dirac equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Dirac equation which is the same as that obtained using the fractional variational principle. Eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard Dirac equation. We also provide expressions for the path integral quantization for the fractional Dirac field which, in the limit α → 1, approaches to the path integral for the regular Dirac field. It is hoped that the fractional Dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanics.

  10. Fractional vector calculus and fluid mechanics

    Science.gov (United States)

    Lazopoulos, Konstantinos A.; Lazopoulos, Anastasios K.

    2017-04-01

    Basic fluid mechanics equations are studied and revised under the prism of fractional continuum mechanics (FCM), a very promising research field that satisfies both experimental and theoretical demands. The geometry of the fractional differential has been clarified corrected and the geometry of the fractional tangent spaces of a manifold has been studied in Lazopoulos and Lazopoulos (Lazopoulos KA, Lazopoulos AK. Progr. Fract. Differ. Appl. 2016, 2, 85-104), providing the bases of the missing fractional differential geometry. Therefore, a lot can be contributed to fractional hydrodynamics: the basic fractional fluid equations (Navier Stokes, Euler and Bernoulli) are derived and fractional Darcy's flow in porous media is studied.

  11. On matrix fractional differential equations

    OpenAIRE

    Adem Kılıçman; Wasan Ajeel Ahmood

    2017-01-01

    The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objec...

  12. Improving Children's Knowledge of Fraction Magnitudes.

    Directory of Open Access Journals (Sweden)

    Lisa K Fazio

    Full Text Available We examined whether playing a computerized fraction game, based on the integrated theory of numerical development and on the Common Core State Standards' suggestions for teaching fractions, would improve children's fraction magnitude understanding. Fourth and fifth-graders were given brief instruction about unit fractions and played Catch the Monster with Fractions, a game in which they estimated fraction locations on a number line and received feedback on the accuracy of their estimates. The intervention lasted less than 15 minutes. In our initial study, children showed large gains from pretest to posttest in their fraction number line estimates, magnitude comparisons, and recall accuracy. In a more rigorous second study, the experimental group showed similarly large improvements, whereas a control group showed no improvement from practicing fraction number line estimates without feedback. The results provide evidence for the effectiveness of interventions emphasizing fraction magnitudes and indicate how psychological theories and research can be used to evaluate specific recommendations of the Common Core State Standards.

  13. Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers

    Science.gov (United States)

    Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru

    2018-06-01

    The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

  14. Fractional CO 2 laser resurfacing as monotherapy in the treatment of atrophic facial acne scars

    Directory of Open Access Journals (Sweden)

    Imran Majid

    2014-01-01

    Full Text Available Background: While laser resurfacing remains the most effective treatment option for atrophic acne scars, the high incidence of post-treatment adverse effects limits its use. Fractional laser photothermolysis attempts to overcome these limitations of laser resurfacing by creating microscopic zones of injury to the dermis with skip areas in between. Aim: The aim of the present study is to assess the efficacy and safety of fractional CO 2 laser resurfacing in atrophic facial acne scars. Materials and Methods: Sixty patients with moderate to severe atrophic facial acne scars were treated with 3-4 sessions of fractional CO 2 laser resurfacing at 6-week intervals. The therapeutic response to treatment was assessed at each follow up visit and then finally 6 months after the last laser session using a quartile grading scale. Response to treatment was labelled as ′excellent′ if there was >50% improvement in scar appearance and texture of skin on the grading scale while 25-50% response and <25% improvement were labelled as ′good′ and ′poor′ response, respectively. The overall satisfaction of the patients and any adverse reactions to the treatment were also noted. Results: Most of the patients showed a combination of different morphological types of acne scars. At the time of final assessment 6 months after the last laser session, an excellent response was observed in 26 patients (43.3% while 15 (25% and 19 patients (31.7% demonstrated a good and poor response respectively. Rolling and superficial boxcar scars responded the best while pitted scars responded the least to fractional laser monotherapy. The commonest reported adverse effect was transient erythema and crusting lasting for an average of 3-4 and 4-6 days, respectively while three patients developed post-inflammatory pigmentation lasting for 8-12 weeks. Conclusions: Fractional laser resurfacing as monotherapy is effective in treating acne scars especially rolling and superficial boxcar

  15. TU-AB-303-12: Towards Inter and Intra Fraction Plan Adaptation for the MR-Linac

    International Nuclear Information System (INIS)

    Kontaxis, C; Bol, G; Lagendijk, J; Raaymakers, B

    2015-01-01

    Purpose: To develop a new sequencer for IMRT that during treatment can account for anatomy changes provided by online and real-time MRI. This sequencer employs a novel inter and intra fraction scheme that converges to the prescribed dose without a final segment weight optimization (SWO) and enables immediate optimization and delivery of radiation adapted to the deformed anatomy. Methods: The sequencer is initially supplied with a voxel-based dose prescription and during the optimization iteratively generates segments that provide this prescribed dose. Every iteration selects the best segment for the current anatomy state, calculates the dose it will deliver, warps it back to the reference prescription grid and subtracts it from the remaining prescribed dose. This process continues until a certain percentage of dose or a number of segments has been delivered. The anatomy changes that occur during treatment require that convergence is achieved without a final SWO. This is resolved by adding the difference between the prescribed and delivered dose up to this fraction to the prescription of the subsequent fraction. This process is repeated for all fractions of the treatment. Results: Two breast cases were selected to stress test the pipeline by producing artificial inter and intra fraction anatomy deformations using a combination of incrementally applied rigid transformations. The dose convergence of the adaptive scheme over the entire treatment, relative to the prescribed dose, was on average 8.6% higher than the static plans delivered to the respective deformed anatomies and only 1.6% less than the static segment weighted plans on the static anatomy. Conclusion: This new adaptive sequencing strategy enables dose convergence without the need of SWO while adapting the plan to intermediate anatomies, which is a prerequisite for online plan adaptation. We are now testing our pipeline on prostate cases using clinical anatomy deformation data from our department. This work

  16. How Weird Are Weird Fractions?

    Science.gov (United States)

    Stuffelbeam, Ryan

    2013-01-01

    A positive rational is a weird fraction if its value is unchanged by an illegitimate, digit-based reduction. In this article, we prove that each weird fraction is uniquely weird and initiate a discussion of the prevalence of weird fractions.

  17. Reduced Order Fractional Fourier Transform A New Variant to Fractional Signal Processing Definition and Properties

    OpenAIRE

    Kumar, Sanjay

    2018-01-01

    In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the proposed Reduced Order Fractional Fourier Transform like shift, modulation, time-frequency shift property are also derived and it is shown mathematically that when the rotation angle of Reduced Order Fractional Fourier Transform approaches 90 degrees, the propos...

  18. Fractional Diffusion Equations and Anomalous Diffusion

    Science.gov (United States)

    Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

    2018-01-01

    Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

  19. Shot-noise evidence of fractional quasiparticle creation in a local fractional quantum Hall state.

    Science.gov (United States)

    Hashisaka, Masayuki; Ota, Tomoaki; Muraki, Koji; Fujisawa, Toshimasa

    2015-02-06

    We experimentally identify fractional quasiparticle creation in a tunneling process through a local fractional quantum Hall (FQH) state. The local FQH state is prepared in a low-density region near a quantum point contact in an integer quantum Hall (IQH) system. Shot-noise measurements reveal a clear transition from elementary-charge tunneling at low bias to fractional-charge tunneling at high bias. The fractional shot noise is proportional to T(1)(1-T(1)) over a wide range of T(1), where T(1) is the transmission probability of the IQH edge channel. This binomial distribution indicates that fractional quasiparticles emerge from the IQH state to be transmitted through the local FQH state. The study of this tunneling process enables us to elucidate the dynamics of Laughlin quasiparticles in FQH systems.

  20. Fractional Stochastic Field Theory

    Science.gov (United States)

    Honkonen, Juha

    2018-02-01

    Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.

  1. On fractional Fourier transform moments

    NARCIS (Netherlands)

    Alieva, T.; Bastiaans, M.J.

    2000-01-01

    Based on the relation between the ambiguity function represented in a quasi-polar coordinate system and the fractional power spectra, the fractional Fourier transform moments are introduced. Important equalities for the global second-order fractional Fourier transform moments are derived and their

  2. COMMERCIAL SNF ACCIDENT RELEASE FRACTIONS

    Energy Technology Data Exchange (ETDEWEB)

    S.O. Bader

    1999-10-18

    The purpose of this design analysis is to specify and document the total and respirable fractions for radioactive materials that are released from an accident event at the Monitored Geologic Repository (MGR) involving commercial spent nuclear fuel (CSNF) in a dry environment. The total and respirable release fractions will be used to support the preclosure licensing basis for the MGR. The total release fraction is defined as the fraction of total CSNF assembly inventory, typically expressed as an activity inventory (e.g., curies), of a given radionuclide that is released to the environment from a waste form. The radionuclides are released from the inside of breached fuel rods (or pins) and from the detachment of radioactive material (crud) from the outside surfaces of fuel rods and other components of fuel assemblies. The total release fraction accounts for several mechanisms that tend to retain, retard, or diminish the amount of radionuclides that are available for transport to dose receptors or otherwise can be shown to reduce exposure of receptors to radiological releases. The total release fraction includes a fraction of airborne material that is respirable and could result in inhalation doses. This subset of the total release fraction is referred to as the respirable release fraction. Potential accidents may involve waste forms that are characterized as either bare (unconfined) fuel assemblies or confined fuel assemblies. The confined CSNF assemblies at the MGR are contained in shipping casks, canisters, or disposal containers (waste packages). In contrast to the bare fuel assemblies, the container that confines the fuel assemblies has the potential of providing an additional barrier for diminishing the total release fraction should the fuel rod cladding breach during an accident. However, this analysis will not take credit for this additional bamer and will establish only the total release fractions for bare unconfined CSNF assemblies, which may however be

  3. COMMERCIAL SNF ACCIDENT RELEASE FRACTIONS

    International Nuclear Information System (INIS)

    S.O. Bader

    1999-01-01

    The purpose of this design analysis is to specify and document the total and respirable fractions for radioactive materials that are released from an accident event at the Monitored Geologic Repository (MGR) involving commercial spent nuclear fuel (CSNF) in a dry environment. The total and respirable release fractions will be used to support the preclosure licensing basis for the MGR. The total release fraction is defined as the fraction of total CSNF assembly inventory, typically expressed as an activity inventory (e.g., curies), of a given radionuclide that is released to the environment from a waste form. The radionuclides are released from the inside of breached fuel rods (or pins) and from the detachment of radioactive material (crud) from the outside surfaces of fuel rods and other components of fuel assemblies. The total release fraction accounts for several mechanisms that tend to retain, retard, or diminish the amount of radionuclides that are available for transport to dose receptors or otherwise can be shown to reduce exposure of receptors to radiological releases. The total release fraction includes a fraction of airborne material that is respirable and could result in inhalation doses. This subset of the total release fraction is referred to as the respirable release fraction. Potential accidents may involve waste forms that are characterized as either bare (unconfined) fuel assemblies or confined fuel assemblies. The confined CSNF assemblies at the MGR are contained in shipping casks, canisters, or disposal containers (waste packages). In contrast to the bare fuel assemblies, the container that confines the fuel assemblies has the potential of providing an additional barrier for diminishing the total release fraction should the fuel rod cladding breach during an accident. However, this analysis will not take credit for this additional bamer and will establish only the total release fractions for bare unconfined CSNF assemblies, which may however be

  4. Analysis and functional consequences of increased Fab-sialylation of intravenous immunoglobulin (IVIG) after lectin fractionation.

    Science.gov (United States)

    Käsermann, Fabian; Boerema, David J; Rüegsegger, Monika; Hofmann, Andreas; Wymann, Sandra; Zuercher, Adrian W; Miescher, Sylvia

    2012-01-01

    It has been proposed that the anti-inflammatory effects of intravenous immunoglobulin (IVIG) might be due to the small fraction of Fc-sialylated IgG. In this study we biochemically and functionally characterized sialic acid-enriched IgG obtained by Sambucus nigra agglutinin (SNA) lectin fractionation. Two main IgG fractions isolated by elution with lactose (E1) or acidified lactose (E2) were analyzed for total IgG, F(ab')(2) and Fc-specific sialic acid content, their pattern of specific antibodies and anti-inflammatory potential in a human in vitro inflammation system based on LPS- or PHA-stimulated whole blood. HPLC and LC-MS testing revealed an increase of sialylated IgG in E1 and more substantially in the E2 fraction. Significantly, the increased amount of sialic acid residues was primarily found in the Fab region whereas only a minor increase was observed in the Fc region. This indicates preferential binding of the Fab sialic acid to SNA. ELISA analyses of a representative range of pathogen and auto-antigens indicated a skewed antibody pattern of the sialylated IVIG fractions. Finally, the E2 fraction exerted a more profound anti-inflammatory effect compared to E1 or IVIG, evidenced by reduced CD54 expression on monocytes and reduced secretion of MCP-1 (CCL2); again these effects were Fab- but not Fc-dependent. Our results show that SNA fractionation of IVIG yields a minor fraction (approx. 10%) of highly sialylated IgG, wherein the sialic acid is mainly found in the Fab region. The tested anti-inflammatory activity was associated with Fab not Fc sialylation.

  5. Analysis and functional consequences of increased Fab-sialylation of intravenous immunoglobulin (IVIG after lectin fractionation.

    Directory of Open Access Journals (Sweden)

    Fabian Käsermann

    Full Text Available It has been proposed that the anti-inflammatory effects of intravenous immunoglobulin (IVIG might be due to the small fraction of Fc-sialylated IgG. In this study we biochemically and functionally characterized sialic acid-enriched IgG obtained by Sambucus nigra agglutinin (SNA lectin fractionation. Two main IgG fractions isolated by elution with lactose (E1 or acidified lactose (E2 were analyzed for total IgG, F(ab'(2 and Fc-specific sialic acid content, their pattern of specific antibodies and anti-inflammatory potential in a human in vitro inflammation system based on LPS- or PHA-stimulated whole blood. HPLC and LC-MS testing revealed an increase of sialylated IgG in E1 and more substantially in the E2 fraction. Significantly, the increased amount of sialic acid residues was primarily found in the Fab region whereas only a minor increase was observed in the Fc region. This indicates preferential binding of the Fab sialic acid to SNA. ELISA analyses of a representative range of pathogen and auto-antigens indicated a skewed antibody pattern of the sialylated IVIG fractions. Finally, the E2 fraction exerted a more profound anti-inflammatory effect compared to E1 or IVIG, evidenced by reduced CD54 expression on monocytes and reduced secretion of MCP-1 (CCL2; again these effects were Fab- but not Fc-dependent. Our results show that SNA fractionation of IVIG yields a minor fraction (approx. 10% of highly sialylated IgG, wherein the sialic acid is mainly found in the Fab region. The tested anti-inflammatory activity was associated with Fab not Fc sialylation.

  6. Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative

    Directory of Open Access Journals (Sweden)

    Ai-Min Yang

    2014-01-01

    Full Text Available The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.

  7. Solution of fractional-order differential equations based on the operational matrices of new fractional Bernstein functions

    Directory of Open Access Journals (Sweden)

    M.H.T. Alshbool

    2017-01-01

    Full Text Available An algorithm for approximating solutions to fractional differential equations (FDEs in a modified new Bernstein polynomial basis is introduced. Writing x→xα(0<α<1 in the operational matrices of Bernstein polynomials, the fractional Bernstein polynomials are obtained and then transformed into matrix form. Furthermore, using Caputo fractional derivative, the matrix form of the fractional derivative is constructed for the fractional Bernstein matrices. We convert each term of the problem to the matrix form by means of fractional Bernstein matrices. A basic matrix equation which corresponds to a system of fractional equations is utilized, and a new system of nonlinear algebraic equations is obtained. The method is given with some priori error estimate. By using the residual correction procedure, the absolute error can be estimated. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.

  8. Application of radial basis functions and sinc method for solving the forced vibration of fractional viscoelastic beam

    Energy Technology Data Exchange (ETDEWEB)

    Permoon, M. R.; Haddadpour, H. [Sharif University of Tech, Tehran (Iran, Islamic Republic of); Rashidinia, J.; Parsa, A.; Salehi, R. [Iran University of Science and Technology, Tehran (Iran, Islamic Republic of)

    2016-07-15

    In this paper, the forced vibrations of the fractional viscoelastic beam with the Kelvin-Voigt fractional order constitutive relationship is studied. The equation of motion is derived from Newton's second law and the Galerkin method is used to discretize the equation of motion in to a set of linear ordinary differential equations. For solving the discretized equations, the radial basis functions and Sinc quadrature rule are used. In order to show the effectiveness and accuracy of this method, some test problem are considered, and it is shown that the obtained results are in very good agreement with exact solution. In the following, the proposed numerical solution is applied to exploring the effects of fractional parameters on the response of the beam and finally some conclusions are outlined.

  9. Design of distributed PID-type dynamic matrix controller for fractional-order systems

    Science.gov (United States)

    Wang, Dawei; Zhang, Ridong

    2018-01-01

    With the continuous requirements for product quality and safety operation in industrial production, it is difficult to describe the complex large-scale processes with integer-order differential equations. However, the fractional differential equations may precisely represent the intrinsic characteristics of such systems. In this paper, a distributed PID-type dynamic matrix control method based on fractional-order systems is proposed. First, the high-order approximate model of integer order is obtained by utilising the Oustaloup method. Then, the step response model vectors of the plant is obtained on the basis of the high-order model, and the online optimisation for multivariable processes is transformed into the optimisation of each small-scale subsystem that is regarded as a sub-plant controlled in the distributed framework. Furthermore, the PID operator is introduced into the performance index of each subsystem and the fractional-order PID-type dynamic matrix controller is designed based on Nash optimisation strategy. The information exchange among the subsystems is realised through the distributed control structure so as to complete the optimisation task of the whole large-scale system. Finally, the control performance of the designed controller in this paper is verified by an example.

  10. Influence of the void fraction in the linear reactivity model

    International Nuclear Information System (INIS)

    Castillo, J.A.; Ramirez, J.R.; Alonso, G.

    2003-01-01

    The linear reactivity model allows the multicycle analysis in pressurized water reactors in a simple and quick way. In the case of the Boiling water reactors the void fraction it varies axially from 0% of voids in the inferior part of the fuel assemblies until approximately 70% of voids to the exit of the same ones. Due to this it is very important the determination of the average void fraction during different stages of the reactor operation to predict the burnt one appropriately of the same ones to inclination of the pattern of linear reactivity. In this work a pursuit is made of the profile of power for different steps of burnt of a typical operation cycle of a Boiling water reactor. Starting from these profiles it builds an algorithm that allows to determine the voids profile and this way to obtain the average value of the same one. The results are compared against those reported by the CM-PRESTO code that uses another method to carry out this calculation. Finally, the range in which is the average value of the void fraction during a typical cycle is determined and an estimate of the impact that it would have the use of this value in the prediction of the reactivity produced by the fuel assemblies is made. (Author)

  11. Characterisation of the biochemical methane potential (BMP) of individual material fractions in Danish source-separated organic household waste

    DEFF Research Database (Denmark)

    Naroznova, Irina; Møller, Jacob; Scheutz, Charlotte

    2016-01-01

    This study is dedicated to characterising the chemical composition and biochemical methane potential (BMP) of individual material fractions in untreated Danish source-separated organic household waste (SSOHW). First, data on SSOHW in different countries, available in the literature, were evaluated...... and then, secondly, laboratory analyses for eight organic material fractions comprising Danish SSOHW were conducted. No data were found in the literature that fully covered the objectives of the present study. Based on laboratory analyses, all fractions were assigned according to their specific properties......) and material degradability (BMP from laboratory incubation tests divided by TBMP) were expressed. Moreover, the degradability of lignocellulose biofibres (the share of volatile lignocellulose biofibre solids degraded in laboratory incubation tests) was calculated. Finally, BMP for average SSOHW composition...

  12. Fractional Reserve in Banking System

    OpenAIRE

    Valkonen, Maria

    2016-01-01

    This thesis is aimed to provide understanding of the role of the fractional reserve in the mod-ern banking system worldwide and particularly in Finland. The fractional reserve banking is used worldwide, but the benefits of this system are very disputable. On the one hand, experts say that the fractional reserve is a necessary instrument for the normal business and profit making. On the other hand, sceptics openly criticize the fractional reserve system and blame it for fiat money (money n...

  13. Fractional Order Element Based Impedance Matching

    KAUST Repository

    Radwan, Ahmed Gomaa

    2014-06-24

    Disclosed are various embodiments of methods and systems related to fractional order element based impedance matching. In one embodiment, a method includes aligning a traditional Smith chart (|.alpha.|=1) with a fractional order Smith chart (|.alpha.|.noteq.1). A load impedance is located on the traditional Smith chart and projected onto the fractional order Smith chart. A fractional order matching element is determined by transitioning along a matching circle of the fractional order Smith chart based at least in part upon characteristic line impedance. In another embodiment, a system includes a fractional order impedance matching application executed in a computing device. The fractional order impedance matching application includes logic that obtains a first set of Smith chart coordinates at a first order, determines a second set of Smith chart coordinates at a second order, and determines a fractional order matching element from the second set of Smith chart coordinates.

  14. Do Children Understand Fraction Addition?

    Science.gov (United States)

    Braithwaite, David W.; Tian, Jing; Siegler, Robert S.

    2017-01-01

    Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, in press) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments…

  15. The random continued fraction transformation

    Science.gov (United States)

    Kalle, Charlene; Kempton, Tom; Verbitskiy, Evgeny

    2017-03-01

    We introduce a random dynamical system related to continued fraction expansions. It uses random combinations of the Gauss map and the Rényi (or backwards) continued fraction map. We explore the continued fraction expansions that this system produces, as well as the dynamical properties of the system.

  16. Fractional Charge Definitions and Conditions

    Energy Technology Data Exchange (ETDEWEB)

    Goldhaber, A.S.

    2004-06-04

    Fractional charge is known through theoretical and experimental discoveries of isolable objects carrying fractions of familiar charge units--electric charge Q, spin S, and the difference of baryon and lepton numbers B-L. With a few simple assumptions all these effects may be described using a generalized version of charge renormalization for locally conserved charges, in which medium correlations yield familiar adiabatic, continuous renormalization, or sometimes nonadiabatic, discrete renormalization. Fractional charges may be carried by fundamental particles or fundamental solitons. Either picture works for the simplest fractional-quantum-Hall-effect quasiholes, though the particle description is far more general. The only known fundamental solitons in three or fewer space dimensions d are the kink (d = 1), the vortex (d = 2), and the magnetic monopole (d = 3). Further, for a charge not intrinsically coupled to the topological charge of a soliton, only the kink and the monopole may carry fractional values. The same reasoning enforces fractional values of B-L for electrically charged elementary particles.

  17. Fractional Charge Definitions and Conditions

    International Nuclear Information System (INIS)

    Goldhaber, A.S.

    2004-01-01

    Fractional charge is known through theoretical and experimental discoveries of isolable objects carrying fractions of familiar charge units--electric charge Q, spin S, and the difference of baryon and lepton numbers B-L. With a few simple assumptions all these effects may be described using a generalized version of charge renormalization for locally conserved charges, in which medium correlations yield familiar adiabatic, continuous renormalization, or sometimes nonadiabatic, discrete renormalization. Fractional charges may be carried by fundamental particles or fundamental solitons. Either picture works for the simplest fractional-quantum-Hall-effect quasiholes, though the particle description is far more general. The only known fundamental solitons in three or fewer space dimensions d are the kink (d = 1), the vortex (d = 2), and the magnetic monopole (d = 3). Further, for a charge not intrinsically coupled to the topological charge of a soliton, only the kink and the monopole may carry fractional values. The same reasoning enforces fractional values of B-L for electrically charged elementary particles

  18. Radiation-induced lung damage in rats: The influence of fraction spacing on effect per fraction

    International Nuclear Information System (INIS)

    Haston, C.K.; Hill, R.P.; Newcomb, C.H.; Van Dyk, J.

