Novel Desorber for Online Drilling Mud Gas Logging.
Lackowski, Marcin; Tobiszewski, Marek; Namieśnik, Jacek
2016-01-01
This work presents the construction solution and experimental results of a novel desorber for online drilling mud gas logging. The traditional desorbers use mechanical mixing of the liquid to stimulate transfer of hydrocarbons to the gaseous phase that is further analyzed. The presented approach is based on transfer of hydrocarbons from the liquid to the gas bubbles flowing through it and further gas analysis. The desorber was checked for gas logging from four different drilling muds collected from Polish boreholes. The results of optimization studies are also presented in this study. The comparison of the novel desorber with a commercial one reveals strong advantages of the novel one. It is characterized by much better hydrocarbons recovery efficiency and allows reaching lower limits of detection of the whole analytical system. The presented desorber seems to be very attractive alternative over widely used mechanical desorbers.
Novel Desorber for Online Drilling Mud Gas Logging
Directory of Open Access Journals (Sweden)
Marcin Lackowski
2016-01-01
Full Text Available This work presents the construction solution and experimental results of a novel desorber for online drilling mud gas logging. The traditional desorbers use mechanical mixing of the liquid to stimulate transfer of hydrocarbons to the gaseous phase that is further analyzed. The presented approach is based on transfer of hydrocarbons from the liquid to the gas bubbles flowing through it and further gas analysis. The desorber was checked for gas logging from four different drilling muds collected from Polish boreholes. The results of optimization studies are also presented in this study. The comparison of the novel desorber with a commercial one reveals strong advantages of the novel one. It is characterized by much better hydrocarbons recovery efficiency and allows reaching lower limits of detection of the whole analytical system. The presented desorber seems to be very attractive alternative over widely used mechanical desorbers.
Apparatus and method for rapid separation and detection of hydrocarbon fractions in a fluid stream
Sluder, Charles S.; Storey, John M.; Lewis, Sr., Samuel A.
2013-01-22
An apparatus and method for rapid fractionation of hydrocarbon phases in a sample fluid stream are disclosed. Examples of the disclosed apparatus and method include an assembly of elements in fluid communication with one another including one or more valves and at least one sorbent chamber for removing certain classifications of hydrocarbons and detecting the remaining fractions using a detector. The respective ratios of hydrocarbons are determined by comparison with a non separated fluid stream.
Directory of Open Access Journals (Sweden)
Mukhopadhyay Nishit K
2008-06-01
Full Text Available Abstract Background Cholesterol-rich membrane microdomains known as lipid rafts have been implicated in diverse physiologic processes including lipid transport and signal transduction. Lipid rafts were originally defined as detergent-resistant membranes (DRMs due to their relative insolubility in cold non-ionic detergents. Recent findings suggest that, although DRMs are not equivalent to lipid rafts, the presence of a given protein within DRMs strongly suggests its potential for raft association in vivo. Therefore, isolation of DRMs represents a useful starting point for biochemical analysis of lipid rafts. The physicochemical properties of DRMs present unique challenges to analysis of their protein composition. Existing methods of isolating DRM-enriched fractions involve flotation of cell extracts in a sucrose density gradient, which, although successful, can be labor intensive, time consuming and results in dilute sucrose-containing fractions with limited utility for direct proteomic analysis. In addition, several studies describing the proteomic characterization of DRMs using this and other approaches have reported the presence of nuclear proteins in such fractions. It is unclear whether these results reflect trafficking of nuclear proteins to DRMs or whether they arise from nuclear contamination during isolation. To address these issues, we have modified a published differential detergent extraction method to enable rapid DRM isolation that minimizes nuclear contamination and yields fractions compatible with mass spectrometry. Results DRM-enriched fractions isolated using the conventional or modified extraction methods displayed comparable profiles of known DRM-associated proteins, including flotillins, GPI-anchored proteins and heterotrimeric G-protein subunits. Thus, the modified procedure yielded fractions consistent with those isolated by existing methods. However, we observed a marked reduction in the percentage of nuclear proteins
The use of desorbing agents in electrodialytic remediation of harbour sediment
DEFF Research Database (Denmark)
Nystrøm, Gunvor Marie; Pedersen, Anne Juul; Ottosen, Lisbeth M.
2006-01-01
Electrodialytic removal of Cu, Zn, Pb and Cd from contaminated harbour sediment was made with the emphasis of testing the effectiveness of different desorbing agents: HCl, NaCl, citric acid, lactic acid, ammonium citrate and distilled water. Extraction experiments with the desorbing agents were...... made prior to the electrodialytic experiments. The extractions showed that HCl was most efficient for metal desorption, probably due to the low pH and complexation with chloride. The metals were not extracted by distilled water. However, in the electrodialytic experiments, the removal was high when...... using distilled water and the desorbing agents did generally not enhance the heavy metal removal compared to distilled water. The only exception was with lactic acid, where the Cu removal was 20% higher compared to the other desorbing agents. The removal was 48% Cu, 80% Zn, 96% Pb and 98% Cd, when using...
Influence of nonlinear sorption kinetics on the slow-desorbing organic contaminant fraction in soil
Schlebaum, W.; Schraa, G.; Riemsdijk, van W.H.
1999-01-01
Release rates of hydrophobic organic compounds (HOCs) from the soil matrix influence the availability of HOCs in soils or sediments for microbial degradation or removal by physical means (e.g., soil washing or soil venting). In this study it was shown that the initial contaminant concentration
Topically applied methotrexate is rapidly delivered into skin by fractional laser ablation
DEFF Research Database (Denmark)
Taudorf, Elisabeth Hjardem; Lerche, Catharina; Vissing, Anne-Cathrine
2015-01-01
/v%) was measured from 0.25 to 24 h through AFXL-processed and intact porcine skin in Franz Cells (n = 46). A 2,940 nm fractional Erbium Yttrium Aluminium Garnet laser generated mid-dermal microchannels at 2.4% density, and 256 mJ/microchannel. HPLC quantified MTX-concentrations in extracts from mid-dermal skin...... sections, donor and receiver compartments. Fluorescence microscopy of UVC-activated MTX-fluorescence and desorption electro-spray ionization mass spectrometry imaging (DESI-MSI) evaluated MTX biodistribution. Results: AFXL-processed skin facilitated rapid MTX delivery through cone-shaped microchannels...... of 690 µm ablation depth, lined by the 47 µm thermal coagulation zone (CZ). Quantitatively, MTX was detectable by HPLC in mid-dermis after 15 min, significantly exceeded deposition in intact skin after 1.5 h, and saturated skin after 7 h at a 10-fold increased MTX-deposition versus intact skin (3.08 vs 0...
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Schwab, K.; Brack, W. [UFZ - Helmholtz Centre or Environmental Research, Leipzig (Germany). Dept. of Effect-Directed Analysis
2007-06-15
Background, Aim and Scope: Effect-directed analysis (EDA) is a powerful tool for the identification of key toxicants in complex environmental samples. In most cases, EDA is based on total extraction of organic contaminants leading to an erroneous prioritization with regard to hazard and risk. Bioaccessibility-directed extraction aims to discriminate between contaminants that take part in partitioning between sediment and biota in a relevant time frame and those that are enclosed in structures, that do not allow rapid desorption. Standard protocols of targeted extraction of rapidly desorbing, and thus bioaccessible fraction using TENAX {sup registered} are based only on small amounts of sediment. In order to get sufficient amounts of extracts for subsequent biotesting, fractionation, and structure elucidation a large volume extraction technique needs to be developed applying one selected extraction time and excluding toxic procedural blanks. Materials and Methods: Desorption behaviour of sediment contaminants was determined by a consecutive solid-solid extraction of sediment using TENAX {sup registered} fitting a tri-compartment model on experimental data. Time needed to remove the rapidly desorbing fraction trap was calculated to select a fixed extraction time for single extraction procedures. Up-scaling by about a factor of 100 provided a large volume extraction technique for EDA. Reproducibility and comparability to small volume approach were proved. Blanks of respective TENAX {sup registered} mass were investigated using Scenedesmus vacuolatus and Artemia salina as test organisms. Results: Desorption kinetics showed that 12 to 30 % of sediment associated pollutants are available for rapid desorption. t{sub r}ap is compound dependent and covers a range of 2 to 18 h. On that basis a fixed extraction time of 24 h was selected. Validation of large volume approach was done by the means of comparison to small method and reproducibility. The large volume showed a good
Determination of Desorbed Species During Heating of AgI-Mordenite Provided by ORNL
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Croes, Kenneth James [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Garino, Terry J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mowry, Curtis D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Nenoff, Tina M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-12-15
This study is focused on describing the desorbed off gases due to heating of the AgIMordenite (MOR) produced at ORNL for iodine (I_{2}) gas capture from nuclear fuel aqueous reprocessing. In particular, the interest is for the incorporation of the AgI-MOR into a waste form, which might be the Sandia developed, low temperature sintering, Bi-Si oxide based, Glass Composite Material (GCM). The GCM has been developed as a waste form for the incorporation any oxide based getter material. In the case where iodine may be released during the sintering process of the GCM, additional Ag flake is added as further insurance in total iodine capture and retention. This has been the case for the incorporated ORNL developed AgIMOR. Thermal analysis studies were carried out to determine off gasing processes of ORNL AgIMOR. Independent of sample size, ~7wt% of total water is desorbed by 225°C. This includes both bulk surface and occluded water, and are monitored as H2O and OH. Of that total, ~5.5wt% is surface water which is removed by 125°C, and 1.5wt% is occluded (in zeolite pore) water. Less than ~1 wt% total water continues to desorb, but is completely removed by 500°C. Above 300°C, the detectable remaining desorbing species observed are iodine containing compounds, including I and I_{2}.