    1994-01-01

    When the linear-quadratic model is used to predict fractionated treatments which are isoeffective, it is usually assumed that each (equal size) treatment fraction has an equal effect, independent of the time at which it was delivered during a course of treatment. Previous work has indicated that this assumption may not be valid in the context of radiation-induced lung damage in rats. Consequently the authors tested directly the validity of the assumption that each fraction has an equal effect, independent of the time it is delivered. An experiment was completed in which fractionated irradiation was given to whole thoraces of Sprague-Dawley rats. All treatment schedules consisted of eleven equal dose fractions in 36 days given as a split course, with some groups receiving the bulk of the doses early in the treatment schedule, before a 27-day gap, and others receiving most of the dose toward the end of the treatment schedule, after the time gap. To monitor the incidence of radiation-induced damage, breathing rate and lethality assays were used. The maximum differences in the LD 50 s and breathing rate ED 50 s for the different fractionation schedules were 4.0% and 7.7% respectively. The lethality data and breathing rate data were consistent with results expected from modelling using the linear-quadratic model with the inclusion of an overall time factor, but not the generalized linear-quadratic model which accounted for fraction spacing. For conventional daily fractionation, and within the range of experimental uncertainties, the results indicate that the effect of a treatment fraction does not depend on the time at which it is given (its position) in the treatment. The results indicate no need to extend isoeffect formulae to consider the effect of each fraction separately for radiation-induced lung damage. 21 refs., 6 figs., 3 tabs

  19. The Fractional Step Method Applied to Simulations of Natural Convective Flows

    Science.gov (United States)

    Westra, Douglas G.; Heinrich, Juan C.; Saxon, Jeff (Technical Monitor)

    2002-01-01

    This paper describes research done to apply the Fractional Step Method to finite-element simulations of natural convective flows in pure liquids, permeable media, and in a directionally solidified metal alloy casting. The Fractional Step Method has been applied commonly to high Reynold's number flow simulations, but is less common for low Reynold's number flows, such as natural convection in liquids and in permeable media. The Fractional Step Method offers increased speed and reduced memory requirements by allowing non-coupled solution of the pressure and the velocity components. The Fractional Step Method has particular benefits for predicting flows in a directionally solidified alloy, since other methods presently employed are not very efficient. Previously, the most suitable method for predicting flows in a directionally solidified binary alloy was the penalty method. The penalty method requires direct matrix solvers, due to the penalty term. The Fractional Step Method allows iterative solution of the finite element stiffness matrices, thereby allowing more efficient solution of the matrices. The Fractional Step Method also lends itself to parallel processing, since the velocity component stiffness matrices can be built and solved independently of each other. The finite-element simulations of a directionally solidified casting are used to predict macrosegregation in directionally solidified castings. In particular, the finite-element simulations predict the existence of 'channels' within the processing mushy zone and subsequently 'freckles' within the fully processed solid, which are known to result from macrosegregation, or what is often referred to as thermo-solutal convection. These freckles cause material property non-uniformities in directionally solidified castings; therefore many of these castings are scrapped. The phenomenon of natural convection in an alloy under-going directional solidification, or thermo-solutal convection, will be explained. The

  20. The Initial Conditions of Fractional Calculus

    International Nuclear Information System (INIS)

    Trigeassou, J. C.; Maamri, N.

    2011-01-01

    During the past fifty years , Fractional Calculus has become an original and renowned mathematical tool for the modelling of diffusion Partial Differential Equations and the design of robust control algorithms. However, in spite of these celebrated results, some theoretical problems have not yet received a satisfying solution. The mastery of initial conditions, either for Fractional Differential Equations (FDEs) or for the Caputo and Riemann-Liouville fractional derivatives, remains an open research domain. The solution of this fundamental problem, also related to the long range memory property, is certainly the necessary prerequisite for a satisfying approach to modelling and control applications. The fractional integrator and its continuously frequency distributed differential model is a valuable tool for the simulation of fractional systems and the solution of initial condition problems. Indeed, the infinite dimensional state vector of fractional integrators allows the direct generalization to fractional calculus of the theoretical results of integer order systems. After a reminder of definitions and properties related to fractional derivatives and systems, this presentation is intended to show, based on the results of two recent publications [1,2], how the fractional integrator provides the solution of the initial condition problem of FDEs and of Caputo and Riemann-Liouville fractional derivatives. Numerical simulation examples illustrate and validate these new theoretical concepts.

  1. Void fraction in horizontal bulk flow boiling at high flow qualities

    International Nuclear Information System (INIS)

    Collado, Fancisco J.; Monne, Carlos; Pascau, Antonio

    2008-01-01

    In this work, a new thermodynamic prediction of the vapor void fraction in bulk flow boiling, which is the core process of many energy conversion systems, is analyzed. The current heat balance is based on the flow quality, which is closely related to the measured void fraction, although some correlation for the vapor-liquid velocity ratio is needed. So here, it is suggested to work with the 'static' or thermodynamic quality, which is directly connected to the void fraction through the densities of the phases. Thus, the relation between heat and the mixture enthalpy (here based on the thermodynamic quality instead of the flow one) should be analyzed in depth. The careful void fraction data taken by Thom during the 'Cambridge project' for horizontal saturated flow boiling with high flow qualities (≤0.8) have been used for this analysis. As main results, first, we have found that the applied heat and the increment of the proposed thermodynamic enthalpy mixture throughout the heated duct do not agree, and for closure, a parameter is needed. Second, it has been checked that this parameter is practically equal to the classic velocity ratio or 'slip' ratio, suggesting that it should be included in a true thermodynamic heat balance. Furthermore, it has been clearly possible to improve the 'Cambridge project' correlations for the 'slip' ratio, here based on inlet pressure and water velocity, and heat flux. The calculated void fractions compare quite well with the measured ones. Finally, the equivalence of the suggested new heat balance with the current one through the 'slip' ratio is addressed. Highlighted is the same new energetic relation for saturated flow boiling that has been recently confirmed by the authors for Knights data, also taken during the 'Cambridge project', which include not only horizontal but also vertical upwards flows with moderate outlet flow quality (≤0.2)

  2. Exact solutions of time-fractional heat conduction equation by the fractional complex transform

    Directory of Open Access Journals (Sweden)

    Li Zheng-Biao

    2012-01-01

    Full Text Available The Fractional Complex Transform is extended to solve exactly time-fractional differential equations with the modified Riemann-Liouville derivative. How to incorporate suitable boundary/initial conditions is also discussed.

  3. Fractional Josephson vortices: oscillating macroscopic spins

    Energy Technology Data Exchange (ETDEWEB)

    Gaber, T.; Buckenmaier, K.; Koelle, D.; Kleiner, R.; Goldobin, E. [Universitaet Tuebingen, Physikalisches Institut - Experimentalphysik II, Tuebingen (Germany)

    2007-11-15

    Fractional Josephson vortices carry a magnetic flux {phi}, which is a fraction of the magnetic flux quantum {phi}{sub 0}{approx}2.07 x 10{sup -15} Wb. We consider a fractional vortex which spontaneously appears at a phase discontinuity. Its properties are very different from the properties of the usual integer fluxon. In particular, a fractional vortex is pinned and may have one of two possible polarities - just like a usual spin 1/2 particle. The fractional vortex may also oscillate around its equilibrium position with an eigenfrequency which is expected to be within the Josephson plasma gap. Using microwave spectroscopy, we investigate the dependence of the eigenfrequency of a fractional Josephson vortex on its magnetic flux {phi} and on the bias current. The experimental results are in good agreement with theoretical predictions. Positive result of this experiment is a cornerstone for further investigation of more complex fractional vortex systems such as fractional vortex molecules and tunable bandgap materials. (orig.)

  4. A Hybrid Dry and Aqueous Fractionation Method to Obtain Protein-Rich Fractions from Quinoa (Chenopodium quinoa Willd)

    NARCIS (Netherlands)

    Avila Ruiz, Geraldine; Arts, Anke; Minor, Marcel; Schutyser, Maarten

    2016-01-01

    Combination of dry and aqueous fractionation is investigated to obtain protein-rich fractions from quinoa in a milder and more sustainable way compared to conventional wet fractionation. Dry fractionation of quinoa involved milling and subsequent air classification, generating a protein-enriched

  5. Fractional Order Generalized Information

    Directory of Open Access Journals (Sweden)

    José Tenreiro Machado

    2014-04-01

    Full Text Available This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.

  6. Pathological Brain Detection by a Novel Image Feature—Fractional Fourier Entropy

    Directory of Open Access Journals (Sweden)

    Shuihua Wang

    2015-12-01

    Full Text Available Aim: To detect pathological brain conditions early is a core procedure for patients so as to have enough time for treatment. Traditional manual detection is either cumbersome, or expensive, or time-consuming. We aim to offer a system that can automatically identify pathological brain images in this paper. Method: We propose a novel image feature, viz., Fractional Fourier Entropy (FRFE, which is based on the combination of Fractional Fourier Transform (FRFT and Shannon entropy. Afterwards, the Welch’s t-test (WTT and Mahalanobis distance (MD were harnessed to select distinguishing features. Finally, we introduced an advanced classifier: twin support vector machine (TSVM. Results: A 10 × K-fold stratified cross validation test showed that this proposed “FRFE + WTT + TSVM” yielded an accuracy of 100.00%, 100.00%, and 99.57% on datasets that contained 66, 160, and 255 brain images, respectively. Conclusions: The proposed “FRFE + WTT + TSVM” method is superior to 20 state-of-the-art methods.

  7. 16 CFR 500.17 - Fractions.

    Science.gov (United States)

    2010-01-01

    ... 16 Commercial Practices 1 2010-01-01 2010-01-01 false Fractions. 500.17 Section 500.17 Commercial... LABELING ACT § 500.17 Fractions. (a) SI metric declarations of net quantity of contents of any consumer commodity may contain only decimal fractions. Other declarations of net quantity of contents may contain...

  8. The fractional dynamics of quantum systems

    Science.gov (United States)

    Lu, Longzhao; Yu, Xiangyang

    2018-05-01

    The fractional dynamic process of a quantum system is a novel and complicated problem. The establishment of a fractional dynamic model is a significant attempt that is expected to reveal the mechanism of fractional quantum system. In this paper, a generalized time fractional Schrödinger equation is proposed. To study the fractional dynamics of quantum systems, we take the two-level system as an example and derive the time fractional equations of motion. The basic properties of the system are investigated by solving this set of equations in the absence of light field analytically. Then, when the system is subject to the light field, the equations are solved numerically. It shows that the two-level system described by the time fractional Schrödinger equation we proposed is a confirmable system.

  9. 12 CFR 5.67 - Fractional shares.

    Science.gov (United States)

    2010-01-01

    ... connection with fractional shares, a national bank issuing additional stock by stock dividend, upon... fair price upon the fraction not being issued through its sale, or the purchase of the additional... stock; (c) Remit the cash equivalent of the fraction not being issued to those to whom fractional shares...

  10. Commercial SNF Accident Release Fractions

    Energy Technology Data Exchange (ETDEWEB)

    J. Schulz

    2004-11-05

    The purpose of this analysis is to specify and document the total and respirable fractions for radioactive materials that could be potentially released from an accident at the repository involving commercial spent nuclear fuel (SNF) in a dry environment. The total and respirable release fractions are used to support the preclosure licensing basis for the repository. The total release fraction is defined as the fraction of total commercial SNF assembly inventory, typically expressed as an activity inventory (e.g., curies), of a given radionuclide that is released to the environment from a waste form. Radionuclides are released from the inside of breached fuel rods (or pins) and from the detachment of radioactive material (crud) from the outside surfaces of fuel rods and other components of fuel assemblies. The total release fraction accounts for several mechanisms that tend to retain, retard, or diminish the amount of radionuclides that are available for transport to dose receptors or otherwise can be shown to reduce exposure of receptors to radiological releases. The total release fraction includes a fraction of airborne material that is respirable and could result in inhalation doses; this subset of the total release fraction is referred to as the respirable release fraction. Accidents may involve waste forms characterized as: (1) bare unconfined intact fuel assemblies, (2) confined intact fuel assemblies, or (3) canistered failed commercial SNF. Confined intact commercial SNF assemblies at the repository are contained in shipping casks, canisters, or waste packages. Four categories of failed commercial SNF are identified: (1) mechanically and cladding-penetration damaged commercial SNF, (2) consolidated/reconstituted assemblies, (3) fuel rods, pieces, and debris, and (4) nonfuel components. It is assumed that failed commercial SNF is placed into waste packages with a mesh screen at each end (CRWMS M&O 1999). In contrast to bare unconfined fuel assemblies, the

  11. Commercial SNF Accident Release Fractions

    International Nuclear Information System (INIS)

    Schulz, J.

    2004-01-01

    The purpose of this analysis is to specify and document the total and respirable fractions for radioactive materials that could be potentially released from an accident at the repository involving commercial spent nuclear fuel (SNF) in a dry environment. The total and respirable release fractions are used to support the preclosure licensing basis for the repository. The total release fraction is defined as the fraction of total commercial SNF assembly inventory, typically expressed as an activity inventory (e.g., curies), of a given radionuclide that is released to the environment from a waste form. Radionuclides are released from the inside of breached fuel rods (or pins) and from the detachment of radioactive material (crud) from the outside surfaces of fuel rods and other components of fuel assemblies. The total release fraction accounts for several mechanisms that tend to retain, retard, or diminish the amount of radionuclides that are available for transport to dose receptors or otherwise can be shown to reduce exposure of receptors to radiological releases. The total release fraction includes a fraction of airborne material that is respirable and could result in inhalation doses; this subset of the total release fraction is referred to as the respirable release fraction. Accidents may involve waste forms characterized as: (1) bare unconfined intact fuel assemblies, (2) confined intact fuel assemblies, or (3) canistered failed commercial SNF. Confined intact commercial SNF assemblies at the repository are contained in shipping casks, canisters, or waste packages. Four categories of failed commercial SNF are identified: (1) mechanically and cladding-penetration damaged commercial SNF, (2) consolidated/reconstituted assemblies, (3) fuel rods, pieces, and debris, and (4) nonfuel components. It is assumed that failed commercial SNF is placed into waste packages with a mesh screen at each end (CRWMS M andO 1999). In contrast to bare unconfined fuel assemblies, the

  12. FGP Approach for Solving Multi-level Multi-objective Quadratic Fractional Programming Problem with Fuzzy parameters

    Directory of Open Access Journals (Sweden)

    m. s. osman

    2017-09-01

    Full Text Available In this paper, we consider fuzzy goal programming (FGP approach for solving multi-level multi-objective quadratic fractional programming (ML-MOQFP problem with fuzzy parameters in the constraints. Firstly, the concept of the ?-cut approach is applied to transform the set of fuzzy constraints into a common deterministic one. Then, the quadratic fractional objective functions in each level are transformed into quadratic objective functions based on a proposed transformation. Secondly, the FGP approach is utilized to obtain a compromise solution for the ML-MOQFP problem by minimizing the sum of the negative deviational variables. Finally, an illustrative numerical example is given to demonstrate the applicability and performance of the proposed approach.

  13. Tests of equal effect per fraction in microcolony assays of survival after fractionated irradiations

    International Nuclear Information System (INIS)

    Taylor, J.M.G.

    1985-01-01

    H.D Thames, Jr. and H.R. Withers propose a test of an equal effect per fraction in microcolony assays after fractionated radiation, in which the total effect is measured by counting microcolonies derived from surviving cells in a tissue. The factors considered to influence the cytocidal effect per fraction are incomplete repair, repopulation, and synchrony. The statistics used in the method are criticized and conditions are given under which the test should not be used. An alternative method of testing for an equal effect per fraction is proposed. The pros and cons of each test are discussed and compared using some mouse jejunal crypt cell survival data

  14. Fractional hydrodynamic equations for fractal media

    International Nuclear Information System (INIS)

    Tarasov, Vasily E.

    2005-01-01

    We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the 'fractional' continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier-Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered

  15. 9 CFR 113.7 - Multiple fractions.

    Science.gov (United States)

    2010-01-01

    ... 9 Animals and Animal Products 1 2010-01-01 2010-01-01 false Multiple fractions. 113.7 Section 113... § 113.7 Multiple fractions. (a) When a biological product contains more than one immunogenic fraction, the completed product shall be evaluated by tests applicable to each fraction. (b) When similar...

  16. Lagrange α-exponential stability and α-exponential convergence for fractional-order complex-valued neural networks.

    Science.gov (United States)

    Jian, Jigui; Wan, Peng

    2017-07-01

    This paper deals with the problem on Lagrange α-exponential stability and α-exponential convergence for a class of fractional-order complex-valued neural networks. To this end, some new fractional-order differential inequalities are established, which improve and generalize previously known criteria. By using the new inequalities and coupling with the Lyapunov method, some effective criteria are derived to guarantee Lagrange α-exponential stability and α-exponential convergence of the addressed network. Moreover, the framework of the α-exponential convergence ball is also given, where the convergence rate is related to the parameters and the order of differential of the system. These results here, which the existence and uniqueness of the equilibrium points need not to be considered, generalize and improve the earlier publications and can be applied to monostable and multistable fractional-order complex-valued neural networks. Finally, one example with numerical simulations is given to show the effectiveness of the obtained results. Copyright © 2017 Elsevier Ltd. All rights reserved.

  17. Fractional finite Fourier transform.

    Science.gov (United States)

    Khare, Kedar; George, Nicholas

    2004-07-01

    We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

  18. Ferroelectric Fractional-Order Capacitors

    KAUST Repository

    Agambayev, Agamyrat; Patole, Shashikant P.; Farhat, Mohamed; Elwakil, Ahmed; Bagci, Hakan; Salama, Khaled N.

    2017-01-01

    Poly(vinylidene fluoride)-based polymers and their blends are used to fabricate electrostatic fractional-order capacitors. This simple but effective method allows us to precisely tune the constant phase angle of the resulting fractional-order capacitor by changing the blend composition. Additionally, we have derived an empirical relation between the ratio of the blend constituents and the constant phase angle to facilitate the design of a fractional order capacitor with a desired constant phase angle. The structural composition of the fabricated blends is investigated using Fourier transform infrared spectroscopy and X-ray diffraction techniques.

  19. Social Trust and Fractionalization:

    DEFF Research Database (Denmark)

    Bjørnskov, Christian

    2008-01-01

    This paper takes a closer look at the importance of fractionalization for the creation of social trust. It first argues that the determinants of trust can be divided into two categories: those affecting individuals' trust radii and those affecting social polarization. A series of estimates using...... a much larger country sample than in previous literature confirms that fractionalization in the form of income inequality and political diversity adversely affects social trust while ethnic diversity does not. However, these effects differ systematically across countries, questioning standard...... interpretations of the influence of fractionalization on trust....

  20. Ferroelectric Fractional-Order Capacitors

    KAUST Repository

    Agambayev, Agamyrat

    2017-07-25

    Poly(vinylidene fluoride)-based polymers and their blends are used to fabricate electrostatic fractional-order capacitors. This simple but effective method allows us to precisely tune the constant phase angle of the resulting fractional-order capacitor by changing the blend composition. Additionally, we have derived an empirical relation between the ratio of the blend constituents and the constant phase angle to facilitate the design of a fractional order capacitor with a desired constant phase angle. The structural composition of the fabricated blends is investigated using Fourier transform infrared spectroscopy and X-ray diffraction techniques.

  1. Fractional order PID controller for load frequency control

    International Nuclear Information System (INIS)

    Sondhi, Swati; Hote, Yogesh V.

    2014-01-01

    Highlights: • The manuscript shows the design of FOPID controller for the load frequency control. • Performance of FOPID is given for non-reheated, reheated and hydro turbine. • Performance of FOPID is compared to IMC-PID and reduced order IMC-PID design scheme. • Performance of FOPID is better than the existing techniques. - Abstract: Load frequency control (LFC) plays a very important role in providing quality power both in the case of isolated as well as interconnected power systems. In order to maintain good quality power supply, the LFC should possess robustness toward the parametric uncertainty of the system and good disturbance rejection capability. The fractional order controller has the properties such as, eliminating steady state error, robustness toward plant gain variations and also good disturbance rejection. This makes the fractional order PID (FOPID) controller quite suitable for the LFC. Therefore, in this paper a FOPID is designed for single area LFC for all three types of turbines i.e., non-reheated, reheated and hydro turbines. It is observed that the FOPID controller shows better robustness toward ±50% parametric uncertainty and disturbance rejection capability than the existing techniques. Finally, the optimization of controller parameters and robustness evaluation of the control technique is done on the basis of the integral error criterion

  2. Passive and active elements using fractional Lβ C α circuit

    KAUST Repository

    Radwan, Ahmed G.

    2011-10-01

    This paper introduces a qualitative revision of the traditional LC tank circuit in the fractional domain. The paper can be divided into six major parts, aiming in turn to establish the various conditions under which L βCα impedance may act as a resistor, negative resistor, or a positive or negative pure imaginary inductor or capacitor, in accordance to new frequency definitions; illustrate the process by which the phase response chooses the shortest path from initial to final phase, and use this illustration to verify the cases discussed in part one; develop the generalized parameters for the bandpass filter response of the L βCα circuit, such as the resonance frequency and quality factor versus α-β plane; discuss sensitivity analyses with respect to the fractional orders, as well as the time domain analyses for the impulse and step responses with their analytical formulas; and lastly, to propose some possible applications for this generalized circuit. Mathematical and PSpice simulation results are included to validate the discussion. © 2011 IEEE.

  3. Teaching stable two-mirror resonators through the fractional Fourier transform

    International Nuclear Information System (INIS)

    Moreno, Ignacio; Garcia-Martinez, Pascuala; Ferreira, Carlos

    2010-01-01

    We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g parameters) and those of the equivalent FRFT systems (the FRFT order and scaling parameters). Expressions connecting Gaussian beam q-transformation with FRFT parameters are derived. In particular, we show that the beam waist of the resonator's mode is located at the plane leading to two FRFT subsystems with equal scaling parameter which, moreover, coincides with the mode Rayleigh range. Finally we analyse the resonator's stability diagram in terms of the fractional orders of each FRFT subsystem, and the round trip propagation. The presented analysis represents an interesting link between two topics (optical resonators and Fourier optics) usually covered in optics and photonics courses at university level, which can be useful to teach and connect the principles of these subjects.

  4. Xenon fractionation in porous planetesimals

    Science.gov (United States)

    Zahnle, Kevin; Pollack, James B.; Kasting, James F.

    1990-01-01

    The distinctively fractionated Xe on Mars and earth may have its root in a common source from which both planets accreted. Beginning with Ozima and Nakazawa's (1980) hypothesis that terrestrial Xe fractionation was caused by gravitational separation of adsorbed solar nebular gases inside large porous planetesimals, it is pointed out that Xe would have been trapped as the planetesimal grew and pores were squeezed shut by lithostatic pressure. It is shown that enough fractionated Xe to supply the earth could have been trapped this way. The degree of fractionation is controlled by the lithostatic pressure at the pore-closing front and so would have been roughly the same for all large planetesimals. The predicted degree of fractionation agrees well with that preserved in terrestrial and Martian Xe. Relative to Xe, this source is strongly depleted in other noble gases. In contrast to the original Ozima and Nakazawa hypothesis, the present hypothesis predicts the observed fractionation, and it allows planetary accretion to occur after the dissipation of the solar nebula.

  5. Xenon fractionation in porous planetesimals

    International Nuclear Information System (INIS)

    Zahnle, K.; Pollack, J.B.; Kasting, J.F.

    1990-01-01

    The distinctively fractionated Xe on Mars and Earth may have its root in a common source from which both planets accreted. We begin with Ozima and Nakazawa's hypothesis that terrestrial Xe fractionation was caused by gravitational separation of adsorbed solar nebular gases inside large porous planetesimals. We point out that Xe would have been trapped as the planetesimal grew and pores were squeezed shut by lithostatic pressure. We show that enough fractionated Xe to supply the Earth could have been trapped this way. The degree of fractionation is controlled by the lithostatic pressure at the pore-closing front and so would have been roughly the same for all large planetesimals. The predicted degree of fractionation agrees well with that preserved in terrestrial and martian Xe. Relative to Xe, this source is strongly depleted in other noble gases. In contrast to the original Ozima and Nakazawa hypothesis, our hypothesis predicts the observed fractionation, and it allows planetary accretion to occur after the dissipation of the solar nebula. The required planetesimals are large, representing a class of object now extinct in the solar system

  6. Ultrastructure and electrophoretic protein pattern of a nuclear fraction enriched in interchromatin granule conglomerations

    Energy Technology Data Exchange (ETDEWEB)

    Krzyzowska-Gruca, S.; Zborek, A.; Gruca, S.

    1986-01-01

    Rats were injected with a cytostatic 1-nitro-9/3'-dimethylpropyloamine/acridine.2HCl to induce aggregation of interchromatin granules (IG). The conglomerations of IG were well preserved in isolated liver nuclei and in nuclear structures deprived of chromatin. This feature enabled obtaining a nuclear fraction enriched in IG. The method consisted in extraction of isolated nuclei with a non-ionic detergent and digestion with DNase I in a high ionic strength. Each step of isolation was ultrastructurally monitored using both the routine electron microscopy as well as a preferential staining of IG with bismuth. Presence of spots of tightly packed granules within IG conglomerations in the final fraction like in the nuclei in situ was a good ultrastructural marker of IG. The resulting fraction consisted predominantly of IG conglomerations. Their preferential staining with bismuth was well preserved. Minute amounts of fibrillar material originating from nuclear matrix and residual nuclei could be observed. Protein composition of the fraction enriched in IG was studied by SDS-polyacrylamide gel electrophoresis. After electrotransfer, nitrocellulose filters were fixed with glutaraldehyde and stained with bismuth method in order to identify IG proteins. The results of ultrastructural and cytochemical studies in comparison to electrophoretic protein pattern are discussed.

  7. Infrared maritime target detection using the high order statistic filtering in fractional Fourier domain

    Science.gov (United States)

    Zhou, Anran; Xie, Weixin; Pei, Jihong

    2018-06-01

    Accurate detection of maritime targets in infrared imagery under various sea clutter conditions is always a challenging task. The fractional Fourier transform (FRFT) is the extension of the Fourier transform in the fractional order, and has richer spatial-frequency information. By combining it with the high order statistic filtering, a new ship detection method is proposed. First, the proper range of angle parameter is determined to make it easier for the ship components and background to be separated. Second, a new high order statistic curve (HOSC) at each fractional frequency point is designed. It is proved that maximal peak interval in HOSC reflects the target information, while the points outside the interval reflect the background. And the value of HOSC relative to the ship is much bigger than that to the sea clutter. Then, search the curve's maximal target peak interval and extract the interval by bandpass filtering in fractional Fourier domain. The value outside the peak interval of HOSC decreases rapidly to 0, so the background is effectively suppressed. Finally, the detection result is obtained by the double threshold segmenting and the target region selection method. The results show the proposed method is excellent for maritime targets detection with high clutters.

  8. A Measurement of the Exclusive Branching Fraction for B → π K at BaBar

    Energy Technology Data Exchange (ETDEWEB)

    Aspinwall, Marie Louise [Imperial College, London (United Kingdom)

    2002-02-01

    This thesis presents an exclusive measurement of the branching fraction B for the rare charmless hadronic B decays to πK final states. A sample of 22.57±0.36 million BB pairs was collected with the BaBar detector at the Stanford Linear Accelerator Center's PEP-II B Factory, during the Run 1 data taking period (1999-2000).

  9. The Ca, Cl, Mg, Na, and P mass fractions in benign and malignant giant cell tumors of bone investigated by neutron activation analysis

    International Nuclear Information System (INIS)

    Vladimir Zaichick; German Davydov; Tatyana Epatova; Sofia Zaichick

    2015-01-01

    The Ca, Cl, Mg, Na, and P content and Ca/P, Ca/Mg, Ca/Na, Cl/Ca, and Cl/Na ratios in samples of intact bone, benign and malignant giant cell tumor (GCT) of bone were investigated by neutron activation analysis with high resolution spectrometry of short-lived radionuclides. It was found that in GCT tissue the mass fractions of Cl and Na are higher and the mass fraction of Ca and P are lower than in normal bone tissues. Moreover, it was shown that higher Cl/Na mass fraction ratios as well as lower Ca/Cl, Ca/Mg, and Ca/Na mass fraction ratios are typical of the GCT tissue compared to intact bone. Finally, we propose to use the estimation of such parameters as the Cl mass fraction and the Ca/Cl mass fraction ratio as an additional test for differential diagnosis between benign and malignant GCT. (author)

  10. Black holes in multi-fractional and Lorentz-violating models

    Energy Technology Data Exchange (ETDEWEB)

    Calcagni, Gianluca [CSIC, Instituto de Estructura de la Materia, Madrid (Spain); Rodriguez Fernandez, David [Universidad de Oviedo, Department of Physics, Oviedo (Spain); Ronco, Michele [Universita di Roma ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); INFN, Rome (Italy)

    2017-05-15

    We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length l{sub *}. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to l{sub *}. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models. (orig.)

  11. Black holes in multi-fractional and Lorentz-violating models

    International Nuclear Information System (INIS)

    Calcagni, Gianluca; Rodriguez Fernandez, David; Ronco, Michele

    2017-01-01

    We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length l_*. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to l_*. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models. (orig.)

  12. Black holes in multi-fractional and Lorentz-violating models.

    Science.gov (United States)

    Calcagni, Gianluca; Rodríguez Fernández, David; Ronco, Michele

    2017-01-01

    We study static and radially symmetric black holes in the multi-fractional theories of gravity with q -derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length [Formula: see text]. In the q -derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to [Formula: see text]. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q -derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models.

  13. Efficacy and Safety of Fractional CO2 Laser Resurfacing in Non-hypertrophic Traumatic and Burn Scars

    Science.gov (United States)

    Majid, Imran; Imran, Saher

    2015-01-01

    Background: Fractional photothermolysis is one of the most effective treatment options used to resurface scars of different aetiologies. Aim: To assess the efficacy and safety of fractional CO2 laser resurfacing treatment in the management of non-hypertrophic traumatic and burn scars. Materials and Methods: Twenty-five patients affected by non-hypertrophic traumatic and burn scars were treated with four sessions of fractional CO2 laser resurfacing treatment at 6-weekly intervals. Patients were photographed at each visit and finally, 3 months after the end of treatment schedule. Response to treatment was assessed clinically as well as by comparing the initial photograph of the patient with the one taken at the last follow-up visit 3-months after the final treatment session. Changes in skin texture, surface irregularity and pigmentation were assessed on a quartile grading scale and scored individually from 0 to 4. A mean of the three individual scores was calculated and the response was labelled as ‘excellent’ if the mean score achieved was >2. A score of 1-2 was labeled as good response while a score below 1 was labeled as ‘poor’ response. The subjective satisfaction of each patient with the treatment offered was also assessed at the last follow-up visit. Results: The commonest site of scarring treated was the face followed by hands. Response to treatment was rated as excellent in 60% (15/25) patients while 24% (6/25) and 16% (4/25) patients were labeled as good and poor responders, respectively. Skin texture showed better response than other variables with average score of 2.44. Linear post-traumatic scars were seen to respond less than other morphological types. Majority of the patients (19 out of 25) were highly satisfied with the treatment offered. No long-term adverse effects were noted in any patient. Conclusions: Fractional photothermolysis with a fractional CO2 laser gives excellent results in patients with post-burn scars with minimal adverse

  14. Efficacy and safety of fractional CO 2 laser resurfacing in non-hypertrophic traumatic and burn scars

    Directory of Open Access Journals (Sweden)

    Imran Majid

    2015-01-01

    Full Text Available Background: Fractional photothermolysis is one of the most effective treatment options used to resurface scars of different aetiologies. Aim: To assess the efficacy and safety of fractional CO 2 laser resurfacing treatment in the management of non-hypertrophic traumatic and burn scars. Materials and Methods: Twenty-five patients affected by non-hypertrophic traumatic and burn scars were treated with four sessions of fractional CO 2 laser resurfacing treatment at 6-weekly intervals. Patients were photographed at each visit and finally, 3 months after the end of treatment schedule. Response to treatment was assessed clinically as well as by comparing the initial photograph of the patient with the one taken at the last follow-up visit 3-months after the final treatment session. Changes in skin texture, surface irregularity and pigmentation were assessed on a quartile grading scale and scored individually from 0 to 4. A mean of the three individual scores was calculated and the response was labelled as ′excellent′ if the mean score achieved was >2. A score of 1-2 was labeled as good response while a score below 1 was labeled as ′poor′ response. The subjective satisfaction of each patient with the treatment offered was also assessed at the last follow-up visit. Results: The commonest site of scarring treated was the face followed by hands. Response to treatment was rated as excellent in 60% (15/25 patients while 24% (6/25 and 16% (4/25 patients were labeled as good and poor responders, respectively. Skin texture showed better response than other variables with average score of 2.44. Linear post-traumatic scars were seen to respond less than other morphological types. Majority of the patients (19 out of 25 were highly satisfied with the treatment offered. No long-term adverse effects were noted in any patient. Conclusions: Fractional photothermolysis with a fractional CO 2 laser gives excellent results in patients with post-burn scars with

  15. Fractional Resonance-Based RLβCα Filters

    Directory of Open Access Journals (Sweden)

    Todd J. Freeborn

    2013-01-01

    Full Text Available We propose the use of a fractional order capacitor and fractional order inductor with orders 0≤α,  β≤1, respectively, in a fractional RLβCα series circuit to realize fractional-step lowpass, highpass, bandpass, and bandreject filters. MATLAB simulations of lowpass and highpass responses having orders of (α+β=1.1, 1.5, and 1.9 and bandpass and bandreject responses having orders of 1.5 and 1.9 are given as examples. PSPICE simulations of 1.1, 1.5, and 1.9 order lowpass and 1.0 and 1.4 order bandreject filters using approximated fractional order capacitors and fractional order inductors verify the implementations.

  16. A uranium enrichment facility safeguards technology based on the separation nozzle process

    International Nuclear Information System (INIS)

    Bahm, W.; Weppner, J.; Didier, H.J.

    1979-01-01

    Under the Trilateral Agreement between Brazil, the Federal Republic of Germany and the IAEA an enrichment plant operating on the basis of the separation nozzle process, will be safeguarded under INFCIRC/66/Rev.2. For nuclear materials balancing purposes the plant has been subdivided into 17 key measuring points to assess the nuclear material flow and the nuclear material inventory. Preliminary studies have indicated that the balancing accuracy required for safeguards purposes cannot be achieved by only using the foreseen in-plant measuring systems, since considerable quantities of enriched uranium cannot be covered in this way. This fraction will merely be estimated by the operator and thus cannot be verified by the inspection authorities. The plant components, whose inventories could not be verified in the first estimate of the balancing accuracy referred to above by means of the in-plant measuring systems, also include the low-temperature separators of the cascade shoulder and the product. Assessing and verifying the inventories of these key measuring points is particularly important because of the enrichment (some 3% 235 U for the product) and the relatively large inventory and, hence, the considerable contribution to the balancing inaccuracy. An estimate of the balancing inaccuracy on the basis of the measuring uncertainties to be expected in the light of the present status of technology indicated values between 0.2 and 0.3% relative to the feed flow with semi-annual inventory-taking. However, this is based on the condition that the experiments planned to determine the inventories of cryogenic separators confirm the measuring uncertainties underlying the calculation

  17. A new procedure for the determination of distillation temperature distribution of high-boiling petroleum products and fractions.

    Science.gov (United States)

    Boczkaj, Grzegorz; Przyjazny, Andrzej; Kamiński, Marian

    2011-03-01

    The distribution of distillation temperatures of liquid and semi-fluid products, including petroleum fractions and products, is an important process and practical parameter. It provides information on properties of crude oil and content of particular fractions, classified on the basis of their boiling points, as well as the optimum conditions of atmospheric or vacuum distillation. At present, the distribution of distillation temperatures is often investigated by simulated distillation (SIMDIS) using capillary gas chromatography (CGC) with a short capillary column with polydimethylsiloxane as the stationary phase. This paper presents the results of investigations on the possibility of replacing currently used CGC columns for SIMDIS with a deactivated fused silica capillary tube without any stationary phase. The SIMDIS technique making use of such an empty fused silica column allows a considerable lowering of elution temperature of the analytes, which results in a decrease of the final oven temperature while ensuring a complete separation of the mixture. This eliminates the possibility of decomposition of less thermally stable mixture components and bleeding of the stationary phase which would result in an increase of the detector signal. It also improves the stability of the baseline, which is especially important in the determination of the end point of elution, which is the basis for finding the final temperature of distillation. This is the key parameter for the safety process of hydrocracking, where an excessively high final temperature of distillation of a batch can result in serious damage to an expensive catalyst bed. This paper compares the distribution of distillation temperatures of the fraction from vacuum distillation of petroleum obtained using SIMDIS with that obtained by the proposed procedure. A good agreement between the two procedures was observed. In addition, typical values of elution temperatures of n-paraffin standards obtained by the two

  18. FRACTIONATION AND CHARACTERISATION OF TECHNICAL AMMONIUM LIGNOSULPHONATE

    Directory of Open Access Journals (Sweden)

    Cheryl Ann Leger

    2010-08-01

    Full Text Available It is difficult to use lignin in any analytical methodology without reducing its considerable polydispersity by fractionation. An ammonium lignosulphonate sample was fractionated using a method of partial solubility in solutions of isopropanol increasingly diluted with distilled water, effectively fractionating by polarity. Selected fractions were characterised by gravimetric determination of the fractions, and determination of acid insoluble lignin, soluble lignin, and carbohydrate contents. Acid-insoluble lignin content was very low, and soluble lignin provided the majority of the lignin content, as should be expected from sulphonated lignin. Carbohydrate contents were also fairly low, the highest percentage at 14.5 being in Fraction 2, with the bulk lignin and Fraction 3 having 6.5% and 3.2%, respectively. Differences in the composition of each fraction support the efficacy of the fractionation process and permitted selection of fractions for use in subsequent studies.

  19. Generalized time fractional IHCP with Caputo fractional derivatives

    International Nuclear Information System (INIS)

    Murio, D A; MejIa, C E

    2008-01-01

    The numerical solution of the generalized time fractional inverse heat conduction problem (GTFIHCP) on a finite slab is investigated in the presence of measured (noisy) data when the time fractional derivative is interpreted in the sense of Caputo. The GTFIHCP involves the simultaneous identification of the heat flux and temperature transient functions at one of the boundaries of the finite slab together with the initial condition of the original direct problem from noisy Cauchy data at a discrete set of points on the opposite (active) boundary. A finite difference space marching scheme with adaptive regularization, using trigonometric mollification techniques and generalized cross validation is introduced. Error estimates for the numerical solution of the mollified problem and numerical examples are provided.

  20. Conformable Fractional Bessel Equation and Bessel Functions

    OpenAIRE

    Gökdoğan, Ahmet; Ünal, Emrah; Çelik, Ercan

    2015-01-01

    In this work, we study the fractional power series solutions around regular singular point x=0 of conformable fractional Bessel differential equation and fractional Bessel functions. Then, we compare fractional solutions with ordinary solutions. In addition, we present certain property of fractional Bessel functions.

  1. Light-mediated 15N fractionation in Caribbean gorgonian octocorals: implications for pollution monitoring

    Science.gov (United States)

    Baker, D. M.; Kim, K.; Andras, J. P.; Sparks, J. P.

    2011-09-01

    The stable nitrogen isotope ratio ( δ 15N) of coral tissue is a useful recorder of anthropogenic pollution in tropical marine ecosystems. However, little is known of the natural environmentally induced fractionations that affect our interpretation of coral δ 15N values. In symbiotic scleractinians, light affects metabolic fractionation of N during photosynthesis, which may confound the identification of N pollution between sites of varied depth or turbidity. Given the superiority of octocorals for δ 15N studies, our goal was to quantify the effect of light on gorgonian δ 15N in the context of monitoring N pollution sources. Using field collections, we show that δ 15N declined by 1.4‰ over 20 m depth in two species of gorgonians, the common sea fan, Gorgonia ventalina, and the slimy sea plume, Pseudopterogorgia americana. An 8-week laboratory experiment with P. americana showed that light, not temperature causes this variation, whereby the lowest fractionation of the N source was observed in the highest light treatment. Finally, we used a yearlong reciprocal depth transplant experiment to quantify the time frame over which δ 15N changes in G. ventalina as a function of light regime . Over the year, δ 15N was unchanged and increased slightly in the deep control colonies and shallow colonies transplanted to the deep site, respectively. Within 6 months, colonies transplanted from deep to shallow became enriched by 0.8‰, mirroring the enrichment observed in the shallow controls, which was likely due to the combined effect of an increase in the source δ 15N and reduced fractionation. We conclude that light affects gorgonian δ 15N fractionation and should be considered in sampling designs for N pollution monitoring. However, these fractionations are small relative to differences observed between natural and anthropogenic N sources.

  2. Identification of antihyperuricemic peptides in the proteolytic digest of shark cartilage water extract using in vivo activity-guided fractionation.

    Science.gov (United States)

    Murota, Itsuki; Taguchi, Satoko; Sato, Nobuyuki; Park, Eun Young; Nakamura, Yasushi; Sato, Kenji

    2014-03-19

    A peptide that exerts antihyperuricemic activity after oral administration was identified from a microbial protease (alcalase) digest of the water extract of shark cartilage by in vivo activity-guided fractionation, using oxonate-induced hyperuricemic rats. Water extract of shark cartilage was first fractionated by preparative ampholine-free isoelectric focusing, followed by preparative reversed-phase liquid chromatography. The antihyperuricemic activity of the alcalse digests of the obtained fractions was evaluated using an animal model. Alcalase digests of the basic and hydrophobic fractions exerted antihyperuricemic activity. A total of 18 peptides were identified in the alcalase digest of the final active fraction. These peptides were chemically synthesized and evaluated for antihyperuricemic activity. Tyr-Leu-Asp-Asn-Tyr and Ser-Pro-Pro-Tyr-Trp-Pro-Tyr lowered the serum uric acid level via intravenous injection at 5 mg/kg of body weight. Furthermore, orally administered Tyr-Leu-Asp-Asn-Tyr showed antihyperuricemic activity. Therefore, these peptides are at least partially responsible for the antihyperuricemic activity of the alcalase digest of shark cartilage.

  3. REFractions: The Representing Equivalent Fractions Game

    Science.gov (United States)

    Tucker, Stephen I.

    2014-01-01

    Stephen Tucker presents a fractions game that addresses a range of fraction concepts including equivalence and computation. The REFractions game also improves students' fluency with representing, comparing and adding fractions.

  4. Some comparison of two fractional oscillators

    International Nuclear Information System (INIS)

    Kang Yonggang; Zhang Xiu'e

    2010-01-01

    The other form of fractional oscillator equation comparing to the widely discussed one is ushered in. The properties of vibration of two fractional oscillators are discussed under the influence of different initial conditions. The interpretation of the characteristics of the fractional oscillators using different method is illustrated. Based on two fractional oscillator equations, two linked bodies and the continuous system are studied.

  5. Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators

    Directory of Open Access Journals (Sweden)

    Sheng-Ping Yan

    2014-01-01

    Full Text Available We perform a comparison between the local fractional Adomian decomposition and local fractional function decomposition methods applied to the Laplace equation. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

  6. Comparative evaluation of multiple fractions per day radiotherapy and conventional fractionated radiotherapy in squamous cell carcinoma of esophagus

    International Nuclear Information System (INIS)

    Andrabi, W.H.; Akhtar, S.; Kharadi, M.Y.; Mushtaq, G.; Zargar, S.A.

    1999-01-01

    Dose fractionated is important in radiotherapy in order to achieve the desired results. There are regimes which are accepted and followed worldwide. Five fractions per week for a full course of treatment is regarded as standard fractionation regimen. Interest has lately been developed to alter this and try regimes like hyper and accelerated fractionations. In the former, smaller doses per fraction than usual are given in several fractions on each treating day, with no change in overall time. In the latter, conventionally sized fractions are given as two or three per day with a shortening of overall time. As the dose fraction in our case is high, we spilt the full course of treatment introducing a gap of one week between the treatment schedules. The results obtained are fairly good in comparison with conventional radiotherapy regimes. (author)

  7. Branching Ratios and Spectral Functions of $\\tau$ Decays final ALEPH measurements and physics implications

    CERN Document Server

    Schael, S.; Bruneliere, R.; De Bonis, I.; Decamp, D.; Goy, C.; Jezequel, S.; Lees, J.-P.; Martin, F.; Merle, E.; Minard, M.-N.; Pietrzyk, B.; Trocme, B.; Bravo, S.; Casado, M.P.; Chmeissani, M.; Crespo, J.M.; Fernandez, E.; Fernandez-Bosman, M.; Garrido, Ll.; Martinez, M.; Pacheco, A.; Ruiz, H.; Colaleo, A.; Creanza, D.; De Filippis, N.; de Palma, M.; Iaselli, G.; Maggi, G.; Maggi, M.; Nuzzo, S.; Ranieri, A.; Raso, G.; Ruggieri, F.; Selvaggi, G.; Silvestris, L.; Tempesta, P.; Tricomi, A.; Zito, G.; Huang, X.; Lin, J.; Ouyang, Q.; Wang, T.; Xie, Y.; Xu, R.; Xue, S.; Zhang, J.; Zhang, L.; Zhao, W.; Abbaneo, D.; Barklow, T.; Buchmuller, O.; Cattaneo, M.; Clerbaux, B.; Drevermann, H.; Forty, R.W.; Frank, M.; Gianotti, F.; Hansen, J.B.; Harvey, J.; Hutchcroft, D.E.; Janot, P.; Jost, B.; Kado, M.; Mato, P.; Moutoussi, A.; Ranjard, F.; Rolandi, L.; Schlatter, D.; Teubert, F.; Valassi, A.; Videau, I.; Badaud, F.; Dessagne, S.; Falvard, A.; Fayolle, D.; Gay, P.; Jousset, J.; Michel, B.; Monteil, S.; Pallin, D.; Pascolo, J.M.; Perret, P.; Hansen, J.D.; Hansen, J.R.; Hansen, P.H.; Kraan, A.C.; Nilsson, B.S.; Kyriakis, A.; Markou, C.; Simopoulou, E.; Vayaki, A.; Zachariadou, K.; Blondel, A.; Brient, J.-C.; Machefert, F.; Rouge, A.; Videau, H.; Ciulli, V.; Focardi, E.; Parrini, G.; Antonelli, A.; Antonelli, M.; Bencivenni, G.; Bossi, F.; Capon, G.; Cerutti, F.; Chiarella, V.; Laurelli, P.; Mannocchi, G.; Murtas, G.P.; Passalacqua, L.; Kennedy, J.; Lynch, J.G.; Negus, P.; O'Shea, V.; Thompson, A.S.; Wasserbaech, S.; Cavanaugh, R.; Dhamotharan, S.; Geweniger, C.; Hanke, P.; Hepp, V.; Kluge, E.E.; Putzer, A.; Stenzel, H.; Tittel, K.; Wunsch, M.; Phys., Kirchhoff Inst.; Beuselinck, R.; Cameron, W.; Davies, G.; Dornan, P.J.; Girone, M.; Marinelli, N.; Nowell, J.; Rutherford, S.A.; Sedgbeer, J.K.; Thompson, J.C.; White, R.; Ghete, V.M.; Girtler, P.; Kneringer, E.; Kuhn, D.; Rudolph, G.; Bouhova-Thacker, E.; Bowdery, C.K.; Clarke, D.P.; Ellis, G.; Finch, A.J.; Foster, F.; Hughes, G.; Jones, R.W.L.; Pearson, M.R.; Robertson, N.A.; Smizanska, M.; van der Aa, O.; Delaere, C.; Leibenguth, G.; Lemaitre, V.; Blumenschein, U.; Holldorfer, F.; Jakobs, K.; Kayser, F.; Muller, A.-S.; Renk, B.; Sander, H.-G.; Schmeling, S.; Wachsmuth, H.; Zeitnitz, C.; Ziegler, T.; Bonissent, A.; Coyle, P.; Curtil, C.; Ealet, A.; Fouchez, D.; Payre, P.; Tilquin, A.; Ragusa, F.; David, A.; Dietl, H.; Ganis, G.; Huttmann, K.; Lutjens, G.; Manner, W.; Moser, H.-G.; Settles, R.; Villegas, M.; Wolf, G.; Boucrot, J.; Callot, O.; Davier, M.; Duflot, L.; Grivaz, J.-F.; Heusse, Ph.; Hocker, Andreas; Jacholkowska, A.; Serin, L.; Veillet, J.-J.; Yuan, C.Z.; Zhang, Z.Q.; Azzurri, P.; Bagliesi, Giuseppe; Boccali, T.; Foa, L.; Giammanco, A.; Giassi, A.; Ligabue, F.; Messineo, A.; Palla, F.; Sanguinetti, G.; Sciaba, A.; Sguazzoni, G.; Spagnolo, P.; Tenchini, R.; Venturi, A.; Verdini, P.G.; Awunor, O.; Blair, G.A.; Cowan, G.; Garcia-Bellido, A.; Green, M.G.; Medcalf, T.; Misiejuk, A.; Strong, J.A.; Teixeira-Dias, P.; Clifft, R.W.; Edgecock, T.R.; Norton, P.R.; Tomalin, I.R.; Ward, J.J.; Bloch-Devaux, Brigitte; Boumediene, D.; Colas, P.; Fabbro, B.; Lancon, E.; Lemaire, M.-C.; Locci, E.; Perez, P.; Rander, J.; Tuchming, B.; Vallage, G.; Litke, A.M.; Taylor, G.; Booth, C.N.; Cartwright, S.; Combley, F.; Hodgson, P.N.; Lehto, M.; Thompson, L.F.; Bohrer, A.; Brandt, S.; Grupen, C.; Hess, J.; Ngac, A.; Prange, G.; Borean, C.; Giannini, G.; He, H.; Putz, J.; Rothberg, J.; Armstrong, S.R.; Berkelman, Karl; Cranmer, K.; Ferguson, D.P.S.; Gao, Y.; Gonzalez, S.; Hayes, O.J.; Hu, H.; Jin, S.; Kile, J.; McNamara, P.A., III; Nielsen, J.; Pan, Y.B.; von Wimmersperg-Toeller, J.H.; Wiedenmann, W.; Wu, J.; Wu, Sau Lan; Wu, X.; Zobernig, G.; Dissertori, G.