Madhavan, Dinesh B; Baldock, Jeff A; Read, Zoe J; Murphy, Simon C; Cunningham, Shaun C; Perring, Michael P; Herrmann, Tim; Lewis, Tom; Cavagnaro, Timothy R; England, Jacqueline R; Paul, Keryn I; Weston, Christopher J; Baker, Thomas G
2017-05-15
Reforestation of agricultural lands with mixed-species environmental plantings can effectively sequester C. While accurate and efficient methods for predicting soil organic C content and composition have recently been developed for soils under agricultural land uses, such methods under forested land uses are currently lacking. This study aimed to develop a method using infrared spectroscopy for accurately predicting total organic C (TOC) and its fractions (particulate, POC; humus, HOC; and resistant, ROC organic C) in soils under environmental plantings. Soils were collected from 117 paired agricultural-reforestation sites across Australia. TOC fractions were determined in a subset of 38 reforested soils using physical fractionation by automated wet-sieving and 13C nuclear magnetic resonance (NMR) spectroscopy. Mid- and near-infrared spectra (MNIRS, 6000-450 cm-1) were acquired from finely-ground soils from environmental plantings and agricultural land. Satisfactory prediction models based on MNIRS and partial least squares regression (PLSR) were developed for TOC and its fractions. Leave-one-out cross-validations of MNIRS-PLSR models indicated accurate predictions (R2 > 0.90, negligible bias, ratio of performance to deviation > 3) and fraction-specific functional group contributions to beta coefficients in the models. TOC and its fractions were predicted using the cross-validated models and soil spectra for 3109 reforested and agricultural soils. The reliability of predictions determined using k-nearest neighbour score distance indicated that >80% of predictions were within the satisfactory inlier limit. The study demonstrated the utility of infrared spectroscopy (MNIRS-PLSR) to rapidly and economically determine TOC and its fractions and thereby accurately describe the effects of land use change such as reforestation on agricultural soils. Copyright © 2017 Elsevier Ltd. All rights reserved.
A rapid method for standardization of the gated radionuclide left ventricular ejection fraction
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Purnell, G.L.; Baker, B.J.; Murphy, M.M.; Boyd, C.M.; Dalrymple, G.V. (Univ. of Arkansas for Medical Sciences (USA))
1990-08-01
Radionuclide ventriculography has become the standard method for serially evaluating left ventricular ejection fraction (EF). The gold standard for evaluating EF is the contrast ventriculogram, which uses mathematical models to arrive at the volumes used to calculate EF. These models are subject to possible error. This paper reports the standardization of volume measurements of a digital angiographic camera system using a series of cardiac phantoms and the correlation of measurement of the EF of a series of patients whose EF was determined by digital angiography and radionuclide ventriculography.
Modeling of adsorber/desorber/catalytic reactor system for ethylene oxide removal
Directory of Open Access Journals (Sweden)
ZELJKO B. GRBAVCIC
2004-12-01
Full Text Available The removal of ethylene oxide (EtO in a combined system adsorber/desorber/catalytic reactor has been investigated. The combined system was a modified draft tube spouted bed reactor loaded with Pt/Al2O3 catalyst. The annular region was divided into two sectons, the hot section contained about 7 % of catalyst and it behaved as a desorber and catalytic incinerator, while the cold section, with the rest of the catalyst, behaved as a sorber. The catalyst particles were circulated between the two sections by use of a draft tube riser. The Computational Fluid Dynamics (CFD program package FLUENT was used for simulations of the operation of the combined system. In addition, a one-dimensional numerical model for the operation of the packed bed reactor was compared with the corresponding FLUENT calculations. The results of the FLUENT simulations are in very good agreement with the experimental observations, as well as with the results of the one-dimensional numerical simulations.
Plume characteristics and dynamics of UV and IR laser-desorbed oligonucleotides.
Merrigan, Tony L; Timson, David J; Hunniford, C Adam; Catney, Martin; McCullough, Robert W
2012-05-01
Laser desorption of dye-tagged oligonucleotides was studied using laser-induced fluorescence imaging. Desorption with ultra violet (UV) and infra-red (IR) lasers resulted in forward directed plumes of molecules. In the case of UV desorption, the initial shot desorbed approximately seven-fold more material than subsequent shots. In contrast, the initial shot in IR desorption resulted in the ejection of less material compared to subsequent shots and these plumes had a component directed along the path of the laser. Thermal equilibrium of the molecules in the plume was achieved after approximately 25 μs with a spread in molecular temperature which was described by a modified Maxwell-Boltzmann equation. Copyright © 2012 Elsevier B.V. All rights reserved.
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Arsenijević Zorana
2008-01-01
Full Text Available The removal of volatile organic compounds (VOCs from numerous emission sources is of crucial importance due to more rigorous demands on air quality. Different technologies can be used to treat the VOCs from effluent gases: absorption, physical adsorption, open flame combustion, thermal and catalytic incineration. Their appropriateness for the specific process depends on several factors such as efficiency, energy consumption, secondary pollution, capital investments etc. The distinctive features of the catalytic combustion are high efficiency and selectivity toward benign products, low energy consumption and absence of secondary pollution. The supported noble catalysts are widely used for catalytic incineration due to their low ignition temperatures and high thermal and chemical stability. In our combined system adsorption and desorption are applied in the spouted bed with draft tube (SBDT unit. The annular zone, loaded with sorbent, was divided in adsorption and desorption section. Draft tube enabled sorbent recirculation between sections. Combustion of desorbed gases to CO2 and water vapor are realized in additive catalytic reactor. This integrated device provided low concentrations VOCs removal with reduced energy consumption. Experiments were conducted on a pilot unit of 220 m3/h nominal capacity. The sorbent was activated carbon, type K81/B - Trayal Corporation, Krusevac. A sphere shaped commercial Pt/Al2O3 catalyst with "egg-shell" macro-distribution was used for the investigation of xylene deep oxidation. Within this paper the investigations of removal of xylene vapors, a typical pollutant in production of liquid pesticides, in combined adsorber/desorber/catalytic reactor system is presented.
Yamamoto, Norio; Yamashita, Yoko; Yoshioka, Yasukiyo; Nishiumi, Shin; Ashida, Hitoshi
2016-08-01
Membrane proteins account for 70% to 80% of all pharmaceutical targets, indicating their clinical relevance and underscoring the importance of identifying differentially expressed membrane proteins that reflect distinct disease properties. The translocation of proteins from the bulk of the cytosol to the plasma membrane is a critical step in the transfer of information from membrane-embedded receptors or transporters to the cell interior. To understand how membrane proteins work, it is important to separate the membrane fraction of cells. This unit provides a protocol for rapidly obtaining plasma membrane fractions for western blot analysis. © 2016 by John Wiley & Sons, Inc. Copyright © 2016 John Wiley & Sons, Inc.
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Pankow, J.F.; Kristensen, T.J.
1983-11-01
One factor limiting adsorption/thermal desorption (ATD) preconcentration techniques is the thermal desorbability of the analyte compounds. The behavior of a set of compounds including polynuclear aromatic hydrocarbons (PAH) and several pesticides on 0.110 g of the sorbent Tenax-GC was investigated as a function of desorption temperature and carrier gas flow rate. The recoveries obtained with helium at 11.2 mL/min are as follows: naphthalene, 99 +/- 1; fluorene, 70 +/- 1; ..cap alpha..-BHC, 97 +/- 8; heptachlor, 26 +/- 5; fluoranthene, 99 +/- 1; pyrene, 93 +/- 1; dieldrin, 120 +/- 3; DDD, 60 +/- 2;DDT 20 +/- 1; benzo(k)fluoranthene, 93 +/- 3; perylene, 89 +/- 2; and benzo(ghi)perylene, 88 +/- 5. The desorbing compounds were trapped on a fused silica capillary column at -30/sup 0/C. Excellent resolution and separation number performance was maintained despite the use of high desorption carrier gas flow rates. Estimates were made of the retention volume and desorbing peak width characteristics of several of the compounds on Tenax-GC at the desorption temperatures studied. 5 figures, 3 tables.
Reeve, Peter J; Fallowfield, Howard J
2017-10-05
Surfactant Modified Zeolite (SMZ) represents a versatile, cost-effective permeable reactive material, capable of treating multiple classes of contaminants. The potential for HDTMA-Br, a cationic surfactant commonly used to modify zeolite, to desorb from the zeolite surface has been identified as a potential issue for the ongoing use of SMZ in water remediation contexts. This paper investigates the toxicity of HDTMA-Br towards enteric virus surrogates, F-RNA bacteriophage MS2 and E. coli, Bacillus subtilis, and soil microflora. The concentration of surfactant desorbing from SMZ was quantified through a bioassay using E. coli. Results showed HDTMA-Br concentrations of ≥10-5M were toxic to MS2, ≥10-4M were toxic to E. coli and ≥10-6M were toxic to B. subtilis. No toxic relationship was established between HDTMA-Br and soil microflora. Desorption of ≥10-4M of HDTMA-Br was shown for the two SMZ samples under the mixing conditions used. Effects of this surfactant on total soil microflora were ambiguous since no toxic relationship could be established, however, HDTMA-Br, at concentrations desorbing from SMZ, were shown to impact the soil bacterium B. subtilis. Further research is required to determine the effect of this surfactant on microbial populations and species diversity in soils. Copyright © 2017 Elsevier B.V. All rights reserved.
Shiratani, Masaharu; Koga, Kazunori; Iwashita, Shinya; Nunomura, Syota
2008-01-01
We have observed transport of nano-particles having, on average, a fractional elementary charge in single pulse and double pulse capacitively-coupled rf discharges both without and with an Amplitude Modulation (AM) of the discharge voltage, using a two-dimensional laser-light scattering method. Rapid transport of nano-particles towards the grounded electrode is realized using rf discharges with AM. Two important parameters for the rapid transport of nano-particles are the discharge voltage and the period of AM. An important key of the rapid transport is fast redistribution of ion current over the whole discharge region; that is, fast change of spatial distribution of forces exerted on nano-particles. The longer period of the modulation is needed for rapid transport for the larger nano-particles. The higher discharge voltage of the modulation is needed for rapid transport of nano-particles having a smaller mean charge. Local perturbation of electric potential using a probe does not bring about global rapid transport of nano-particles, whereas it leads to their local transport near the probe.