    2005-01-01

    The full LEP-1 data set collected with the ALEPH detector at the $Z$ pole during 1991-1995 is analysed in order to measure the $\\tau$ decay branching fractions. The analysis follows the global method used in the published study based on 1991-1993 data, but several improvements are introduced, especially concerning the treatment of photons and $\\pi^0$'s. Extensive systematic studies are performed, in order to match the large statistics of the data sample corresponding to over 300\\,000 measured and identified $\\tau$ decays. Branching fractions are obtained for the two leptonic channels and eleven hadronic channels defined by their respective numbers of charged particles and $\\pi^0$'s. Using previously published ALEPH results on final states with charged and neutral kaons, corrections are applied to the hadronic channels to derive branching ratios for exclusive final states without kaons. Thus the analyses of the full LEP-1 ALEPH data are combined to yield a complete description of $\\tau$ decays, encompassing 22...

  8. Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

    OpenAIRE

    Xiao-Li Ding; Juan J. Nieto

    2018-01-01

    In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochast...

  9. A new fractional wavelet transform

    Science.gov (United States)

    Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

    2017-03-01

    The fractional Fourier transform (FRFT) is a potent tool to analyze the time-varying signal. However, it fails in locating the fractional Fourier domain (FRFD)-frequency contents which is required in some applications. A novel fractional wavelet transform (FRWT) is proposed to solve this problem. It displays the time and FRFD-frequency information jointly in the time-FRFD-frequency plane. The definition, basic properties, inverse transform and reproducing kernel of the proposed FRWT are considered. It has been shown that an FRWT with proper order corresponds to the classical wavelet transform (WT). The multiresolution analysis (MRA) associated with the developed FRWT, together with the construction of the orthogonal fractional wavelets are also presented. Three applications are discussed: the analysis of signal with time-varying frequency content, the FRFD spectrum estimation of signals that involving noise, and the construction of fractional Harr wavelet. Simulations verify the validity of the proposed FRWT.

  10. Anti-inflammatory effects of chloroform soluble fraction from Perilla frutescens britton leaves produced by radiation breeding in RAW264.7 cells

    Energy Technology Data Exchange (ETDEWEB)

    Jo, Yun Ho; So, Yang Kang; Kim, Jin Baek; Jin, Chang Hyun [Advance Radiation Technology Institute, Korea Atomic Energy Research Institute, Jeongeup (Korea, Republic of); Lee, Jun Soo [Dept. Food Science and Technology Graduate School, Chungbuk National University, Cheongju (Korea, Republic of); Lee, Seung Young [Freshwater Bioresources Utilization Division, Nakdonggang National Institute of Biological Resources, Sangju (Korea, Republic of)

    2016-11-15

    The present study aimed to determine the anti-inflammatory effects of each solvent fraction of a mutant Perilla frutescens produced by radiation breeding. Following extraction with 80% methanol, P. frutescens was fractionated in the order of hexane, chloroform, ethyl acetate, and butanol; the chloroform fraction exhibited less cytotoxicity, the greatest inhibitory effect on the production of nitric oxide (NO), and the highest rate of inhibition on the generation of tumor necrosis factor-α (TNF-α), interleukin-6 (IL-6), monocyte chemoattractant protein-1 (MCP-1), and interferon-β (IFN-β). The chloroform fraction also suppressed the mRNA and protein levels of inducible nitric oxide synthase (iNOS) and reduced the activation of nuclear factor-{sub κ}B (NF-{sub κ}B) in lipopolysaccharide (LPS)-stimulated RAW264.7 cells. Finally, the presence of corosolic acid in the chloroform fraction was identifed. Taken together, the present fndings indicate that the chloroform fraction obtained from mutant P. frutescens inhibited NO production in LPSstimulated RAW264.7 cells via the suppression of iNOS expression and the inactivation of NF-{sub κ}B.

  11. The Norwegian Plasma Fractionation Project--a 12 year clinical and economic success story.

    Science.gov (United States)

    Flesland, O; Seghatchian, J; Solheim, B G

    2003-02-01

    The establishment of the Norwegian Fractionation Project (Project) was of major importance in preserving national self-sufficiency when plasma, cryoprecipitate and small batch factor IX-concentrates were replaced by virus inactivated products in the last part of the 1980s. Fractionation was performed abroad by contract with Octapharma after tenders on the European market. All Norwegian blood banks (>50) participated in the Project. Total yearly production was 50-60 tons of mainly recovered plasma. From 1993 solvent detergent (SD) treated plasma has replaced other plasma for transfusion. The blood banks paid for the fractionation and/or viral inactivation process, while the plasma remained the property of the blood banks and the final products were returned to the blood banks. The Project sold surplus products to other Norwegian blood banks and the majority of the coagulation factor concentrates to The Institute of Haemophilia and Rikshospitalet University Hospital. Both plasma and blood bank quality was improved by the Project. Clinical experience with the products has been satisfactory and self-sufficiency has been achieved for all major plasma proteins and SD plasma, but a surplus exceeding 3 years consumption of albumin has accumulated due to decreasing clinical use.The Project has secured high yields of the fractionated products and the net income from the produced products is NOK 1115 (140 Euros or US dollars) per litre plasma. An increasing surplus of albumin and the possibility of significant sales abroad of currently not fractionated IVIgG, could lead to a reorganisation of the Project from that of a co-ordinator to a national plasma handling unit. This unit could buy the plasma from the blood banks and have the plasma fractionated by contract after tender, before selling the products back for cost recovery. The small blood banks could produce plasma for products for the Norwegian market, while surplus products from the larger blood banks which are

  12. Influence of the time interval between two daily fractions during fractionated radiotherapy of the R1H-tumor

    International Nuclear Information System (INIS)

    Beck-Bornholdt, H.P.; Kleineidam, M.; Pieconka, A.

    1994-01-01

    Tumors were exposed to irradiation five days per week over six weeks. A standard treatment of 30 fractions, i.e. one fraction per day (200 kVp X-rays) was compared with a hyperfractionated schedule of 60 fractions, i.e. two fractions per day, with time invervals of either one, two, three, five or six hours between the two daily fractions. Compared with standard treatment a significant reduction (p [de

  13. Joint estimation of the fractional differentiation orders and the unknown input for linear fractional non-commensurate system

    KAUST Repository

    Belkhatir, Zehor

    2015-11-05

    This paper deals with the joint estimation of the unknown input and the fractional differentiation orders of a linear fractional order system. A two-stage algorithm combining the modulating functions with a first-order Newton method is applied to solve this estimation problem. First, the modulating functions approach is used to estimate the unknown input for a given fractional differentiation orders. Then, the method is combined with a first-order Newton technique to identify the fractional orders jointly with the input. To show the efficiency of the proposed method, numerical examples illustrating the estimation of the neural activity, considered as input of a fractional model of the neurovascular coupling, along with the fractional differentiation orders are presented in both noise-free and noisy cases.

  14. Experimental facility and void fraction calibration methods for impedance probes

    Energy Technology Data Exchange (ETDEWEB)

    Oliveira, Fernando L. de; Rocha, Marcelo S., E-mail: floliveira@ipen.br, E-mail: msrocha@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)

    2013-07-01

    An experimental facility was designed and constructed with aims of to calibrate a capacitance probe for gas-liquid flow void fraction measurements. The facility is composed of a metallic hack with a vertical 2,300 mm high glass tube with 38 mm ID with stagnant water and compressed air bubbling system simulating the gas phase (vapor). At the lower part, a mixing section with a porous media element releases the air bubbles into the water, and the compressed air flow is measured by two calibrated rotameters. At the upper part a stagnant water tank separates the liquid and gas. Two pressure taps are located near the lower and upper sides of the glass tube for pressure difference measurement. The pressure difference is used for low void fraction values (0-15%) calibration methods, as described in the work. Two electrically controlled quick closing valves are installed between the porous media element and the upward separation tank for high void fraction values measurement (15-50%) used to calibrate the capacitance probe. The experimental facility design, construction, capacitance probe calibration methods and results, as well as flow pattern visualization, are presented. Finally, the capacitance probe will be installed on a natural circulation circuit mounted at the Nuclear Engineering Center (CEN/IPEN/CNEN-SP) for measurement of the instantaneous bulk void. Instantaneous signals generated by the capacitance probe will allow the determination of natural circulation loop global energy balance. (author)

  15. Experimental facility and void fraction calibration methods for impedance probes

    International Nuclear Information System (INIS)

    Oliveira, Fernando L. de; Rocha, Marcelo S.

    2013-01-01

    An experimental facility was designed and constructed with aims of to calibrate a capacitance probe for gas-liquid flow void fraction measurements. The facility is composed of a metallic hack with a vertical 2,300 mm high glass tube with 38 mm ID with stagnant water and compressed air bubbling system simulating the gas phase (vapor). At the lower part, a mixing section with a porous media element releases the air bubbles into the water, and the compressed air flow is measured by two calibrated rotameters. At the upper part a stagnant water tank separates the liquid and gas. Two pressure taps are located near the lower and upper sides of the glass tube for pressure difference measurement. The pressure difference is used for low void fraction values (0-15%) calibration methods, as described in the work. Two electrically controlled quick closing valves are installed between the porous media element and the upward separation tank for high void fraction values measurement (15-50%) used to calibrate the capacitance probe. The experimental facility design, construction, capacitance probe calibration methods and results, as well as flow pattern visualization, are presented. Finally, the capacitance probe will be installed on a natural circulation circuit mounted at the Nuclear Engineering Center (CEN/IPEN/CNEN-SP) for measurement of the instantaneous bulk void. Instantaneous signals generated by the capacitance probe will allow the determination of natural circulation loop global energy balance. (author)

  16. Discrete fractional solutions of a Legendre equation

    Science.gov (United States)

    Yılmazer, Resat

    2018-01-01

    One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus has also an important position in fractional calculus. In this work, we acquire new discrete fractional solutions of the homogeneous and non homogeneous Legendre differential equation by using discrete fractional nabla operator.

  17. Separation, fractionation, concentration and drying of food products: Final report, March 4, 1987--March 31, 1988

    Energy Technology Data Exchange (ETDEWEB)

    Merlo, C.A.; Rose, W.W.; Pedersen, L.D.; Brewbaker, P.L.

    1988-03-01

    This project studied energy efficient processes for separation, fractionation, concentration, drying, and recombination of food products, in order to reduce energy requirements for processing, preservation, and transportation. The project had three phases. In the laboratory-scale phase, results of which are summarized in this report, tomato puree was separated by three methods: conventional vacuum filtration, centrifugation, and crossflow microfiltration to produce pulp and serum. Three methods of recombination were examined: homogenizing, stomacher blending, and static (in-line) mixing. Satisfactory recombined purees were obtained. In addition, after centrifugation, the pulp was rinsed producing rinsed-pulp, and the rinse water was added to the serum producing rinse/serum. The rinse/serum was concentrated by evaporation. This was recombined with the rinsed-pulp and water producing satisfactory puree. 11 refs., 18 figs., 18 tabs.

  18. dimensional generalised time-fractional Hirota equation

    Indian Academy of Sciences (India)

    Youwei Zhang

    2018-02-09

    Feb 9, 2018 ... Fractional calculus has attracted much attention in ... cally proved that the fractional calculus theory is non- ... calculus and various definitions of fractional integration .... basic features of the tanh-expansion are outlined as.

  19. Can Kindergartners Do Fractions?

    Science.gov (United States)

    Cwikla, Julie

    2014-01-01

    Mathematics professor Julie Cwikla decided that she needed to investigate young children's understandings and see what precurricular partitioning notions young minds bring to the fraction table. Cwikla realized that only a handful of studies have examined how preschool-age and early elementary school-age students solve fraction problems (Empson…

  20. Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion

    Science.gov (United States)

    Zhang, Wei-Guo; Li, Zhe; Liu, Yong-Jun

    2018-01-01

    In this paper, we study the pricing problem of the continuously monitored fixed and floating strike geometric Asian power options in a mixed fractional Brownian motion environment. First, we derive both closed-form solutions and mixed fractional partial differential equations for fixed and floating strike geometric Asian power options based on delta-hedging strategy and partial differential equation method. Second, we present the lower and upper bounds of the prices of fixed and floating strike geometric Asian power options under the assumption that both risk-free interest rate and volatility are interval numbers. Finally, numerical studies are performed to illustrate the performance of our proposed pricing model.

  1. Treatment of acne scarring using a dual-spot-size ablative fractionated carbon dioxide laser: review of the literature.

    Science.gov (United States)

    Tierney, Emily P

    2011-07-01

    Fractional photothermolysis has been reported in the literature to improve pigmentary and textural changes associated with acne scarring. To review the literature for the treatment of acne scarring using nonablative fractional laser (NAFL) and ablative fractional laser (AFL) resurfacing. Review of the Medline literature evaluating NAFL and AFL for acne scarring. NAFL and AFL are safe and effective treatments for acne scarring. It is likely that the controlled, limited dermal heating of fractional resurfacing initiates a cascade of events in which normalization of the collagenesis-collagenolysis cycle occurs. We present the results of a patient treated using a novel dual-spot-size AFL device. Three months after the final treatment, the patient reported 75% improvement in acne scarring and 63% overall improvement in photoaging. Fractionated resurfacing for the treatment of acne scarring is associated with lesser risks of side effects of prolonged erythema and risks of delayed-onset dyspigmentation and scarring which complicate traditional ablative laser resurfacing approaches. We present herein preliminary data suggesting that a dual-spot-size AFL device presents novel advantages of improving texture and pigmentation in acne scarring and photoaging. © 2011 by the American Society for Dermatologic Surgery, Inc.

  2. Can Fractional Crystallization of a Lunar Magma Ocean Produce the Lunar Crust?

    Science.gov (United States)

    Rapp, Jennifer F.; Draper, David S.

    2013-01-01

    New techniques enable the study of Apollo samples and lunar meteorites in unprecedented detail, and recent orbital spectral data reveal more about the lunar farside than ever before, raising new questions about the supposed simplicity of lunar geology. Nevertheless, crystallization of a global-scale magma ocean remains the best model to account for known lunar lithologies. Crystallization of a lunar magma ocean (LMO) is modeled to proceed by two end-member processes - fractional crystallization from (mostly) the bottom up, or initial equilibrium crystallization as the magma is vigorously convecting and crystals remain entrained, followed by crystal settling and a final period of fractional crystallization [1]. Physical models of magma viscosity and convection at this scale suggest that both processes are possible. We have been carrying out high-fidelity experimental simulations of LMO crystallization using two bulk compositions that can be regarded as end-members in the likely relevant range: Taylor Whole Moon (TWM) [2] and Lunar Primitive Upper Mantle (LPUM) [3]. TWM is enriched in refractory elements by 1.5 times relative to Earth, whereas LPUM is similar to the terrestrial primitive upper mantle, with adjustments made for the depletion of volatile alkalis observed on the Moon. Here we extend our earlier equilibrium-crystallization experiments [4] with runs simulating full fractional crystallization

  3. Generalized dislocated lag function projective synchronization of fractional order chaotic systems with fully uncertain parameters

    International Nuclear Information System (INIS)

    Wang, Cong; Zhang, Hong-li; Fan, Wen-hui

    2017-01-01

    In this paper, we propose a new method to improve the safety of secure communication. This method uses the generalized dislocated lag projective synchronization and function projective synchronization to form a new generalized dislocated lag function projective synchronization. Moreover, this paper takes the examples of fractional order Chen system and Lü system with uncertain parameters as illustration. As the parameters of the two systems are uncertain, the nonlinear controller and parameter update algorithms are designed based on the fractional stability theory and adaptive control method. Moreover, this synchronization form and method of control are applied to secure communication via chaotic masking modulation. Many information signals can be recovered and validated. Finally, simulations are used to show the validity and feasibility of the proposed scheme.

  4. Optimization of spatiotemporally fractionated radiotherapy treatments with bounds on the achievable benefit

    Science.gov (United States)

    Gaddy, Melissa R.; Yıldız, Sercan; Unkelbach, Jan; Papp, Dávid

    2018-01-01

    Spatiotemporal fractionation schemes, that is, treatments delivering different dose distributions in different fractions, can potentially lower treatment side effects without compromising tumor control. This can be achieved by hypofractionating parts of the tumor while delivering approximately uniformly fractionated doses to the surrounding tissue. Plan optimization for such treatments is based on biologically effective dose (BED); however, this leads to computationally challenging nonconvex optimization problems. Optimization methods that are in current use yield only locally optimal solutions, and it has hitherto been unclear whether these plans are close to the global optimum. We present an optimization framework to compute rigorous bounds on the maximum achievable normal tissue BED reduction for spatiotemporal plans. The approach is demonstrated on liver tumors, where the primary goal is to reduce mean liver BED without compromising any other treatment objective. The BED-based treatment plan optimization problems are formulated as quadratically constrained quadratic programming (QCQP) problems. First, a conventional, uniformly fractionated reference plan is computed using convex optimization. Then, a second, nonconvex, QCQP model is solved to local optimality to compute a spatiotemporally fractionated plan that minimizes mean liver BED, subject to the constraints that the plan is no worse than the reference plan with respect to all other planning goals. Finally, we derive a convex relaxation of the second model in the form of a semidefinite programming problem, which provides a rigorous lower bound on the lowest achievable mean liver BED. The method is presented on five cases with distinct geometries. The computed spatiotemporal plans achieve 12-35% mean liver BED reduction over the optimal uniformly fractionated plans. This reduction corresponds to 79-97% of the gap between the mean liver BED of the uniform reference plans and our lower bounds on the lowest

  5. Norm- and hypo-fractionated radiotherapy is capable of activating human dendritic cells.

    Science.gov (United States)

    Kulzer, Lorenz; Rubner, Yvonne; Deloch, Lisa; Allgäuer, Andrea; Frey, Benjamin; Fietkau, Rainer; Dörrie, Jan; Schaft, Niels; Gaipl, Udo S

    2014-10-01

    Despite the transient immunosuppressive properties of local radiotherapy (RT), this classical treatment modality of solid tumors is capable of inducing immunostimulatory forms of tumor-cell death. The resulting 'immunotoxicity' in the tumor, but not in healthy tissues, may finally lead to immune-mediated destruction of the tumor. However, little is known about the best irradiation scheme in this setting. This study examines the immunological effects of differently irradiated human colorectal tumor cells on human monocyte-derived dendritic cells (DC). Human SW480 tumor cells were irradiated with a norm-fractionation scheme (5 × 2 Gy), a hypo-fractionated protocol (3 × 5 Gy), and with a high single irradiation dose (radiosurgery; 1 × 15 Gy). Subsequently, human immature DC (iDC) were co-incubated with supernatants (SN) of these differently treated tumor cells. Afterwards, DC were analyzed regarding the expression of maturation markers, the release of cytokines, and the potential to stimulate CD4(+) T-cells. The co-incubation of iDC with SN of tumor cells exposed to norm- or hypo-fractionated RT resulted in a significantly increased secretion of the immune activating cytokines IL-12p70, IL-8, IL-6, and TNFα, compared to iDC co-incubated with SN of tumor cells that received a high single irradiation dose or were not irradiated. In addition, DC-maturation markers CD80, CD83, and CD25 were also exclusively elevated after co-incubation with the SN of fractionated irradiated tumor cells. Furthermore, the SN of tumor cells that were irradiated with norm- or hypo-fractionated RT triggered iDC to stimulate CD4(+) T-cells not only in an allogenic, but also in an antigen-specific manner like mature DC. Collectively, these results demonstrate that norm- and hypo-fractionated RT induces a fast human colorectal tumor-cell death with immunogenic potential that can trigger DC maturation and activation in vitro. Such findings may contribute to the improvement of

  6. Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion.

    Science.gov (United States)

    Sun, Jiao-Jiao; Zhou, Shengwu; Zhang, Yan; Han, Miao; Wang, Fei

    2014-01-01

    The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed.

  7. Regularized Fractional Power Parameters for Image Denoising Based on Convex Solution of Fractional Heat Equation

    Directory of Open Access Journals (Sweden)

    Hamid A. Jalab

    2014-01-01

    Full Text Available The interest in using fractional mask operators based on fractional calculus operators has grown for image denoising. Denoising is one of the most fundamental image restoration problems in computer vision and image processing. This paper proposes an image denoising algorithm based on convex solution of fractional heat equation with regularized fractional power parameters. The performances of the proposed algorithms were evaluated by computing the PSNR, using different types of images. Experiments according to visual perception and the peak signal to noise ratio values show that the improvements in the denoising process are competent with the standard Gaussian filter and Wiener filter.

  8. Comparison of Radiation-Induced Bystander Effect in QU-DB Cells after Acute and Fractionated Irradiation: An In Vitro Study.

    Science.gov (United States)

    Soleymanifard, Shokouhozaman; Bahreyni Toossi, Mohammad Taghi; Kamran Samani, Roghayeh; Mohebbi, Shokoufeh

    2016-01-01

    Radiation effects induced in non-irradiated cells are termed radiation-induced bystander effects (RIBE). The present study intends to examine the RIBE response of QU-DB bystander cells to first, second and third radiation fractions and compare their cumulative outcome with an equal, single acute dose. This experimental study irradiated three groups of target cells for one, two and three times with(60)Co gamma rays. One hour after irradiation, we transferred their culture media to non-irradiated (bystander) cells. We used the cytokinesis block micronucleus assay to evaluate RIBE response in the bystander cells. The numbers of micronuclei generated in bystander cells were determined. RIBE response to single acute doses increased up to 4 Gy, then decreased, and finally at the 8 Gy dose disappeared. The second and third fractions induced RIBE in bystander cells, except when RIBE reached to the maximum level at the first fraction. We split the 4 Gy acute dose into two fractions, which decreased the RIBE response. However, fractionation of 6 Gy (into two fractions of 3 Gy or three fractions of 2 Gy) had no effect on RIBE response. When we split the 8 Gy acute dose into two fractions we observed RIBE, which had disappeared following the single 8 Gy dose. The impact of dose fractionation on RIBE induced in QU-DB cells de- pended on the RIBE dose-response relationship. Where RIBE increased proportion- ally with the dose, fractionation reduced the RIBE response. In contrast, at high dos- es where RIBE decreased proportionally with the dose, fractionation either did not change RIBE (at 6 Gy) or increased it (at 8 Gy).

  9. Improving Children’s Knowledge of Fraction Magnitudes

    Science.gov (United States)

    Fazio, Lisa K.; Kennedy, Casey A.; Siegler, Robert S.

    2016-01-01

    We examined whether playing a computerized fraction game, based on the integrated theory of numerical development and on the Common Core State Standards’ suggestions for teaching fractions, would improve children’s fraction magnitude understanding. Fourth and fifth-graders were given brief instruction about unit fractions and played Catch the Monster with Fractions, a game in which they estimated fraction locations on a number line and received feedback on the accuracy of their estimates. The intervention lasted less than 15 minutes. In our initial study, children showed large gains from pretest to posttest in their fraction number line estimates, magnitude comparisons, and recall accuracy. In a more rigorous second study, the experimental group showed similarly large improvements, whereas a control group showed no improvement from practicing fraction number line estimates without feedback. The results provide evidence for the effectiveness of interventions emphasizing fraction magnitudes and indicate how psychological theories and research can be used to evaluate specific recommendations of the Common Core State Standards. PMID:27768756

  10. Fractional variational principles in action

    Energy Technology Data Exchange (ETDEWEB)

    Baleanu, Dumitru [Department of Mathematics and Computer Science, Faculty of Art and Sciences, Cankaya University, 06530 Ankara (Turkey); Institute of Space Sciences, PO Box MG-23, R 76900, Magurele-Bucharest (Romania)], E-mail: dumitru@cankaya.edu.tr

    2009-10-15

    The fractional calculus has gained considerable importance in various fields of science and engineering, especially during the last few decades. An open issue in this emerging field is represented by the fractional variational principles area. Therefore, the fractional Euler-Lagrange and Hamilton equations started to be examined intensely during the last decade. In this paper, we review some new trends in this field and we discuss some of their potential applications.

  11. Optical image encryption using chaos-based compressed sensing and phase-shifting interference in fractional wavelet domain

    Science.gov (United States)

    Liu, Qi; Wang, Ying; Wang, Jun; Wang, Qiong-Hua

    2018-02-01

    In this paper, a novel optical image encryption system combining compressed sensing with phase-shifting interference in fractional wavelet domain is proposed. To improve the encryption efficiency, the volume data of original image are decreased by compressed sensing. Then the compacted image is encoded through double random phase encoding in asymmetric fractional wavelet domain. In the encryption system, three pseudo-random sequences, generated by three-dimensional chaos map, are used as the measurement matrix of compressed sensing and two random-phase masks in the asymmetric fractional wavelet transform. It not only simplifies the keys to storage and transmission, but also enhances our cryptosystem nonlinearity to resist some common attacks. Further, holograms make our cryptosystem be immune to noises and occlusion attacks, which are obtained by two-step-only quadrature phase-shifting interference. And the compression and encryption can be achieved in the final result simultaneously. Numerical experiments have verified the security and validity of the proposed algorithm.