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Gasper, Gerald L. [Department of Chemistry, University of Illinois at Chicago, 845 W. Taylor Street (m/c 111), Chicago, IL 60607 (United States); Takahashi, Lynelle K. [Department of Chemistry, University of California, Berkeley, Room 419 Latimer Hall, Berkeley, CA 94720-1460 (United States); Chemical Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720 (United States); Zhou Jia; Ahmed, Musahid [Chemical Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720 (United States); Moore, Jerry F. [MassThink LLC, 500 East Ogden Avenue Suite 200, Naperville, IL 60563 (United States); Hanley, Luke, E-mail: lhanley@uic.edu [Department of Chemistry, University of Illinois at Chicago, 845 W. Taylor Street (m/c 111), Chicago, IL 60607 (United States)
2011-09-01
Vacuum and extreme ultraviolet radiation from 8 to 24 eV generated at a synchrotron was used to postionize laser desorbed neutrals of antibiotic-treated biofilms and a modified fullerene using laser desorption postionization mass spectrometry (LDPI-MS). Results show detection of the parent ion, various fragments, and extracellular material from biofilms using LDPI-MS with both vacuum and extreme ultraviolet photons. Parent ions were observed for both cases, but extreme ultraviolet photons (16-24 eV) induced more fragmentation than vacuum ultraviolet (8-14 eV) photons.
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Gaspera, Gerald L.; Takahashi, Lynelle K.; Zhou, Jia; Ahmed, Musahid; Moored, Jerry F.; Hanley, Luke
2010-12-08
Vacuum and extreme ultraviolet radiation from 8 - 24 eV generated at a synchrotron was used to postionize laser desorbed neutrals of antibiotic-treated biofilms and a modified fullerene using laser desorption postionization mass spectrometry (LDPI-MS). Results show detection of the parent ion, various fragments, and extracellular material from biofilms using LDPI-MS with both vacuum and extreme ultraviolet photons. Parent ions were observed for both cases, but extreme ultraviolet photons (16-24 eV) induced more fragmentation than vacuum ultraviolet (8-14 eV) photons.
Directory of Open Access Journals (Sweden)
Mohammad Amir Amirkhani
2016-06-01
Conclusion: The current protocol based on the sonication-mediated cavitation is a rapid, safe and cost-effective method, which is proposed for isolation of SVF and of course ADSCs cultures in a large scale for the clinical trials or therapeutic purposes.
Wang, Tao; Elbaz, D.; Alexander, D. M.; Xue, Y. Q.; Gabor, J. M.; Juneau, S.; Schreiber, C.; Zheng, X.-Z.; Wuyts, S.; Shi, Y.; Daddi, E.; Shu, X.-W.; Fang, G.-W.; Huang, J.-S.; Luo, B.; Gu, Q.-S.
2017-05-01
We explore the dependence of the incidence of moderate-luminosity (L0.5-8 keV = 1041.9-43.7 erg s-1) active galactic nuclei (AGNs) and the distribution of their accretion rates on host color at 0.5 mass-complete parent galaxy sample down to M∗ > 1010 M⊙. We use extinction-corrected rest-frame U-V colors to divide both AGN hosts and non-AGN galaxies into red sequence (red), green valley (green), and blue cloud (blue) populations. We find that the fraction of galaxies hosting an AGN at fixed X-ray luminosity increases with stellar mass and redshift for all the three galaxy populations, independent of their colors. However, both the AGN fraction at fixed stellar mass and its evolution with redshift are clearly dependent on host colors. Most notably, red galaxies have the lowest AGN fraction ( 5%) at z 1 yet with most rapid evolution with redshift, increasing by a factor of 5 (24%) at z 2. Green galaxies exhibit the highest AGN fraction across all redshifts, which is most pronounced at z 2 with more than half of them hosting an AGN at M∗ > 1010.6 M⊙. Together with the high AGN fraction in red galaxies at z 2, this indicates that (X-ray) AGNs could be important in both transforming (quenching) star-forming galaxies into quiescent ones and subsequently maintaining their quiescence at high redshift. Furthermore, consistent with previous studies at lower redshifts, we show that the probability of hosting an AGN for the total galaxy population can be characterized by a universal Eddington ratio (as approximated by LX/M∗) distribution (p(λEdd) λEdd-0.4), which is independent on host mass. Yet consistent with their different AGN fractions, galaxies with different colors appear to also have different p(λEdd) with red galaxies exhibiting more rapid redshift evolution compared with that for green and blue galaxies. Evidence for a steeper power-law distribution of p(λEdd) in red galaxies (p(λEdd) λEdd-0.6) is also presented, though larger samples are needed to
Ugliano, Maurizio
2016-12-01
This work describes the application of disposable screen printed carbon paste sensors for the analysis of the main white wine oxidizable compounds as well as for the rapid fingerprinting and classification of white wines from different grape varieties. The response of individual white wine antioxidants such as flavanols, flavanol derivatives, phenolic acids, SO2 and ascorbic acid was first assessed in model wine. Analysis of commercial white wines gave voltammograms featuring two unresolved anodic waves corresponding to the oxidation of different compounds, mostly phenolic antioxidants. Calculation of the first order derivative of measured current vs. applied potential allowed resolving these two waves, highlighting the occurrence of several electrode processes corresponding to the oxidation of individual wine components. Through the application of Principal Component Analysis (PCA), derivative voltammograms were used to discriminate among wines of different varieties. Copyright © 2016 Elsevier Ltd. All rights reserved.