  12. Fractionating power and outlet stream polydispersity in asymmetrical flow field-flow fractionation. Part I: isocratic operation.

    Science.gov (United States)

    Williams, P Stephen

    2016-05-01

    Asymmetrical flow field-flow fractionation (As-FlFFF) has become the most commonly used of the field-flow fractionation techniques. However, because of the interdependence of the channel flow and the cross flow through the accumulation wall, it is the most difficult of the techniques to optimize, particularly for programmed cross flow operation. For the analysis of polydisperse samples, the optimization should ideally be guided by the predicted fractionating power. Many experimentalists, however, neglect fractionating power and rely on light scattering detection simply to confirm apparent selectivity across the breadth of the eluted peak. The size information returned by the light scattering software is assumed to dispense with any reliance on theory to predict retention, and any departure of theoretical predictions from experimental observations is therefore considered of no importance. Separation depends on efficiency as well as selectivity, however, and efficiency can be a strong function of retention. The fractionation of a polydisperse sample by field-flow fractionation never provides a perfectly separated series of monodisperse fractions at the channel outlet. The outlet stream has some residual polydispersity, and it will be shown in this manuscript that the residual polydispersity is inversely related to the fractionating power. Due to the strong dependence of light scattering intensity and its angular distribution on the size of the scattering species, the outlet polydispersity must be minimized if reliable size data are to be obtained from the light scattering detector signal. It is shown that light scattering detection should be used with careful control of fractionating power to obtain optimized analysis of polydisperse samples. Part I is concerned with isocratic operation of As-FlFFF, and part II with programmed operation.

  13. Intelligent distributed control for nuclear power plants

    International Nuclear Information System (INIS)

    Klevans, E.H.

    1993-01-01

    This project was initiated in September 1989 as a three year project to develop and demonstrate Intelligent Distributed Control (IDC) for Nuclear Power Plants. There were two primary goals of this research project. The first goal was to combine diagnostics and control to achieve a highly automated power plant as described by M.A. Schultz. The second goal was to apply this research to develop a prototype demonstration on an actual power plant system, the EBR-2 steam plant. Described in this Final (Third Annual) Technical Progress Report is the accomplishment of the project's final milestone, an in-plant intelligent control experiment conducted on April 1, 1993. The development of the experiment included: simulation validation, experiment formulation and final programming, procedure development and approval, and experimental results. Other third year developments summarized in this report are: (1) a theoretical foundation for Reconfigurable Hybrid Supervisory Control, (2) a steam plant diagnostic system, (3) control console design tools and (4) other advanced and intelligent control

  14. Ultracentrifugation for ultrafine nanodiamond fractionation

    Science.gov (United States)

    Koniakhin, S. V.; Besedina, N. A.; Kirilenko, D. A.; Shvidchenko, A. V.; Eidelman, E. D.

    2018-01-01

    In this paper we propose a method for ultrafine fractionation of nanodiamonds using the differential centrifugation in the fields up to 215000g. The developed protocols yield 4-6 nm fraction giving main contribution to the light scattering intensity. The desired 4-6 nm fraction can be obtained from various types of initial nanodiamonds: three types of detonation nanodiamonds differing in purifying methods, laser synthesis nanodiamonds and nanodiamonds made by milling. The characterization of the obtained hydrosols was conducted with Dynamic Light Scattering, Zeta potential measurements, powder XRD and TEM. According to powder XRD and TEM data ultracentrifugation also leads to a further fractionation of the primary diamond nanocrystallites in the hydrosols from 4 to 2 nm.

  15. Airborne release fractions/rates and respirable fractions for nonreactor nuclear facilities. Volume 2, Appendices

    International Nuclear Information System (INIS)

    1994-12-01

    This document contains compiled data from the DOE Handbook on Airborne Release Fractions/Rates and Respirable Fractions for Nonreactor Nuclear facilities. Source data and example facilities utilized, such as the Plutonium Recovery Facility, are included

  16. Second Study of Hyper-Fractionated Radiotherapy

    Directory of Open Access Journals (Sweden)

    R. Jacob

    1999-01-01

    Full Text Available Purpose and Method. Hyper-fractionated radiotherapy for treatment of soft tissue sarcomas is designed to deliver a higher total dose of radiation without an increase in late normal tissue damage. In a previous study at the Royal Marsden Hospital, a total dose of 75 Gy using twice daily 1.25 Gy fractions resulted in a higher incidence of late damage than conventional radiotherapy using 2 Gy daily fractions treating to a total of 60 Gy. The current trial therefore used a lower dose per fraction of 1.2 Gy and lower total dose of 72 Gy, with 60 fractions given over a period of 6 weeks.

  17. Fractions Learning in Children With Mathematics Difficulties.

    Science.gov (United States)

    Tian, Jing; Siegler, Robert S

    Learning fractions is difficult for children in general and especially difficult for children with mathematics difficulties (MD). Recent research on developmental and individual differences in fraction knowledge of children with MD and typically achieving (TA) children has demonstrated that U.S. children with MD start middle school behind their TA peers in fraction understanding and fall further behind during middle school. In contrast, Chinese children, who like the MD children in the United States score in the bottom one third of the distribution in their country, possess reasonably good fraction understanding. We interpret these findings within the framework of the integrated theory of numerical development. By emphasizing the importance of fraction magnitude knowledge for numerical understanding in general, the theory proved useful for understanding differences in fraction knowledge between MD and TA children and for understanding how knowledge can be improved. Several interventions demonstrated the possibility of improving fraction magnitude knowledge and producing benefits that generalize to fraction arithmetic learning among children with MD. The reasonably good fraction understanding of Chinese children with MD and several successful interventions with U.S. students provide hope for the improvement of fraction knowledge among American children with MD.

  18. An Appetite for Fractions

    Science.gov (United States)

    Wilkerson, Trena L.; Bryan, Tommy; Curry, Jane

    2012-01-01

    This article describes how using candy bars as models gives sixth-grade students a taste for learning to represent fractions whose denominators are factors of twelve. Using paper models of the candy bars, students explored and compared fractions. They noticed fewer different representations for one-third than for one-half. The authors conclude…

  19. Fractional-order devices

    CERN Document Server

    Biswas, Karabi; Caponetto, Riccardo; Mendes Lopes, António; Tenreiro Machado, José António

    2017-01-01

    This book focuses on two specific areas related to fractional order systems – the realization of physical devices characterized by non-integer order impedance, usually called fractional-order elements (FOEs); and the characterization of vegetable tissues via electrical impedance spectroscopy (EIS) – and provides readers with new tools for designing new types of integrated circuits. The majority of the book addresses FOEs. The interest in these topics is related to the need to produce “analogue” electronic devices characterized by non-integer order impedance, and to the characterization of natural phenomena, which are systems with memory or aftereffects and for which the fractional-order calculus tool is the ideal choice for analysis. FOEs represent the building blocks for designing and realizing analogue integrated electronic circuits, which the authors believe hold the potential for a wealth of mass-market applications. The freedom to choose either an integer- or non-integer-order analogue integrator...

  20. Fractional Bateman—Feshbach Tikochinsky Oscillator

    Science.gov (United States)

    Dumitru, Baleanu; Jihad, H. Asad; Ivo, Petras

    2014-02-01

    In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these things in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman—Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grünwald—Letnikov approach, which is power series expansion of the generating function.

  1. On the Fractional Mean Value

    OpenAIRE

    Hosseinabadi, Abdolali Neamaty; Nategh, Mehdi

    2014-01-01

    This work, dealt with the classical mean value theorem and took advantage of it in the fractional calculus. The concept of a fractional critical point is introduced. Some sufficient conditions for the existence of a critical point is studied and an illustrative example rele- vant to the concept of the time dilation effect is given. The present paper also includes, some connections between convexity (and monotonicity) with fractional derivative in the Riemann-Liouville sense.

  2. A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

    Science.gov (United States)

    Bhrawy, A. H.; Zaky, M. A.

    2015-01-01

    In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.

  3. Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms

    Directory of Open Access Journals (Sweden)

    Abir Lassoued

    2017-01-01

    Full Text Available A novel hyperchaotic system with fractional-order (FO terms is designed. Its highly complex dynamics are investigated in terms of equilibrium points, Lyapunov spectrum, and attractor forms. It will be shown that the proposed system exhibits larger Lyapunov exponents than related hyperchaotic systems. Finally, to enhance its potential application, a related circuit is designed by using the MultiSIM Software. Simulation results verify the effectiveness of the suggested circuit.

  4. Fractional Euler Limits and Their Applications

    OpenAIRE

    MacNamara, Shev; Henry, Bruce I; McLean, William

    2016-01-01

    Generalisations of the classical Euler formula to the setting of fractional calculus are discussed. Compound interest and fractional compound interest serve as motivation. Connections to fractional master equations are highlighted. An application to the Schlogl reactions with Mittag-Leffler waiting times is described.

  5. The come-back of hypo fractionation?

    International Nuclear Information System (INIS)

    Cosset, J.M.

    2005-01-01

    Hypo-fractionation (i.e. the use of fewer higher fractional doses than usual) is not a new concept. It had actually been proposed in the early year of Radiotherapy by the German and Austrian specialists. In the seventy's, supported by the - wrong - hypotheses which gave birth to the NSD (Nominal Standard Dose), hypo-fractionation reappears. The consequential increase of late complications which was observed led the radiation oncologists to give up again using large doses per fraction, except for a few specific situations, such as palliative treatments. We are recently facing a new 'come-back' of hypo-fractionation, in particular for breast and prostate cancers. In the case of breast cancer, the aim is clearly to look for more 'convenience' for both the patients and the physicians, proposing shorter irradiation schedules including a lesser number of fractions. Some 'modestly' hypo-fractionated schemes have been proposed and used, without apparently altering the efficacy/toxicity ratio, but these results have been seriously questioned. As for prostate cancer, the situation is different, since in that case new radiobiological data are at the origin of the newly proposed hypo-fractionation schedules. A number of papers actually strongly suggested that the fractionation sensitivity of prostate cancer could be higher than the one of the tissues responsible for late toxicity (i.e the exact opposite of the classical dogma). Based on those data, several hypo-fractionated schemes have been proposed, with a few preliminary results looking similar to the ones obtained by the classical schedules. However, no randomized study is available so far, and a few recent radiobiological data are now questioning the new dogma of the high fractionation sensitivity of prostate cancer. For those two - frequent - cancers, it seems therefore that prudence should prevail before altering classical irradiation schedules which have proven their efficacy, while staying open to new concepts and

  6. Fractional Poisson process (II)

    International Nuclear Information System (INIS)

    Wang Xiaotian; Wen Zhixiong; Zhang Shiying

    2006-01-01

    In this paper, we propose a stochastic process W H (t)(H-bar (12,1)) which we call fractional Poisson process. The process W H (t) is self-similar in wide sense, displays long range dependence, and has more fatter tail than Gaussian process. In addition, it converges to fractional Brownian motion in distribution

  7. Momentum fractionation on superstrata

    International Nuclear Information System (INIS)

    Bena, Iosif; Martinec, Emil; Turton, David; Warner, Nicholas P.

    2016-01-01

    Superstrata are bound states in string theory that carry D1, D5, and momentum charges, and whose supergravity descriptions are parameterized by arbitrary functions of (at least) two variables. In the D1-D5 CFT, typical three-charge states reside in high-degree twisted sectors, and their momentum charge is carried by modes that individually have fractional momentum. Understanding this momentum fractionation holographically is crucial for understanding typical black-hole microstates in this system. We use solution-generating techniques to add momentum to a multi-wound supertube and thereby construct the first examples of asymptotically-flat superstrata. The resulting supergravity solutions are horizonless and smooth up to well-understood orbifold singularities. Upon taking the AdS_3 decoupling limit, our solutions are dual to CFT states with momentum fractionation. We give a precise proposal for these dual CFT states. Our construction establishes the very nontrivial fact that large classes of CFT states with momentum fractionation can be realized in the bulk as smooth horizonless supergravity solutions.

  8. Spectroscopy of fractional Josephson vortex molecules

    Energy Technology Data Exchange (ETDEWEB)

    Goldobin, Edward; Gaber, Tobias; Buckenmaier, Kai; Kienzle, Uta; Sickinger, Hanna; Koelle, Dieter; Kleiner, Reinhold [Physikalisches Institut - Experimentalphysik II, Center for Collective Quantum Phenomena, Universitaet Tuebingen, Auf der Morgenstelle 14, D-72076 Tuebingen (Germany)

    2010-07-01

    Using tiny current injectors we create {kappa} discontinuities of the Josephson phase in a long Josephson junction. The junction reacts at the discontinuities by creating fractional Josephson vortices of size {lambda}{sub J} pinned at them. Such vortices carry the flux {phi}, which is a fraction of the magnetic flux quantum {phi}{sub 0}{approx}2.07 x 10{sup -15} Wb. Being pinned, a fractional vortex has an eigenfrequency (localized mode), which depends on {kappa} and applied bias current, and which lays within the plasma gap. If one considers a molecule consisting of several coupled fractional vortices, the eigenfrequency will split into several modes. We report on spectroscopy of a fractional vortex molecule performed in the thermal regime.

  9. Nonlinear dynamics of fractional order Duffing system

    International Nuclear Information System (INIS)

    Li, Zengshan; Chen, Diyi; Zhu, Jianwei; Liu, Yongjian

    2015-01-01

    In this paper, we analyze the nonlinear dynamics of fractional order Duffing system. First, we present the fractional order Duffing system and the numerical algorithm. Second, nonlinear dynamic behaviors of Duffing system with a fixed fractional order is studied by using bifurcation diagrams, phase portraits, Poincare maps and time domain waveforms. The fractional order Duffing system shows some interesting dynamical behaviors. Third, a series of Duffing systems with different fractional orders are analyzed by using bifurcation diagrams. The impacts of fractional orders on the tendency of dynamical motion, the periodic windows in chaos, the bifurcation points and the distance between the first and the last bifurcation points are respectively studied, in which some basic laws are discovered and summarized. This paper reflects that the integer order system and the fractional order one have close relationship and an integer order system is a special case of fractional order ones.

  10. Fractional fermions

    International Nuclear Information System (INIS)

    Jackiw, R.; Massachusetts Inst. of Tech., Cambridge; Massachusetts Inst. of Tech., Cambridge

    1984-01-01

    The theory of fermion fractionization due to topologically generated fermion ground states is presented. Applications to one-dimensional conductors, to the MIT bag, and to the Hall effect are reviewed. (author)

  11. INDICATION OF INSENSITIVITY OF PLANETARY WEATHERING BEHAVIOR AND HABITABLE ZONE TO SURFACE LAND FRACTION

    International Nuclear Information System (INIS)

    Abbot, Dorian S.; Ciesla, Fred J.; Cowan, Nicolas B.

    2012-01-01

    It is likely that unambiguous habitable zone terrestrial planets of unknown water content will soon be discovered. Water content helps determine surface land fraction, which influences planetary weathering behavior. This is important because the silicate-weathering feedback determines the width of the habitable zone in space and time. Here a low-order model of weathering and climate, useful for gaining qualitative understanding, is developed to examine climate evolution for planets of various land-ocean fractions. It is pointed out that, if seafloor weathering does not depend directly on surface temperature, there can be no weathering-climate feedback on a waterworld. This would dramatically narrow the habitable zone of a waterworld. Results from our model indicate that weathering behavior does not depend strongly on land fraction for partially ocean-covered planets. This is powerful because it suggests that previous habitable zone theory is robust to changes in land fraction, as long as there is some land. Finally, a mechanism is proposed for a waterworld to prevent complete water loss during a moist greenhouse through rapid weathering of exposed continents. This process is named a 'waterworld self-arrest', and it implies that waterworlds can go through a moist greenhouse stage and end up as planets like Earth with partial ocean coverage. This work stresses the importance of surface and geologic effects, in addition to the usual incident stellar flux, for habitability.

  12. INDICATION OF INSENSITIVITY OF PLANETARY WEATHERING BEHAVIOR AND HABITABLE ZONE TO SURFACE LAND FRACTION

    Energy Technology Data Exchange (ETDEWEB)

    Abbot, Dorian S.; Ciesla, Fred J. [Department of the Geophysical Sciences, University of Chicago, 5734 South Ellis Avenue, Chicago, IL 60637 (United States); Cowan, Nicolas B., E-mail: abbot@uchicago.edu [Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, 2131 Tech Drive, Evanston, IL 60208 (United States)

    2012-09-10

    It is likely that unambiguous habitable zone terrestrial planets of unknown water content will soon be discovered. Water content helps determine surface land fraction, which influences planetary weathering behavior. This is important because the silicate-weathering feedback determines the width of the habitable zone in space and time. Here a low-order model of weathering and climate, useful for gaining qualitative understanding, is developed to examine climate evolution for planets of various land-ocean fractions. It is pointed out that, if seafloor weathering does not depend directly on surface temperature, there can be no weathering-climate feedback on a waterworld. This would dramatically narrow the habitable zone of a waterworld. Results from our model indicate that weathering behavior does not depend strongly on land fraction for partially ocean-covered planets. This is powerful because it suggests that previous habitable zone theory is robust to changes in land fraction, as long as there is some land. Finally, a mechanism is proposed for a waterworld to prevent complete water loss during a moist greenhouse through rapid weathering of exposed continents. This process is named a 'waterworld self-arrest', and it implies that waterworlds can go through a moist greenhouse stage and end up as planets like Earth with partial ocean coverage. This work stresses the importance of surface and geologic effects, in addition to the usual incident stellar flux, for habitability.

  13. Cesium distribution in the milling fractions of contaminated cereal crops: their decontamination, is it possible?

    International Nuclear Information System (INIS)

    Arapis, G.; Marti, J.M.; Gutierrez, J.; Kouskoutopoulos, A.

    1991-01-01

    A study of radioactivity transfer during an experimental milling of selected seeds of wheat and barley from Greek crops contaminated by the accident of Chernobyl was conducted. The Cs-137 and Ce-134 activities of the whole seeds, the flour fractions (three break and three reduction), the shorts and the bran were measured. The possibility of decontamination of seeds and bran was also investigated. The activity of whole seeds and bran, after cleaning with normal and saline (1M NaCl) water respectively, was measured. For wheat and barley, in both cases, the average activity concentration (Bq/g) of the 'reduction flour' fractions is about the half that of the whole seeds. Also, the average activity concentration for the total flours' fractions remains 60% less than the activity concentration of the whole seed. However, in the total 'break' and 'reduction' flour fractions only about 20% of the seed radioactivity remains. In the fraction of bran, the activity concentration appears to double the value of the seed and to be four times higher than the flours. After cleaning with normal water, the activity concentration in the whole seed was only 10% less than the original one. Finally, the activity concentration of bran after cleaning with saline water was reduced by a factor of 3 for wheat and of 2.4 for barley. But this diminution of activity concentration was found to represent only the 20% of the whole see activity. (author)

  14. Local control stations: Human engineering issues and insights

    International Nuclear Information System (INIS)

    Brown, W.S.; Higgins, J.C.; O'Hara, J.M.

    1994-09-01

    The objective of this research project was to evaluate current human engineering at local control stations (LCSs) in nuclear power plants, and to identify good human engineering practices relevant to the design of these operator interfaces. General literature and reports of operating experience were reviewed to determine the extent and type of human engineering deficiencies at LCSs in nuclear power plants. In-plant assessments were made of human engineering at single-function as well as multifunction LCSs. Besides confirming the existence of human engineering deficiencies at LCSs, the in-plant assessments provided information about the human engineering upgrades that have been made at nuclear power plants. Upgrades were typically the result of any of three influences regulatory activity, broad industry initiatives such as INPO, and specific in-plant programs (e.g. activities related to training). It is concluded that the quality of LCSs is quite variable and might be improved if there were greater awareness of good practices and existing human engineering guidance relevant to these operator interfaces, which is available from a variety of sources. To make such human engineering guidance more readily accessible, guidelines were compiled from such sources and included in the report as an appendix

  15. Fractional Calculus and Shannon Wavelet

    Directory of Open Access Journals (Sweden)

    Carlo Cattani

    2012-01-01

    Full Text Available An explicit analytical formula for the any order fractional derivative of Shannon wavelet is given as wavelet series based on connection coefficients. So that for any 2(ℝ function, reconstructed by Shannon wavelets, we can easily define its fractional derivative. The approximation error is explicitly computed, and the wavelet series is compared with Grünwald fractional derivative by focusing on the many advantages of the wavelet method, in terms of rate of convergence.

  16. Estimation of Multiple Point Sources for Linear Fractional Order Systems Using Modulating Functions

    KAUST Repository

    Belkhatir, Zehor

    2017-06-28

    This paper proposes an estimation algorithm for the characterization of multiple point inputs for linear fractional order systems. First, using polynomial modulating functions method and a suitable change of variables the problem of estimating the locations and the amplitudes of a multi-pointwise input is decoupled into two algebraic systems of equations. The first system is nonlinear and solves for the time locations iteratively, whereas the second system is linear and solves for the input’s amplitudes. Second, closed form formulas for both the time location and the amplitude are provided in the particular case of single point input. Finally, numerical examples are given to illustrate the performance of the proposed technique in both noise-free and noisy cases. The joint estimation of pointwise input and fractional differentiation orders is also presented. Furthermore, a discussion on the performance of the proposed algorithm is provided.

  17. Effect of experimentally observed hydrogenic fractionation on inertial confinement fusion ignition target performance

    International Nuclear Information System (INIS)

    McKenty, P. W.; Wittman, M. D.; Harding, D. R.

    2006-01-01

    The need of cryogenic hydrogenic fuels in inertial confinement fusion (ICF) ignition targets has been long been established. Efficient implosion of such targets has mandated keeping the adiabat of the main fuel layer at low levels to ensure drive energies are kept at reasonable minima. The use of cryogenic fuels helps meet this requirement and has therefore become the standard in most ICF ignition designs. To date most theoretical ICF ignition target designs have assumed a homogeneous layer of deuterium-tritium (DT) fuel kept slightly below the triple point. However, recent work has indicated that, as cryogenic fuel layers are formed inside an ICF capsule, isotopic dissociation of the tritium (T), deuterium (D), and DT takes place leading to a 'fractionation' of the final ice layer. This paper will numerically investigate the effects that various scenarios of fractionation have on hot-spot formation, ignition, and burn in ICF ignition target designs

  18. Comment on "Fractional quantum mechanics" and "Fractional Schrödinger equation".

    Science.gov (United States)

    Wei, Yuchuan

    2016-06-01

    In this Comment we point out some shortcomings in two papers [N. Laskin, Phys. Rev. E 62, 3135 (2000)10.1103/PhysRevE.62.3135; N. Laskin, Phys. Rev. E 66, 056108 (2002)10.1103/PhysRevE.66.056108]. We prove that the fractional uncertainty relation does not hold generally. The probability continuity equation in fractional quantum mechanics has a missing source term, which leads to particle teleportation, i.e., a particle can teleport from a place to another. Since the relativistic kinetic energy can be viewed as an approximate realization of the fractional kinetic energy, the particle teleportation should be an observable relativistic effect in quantum mechanics. With the help of this concept, superconductivity could be viewed as the teleportation of electrons from one side of a superconductor to another and superfluidity could be viewed as the teleportation of helium atoms from one end of a capillary tube to the other. We also point out how to teleport a particle to an arbitrary destination.

  19. Void fraction in horizontal bulk flow boiling at high flow qualities

    Energy Technology Data Exchange (ETDEWEB)

    Collado, Fancisco J.; Monne, Carlos [Dpto. de Ingenieria Mecanica, Universidad de Zaragoza-CPS, Maria de Luna 3, 50018-Zaragoza (Spain); Pascau, Antonio [Dpto. de Ciencia de los Materiales y Fluidos, Universidad de Zaragoza-CPS, Maria de Luna 3, 50018-Zaragoza (Spain)

    2008-04-15

    In this work, a new thermodynamic prediction of the vapor void fraction in bulk flow boiling, which is the core process of many energy conversion systems, is analyzed. The current heat balance is based on the flow quality, which is closely related to the measured void fraction, although some correlation for the vapor-liquid velocity ratio is needed. So here, it is suggested to work with the 'static' or thermodynamic quality, which is directly connected to the void fraction through the densities of the phases. Thus, the relation between heat and the mixture enthalpy (here based on the thermodynamic quality instead of the flow one) should be analyzed in depth. The careful void fraction data taken by Thom during the 'Cambridge project' for horizontal saturated flow boiling with high flow qualities ({<=}0.8) have been used for this analysis. As main results, first, we have found that the applied heat and the increment of the proposed thermodynamic enthalpy mixture throughout the heated duct do not agree, and for closure, a parameter is needed. Second, it has been checked that this parameter is practically equal to the classic velocity ratio or 'slip' ratio, suggesting that it should be included in a true thermodynamic heat balance. Furthermore, it has been clearly possible to improve the 'Cambridge project' correlations for the 'slip' ratio, here based on inlet pressure and water velocity, and heat flux. The calculated void fractions compare quite well with the measured ones. Finally, the equivalence of the suggested new heat balance with the current one through the 'slip' ratio is addressed. Highlighted is the same new energetic relation for saturated flow boiling that has been recently confirmed by the authors for Knights data, also taken during the 'Cambridge project', which include not only horizontal but also vertical upwards flows with moderate outlet flow quality ({<=}0.2). (author)

  20. Fractional CO2 Laser Resurfacing as Monotherapy in the Treatment of Atrophic Facial Acne Scars.

    Science.gov (United States)

    Majid, Imran; Imran, Saher

    2014-04-01

    While laser resurfacing remains the most effective treatment option for atrophic acne scars, the high incidence of post-treatment adverse effects limits its use. Fractional laser photothermolysis attempts to overcome these limitations of laser resurfacing by creating microscopic zones of injury to the dermis with skip areas in between. The aim of the present study is to assess the efficacy and safety of fractional CO2 laser resurfacing in atrophic facial acne scars. Sixty patients with moderate to severe atrophic facial acne scars were treated with 3-4 sessions of fractional CO2 laser resurfacing at 6-week intervals. The therapeutic response to treatment was assessed at each follow up visit and then finally 6 months after the last laser session using a quartile grading scale. Response to treatment was labelled as 'excellent' if there was >50% improvement in scar appearance and texture of skin on the grading scale while 25-50% response and resurfacing as monotherapy is effective in treating acne scars especially rolling and superficial boxcar scars with minimal adverse effects.

  1. Guaranteed Cost Finite-Time Control of Fractional-Order Positive Switched Systems

    Directory of Open Access Journals (Sweden)

    Leipo Liu

    2017-01-01

    Full Text Available The problem of guaranteed cost finite-time control of fractional-order positive switched systems (FOPSS is considered in this paper. Firstly, a new cost function is defined. Then, by constructing linear copositive Lyapunov functions and using the average dwell time (ADT approach, a state feedback controller and a static output feedback controller are constructed, respectively, and sufficient conditions are derived to guarantee that the corresponding closed-loop systems are guaranteed cost finite-time stable (GCFTS. Such conditions can be easily solved by linear programming. Finally, two examples are given to illustrate the effectiveness of the proposed method.

  2. Fractional charge definitions and conditions

    International Nuclear Information System (INIS)

    Goldhaber, Alfred Scharff

    2003-01-01

    The phenomenon of fractional charge has come to prominence in recent decades through theoretical and experimental discoveries of isolable objects which carry fractions of familiar charge units--electric charge Q, spin S, baryon number B and lepton number L. It is shown here on the basis of a few simple assumptions that all these effects may be described using a generalized version of charge renormalization for locally conserved charges, in which many-body correlations can produce familiar adiabatic, continuous renormalization, and in some circumstances nonadiabatic, discrete renormalization. The fractional charges may be carried either by fundamental particles or by fundamental solitons. This excludes nontopological solitons and also skyrmions: The only known fundamental solitons in three or fewer space dimensions d are the kink (d=1), the vortex (d=2), and the magnetic monopole (d=3). Further, for a charge which is not intrinsically coupled to the topological charge of a soliton, only the kink and the monopole may carry fractional values. The same reasoning enforces fractional local values of B-L for electrically charged elementary particles

  3. Distributed-order fractional diffusions on bounded domains

    OpenAIRE

    Meerschaert, Mark M.; Nane, Erkan; Vellaisamy, P.

    2011-01-01

    In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. The fractional derivative models time delays in a diffusion process. The order of the fractional derivative can be distributed over the unit interval, to model a mixture of delay sources. In this paper, we provide explicit strong solutions and stochastic analogues for distributed-order fractional Cauchy problems on bounded domains with Dirichlet boundary conditions. Stochastic solutio...

  4. Fractional RC and LC Electrical Circuits

    Directory of Open Access Journals (Sweden)

    Gómez-Aguilar José Francisco

    2014-04-01

    Full Text Available In this paper we propose a fractional differential equation for the electrical RC and LC circuit in terms of the fractional time derivatives of the Caputo type. The order of the derivative being considered is 0 < ɣ ≤1. To keep the dimensionality of the physical parameters R, L, C the new parameter σ is introduced. This parameter characterizes the existence of fractional structures in the system. A relation between the fractional order time derivative ɣ and the new parameter σ is found. The numeric Laplace transform method was used for the simulation of the equations results. The results show that the fractional differential equations generalize the behavior of the charge, voltage and current depending of the values of ɣ. The classical cases are recovered by taking the limit when ɣ = 1. An analysis in the frequency domain of an RC circuit shows the application and use of fractional order differential equations.

  5. Adaptive neural network backstepping control for a class of uncertain fractional-order chaotic systems with unknown backlash-like hysteresis

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Yimin [School of Mathematics and Statistics, Suzhou University, Suzhou 234000 (China); Lv, Hui, E-mail: lvhui207@gmail.com [Department of Applied Mathematics, Huainan Normal University, Huainan 232038 (China)

    2016-08-15

    In this paper, we consider the control problem of a class of uncertain fractional-order chaotic systems preceded by unknown backlash-like hysteresis nonlinearities based on backstepping control algorithm. We model the hysteresis by using a differential equation. Based on the fractional Lyapunov stability criterion and the backstepping algorithm procedures, an adaptive neural network controller is driven. No knowledge of the upper bound of the disturbance and system uncertainty is required in our controller, and the asymptotical convergence of the tracking error can be guaranteed. Finally, we give two simulation examples to confirm our theoretical results.

  6. Limited Intervention at Sub Concept of Fractions in the Object Conversion into Fractions

    Science.gov (United States)

    Kurniawan, Henry; Nusantara, Toto; Subanji; Susiswo; Setiawan, Iwan; Sutawidjaja, Akbar; As'ari, Abdur Rahman; Muksar, Makbul

    2016-01-01

    This research is an exploratory study with a qualitative approach, which is based on interviews with a task-based the purpose of this study is to describe the understanding of elementary school students in interpreting sub concept fractions in changing of the object is given to fractions with limit intervention. While intervention on problems…

  7. Utilization of Different Corn Fractions by Broilers

    Directory of Open Access Journals (Sweden)

    SIFR Costa

    2015-09-01

    Full Text Available ABSTRACTThis study was conducted to evaluate the nutritional values of fractions of damaged corn. One hundred and eighty 22-d-old Cobb 500 male broilers were distributed in batteries according to a completely randomized design with six treatments of six replicates each. The treatments consisted of diets containing five corn fractions, classified as sound, fermented, insect-damaged, mold-damaged, or reference corn. The test diets consisted of 60% of reference diet + 40% of each corn fraction. Only the reference corn fraction included all the fractions at different proportions (0.8% fermented, 0.05% insect-damaged, 3.3% mold-damaged, and 95.85% sound grains. The method of total excreta collection was used to determine AMEn values and metabolizability coefficients of dry matter (MDM, crude protein (MCP, ether extract (MEE, and gross energy (MGE of the reference corn and its fractions. The density values of the corn fractions were used to calculate the correlations among the evaluated parameters. The evaluated corn fractions presented different compositions values. The insect-damaged and mold-damaged grains presented higher CP level, lower density, and MDM and MCP coefficients compared with the other fractions. However, calculated AMEn values were not significantly different (p>0.05 among corn fractions. A low correlation between density and AMEn content (r0.8 were calculated. Although the evaluated corn fractions presented different nutritional values, there were no marked differences in their utilization by broilers.

  8. Teaching Fractions. Educational Practices Series-22

    Science.gov (United States)

    Fazio, Lisa; Siegler, Robert

    2011-01-01

    Students around the world have difficulties in learning about fractions. In many countries, the average student never gains a conceptual knowledge of fractions. This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on a…

  9. Fractional Bateman—Feshbach Tikochinsky Oscillator

    International Nuclear Information System (INIS)

    Baleanu, Dumitru; Asad, Jihad H.; Petras Ivo

    2014-01-01

    In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these things in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman—Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grünwald—Letnikov approach, which is power series expansion of the generating function. (physics of elementary particles and fields)

  10. Fractional Bhatnagar-Gross-Krook kinetic equation

    Science.gov (United States)

    Goychuk, Igor

    2017-11-01

    The linear Boltzmann equation (LBE) approach is generalized to describe fractional superdiffusive transport of the Lévy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and infinite variance. It is completely characterized by the two scattering rates, one fractional and a normal one, which defines also the mean scattering rate. We formulate a general fractional LBE approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral leading to a fractional generalization of the Bhatnagar, Gross and Krook (BGK) kinetic equation. Here, at each scattering event the particle velocity is completely randomized and takes a value from equilibrium Maxwell distribution at a given fixed temperature. We show that the retardation effects are indispensable even in the limit of infinite mean scattering rate and argue that this novel fractional kinetic equation provides a viable alternative to the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and its generalization by Friedrich et al. based on the picture of divergent mean time between scattering events. The case of divergent mean time is also discussed at length and compared with the earlier results obtained within the fractional KFP. Also a phenomenological fractional BGK equation without retardation effects is proposed in the limit of infinite scattering rates. It cannot be, however, rigorously derived from a scattering model, being rather clever postulated. It this respect, this retardationless equation is similar to the fractional KFP by Barkai and Silbey. However, it corresponds to the opposite, much more physical limit and, therefore, also presents a viable alternative.

  11. Integro-differential equations of fractional order with nonlocal fractional boundary conditions associated with financial asset model

    Directory of Open Access Journals (Sweden)

    Bashir Ahmad

    2013-02-01

    Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented.

  12. On fractal space-time and fractional calculus

    Directory of Open Access Journals (Sweden)

    Hu Yue

    2016-01-01

    Full Text Available This paper gives an explanation of fractional calculus in fractal space-time. On observable scales, continuum models can be used, however, when the scale tends to a smaller threshold, a fractional model has to be adopted to describe phenomena in micro/nano structure. A time-fractional Fornberg-Whitham equation is used as an example to elucidate the physical meaning of the fractional order, and its solution process is given by the fractional complex transform.

  13. Electronic realization of the fractional-order systems

    Directory of Open Access Journals (Sweden)

    Františka Dorčáková

    2007-10-01

    Full Text Available This article is devoted to the electronic (analogue realization of the fractional-order systems – controllers or controlled objects whose we earlier used, identified, and analyzed as a mathematical models only ��� namely a fractional-order differential equation, and solved numerically using a method based on the truncated version of the Grunwald - Letnikov formula for fractional derivative. The electronic realization of the fractional derivative is based on the continued fraction expansion of the rational approximation of the fractional differentiator from which we obtained the values of the resistors and capacitors of the electronic circuit. Along with the mathematical description are presented also simulation and measurement results.

  14. On generalized fractional vibration equation

    International Nuclear Information System (INIS)

    Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

    2017-01-01

    Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

  15. Comparisons of Modeling and State of Charge Estimation for Lithium-Ion Battery Based on Fractional Order and Integral Order Methods

    Directory of Open Access Journals (Sweden)

    Renxin Xiao

    2016-03-01

    Full Text Available In order to properly manage lithium-ion batteries of electric vehicles (EVs, it is essential to build the battery model and estimate the state of charge (SOC. In this paper, the fractional order forms of Thevenin and partnership for a new generation of vehicles (PNGV models are built, of which the model parameters including the fractional orders and the corresponding resistance and capacitance values are simultaneously identified based on genetic algorithm (GA. The relationships between different model parameters and SOC are established and analyzed. The calculation precisions of the fractional order model (FOM and integral order model (IOM are validated and compared under hybrid test cycles. Finally, extended Kalman filter (EKF is employed to estimate the SOC based on different models. The results prove that the FOMs can simulate the output voltage more accurately and the fractional order EKF (FOEKF can estimate the SOC more precisely under dynamic conditions.

  16. Complexified quantum field theory and 'mass without mass' from multidimensional fractional actionlike variational approach with dynamical fractional exponents

    International Nuclear Information System (INIS)

    El-Nabulsi, Ahmad Rami

    2009-01-01

    Multidimensional fractional actionlike variational problem with time-dependent dynamical fractional exponents is constructed. Fractional Euler-Lagrange equations are derived and discussed in some details. The results obtained are used to explore some novel aspects of fractional quantum field theory where many interesting consequences are revealed, in particular the complexification of quantum field theory, in particular Dirac operators and the novel notion of 'mass without mass'.

  17. Fractionalizing Majorana Fermions: Non-Abelian Statistics on the Edges of Abelian Quantum Hall States

    Directory of Open Access Journals (Sweden)

    Netanel H. Lindner

    2012-10-01

    Full Text Available We study the non-Abelian statistics characterizing systems where counterpropagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity coupling to superconductors and ferromagnets. The most transparent example is that of a fractional quantum spin Hall state, in which electrons of one spin direction occupy a fractional quantum Hall state of ν=1/m, while electrons of the opposite spin occupy a similar state with ν=-1/m. However, we also propose other examples of such systems, which are easier to realize experimentally. We find that each interface between a region on the edge coupled to a superconductor and a region coupled to a ferromagnet corresponds to a non-Abelian anyon of quantum dimension sqrt[2m]. We calculate the unitary transformations that are associated with the braiding of these anyons, and we show that they are able to realize a richer set of non-Abelian representations of the braid group than the set realized by non-Abelian anyons based on Majorana fermions. We carry out this calculation both explicitly and by applying general considerations. Finally, we show that topological manipulations with these anyons cannot realize universal quantum computation.

  18. Isotope fractionation during the anaerobic consumption of acetate by methanogenic and sulfate-reducing microorganisms

    Science.gov (United States)

    Gövert, D.; Conrad, R.

    2009-04-01

    During the anaerobic degradation of organic matter in anoxic sediments and soils acetate is the most important substrate for the final step in production of CO2 and/or CH4. Sulfate-reducing bacteria (SRB) and methane-producing archaea both compete for the available acetate. Knowledge about the fractionation of 13C/12C of acetate carbon by these microbial groups is still limited. Therefore, we determined carbon isotope fractionation in different cultures of acetate-utilizing SRB (Desulfobacter postgatei, D. hydrogenophilus, Desulfobacca acetoxidans) and methanogens (Methanosarcina barkeri, M. acetivorans). Including literature values (e.g., Methanosaeta concilii), isotopic enrichment factors (epsilon) ranged between -35 and +2 permil, possibly involving equilibrium isotope effects besides kinetic isotope effects. The values of epsilon were dependent on the acetate-catabolic pathway of the particular microorganism, the methyl or carboxyl position of acetate, and the relative availability or limitation of the substrate acetate. Patterns of isotope fractionation in anoxic lake sediments and rice field soil seem to reflect the characteristics of the microorganisms actively involved in acetate catabolism. Hence, it might be possible using environmental isotopic information to determine the type of microbial metabolism converting acetate to CO2 and/or CH4.

  19. nduced hyperlipidemic rats. Methods: Column chromatographic fractionation of butanol fraction of total methanol extract of leaves of Bauhinia variegata (Linn. yields four sub-fractions (sub-fraction A-D. All sub-fractions tested for their anti-hyperlipidemic activity. Sub-fractions administered at a dose of 65 mg/kg (oral to the Triton WR-1339 induced hyperlipidemic rats and total cholesterol, triglycerides, HDL, LDL and VLDL

    Directory of Open Access Journals (Sweden)

    Deepak Kumar

    2012-10-01

    Full Text Available Objective: To investigate the effect and evaluation of Anti-hyperlipidemic activity guided subfraction isolated from total methanolic extract of Bauhinia variegata (Linn. leaves on Triton WR-1339 induced hyperlipidemic rats. Methods: Column chromatographic fractionation of butanol fraction of total methanol extract of leaves of Bauhinia variegata (Linn. yields four subfractions (sub-fraction A-D. All sub-fractions tested for their anti-hyperlipidemic activity. Subfractions administered at a dose of 65 mg/kg (oral to the Triton WR-1339 induced hyperlipidemic rats and total cholesterol, triglycerides, HDL, LDL and VLDL level in the blood were checked. Results: Sub-fraction D showed significant reduction (P<0.05 among four sub-fraction in comparison with standard drug fenofibrate. Conclusions: From the above study it could be concluded that butanol sub-fraction D of Bauhinia variegata (Linn. not only have resulted in significant reduction in cholesterol, triglyceride, LDL, VLDL level but also increases the HDL level at a reduced dose level.

  20. Combining electrophoresis with detection under ultraviolet light and multiple ultrafiltration for isolation of humic fluorescence fractions.

    Science.gov (United States)

    Trubetskaya, Olga E; Shaloiko, Lubov A; Demin, Dmitrii V; Marchenkov, Victor V; Proskuryakov, Ivan I; Coelho, Christian; Trubetskoj, Oleg A

    2011-04-01

    Polyacrylamide gel electrophoresis of chernozem soil humic acids (HAs) followed by observation under UV (312 nm) excitation light reveals new low molecular weight (MW) fluorescent fractions. Ultrafiltration of HAs sample in 7 M urea on a membrane of low nominal MW retention (NMWR, 5 kDa) was repetitively used for separation of fluorescent and non-fluorescent species. Thirty ultrafiltrates and the final retentate R were obtained. Fluorescence maxima of separate ultrafiltrates were different and non-monotonously changed in the range of 475-505 nm. Fluorescence maxima of less than 490 nm were detected only in the four first utrafiltrates. For further physical-chemical analyses all utrafiltrates were combined into a fraction called UFchernozem soil HAs complex. Copyright © 2011 Elsevier B.V. All rights reserved.

  1. Propagation of registration uncertainty during multi-fraction cervical cancer brachytherapy

    Science.gov (United States)

    Amir-Khalili, A.; Hamarneh, G.; Zakariaee, R.; Spadinger, I.; Abugharbieh, R.

    2017-10-01

    Multi-fraction cervical cancer brachytherapy is a form of image-guided radiotherapy that heavily relies on 3D imaging during treatment planning, delivery, and quality control. In this context, deformable image registration can increase the accuracy of dosimetric evaluations, provided that one can account for the uncertainties associated with the registration process. To enable such capability, we propose a mathematical framework that first estimates the registration uncertainty and subsequently propagates the effects of the computed uncertainties from the registration stage through to the visualizations, organ segmentations, and dosimetric evaluations. To ensure the practicality of our proposed framework in real world image-guided radiotherapy contexts, we implemented our technique via a computationally efficient and generalizable algorithm that is compatible with existing deformable image registration software. In our clinical context of fractionated cervical cancer brachytherapy, we perform a retrospective analysis on 37 patients and present evidence that our proposed methodology for computing and propagating registration uncertainties may be beneficial during therapy planning and quality control. Specifically, we quantify and visualize the influence of registration uncertainty on dosimetric analysis during the computation of the total accumulated radiation dose on the bladder wall. We further show how registration uncertainty may be leveraged into enhanced visualizations that depict the quality of the registration and highlight potential deviations from the treatment plan prior to the delivery of radiation treatment. Finally, we show that we can improve the transfer of delineated volumetric organ segmentation labels from one fraction to the next by encoding the computed registration uncertainties into the segmentation labels.

  2. Constraints on exclusive branching fractions Bi(B+ → Xcil+ν) from moment measurements in inclusive B → Xclν decays

    International Nuclear Information System (INIS)

    Bernlochner, Florian U.; Lueck, Thomas; Biedermann, Dustin; Lacker, Heiko

    2014-01-01

    As an alternative to direct measurements, we extract the branching fractions B i (B + → X c i l + ν) with X c i = D, D * , D 0 , D 1 ' , D 1 , D 2 , D ' , D '* and non-resonant final states (D (*) π) nr , from a fit to electron energy, hadronic mass and combined hadronic mass.energy moments measured in inclusive B → X c lν decays. The fit is performed by constraining the sum of exclusive branching fractions to the measured B(B + → X c l + ν) value, and with different sets of additional constraints for the directly measured branching fractions. There is no fit scenario in which a single branching fraction can close the gap between B(B + → X c l + ν) and the sum of known branching fractions B i (B + → X c i l + ν). The fitted B(B + → anti D *0 l + ν) is found to be significantly larger than its direct measurement. B(B + → anti D 0 l + ν) is in good agreement with the direct measurement; when B(B + → anti D *0 l + ν) is constrained the fitted B(B + → anti D 0 l + ν) increases. Within large uncertainties, B(B + → anti D 1 '0 l + ν) agrees with direct measurements. Depending on the fit scenario, B(B + → anti D 0 0 l + ν) is consistent with or larger than its direct measurement. The fit is not able to easily disentangle B + → anti D 1 0 l + ν and B + → anti D 2 0 l + ν, and tends to increase the sum of these two branching fractions. B(B + → (D (*) π) nr l + ν) with nonresonant (D (*) π) nr final states is found to be of the order 0.3 %. No indication is found for significant contributions from so far unmeasured B + → anti D '(*)0 l + ν decays. (orig.)

  3. Some composition formulae for the M-S-M fractional integral operator with the multi-index Mittag-Leffler functions

    Science.gov (United States)

    Jain, Shilpi; Agarwal, Praveen; Kıymaz, I. Onur; ćetinkaya, Ayá¹£egül

    2018-01-01

    Authors presented some composition formulae for the Marichev-Saigo-Maeda (M-S-M) fractional integral operator with the multi-index Mittag-Leffler functions. Our results are generalizes the results obtained by Choi and Agarwal [3]. Here, we record some particular cases of our main result. Finally, we obtain Laplace transforms of the composition formulae.

  4. On the first crossing distributions in fractional Brownian motion and the mass function of dark matter haloes

    Energy Technology Data Exchange (ETDEWEB)

    Hiotelis, Nicos [1st Lyceum of Athens, Ipitou 15, Plaka, 10557, Athens (Greece); Popolo, Antonino Del, E-mail: adelpopolo@oact.inaf.it, E-mail: hiotelis@ipta.demokritos.gr [Dipartimento di Fisica e Astronomia, University Of Catania, Viale Andrea Doria 6, 95125, Catania (Italy)

    2017-03-01

    We construct an integral equation for the first crossing distributions for fractional Brownian motion in the case of a constant barrier and we present an exact analytical solution. Additionally we present first crossing distributions derived by simulating paths from fractional Brownian motion. We compare the results of the analytical solutions with both those of simulations and those of some approximated solutions which have been used in the literature. Finally, we present multiplicity functions for dark matter structures resulting from our analytical approach and we compare with those resulting from N-body simulations. We show that the results of analytical solutions are in good agreement with those of path simulations but differ significantly from those derived from approximated solutions. Additionally, multiplicity functions derived from fractional Brownian motion are poor fits of the those which result from N-body simulations. We also present comparisons with other models which are exist in the literature and we discuss different ways of improving the agreement between analytical results and N-body simulations.

  5. Chaos Suppression of an Electrically Actuated Microresonator Based on Fractional-Order Nonsingular Fast Terminal Sliding Mode Control

    Directory of Open Access Journals (Sweden)

    Jianxin Han

    2017-01-01

    Full Text Available This paper focuses on chaos suppression strategy of a microresonator actuated by two symmetrical electrodes. Dynamic behavior of this system under the case where the origin is the only stable equilibrium is investigated first. Numerical simulations reveal that system may exhibit chaotic motion under certain excitation conditions. Then, bifurcation diagrams versus amplitude or frequency of AC excitation are drawn to grasp system dynamics nearby its natural frequency. Results show that the vibration is complex and may exhibit period-doubling bifurcation, chaotic motion, or dynamic pull-in instability. For the suppression of chaos, a novel control algorithm, based on an integer-order nonsingular fast terminal sliding mode and a fractional-order switching law, is proposed. Fractional Lyapunov Stability Theorem is used to guarantee the asymptotic stability of the system. Finally, numerical results with both fractional-order and integer-order control laws show that our proposed control law is effective in controlling chaos with system uncertainties and external disturbances.

  6. Determination of hepatic fractional clearance of radioactive gold colloids for a measure of effective hepatic blood flow

    International Nuclear Information System (INIS)

    Fujii, Masahiro

    1979-01-01

    For a measure of effective blood flow, a hepatic fractional clearance of 198 Au-colloids was determined, which was obtained from the disappearance rate multiplied by the fraction of injected dose taken up by the liver. The hepatic uptake was determined with a gamma camera. The counts over the liver was corrected for body weight and height. The method was considered sufficiently simple for routine use. 198 Au-colloids were obtained from Dainabot Lab. and CIS. The former gave 64% higher values of disappearance rate than the latter, without any change in the organ distribution. A quality control tests were applied over a six-year period to the disappearance rates. Reproducibility within 95 to confidence limits was found for both groups. In 28 normal control subjects, hepatic fractional clearance of the colloids from Dainabot Lab. was 18.5 +- 3.4%/min. In patients with progressed hepatic disease, both hepatic fractional clearance and final hepatic uptake were decreased, showing that the determination of hepatic uptake is necessary in measuring effective hepatic blood flow by the colloidal clearance method. The influence of splenic uptake is discussed in relation to hepatic blood flow measurement. (author)

  7. Single fraction versus multiple fraction radiotherapy for palliation of painful vertebral bone metastases: A prospective study

    Directory of Open Access Journals (Sweden)

    Dipanjan Majumder

    2012-01-01

    Conclusions: Different fractionation of radiation has same response and toxicity in treatment of vertebral bone metastasis. Single fraction RT may be safely used to treat these cases as this is more cost effective and less time consuming. Studies may be conducted to find out particular subgroup of patients to be benefitted more by either fractionation schedule; however, our study cannot comment on that issue.