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Jani, Ashish; Shaikh, Fauzia; Barton, Sunjay [Department of Radiation Oncology, Columbia University Medical Center, New York, New York (United States); Willis, Callen [Department of Surgery, Columbia University Medical Center, New York, New York (United States); Banerjee, Debarshi [Department of Pediatrics, Columbia University Medical Center, New York, New York (United States); Mitchell, Jason [Department of Surgery, Columbia University Medical Center, New York, New York (United States); Hernandez, Sonia L. [Department of Surgery, University of Chicago, Chicago, Illinois (United States); Hei, Tom [Department of Radiation Oncology, Columbia University Medical Center, New York, New York (United States); Kadenhe-Chiweshe, Angela [Department of Surgery, Columbia University Medical Center, New York, New York (United States); Yamashiro, Darrell J. [Department of Surgery, Columbia University Medical Center, New York, New York (United States); Department of Pediatrics, Columbia University Medical Center, New York, New York (United States); Department of Pathology and Cell Biology, Columbia University Medical Center, New York, New York (United States); Connolly, Eileen P., E-mail: epc2116@cumc.columbia.edu [Department of Radiation Oncology, Columbia University Medical Center, New York, New York (United States)
2016-04-01
Purpose: To characterize the effects of high-dose radiation therapy (HDRT) on neuroblastoma tumor vasculature, including the endothelial cell (EC)–pericyte interaction as a potential target for combined treatment with antiangiogenic agents. Methods and Materials: The vascular effects of radiation therapy were examined in a xenograft model of high-risk neuroblastoma. In vivo 3-dimensional contrast-enhanced ultrasonography (3D-CEUS) imaging and immunohistochemistry (IHC) were performed. Results: HDRT significantly reduced tumor blood volume 6 hours after irradiation compared with the lower doses used in conventionally fractionated radiation. There was a 63% decrease in tumor blood volume after 12-Gy radiation compared with a 24% decrease after 2 Gy. Analysis of tumor vasculature by lectin angiography showed a significant loss of small vessel ends at 6 hours. IHC revealed a significant loss of ECs at 6 and 72 hours after HDRT, with an accompanying loss of immature and mature pericytes at 72 hours. Conclusions: HDRT affects tumor vasculature in a manner not observed at lower doses. The main observation was an early reduction in tumor perfusion resulting from a reduction of small vessel ends with a corresponding loss of endothelial cells and pericytes.
Yuan, XiaoDong; Tang, Wei; Shi, WenWei; Yu, Libao; Zhang, Jing; Yuan, Qing; You, Shan; Wu, Ning; Ao, Guokun; Ma, Tingting
2018-02-09
To develop a convenient and rapid single-kidney CT-GFR technique. One hundred and twelve patients referred for multiphasic renal CT and 99mTc-DTPA renal dynamic imaging Gates-GFR measurement were prospectively included and randomly divided into two groups of 56 patients each: the training group and the validation group. On the basis of the nephrographic phase images, the fractional renal accumulation (FRA) was calculated and correlated with the Gates-GFR in the training group. From this correlation a formula was derived for single-kidney CT-GFR calculation, which was validated by a paired t test and linear regression analysis with the single-kidney Gates-GFR in the validation group. In the training group, the FRA (x-axis) correlated well (r = 0.95, p < 0.001) with single-kidney Gates-GFR (y-axis), producing a regression equation of y = 1665x + 1.5 for single-kidney CT-GFR calculation. In the validation group, the difference between the methods of single-kidney GFR measurements was 0.38 ± 5.57 mL/min (p = 0.471); the regression line is identical to the diagonal (intercept = 0 and slope = 1) (p = 0.727 and p = 0.473, respectively), with a standard deviation of residuals of 5.56 mL/min. A convenient and rapid single-kidney CT-GFR technique was presented and validated in this investigation. • The new CT-GFR method takes about 2.5 min of patient time. • The CT-GFR method demonstrated identical results to the Gates-GFR method. • The CT-GFR method is based on the fractional renal accumulation of iodinated CM. • The CT-GFR method is achieved without additional radiation dose to the patient.
Giardina, Bennett J; Stein, Kathryn; Chiang, Hui-Ling
2014-01-01
Protein secretion is a fundamental process in all living cells. Gluconeogenic enzymes are secreted when Saccharomyces cerevisiae are grown in media containing low glucose. However, when cells are transferred to media containing high glucose, they are internalized. We investigated whether or not gluconeogenic enzymes were associated with extracellular vesicles in glucose-starved cells. We also examined the role that the endocytosis gene END3 plays in the internalization of extracellular proteins/vesicles in response to glucose addition. Transmission electron microscopy was performed to determine the presence of extracellular vesicles in glucose-starved wild-type cells and the dynamics of vesicle transport in cells lacking the END3 gene. Proteomics was used to identify extracellular proteins that associated with these vesicles. Total extracts prepared from glucose-starved cells consisted of about 95% small vesicles (30-50 nm) and 5% large structures (100-300 nm). The addition of glucose caused a rapid decline in small extracellular vesicles in wild-type cells. However, most of the extracellular vesicles were still observed in cells lacking the END3 gene following glucose replenishment. Proteomics was used to identify 72 extracellular proteins that may be associated with these vesicles. Gluconeogenic enzymes fructose-1,6-bisphosphatase, malate dehydrogenase, isocitrate lyase, and phosphoenolpyruvate carboxykinase, as well as non-gluconeogenic enzymes glyceraldehyde-3-phosphate dehydrogenase and cyclophilin A, were distributed in the vesicle-enriched fraction in total extracts prepared from cells grown in low glucose. Distribution of these proteins in the vesicle-enriched fraction required the integrity of the membranes. When glucose was added to glucose-starved wild-type cells, levels of extracellular fructose-1,6-bisphosphatase, malate dehydrogenase, isocitrate lyase, phosphoenolpyruvate carboxykinase, glyceraldehyde-3-phosphate dehydrogenase, and cyclophilin A were
Sharapov, V. I.; Kudryavtseva, E. V.
2017-11-01
The technology of low-temperature deaeration of water in thermal power plants was developed. It is proposed to use natural gas supplied to the furnace as desorbing agent in the deaerator instead steam or superheated water. Natural gas has low, often - negative temperature after reducing installs. At the same time, it contains virtually no corrosive gases, oxygen and carbon dioxide, thereby successfully may be used as a stripping agent in water deaeration. The calculation of the energy efficiency of the technology for a typical unit of CHP has shown that achieved a significant annual saving of fuel equivalent in the transition from the traditional method of deaeration of water in the low temperature deaeration. Hydrodynamic and mass transfer indicators were determined for the deaerator thermal power plants using as stripping medium natural gas supplied to the boiler burners. Theoretically required amount and the real specific consumption of natural gas were estimated for deaeration of water standard quality. The calculation of the hydrodynamic characteristics was presented for jet-bubbling atmospheric deaerator with undescended perforated plate when operating on natural gas. The calculation shows the possibility of using commercially available atmospheric deaerators for the application of the new low-temperature water deaeration technology.
Uhlemann, Thomas; Seidel, Sebastian; Müller, Christian W.
2017-06-01
Molecules containing the sulfonamide group R^{1}-SO_2-NHR^{2} have a longstanding history as antimicrobial agents. Even though nowadays they are not commonly used in treating humans anymore, they continue to be studied as effective inhibitors of metalloenzyme carbonic anhydrases. These enzymes are important targets for a variety of diseases, such as, for instance, breast cancer, glaucoma, and obesity. Here we present the results of our laser desorption single-conformation UV and IR study of sulfanilamide (NH_2Ph-SO_2-NHR, R=H), a variety of singly substituted derivatives, and their monohydrated complexes. Depending on the substituent, the sulfonamide group can either adopt an amino or an imino tautomeric form. The form prevalent in the crystal is not necessarily also the tautomeric form we identified in the molecular beam after laser desorbing the sample. Furthermore, we explored the effect of complexation with a single water molecule on the tautomeric and conformational preferences of the sulfonamides. Our conformer-specific IR spectra in the NH and OH stretch region (3200-3750 \\wn) suggest that the intra- and intermolecular interactions governing the structures of the monomers and water complexes are surprisingly diverse. We have undertaken both Quantum Theory of Atoms in Molecules (QTAIM) and Interacting Quantum Atoms (IQA) analyses of calculated electron densities to quantitatively characterize the nature and strengths of the intra- and intermolecular interactions prevalent in the monomer and water complex structures.