  8. Parameters and Fractional Differentiation Orders Estimation for Linear Continuous-Time Non-Commensurate Fractional Order Systems

    KAUST Repository

    Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem

    2017-01-01

    This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.

  9. Parameters and Fractional Differentiation Orders Estimation for Linear Continuous-Time Non-Commensurate Fractional Order Systems

    KAUST Repository

    Belkhatir, Zehor

    2017-05-31

    This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.

  10. Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries.

    Science.gov (United States)

    Jeon, Jae-Hyung; Metzler, Ralf

    2010-02-01

    Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.

  11. Test of equal effect per fraction and estimation of initial clonogen number in microcolony assays of survival after fractionated irradiation

    International Nuclear Information System (INIS)

    Thames, H.D.; Withers, H.R.

    1980-01-01

    In the use of multifraction microcolony assays to infer the low-dose response of in situ renewal systems such as intestinal crypts, the assumption of equal effect per dose fraction is required. Moreover, the construction of a cell-survival curve requires knowledge of the initial count of cells capable of repopulating each renewal structure. We describe a method of designing fractionation protocols which provides a regression estimate of the initial number of clonogens per renewal structure and a test of the hypothesis of equal effect per fraction. The essential factor in the experimental design is the use of common dose fractions (use of the same dose per fraction in series with different numbers of fractions). Applications of the method to data for which the assumption of equal effect per fraction holds (four-hour fractionation interval murine testis study) and does not hold (one-hour fractionation interval murine jejunal crypt study) are presented. (author)

  12. On the fractional calculus of Besicovitch function

    International Nuclear Information System (INIS)

    Liang Yongshun

    2009-01-01

    Relationship between fractional calculus and fractal functions has been explored. Based on prior investigations dealing with certain fractal functions, fractal dimensions including Hausdorff dimension, Box dimension, K-dimension and Packing dimension is shown to be a linear function of order of fractional calculus. Both Riemann-Liouville fractional calculus and Weyl-Marchaud fractional derivative of Besicovitch function have been discussed.

  13. Bio-oil fractionation and condensation

    Science.gov (United States)

    Brown, Robert C; Jones, Samuel T; Pollard, Anthony

    2013-07-02

    A method of fractionating bio-oil vapors which involves providing bio-oil vapors comprising bio-oil constituents is described. The bio-oil vapors are cooled in a first stage which comprises a condenser having passages for the bio-oil separated by a heat conducting wall from passages for a coolant. The coolant in the condenser of the first stage is maintained at a substantially constant temperature, set at a temperature in the range of 75 to 100.degree. C., to condense a first liquid fraction of liquefied bio-oil constituents in the condenser of the first stage. The first liquid fraction of liquified bio-oil constituents from the condenser in the first stage is collected. Also described are steps for subsequently recovering further liquid fractions of liquefied bio-oil constituents. Particular compositions of bio-oil condensation products are also described.

  14. On Generalized Fractional Differentiator Signals

    Directory of Open Access Journals (Sweden)

    Hamid A. Jalab

    2013-01-01

    Full Text Available By employing the generalized fractional differential operator, we introduce a system of fractional order derivative for a uniformly sampled polynomial signal. The calculation of the bring in signal depends on the additive combination of the weighted bring-in of N cascaded digital differentiators. The weights are imposed in a closed formula containing the Stirling numbers of the first kind. The approach taken in this work is to consider that signal function in terms of Newton series. The convergence of the system to a fractional time differentiator is discussed.

  15. Adaptive Synchronization of Fractional Order Complex-Variable Dynamical Networks via Pinning Control

    Science.gov (United States)

    Ding, Da-Wei; Yan, Jie; Wang, Nian; Liang, Dong

    2017-09-01

    In this paper, the synchronization of fractional order complex-variable dynamical networks is studied using an adaptive pinning control strategy based on close center degree. Some effective criteria for global synchronization of fractional order complex-variable dynamical networks are derived based on the Lyapunov stability theory. From the theoretical analysis, one concludes that under appropriate conditions, the complex-variable dynamical networks can realize the global synchronization by using the proper adaptive pinning control method. Meanwhile, we succeed in solving the problem about how much coupling strength should be applied to ensure the synchronization of the fractional order complex networks. Therefore, compared with the existing results, the synchronization method in this paper is more general and convenient. This result extends the synchronization condition of the real-variable dynamical networks to the complex-valued field, which makes our research more practical. Finally, two simulation examples show that the derived theoretical results are valid and the proposed adaptive pinning method is effective. Supported by National Natural Science Foundation of China under Grant No. 61201227, National Natural Science Foundation of China Guangdong Joint Fund under Grant No. U1201255, the Natural Science Foundation of Anhui Province under Grant No. 1208085MF93, 211 Innovation Team of Anhui University under Grant Nos. KJTD007A and KJTD001B, and also supported by Chinese Scholarship Council

  16. Resonant spin-flavor conversion of supernova neutrinos: Dependence on electron mole fraction

    International Nuclear Information System (INIS)

    Yoshida, Takashi; Takamura, Akira; Kimura, Keiichi; Yokomakura, Hidekazu; Kawagoe, Shio; Kajino, Toshitaka

    2009-01-01

    Detailed dependence of resonant spin-flavor (RSF) conversion of supernova neutrinos on electron mole fraction Y e is investigated. Supernova explosion forms a hot-bubble and neutrino-driven wind region of which electron mole fraction exceeds 0.5 in several seconds after the core collapse. When a higher resonance of the RSF conversion is located in the innermost region, flavor change of the neutrinos strongly depends on the sign of 1-2Y e . At an adiabatic high RSF resonance the flavor conversion of ν e ↔ν μ,τ occurs in Y e e >0.5 and inverted mass hierarchy. In other cases of Y e values and mass hierarchies, the conversion of ν e ↔ν μ,τ occurs. The final ν e spectrum is evaluated in the cases of Y e e >0.5 taking account of the RSF conversion. Based on the obtained result, time variation of the event number ratios of low ν e energy to high ν e energy is discussed. In normal mass hierarchy, an enhancement of the event ratio should be seen in the period when the electron fraction in the innermost region exceeds 0.5. In inverted mass hierarchy, on the other hand, a dip of the event ratio should be observed. Therefore, the time variation of the event number ratio is useful to investigate the effect of the RSF conversion.

  17. Generalized variational formulations for extended exponentially fractional integral

    Directory of Open Access Journals (Sweden)

    Zuo-Jun Wang

    2016-01-01

    Full Text Available Recently, the fractional variational principles as well as their applications yield a special attention. For a fractional variational problem based on different types of fractional integral and derivatives operators, corresponding fractional Lagrangian and Hamiltonian formulation and relevant Euler–Lagrange type equations are already presented by scholars. The formulations of fractional variational principles still can be developed more. We make an attempt to generalize the formulations for fractional variational principles. As a result we obtain generalized and complementary fractional variational formulations for extended exponentially fractional integral for example and corresponding Euler–Lagrange equations. Two illustrative examples are presented. It is observed that the formulations are in exact agreement with the Euler–Lagrange equations.

  18. The application of the linear-quadratic model to fractionated radiotherapy when there is incomplete normal tissue recovery between fractions, and possible implications for treatments involving multiple fractions per day

    International Nuclear Information System (INIS)

    Dale, R.G.

    1986-01-01

    By extending a previously developed mathematical model based on the linear-quadratic dose-effect relationship, it is possible to examine the consequences of performing fractionated treatments for which there is insufficient time between fractions to allow complete damage repair. Equations are derived which give the relative effectiveness of such treatments in terms of tissue-repair constants (μ values) and α/β ratios, and these are then applied to some examples of treatments involving multiple fractions per day. The interplay of the various mechanisms involved (including repopulation effects) and their possible influence on treatments involving closely spaced fractions are examined. If current indications of the differences in recovery rates between early- and late-reacting normal tissues are representative, then it is shown that such differences may limit the clinical potential of accelerated fractionation regimes, where several fractions per day are given in a relatively short overall time. (author)

  19. Adaptive fractionation therapy: I. Basic concept and strategy

    International Nuclear Information System (INIS)

    Lu Weiguo; Chen Mingli; Chen Quan; Ruchala, Kenneth; Olivera, Gustavo

    2008-01-01

    Radiotherapy is fractionized to increase the therapeutic ratio. Fractionation in conventional treatment is determined as part of the prescription, and a fixed fraction size is used for the whole course of treatment. Due to patients' day-to-day variations on the relative distance between the tumor and the organs at risk (OAR), a better therapeutic ratio may be attained by using an adaptive fraction size. Intuitively, we want to use a larger fraction size when OAR and the tumor are far apart and a smaller fraction size when OAR and the tumor are close to each other. The concept and strategies of adaptive fractionation therapy (AFT) are introduced in this paper. AFT is an on-line adaptive technique that utilizes the variations of internal structures to get optimal OAR sparing. Changes of internal structures are classified as different configurations according to their feasibility to the radiation delivery. A priori knowledge is used to describe the probability distribution of these configurations. On-line processes include identifying the configuration via daily image guidance and optimizing the current fraction size. The optimization is modeled as a dynamic linear programming problem so that at the end of the treatment course, the tumor receives the same planned dose while OAR receives less dose than the regular fractionation delivery. Extensive simulations, which include thousands of treatment courses with each course consisting of 40 fractions, are used to test the efficiency and robustness of the presented technique. The gains of OAR sparing depend on the variations on configurations and the bounds of the fraction size. The larger the variations and the looser the bounds are, the larger the gains will be. Compared to the conventional fractionation technique with 2 Gy/fraction in 40 fractions, for a 20% variation on tumor-OAR configurations and [1 Gy, 3 Gy] fraction size bounds, the cumulative OAR dose with adaptive fractionation is 3-8 Gy, or 7-20% less than that

  20. Multivariate fractional Poisson processes and compound sums

    OpenAIRE

    Beghin, Luisa; Macci, Claudio

    2015-01-01

    In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also consider compound processes. We obtain some equations in terms of some suitable fractional derivatives and fractional difference operators, which provides the extension of known equations for the univariate processes.

  1. Generalized Fractional Derivative Anisotropic Viscoelastic Characterization

    Directory of Open Access Journals (Sweden)

    Harry H. Hilton

    2012-01-01

    Full Text Available Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated.

  2. Error analysis of pupils in calculating with fractions

    OpenAIRE

    Uranič, Petra

    2016-01-01

    In this thesis I examine the correlation between the frequency of errors that seventh grade pupils make in their calculations with fractions and their level of understanding of fractions. Fractions are a relevant and demanding theme in the mathematics curriculum. Although we use fractions on a daily basis, pupils find learning fractions to be very difficult. They generally do not struggle with the concept of fractions itself, but they frequently have problems with mathematical operations ...

  3. The fractional oscillator process with two indices

    International Nuclear Information System (INIS)

    Lim, S C; Teo, L P

    2009-01-01

    We introduce a new fractional oscillator process which can be obtained as a solution of a stochastic differential equation with two fractional orders. Basic properties such as fractal dimension and short-range dependence of the process are studied by considering the asymptotic properties of its covariance function. By considering the fractional oscillator process as the velocity of a diffusion process, we derive the corresponding diffusion constant, fluctuation-dissipation relation and mean-square displacement. The fractional oscillator process can also be regarded as a one-dimensional fractional Euclidean Klein-Gordon field, which can be obtained by applying the Parisi-Wu stochastic quantization method to a nonlocal Euclidean action. The Casimir energy associated with the fractional field at positive temperature is calculated by using the zeta function regularization technique

  4. Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate

    Directory of Open Access Journals (Sweden)

    Adnane Boukhouima

    2017-01-01

    Full Text Available We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV infection. In the model, the infection transmission process is modeled by a specific functional response. First, we show that the model is mathematically and biologically well posed. Second, the local and global stabilities of the equilibria are investigated. Finally, some numerical simulations are presented in order to illustrate our theoretical results.

  5. Modeling single-file diffusion with step fractional Brownian motion and a generalized fractional Langevin equation

    International Nuclear Information System (INIS)

    Lim, S C; Teo, L P

    2009-01-01

    Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann–Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion

  6. Numerical Solution of a Fractional Order Model of HIV Infection of CD4+T Cells Using Müntz-Legendre Polynomials

    Directory of Open Access Journals (Sweden)

    Mojtaba Rasouli Gandomani

    2016-06-01

    Full Text Available In this paper, the model of HIV infection of CD4+ T cells is considered as a system of fractional differential equations. Then, a numerical method by using collocation method based on the Müntz-Legendre polynomials to approximate solution of the model is presented. The application of the proposed numerical method causes fractional differential equations system to convert into the algebraic equations system. The new system can be solved by one of the existing methods. Finally, we compare the result of this numerical method with the result of the methods have already been presented in the literature.

  7. Void fraction correlations analysis and their influence on heat transfer of helical double-pipe vertical evaporator

    International Nuclear Information System (INIS)

    Parrales, Arianna; Colorado, Dario; Huicochea, Armando; Díaz, Juan; Alfredo Hernández, J.

    2014-01-01

    Highlights: • 50 void fraction correlations were evaluated on heat transfer in vertical evaporators. • Two-phase flow model based on control volume formulation was used. • The drift flux parameter is common in all correlations with satisfactory results. - Abstract: An analysis of 50 void fraction correlations available in the literature was performed to describe two-phase flow mechanism inside two helical double-pipe vertical evaporators. The evaporators considered water as working fluid connected in countercurrent so the change of phase was carried out into the internal tube. The discretized equations of continuity, momentum and energy in each flow were coupled using an implicit step by step method. The selection of the void fraction correlations for the mathematical model was based on inclusion of some theoretical limits. The results of this analysis were compared with the experimental data in steady state for two different evaporators, obtaining good agreement in the evaporation process for only 7 void fraction correlations. The Armand and Massena correlation had a mean percentage error (MPE) of 3.08%, followed by Rouhanni and Axelsson I adquired MPE=3.16%, Chisholm and Armand obtained MPE=3.18%, Steiner as well as Rouhanni and Axelsson II with MPE=3.19%, Bestion reached MPE=3.20% and Flanigan presented MPE=3.21%. Furthermore, the experimental and simulated heat flux were acceptable (R 2 =0.939). Finally, the results showed that the drift flux parameter was important to evaluate the void fraction

  8. Single-fraction vs. fractionated linac-based stereotactic radiosurgery for vestibular schwannoma: a single-institution study

    NARCIS (Netherlands)

    Meijer, O. W. M.; Vandertop, W. P.; Baayen, J. C.; Slotman, B. J.

    2003-01-01

    PURPOSE: In this single-institution trial, we investigated whether fractionated stereotactic radiation therapy is superior to single-fraction linac-based radiosurgery with respect to treatment-related toxicity and local control in patients with vestibular schwannoma. METHODS AND MATERIALS: All 129

  9. Fractional, biodegradable and spectral characteristics of extracted and fractionated sludge extracellular polymeric substances.

    Science.gov (United States)

    Wei, Liang-Liang; Wang, Kun; Zhao, Qing-Liang; Jiang, Jun-Qiu; Kong, Xiang-Juan; Lee, Duu-Jong

    2012-09-15

    Correlation between fractional, biodegradable and spectral characteristics of sludge extracellular polymeric substances (EPS) by different protocols has not been well established. This work extracted sludge EPS using alkaline extractants (NH₄OH and formaldehyde + NaOH) and physical protocols (ultrasonication, heating at 80 °C or cation exchange resin (CER)) and then fractionated the extracts using XAD-8/XAD-4 resins. The alkaline extractants yielded more sludge EPS than the physical protocols. However, the physical protocols extracted principally the hydrophilic components which were readily biodegradable by microorganisms. The alkaline extractants dissolved additional humic-like substances from sludge solids which were refractory in nature. Different extraction protocols preferably extracted EPS with distinct fractional, biodegradable and spectral characteristics which could be applied in specific usages. Copyright © 2012 Elsevier Ltd. All rights reserved.

  10. The improved fractional sub-equation method and its applications to the space–time fractional differential equations in fluid mechanics

    International Nuclear Information System (INIS)

    Guo, Shimin; Mei, Liquan; Li, Ying; Sun, Youfa

    2012-01-01

    By introducing a new general ansätz, the improved fractional sub-equation method is proposed to construct analytical solutions of nonlinear evolution equations involving Jumarie's modified Riemann–Liouville derivative. By means of this method, the space–time fractional Whitham–Broer–Kaup and generalized Hirota–Satsuma coupled KdV equations are successfully solved. The obtained results show that the proposed method is quite effective, promising and convenient for solving nonlinear fractional differential equations. -- Highlights: ► We propose a novel method for nonlinear fractional differential equations. ► Two important fractional differential equations in fluid mechanics are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained. ► These solutions will advance the understanding of nonlinear physical phenomena.

  11. Water dynamics in different biochar fractions.

    Science.gov (United States)

    Conte, Pellegrino; Nestle, Nikolaus

    2015-09-01

    Biochar is a carbonaceous porous material deliberately applied to soil to improve its fertility. The mechanisms through which biochar acts on fertility are still poorly understood. The effect of biochar texture size on water dynamics was investigated here in order to provide information to address future research on nutrient mobility towards plant roots as biochar is applied as soil amendment. A poplar biochar has been stainless steel fractionated in three different textured fractions (1.0-2.0 mm, 0.3-1.0 mm and <0.3 mm, respectively). Water-saturated fractions were analyzed by fast field cycling (FFC) NMR relaxometry. Results proved that 3D exchange between bound and bulk water predominantly occurred in the coarsest fraction. However, as porosity decreased, water motion was mainly associated to a restricted 2D diffusion among the surface-site pores and the bulk-site ones. The X-ray μ-CT imaging analyses on the dry fractions revealed the lowest surface/volume ratio for the coarsest fraction, thereby corroborating the 3D water exchange mechanism hypothesized by FFC NMR relaxometry. However, multi-micrometer porosity was evidenced in all the samples. The latter finding suggested that the 3D exchange mechanism cannot even be neglected in the finest fraction as previously excluded only on the basis of NMR relaxometry results. X-ray μ-CT imaging showed heterogeneous distribution of inorganic materials inside all the fractions. The mineral components may contribute to the water relaxation mechanisms by FFC NMR relaxometry. Further studies are needed to understand the role of the inorganic particles on water dynamics. Copyright © 2015 John Wiley & Sons, Ltd.

  12. Fractional Fick's law: the direct way

    International Nuclear Information System (INIS)

    Neel, M C; Abdennadher, A; Joelson, M

    2007-01-01

    Levy flights, which are Markovian continuous time random walks possibly accounting for extreme events, serve frequently as small-scale models for the spreading of matter in heterogeneous media. Among them, Brownian motion is a particular case where Fick's law holds: for a cloud of walkers, the flux is proportional to the gradient of the probability density of finding a particle at some place. Levy flights resemble Brownian motion, except that jump lengths are distributed according to an α-stable Levy law, possibly showing heavy tails and skewness. For α between 1 and 2, a fractional form of Fick's law is known to hold in infinite media: that the flux is proportional to a combination of fractional derivatives or the order of α - 1 of the density of walkers was obtained as a consequence of a fractional dispersion equation. We present a direct and natural proof of this result, based upon a novel definition of usual fractional derivatives, involving a convolution and a limiting process. Taking account of the thus obtained fractional Fick's law yields fractional dispersion equation for smooth densities. The method adapts to domains, limited by boundaries possibly implying non-trivial modifications to this equation

  13. Generalized continued fractions and ergodic theory

    International Nuclear Information System (INIS)

    Pustyl'nikov, L D

    2003-01-01

    In this paper a new theory of generalized continued fractions is constructed and applied to numbers, multidimensional vectors belonging to a real space, and infinite-dimensional vectors with integral coordinates. The theory is based on a concept generalizing the procedure for constructing the classical continued fractions and substantially using ergodic theory. One of the versions of the theory is related to differential equations. In the finite-dimensional case the constructions thus introduced are used to solve problems posed by Weyl in analysis and number theory concerning estimates of trigonometric sums and of the remainder in the distribution law for the fractional parts of the values of a polynomial, and also the problem of characterizing algebraic and transcendental numbers with the use of generalized continued fractions. Infinite-dimensional generalized continued fractions are applied to estimate sums of Legendre symbols and to obtain new results in the classical problem of the distribution of quadratic residues and non-residues modulo a prime. In the course of constructing these continued fractions, an investigation is carried out of the ergodic properties of a class of infinite-dimensional dynamical systems which are also of independent interest

  14. Generalized hydrodynamic correlations and fractional memory functions

    Science.gov (United States)

    Rodríguez, Rosalio F.; Fujioka, Jorge

    2015-12-01

    A fractional generalized hydrodynamic (GH) model of the longitudinal velocity fluctuations correlation, and its associated memory function, for a complex fluid is analyzed. The adiabatic elimination of fast variables introduces memory effects in the transport equations, and the dynamic of the fluctuations is described by a generalized Langevin equation with long-range noise correlations. These features motivate the introduction of Caputo time fractional derivatives and allows us to calculate analytic expressions for the fractional longitudinal velocity correlation function and its associated memory function. Our analysis eliminates a spurious constant term in the non-fractional memory function found in the non-fractional description. It also produces a significantly slower power-law decay of the memory function in the GH regime that reduces to the well-known exponential decay in the non-fractional Navier-Stokes limit.

  15. Main activities in Kazakhstan aimed to substantiate ITER and demo reactors safety

    International Nuclear Information System (INIS)

    Shestakov, V.; Chikhray, Y.; Tazhibayeva, I.; Kenzhin, Ye.; Dzhakishev, M.; Goryaev, G.; Gagarin, A.; Shakhvorostov, Yr.; Savchuk, V.

    2004-01-01

    The first stage of such activity is examinations of physicochemical properties of compact beryllium. This work is carrying out Ulba Plant - worl known beryllium producer. Quality control of compact beryllium products includes step-by-step operational control and attestation control of final products for compliancy with customer's requirements. Step-by-step control is carried out along the whole production process and includes the control of the following: temperature, pressure, duration of the process and other process parameter, listed in the in-plant documentation; quality of intermediate semi products (chemical, physical and mechanical properties, defects, appearance, dimension, etc). The process control is carried out by personnel and by an independent inspection service. The attestation control of final products is carried out for compliancy of products with requirement of consumers and includes the following: chemical analysis, mechanical testing, radiographic testing, ultrasonic testing, appearance inspection, dimension inspection, density testing, and metallographic inspection. The attestation control is carried out by a special service independent of technologists. This is the service that makes a final report on the compliancy of the product with requirements of customers and gives permission for shipping the products. The process and attestation control is carried out with the use of equipment, apparatuses and devices, which are checked regularly by special instrumentation service. If they do not meet the requirements in precision, reliability and stability they are removed from service and not approved for measurements. Methods of control of specific values and characteristics, the apparatuses used and allowed classes of accuracy are specified in state standards, tensile specifications of products and in-plant standards or in agreements between a producer and a customer. The next stage will be manufacturing of mock-ups of reactor's first wall elements

  16. Mo isotope fractionation during hydrothermal evolution of porphyry Cu systems

    Science.gov (United States)

    Shafiei, Behnam; Shamanian, GholamHossein; Mathur, Ryan; Mirnejad, Hassan

    2015-03-01

    We present Mo isotope compositions of molybdenite types from three successive stages of ore deposition in several porphyry copper deposits of the Kerman region, Iran. The data provide new insights into controlling processes on Mo isotope fractionation during the hydrothermal evolution of porphyry systems. The Mo isotope compositions of 27 molybdenite samples show wide variations in δ97Mo ranging from -0.37 to +0.92 ‰. The data reveal that molybdenites in the early and transitional stages of mineralization (preferentially 2H polytypes; δ97Mo mean = 0.35 ‰) have higher δ97Mo values than late stage (mainly 3R polytypes; δ97Mo mean = 0.02 ‰) molybdenites. This trend suggests that fractionation of Mo isotopes occurred in high-temperature stages of mineralization and that hydrothermal systems generally evolve towards precipitation of molybdenite with lower δ97Mo values. Taking into account the genetic models proposed for porphyry Cu deposits along with the temperature-dependent fractionation of Mo isotope ratios, it is proposed that large variations of Mo isotopes in the early and the transitional stages of ore deposition could be controlled by the separation of the immiscible ore-forming fluid phases with different density, pH, and ƒO2 properties (i.e., brine and vapor). The fractionation of Mo isotopes during fluid boiling and Rayleigh distillation processes likely dominates the Mo isotope budget of the remaining ore-forming fluids for the late stage of mineralization. The lower δ97Mo values in the late stage of mineralization can be explained by depletion of the late ore-forming hydrothermal solutions in 97Mo, as these fluids have moved to considerable distance from the source. Finally, the relationship observed between MoS2 polytypes (2H and 3R) and their Mo isotopic compositions can be explained by the molecular vibration theory, in which heavier isotopes are preferentially partitioned into denser primary 2H MoS2 crystals.

  17. Charmless hadronic three-body decays of neutral $B$ mesons with a $K^0_s$ in the final state in the LHCb experiment: branching fractions and an amplitude analysis Désintégrations hadroniques à trois corps sans charme de mésons $B$ avec un $K^0_s$ dans l'état final dans l'expérience LHCb : mesure de rapports d'embranchement et une analyse en amplitude

    CERN Document Server

    AUTHOR|(INSPIRE)INSPIRE-00390866

    This dissertation presents several studies of the decays of both $B_d$ and $B_s$ mesons to charmless three-body final states including a $K_{\\rm S}^0$ meson. They use the data recorded by the LHCb experiment during Run I of LHC, corresponding to an integrated luminosity of $\\int\\mathcal{L}=3\\rm fb^{-1}$. A first analysis consists of the measurement of the branching fractions of $B_{d,s}\\rightarrow K_{\\rm S}^0h^{+}h^{'-}$ decays, where $h^{(')}$ designates a kaon or a pion. Preceding LHCb measurements of branching fractions for all decay channels, relative to that of $B_d\\rightarrow K_{\\rm S}^0\\pi^{+}\\pi^{-}$, are updated. Furthermore, the primary goal of this analysis is to search for the, as yet, unobserved decay $B_s\\rightarrow K_{\\rm S}^0K^+K^-$. The relative branching fractions are measured to be: \\begin{align} \\frac{\\mathcal{B}\\left(B_s\\rightarrow K_{\\rm S}^0\\pi^{+}\\pi^{-}\\right)}{\\mathcal{B}\\left(B_d\\rightarrow K_{\\rm S}^0\\pi^{+}\\pi^{-}\\right)} &= 0.26 \\pm 0.04\\mathrm{(stat.)} \\pm 0.02\\mathrm{(sy...

  18. Unwrapping Students' Ideas about Fractions

    Science.gov (United States)

    Lewis, Rebecca M.; Gibbons, Lynsey K.; Kazemi, Elham; Lind, Teresa

    2015-01-01

    Supporting students to develop an understanding of the meaning of fractions is an important goal of elementary school mathematics. This involves developing partitioning strategies, creating representations, naming fractional quantities, and using symbolic notation. This article describes how teachers can use a formative assessment problem to…

  19. Deterministic ratchets for suspension fractionation

    NARCIS (Netherlands)

    Kulrattanarak, T.

    2010-01-01

    Driven by the current insights in sustainability and technological development in
    biorefining natural renewable resources, the food industry has taken an interest in
    fractionation of agrofood materials, like milk and cereal crops. The purpose of fractionation
    is to split the raw

  20. Fractional order control and synchronization of chaotic systems

    CERN Document Server

    Vaidyanathan, Sundarapandian; Ouannas, Adel

    2017-01-01

    The book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining the concepts involved in a clear, matter-of-fact style. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories, methods and applications in a number of research areas related to fractional order control and synchronization of chaotic systems, such as: fractional chaotic systems, hyperchaotic systems, complex systems, fractional order discrete chaotic systems, chaos control, chaos synchronization, jerk circuits, fractional chaotic systems with hidden attractors, neural network, fuzzy logic controllers, behavioral modeling, robust and adaptive control, sliding mode control, different types of synchronization, circuit realization of chaotic systems, etc. In addition to providing readers extensive information on chaos fundamentals, fractional calculus, fractional differential equations, fractional contro...

  1. Observation of Exclusive {ital B} Decays to Final States Containing a Charmed Baryon

    Energy Technology Data Exchange (ETDEWEB)

    Fu, X.; Nemati, B.; Richichi, S.J.; Ross, W.R.; Skubic, P.; Wood, M. [University of Oklahoma, Norman, Oklahoma 73019 (United States); Bishai, M.; Fast, J.; Gerndt, E.; Hinson, J.W.; Miao, T.; Miller, D.H.; Modesitt, M.; Shibata, E.I.; Shipsey, I.P.; Wang, P.N. [Purdue University, West Lafayette, Indiana 47907 (United States); Gibbons, L.; Johnson, S.D.; Kwon, Y.; Roberts, S.; Thorndike, E.H. [University of Rochester, Rochester, New York 14627 (United States); Jessop, C.P.; Lingel, K.; Marsiske, H.; Perl, M.L.; Schaffner, S.F.; Wang, R. [Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 (United States); Coan, T.E.; Dominick, J.; Fadeyev, V.; Korolkov, I.; Lambrecht, M.; Sanghera, S.; Shelkov, V.; Stroynowski, R.; Volobouev, I.; Wei, G. [Southern Methodist University, Dallas, Texas 75275 (United States); Artuso, M.; Efimov, A.; Gao, M.; Goldberg, M.; He, D.; Horwitz, N.; Kopp, S.; Moneti, G.C.; Mountain, R.; Mukhin, Y.; Playfer, S.; Skwarnicki, T.; Stone, S.; Xing, X. [Syracuse University, Syracuse, New York 13244 (United States); Bartelt, J.; Csorna, S.E.; Jain, V.; Marka, S. [Vanderbilt University, Nashville, Tennessee 37235 (United States); Freyberger, A.; Gibaut, D.; Kinoshita, K.; Pomianowski, P.; Schrenk, S. [Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 (United States); Cinabro, D. [Wayne State University, Detroit, Michigan 48202 (United States); Barish, B.; Chadha, M.; Chan, S.; Eigen, G.; Miller, J.S.; OGrady, C.; Schmidtler, M.; Urheim, J.; Weinstein, A.J.; Wuerthwein, F. [California Institute of Technology, Pasadena, California 91125 (United States); Asner, D.M.; Athanas, M.; Bliss, D.W.; Brower, W.S.; Masek, G.; Paar, H.P. [University of California, San Diego, La Jolla, California 92093 (United States); Gronberg, J.; Korte, C.M.; Kutschke, R.; Menary, S.; Morrison, R.J.; Nakanishi, S.; Nelson, H.N.; Nelson, T.K.; Qiao, C.; Richman, J.D.; Roberts, D.; Ryd, A.; and others

    1997-10-01

    Using data collected in the region of the {Upsilon}(4S) resonance with the CLEO-II detector, we report on the first observation of exclusive decays of the B meson to final states with a charmed baryon. We have measured the branching fractions B(B{sup {minus}}{r_arrow}{Lambda}{sup +}{sub c}{ovr p}{pi}{sup {minus}})=( 0.62{sup +0.23}{sub {minus}0.20}{plus_minus}0.11{plus_minus}0.10) {times}10{sup {minus}3} and B({ovr B}{sup 0}{r_arrow}{Lambda}{sup +}{sub c}{ovr p}{pi}{sup +}{pi}{sup {minus}})=(1.33{sup +0.46}{sub {minus}0.42}{plus_minus}0.31{plus_minus}0.21){times}10{sup {minus}3} , where the first error is statistical, the second is systematic, and the third is due to uncertainty in the {Lambda}{sup +}{sub c} branching fractions. In addition, we report upper limits for final states of the form {ovr B}{r_arrow}{Lambda}{sup +}{sub c}{ovr p} (n{pi}) and {Lambda}{sup +}{sub c}{ovr p}(n{pi}) {pi}{sup 0} , where (n{pi}) denotes up to four charged pions. {copyright} {ital 1997} {ital The American Physical Society}

  2. Fractional Klein-Gordon equation composed of Jumarie fractional derivative and its interpretation by a smoothness parameter

    Science.gov (United States)

    Ghosh, Uttam; Banerjee, Joydip; Sarkar, Susmita; Das, Shantanu

    2018-06-01

    Klein-Gordon equation is one of the basic steps towards relativistic quantum mechanics. In this paper, we have formulated fractional Klein-Gordon equation via Jumarie fractional derivative and found two types of solutions. Zero-mass solution satisfies photon criteria and non-zero mass satisfies general theory of relativity. Further, we have developed rest mass condition which leads us to the concept of hidden wave. Classical Klein-Gordon equation fails to explain a chargeless system as well as a single-particle system. Using the fractional Klein-Gordon equation, we can overcome the problem. The fractional Klein-Gordon equation also leads to the smoothness parameter which is the measurement of the bumpiness of space. Here, by using this smoothness parameter, we have defined and interpreted the various cases.

  3. Semi-infinite fractional programming

    CERN Document Server

    Verma, Ram U

    2017-01-01

    This book presents a smooth and unified transitional framework from generalised fractional programming, with a finite number of variables and a finite number of constraints, to semi-infinite fractional programming, where a number of variables are finite but with infinite constraints. It focuses on empowering graduate students, faculty and other research enthusiasts to pursue more accelerated research advances with significant interdisciplinary applications without borders. In terms of developing general frameworks for theoretical foundations and real-world applications, it discusses a number of new classes of generalised second-order invex functions and second-order univex functions, new sets of second-order necessary optimality conditions, second-order sufficient optimality conditions, and second-order duality models for establishing numerous duality theorems for discrete minmax (or maxmin) semi-infinite fractional programming problems.   In the current interdisciplinary supercomputer-oriented research envi...

  4. Studies on proinsulin and proglucagon biosynthesis and conversion at the subcellular level: I. Fractionation procedure and characterization of the subcellular fractions

    Science.gov (United States)

    Noe, BD; Baste, CA; Bauer, GE

    1977-01-01

    Anglerfish islets were homogenized in 0.25 M sucrose and separated into seven separate subcellular fractions by differential and discontinuous density gradient centrifugation. The objective was to isolate microsomes and secretory granules in a highly purified state. The fractions were characterized by electron microscopy and chemical analyses. Each fraction was assayed for its content of protein, RNA, DNA, immunoreactive insulin (IRI), and immunoreactive glucagon (IRG). Ultrastructural examination showed that two of the seven subcellular fractions contain primarily mitochondria, and that two others consist almost exclusively of secretory granules. A fifth fraction contains rough and smooth microsomal vesicles. The remaining two fractions are the cell supernate and the nuclei and cell debris. The content of DNA and RNA in all fractions is consistent with the observed ultrastructure. More than 82 percent of the total cellular IRI and 89(percent) of the total cellular IRG are found in the fractions of secretory granules. The combined fractions of secretory granules and microsomes consistently yield >93 percent of the total IRG. These results indicate that the fractionation procedure employed yields fractions of microsomes and secretory granules that contain nearly all the immunoassayable insulin and glucagons found in whole islet tissue. These fractions are thus considered suitable for study of proinsulin and proglucagon biosynthesis and their metabolic conversion at the subcellular level. PMID:328517

  5. Characterization of federated oil fractions used for the PTAC project to study the petroleum fraction-specific toxicity to soils

    International Nuclear Information System (INIS)

    Wang, Z.; Jokuty, P.; Fingas, M.; Sigouin, L.

    2001-01-01

    In 1998, the Petroleum Technology Alliance of Canada (PTAC) and the Canadian Association of Petroleum Producers (CAPP) launched an important research project for the oil and gas industry entitled A Fraction-Specific Toxicity and Derivation of Recommended Soil Quality Guidelines for Crude Oil in Agricultural Soils. The objective was to generate useful and relevant data that could be used to develop soil quality guidelines for petroleum hydrocarbon residuals in agricultural soils. The oil used in the study was Federated crude oil which was fractionated into four fractions using a distillation method. The fraction-based approach was used to support ecologically-relevant, risk-based, soil quality criteria for the protection of environmental health. This paper presented the nominal carbon number and boiling point ranges of these fractions and described the distillation procedures for producing the fractions from the Federated crude oil. The paper also presented the detailed chemical characterization results of each distillation fraction. The toxicity of the crude oil mixture to plants and soil invertebrates was also assessed using standardized toxicity tests. Tests were also conducted to assess the toxicity of fractions of the crude oil and the toxic interactions of the fractions responsible for a significant proportion of the toxicity. Phase 2 of the project was designed to determine if hydrocarbon residuals exceeding 1000 μg/g and weathered for short or long periods of time, posed an ecotoxicological risk or impaired soil physical, chemical and biological properties such that productivity of the agricultural soils was compromised. The objectives of phase 2 were to amend differently textured soils in field plots at sites with fresh crude oil and to monitor their toxicity to terrestrial organisms using laboratory-based ecotoxicity tests. The study showed that because of the nature of the chemical composition of hydrocarbons (such as boiling points, nominal carbon range

  6. Understanding Magnitudes to Understand Fractions

    Science.gov (United States)

    Gabriel, Florence

    2016-01-01

    Fractions are known to be difficult to learn and difficult to teach, yet they are vital for students to have access to further mathematical concepts. This article uses evidence to support teachers employing teaching methods that focus on the conceptual understanding of the magnitude of fractions.

  7. Generation of fractional acoustic vortex with a discrete Archimedean spiral structure plate

    Science.gov (United States)

    Jia, Yu-Rou; Wei, Qi; Wu, Da-Jian; Xu, Zheng; Liu, Xiao-Jun

    2018-04-01

    Artificial structure plates engraved with discrete Archimedean spiral slits have been well designed to achieve fractional acoustic vortices (FAVs). The phase and pressure field distributions of FAVs are investigated theoretically and demonstrated numerically. It is found that the phase singularities relating to the integer and fractional parts of the topological charge (TC) result in dark spots in the upper half of the pressure field profile and a low-intensity stripe in the lower half of the pressure field profile, respectively. The dynamic progress of the FAV is also discussed in detail as TC increases from 1 to 2. With increasing TC from 1 to 1.5, the splitting of the phase singularity leads to the deviation of the phase of the FAV from the integer case and hence a new phase singularity occurs. As TC m increases from 1.5 to 2, two phase singularities of the FAV approach together and finally merge as a new central phase singularity. We further perform an experiment based on the Schlieren method to demonstrate the generation of the FAV.

  8. On a Fractional Binomial Process

    Science.gov (United States)

    Cahoy, Dexter O.; Polito, Federico

    2012-02-01

    The classical binomial process has been studied by Jakeman (J. Phys. A 23:2815-2825, 1990) (and the references therein) and has been used to characterize a series of radiation states in quantum optics. In particular, he studied a classical birth-death process where the chance of birth is proportional to the difference between a larger fixed number and the number of individuals present. It is shown that at large times, an equilibrium is reached which follows a binomial process. In this paper, the classical binomial process is generalized using the techniques of fractional calculus and is called the fractional binomial process. The fractional binomial process is shown to preserve the binomial limit at large times while expanding the class of models that include non-binomial fluctuations (non-Markovian) at regular and small times. As a direct consequence, the generality of the fractional binomial model makes the proposed model more desirable than its classical counterpart in describing real physical processes. More statistical properties are also derived.

  9. q-fractional calculus and equations

    CERN Document Server

    Annaby, Mahmoud H

    2012-01-01

    This nine-chapter monograph introduces a rigorous investigation of q-difference operators in standard and fractional settings. It starts with elementary calculus of q-differences and integration of Jackson’s type before turning to q-difference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular  q-Sturm–Liouville theory is also introduced; Green’s function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional q-calculi. Hence fractional q-calculi of the types Riemann–Liouville; Grünwald–Letnikov;  Caputo;  Erdélyi–Kober and Weyl are defined analytically. Fractional q-Leibniz rules with applications  in q-series are  also obtained with rigorous proofs of the formal  results of  Al-Salam-Verma, which remained unproved for decades. In working ...

  10. Mass fractionation processes of transition metal isotopes

    Science.gov (United States)

    Zhu, X. K.; Guo, Y.; Williams, R. J. P.; O'Nions, R. K.; Matthews, A.; Belshaw, N. S.; Canters, G. W.; de Waal, E. C.; Weser, U.; Burgess, B. K.; Salvato, B.

    2002-06-01

    Recent advances in mass spectrometry make it possible to utilise isotope variations of transition metals to address some important issues in solar system and biological sciences. Realisation of the potential offered by these new isotope systems however requires an adequate understanding of the factors controlling their isotope fractionation. Here we show the results of a broadly based study on copper and iron isotope fractionation during various inorganic and biological processes. These results demonstrate that: (1) naturally occurring inorganic processes can fractionate Fe isotope to a detectable level even at temperature ˜1000°C, which challenges the previous view that Fe isotope variations in natural system are unique biosignatures; (2) multiple-step equilibrium processes at low temperatures may cause large mass fractionation of transition metal isotopes even when the fractionation per single step is small; (3) oxidation-reduction is an importation controlling factor of isotope fractionation of transition metal elements with multiple valences, which opens a wide range of applications of these new isotope systems, ranging from metal-silicate fractionation in the solar system to uptake pathways of these elements in biological systems; (4) organisms incorporate lighter isotopes of transition metals preferentially, and transition metal isotope fractionation occurs stepwise along their pathways within biological systems during their uptake.

  11. Acute hematological tolerance to multiple fraction, whole body, low dose irradiation in an experimental murine system

    International Nuclear Information System (INIS)

    Melamed, J.S.; Chen, M.G.; Brown, J.W.; Katagiri, C.A.

    1980-01-01

    Using a dose fractionation scheme patterned after the current regimen for treatment of disseminated non-Hodgkin lymphoma, the authors studied the effects of irradation on progenitor and effector cells for hematopoiesis in five-month-old BC3F 1 mice. Fractions of 20 or 50 rad (0.2 or 0.5 Gy) total body irradation were given twice weekly to a final total dose of 200 or 500 rad (2 or 5 Gy), respectively. Weekly assays revealed a marked, sustained depression of stem cell activity, measured as numbers of spleen colony-forming units (CFU-S) and in vitro colony-forming cells (CFU-C), without corresponding depression of effector cells (red and white cells, and platelets). The lack of correlation between numbers of stem cells and peripheral elements is relevant to clinical assessment of marrow reserve

  12. Controllability Problem of Fractional Neutral Systems: A Survey

    Directory of Open Access Journals (Sweden)

    Artur Babiarz

    2017-01-01

    Full Text Available The following article presents recent results of controllability problem of dynamical systems in infinite-dimensional space. Generally speaking, we describe selected controllability problems of fractional order systems, including approximate controllability of fractional impulsive partial neutral integrodifferential inclusions with infinite delay in Hilbert spaces, controllability of nonlinear neutral fractional impulsive differential inclusions in Banach space, controllability for a class of fractional neutral integrodifferential equations with unbounded delay, controllability of neutral fractional functional equations with impulses and infinite delay, and controllability for a class of fractional order neutral evolution control systems.

  13. On some fractional order hardy inequalities

    Directory of Open Access Journals (Sweden)

    Kufner Alois

    1997-01-01

    Full Text Available Weighted inequalities for fractional derivatives ( fractional order Hardy-type inequalities have recently been proved in [4] and [1]. In this paper, new inequalities of this type are proved and applied. In particular, the general mixed norm case and a general twodimensional weight are considered. Moreover, an Orlicz norm version and a multidimensional fractional order Hardy inequality are proved. The connections to related results are pointed out.

  14. Particle size fractionation of paralytic shellfish toxins (PSTs): seasonal distribution and bacterial production in the St Lawrence estuary, Canada.

    Science.gov (United States)

    Michaud, S; Levasseur, M; Doucette, G; Cantin, G

    2002-10-01

    We determined the seasonal distribution of paralytic shellfish toxins (PSTs) and PST producing bacteria in > 15, 5-15, and 0.22-5 microm size fractions in the St Lawrence. We also measured PSTs in a local population of Mytilus edulis. PST concentrations were determined in each size fraction and in laboratory incubations of sub-samples by high performance liquid chromatography (HPLC), including the rigorous elimination of suspected toxin 'imposter' peaks. Mussel toxin levels were determined by mouse bioassay and HPLC. PSTs were detected in all size fractions during the summer sampling season, with 47% of the water column toxin levels associated with particles smaller than Alexandrium tamarense ( 15 microm size fraction, we estimated that as much as 92% of PSTs could be associated with particles other than A. tamarense. Our results stress the importance of taking into account the potential presence of PSTs in size fractions other than that containing the known algal producer when attempting to model shellfish intoxication, especially during years of low cell abundance. Finally, our HPLC results confirmed the presence of bacteria capable of autonomous PST production in the St Lawrence as well as demonstrating their regular presence and apparent diversity in the plankton. Copyright 2002 Elsevier Science Ltd.

  15. Fractional Dynamics Applications of Fractional Calculus to Dynamics of Particles, Fields and Media

    CERN Document Server

    Tarasov, Vasily E

    2010-01-01

    "Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and...

  16. The Fractional Orthogonal Difference with Applications

    Directory of Open Access Journals (Sweden)

    Enno Diekema

    2015-06-01

    Full Text Available This paper is a follow-up of a previous paper of the author published in Mathematics journal in 2015, which treats the so-called continuous fractional orthogonal derivative. In this paper, we treat the discrete case using the fractional orthogonal difference. The theory is illustrated with an application of a fractional differentiating filter. In particular, graphs are presented of the absolutel value of the modulus of the frequency response. These make clear that for a good insight into the behavior of a fractional differentiating filter, one has to look for the modulus of its frequency response in a log-log plot, rather than for plots in the time domain.

  17. Fractional Diffusion in Gaussian Noisy Environment

    Directory of Open Access Journals (Sweden)

    Guannan Hu

    2015-03-01

    Full Text Available We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic heat equations of the following form: \\(D_t^{(\\alpha} u(t, x=\\textit{B}u+u\\cdot \\dot W^H\\, where \\(D_t^{(\\alpha}\\ is the Caputo fractional derivative of order \\(\\alpha\\in (0,1\\ with respect to the time variable \\(t\\, \\(\\textit{B}\\ is a second order elliptic operator with respect to the space variable \\(x\\in\\mathbb{R}^d\\ and \\(\\dot W^H\\ a time homogeneous fractional Gaussian noise of Hurst parameter \\(H=(H_1, \\cdots, H_d\\. We obtain conditions satisfied by \\(\\alpha\\ and \\(H\\, so that the square integrable solution \\(u\\ exists uniquely.

  18. Topologically induced fractional Hall steps in the integer quantum Hall regime of MoS 2

    Science.gov (United States)

    Firoz Islam, SK; Benjamin, Colin

    2016-09-01

    The quantum magnetotransport properties of a monolayer of molybdenum disulfide are derived using linear response theory. In particular, the effect of topological terms on longitudinal and Hall conductivity is analyzed. The Hall conductivity exhibits fractional steps in the integer quantum Hall regime. Further complete spin and valley polarization of the longitudinal conductivitity is seen in presence of these topological terms. Finally, the Shubnikov-de Hass oscillations are suppressed or enhanced contingent on the sign of these topological terms.

  19. Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation

    CERN Document Server

    Petráš, Ivo

    2011-01-01

    "Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...

  20. Justification for inter-fraction correction of catheter movement in fractionated high dose-rate brachytherapy treatment of prostate cancer

    International Nuclear Information System (INIS)

    Simnor, Tania; Li, Sonia; Lowe, Gerry; Ostler, Peter; Bryant, Linda; Chapman, Caroline; Inchley, Dave; Hoskin, Peter J.

    2009-01-01

    Background and purpose: Fractionated high dose-rate (HDR) brachytherapy in the treatment of prostate cancer relies on reproducible catheter positions for each fraction to ensure adequate tumour coverage while minimising dose to normal tissues. Peri-prostatic oedema may cause caudal displacement of the catheters relative to the prostate gland between fractions. This can be corrected for by changing source dwell positions or by physical re-advancement of catheters before treatment. Materials and methods: Data for 20 consecutive monotherapy patients receiving three HDR fractions of 10.5 Gy per fraction over 2 days were analysed retrospectively. Pre-treatment CT scans were used to assess the effect of catheter movement between fractions on implant quality, with and without movement correction. Implant quality was evaluated using dosimetric parameters. Results: Compared to the first fraction (f1) the mean inter-fraction caudal movement relative to the prostate base was 7.9 mm (f2) (range 0-21 mm) and 3.9 mm (f3) (range 0-25.5 mm). PTV D90% was reduced without movement correction by a mean of 27.8% (f2) and 32.3% (f3), compared with 5.3% and 5.1%, respectively, with catheter movement correction. Dose to 2 cc of the rectum increased by a mean of 0.69 (f2) and 0.76 Gy (f3) compared with an increase of 0.03 and 0.04 Gy, respectively, with correction. The urethra V12 also increased by a mean of 0.36 (f2) and 0.39 Gy (f3) compared with 0.06 and 0.16 Gy, respectively, with correction. Conclusions: Inter-fraction correction for catheter movement using pre-treatment imaging is critical to maintain the quality of an implant. Without movement correction there is significant risk of tumour under-dosage and normal tissue over-dosage. The findings of this study justify additional imaging between fractions in order to carry out correction.

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