Imukova, Kristina; Ingwersen, Joachim; Streck, Thilo
2014-05-01
The green vegetation fraction (GVF) is a key input variable to the evapotranspiration scheme applied in the widely used NOAH land surface model (LSM). In standard applications of the NOAH LSM, the GVF is taken from a global map with a 15 km×15 km resolution. The central objective of the present study was (a) to derive gridded GVF data in a high spatial and temporal resolution from RapidEye images for a region in Southwest Germany, and (b) to improve the representation of the GVF dynamics of croplands in the NOAH LSM for a better simulation of water and energy exchange between land surface and atmosphere. For the region under study we obtained monthly RapidEye satellite images with a resolution 5 m×5 m by the German Aerospace Center (DLR). The images hold five spectral bands: blue, green, red, red-edge and near infrared (NIR). The GVF dynamics were determined based on the Normalized Difference Vegetation Index (NDVI) calculated from the red and near-infrared bands of the satellite images. The satellite GVF data were calibrated and validated against ground truth measurements. Digital colour photographs above the canopy were taken with a boom-mounted digital camera at fifteen permanently marked plots (1 m×1 m). Crops under study were winter wheat, winter rape and silage maize. The GVF was computed based on the red and the green band of the photographs according to Rundquist's method (2002). Based on the obtained calibration scheme GVF maps were derived in a monthly resolution for the region. Our results confirm a linear relationship between GVF and NDVI and demonstrate that it is possible to determine the GVF of croplands from RapidEye images based on a simple two end-member mixing model. Our data highlight the high variability of the GVF in time and space. At the field scale, the GVF was normally distributed with a coefficient of variation of about 32%. Variability was mainly caused by soil heterogeneities and management differences. At the regional scale the GVF
Yang, Zhong; Li, Kang; Zhang, Maomao; Xin, Donglin; Zhang, Junhua
2016-01-01
During conversion of bamboo into biofuels and chemicals, it is necessary to efficiently predict the chemical composition and digestibility of biomass. However, traditional methods for determination of lignocellulosic biomass composition are expensive and time consuming. In this work, a novel and fast method for quantitative and qualitative analysis of chemical composition and enzymatic digestibilities of juvenile bamboo and mature bamboo fractions (bamboo green, bamboo timber, bamboo yellow, bamboo node, and bamboo branch) using visible-near infrared spectra was evaluated. The developed partial least squares models yielded coefficients of determination in calibration of 0.88, 0.94, and 0.96, for cellulose, xylan, and lignin of bamboo fractions in raw spectra, respectively. After visible-near infrared spectra being pretreated, the corresponding coefficients of determination in calibration yielded by the developed partial least squares models are 0.994, 0.990, and 0.996, respectively. The score plots of principal component analysis of mature bamboo, juvenile bamboo, and different fractions of mature bamboo were obviously distinguished in raw spectra. Based on partial least squares discriminant analysis, the classification accuracies of mature bamboo, juvenile bamboo, and different fractions of bamboo (bamboo green, bamboo timber, bamboo yellow, and bamboo branch) all reached 100 %. In addition, high accuracies of evaluation of the enzymatic digestibilities of bamboo fractions after pretreatment with aqueous ammonia were also observed. The results showed the potential of visible-near infrared spectroscopy in combination with multivariate analysis in efficiently analyzing the chemical composition and hydrolysabilities of lignocellulosic biomass, such as bamboo fractions.
Mendlovic, D; Ozaktas, H M; Lohmann, A W
1995-01-10
Recently, optical interpretations of the fractional-Fourier-transform operator have been introduced. On the basis of this operator the fractional correlation operator is defined in two different ways that are both consistent with the definition of conventional correlation. Fractional correlation is not always a shift-invariant operation. This property leads to some new applications for fractional correlation as shift-variant image detection. A bulk-optics implementation of fractional correlation is suggested and demonstrated with computer simulations.
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 ...
Papaemmanouil, Christina; Tsiafoulis, Constantinos G; Alivertis, Dimitrios; Tzamaloukas, Ouranios; Miltiadou, Despoina; Tzakos, Andreas G; Gerothanassis, Ioannis P
2015-06-10
We report a rapid, direct, and unequivocal spin-chromatographic separation and identification of minor components in the lipid fraction of milk and common dairy products with the use of selective one-dimensional (1D) total correlation spectroscopy (TOCSY) nuclear magnetic resonance (NMR) experiments. The method allows for the complete backbone spin-coupling network to be elucidated even in strongly overlapped regions and in the presence of major components from 4 × 10(2) to 3 × 10(3) stronger NMR signal intensities. The proposed spin-chromatography method does not require any derivatization steps for the lipid fraction, is selective with excellent resolution, is sensitive with quantitation capability, and compares favorably to two-dimensional (2D) TOCSY and gas chromatography-mass spectrometry (GC-MS) methods of analysis. The results of the present study demonstrated that the 1D TOCSY NMR spin-chromatography method can become a procedure of primary interest in food analysis and generally in complex mixture analysis.
Energy Technology Data Exchange (ETDEWEB)
Rahimpour, M.R.; Mottaghi, H.R.; Barmaki, M.M. [Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz71345 (Iran)
2010-06-15
This work presents novel application of palladium-based membrane in a wastewater treatment loop of urea plant for hydrogen production. Urea wastewater treatment loop is based on combined thermal hydrolysis-desorption operations. The wastewater of urea plant includes ammonia and urea which in the current treatment loop; urea decomposes to ammonia and carbon dioxide. The catalytic hydrogen-permselective membrane reactor is proposed for hydrogen production from desorbed ammonia of urea wastewater which much of it discharges to air and causes environmental pollution. Therefore hydrogen is produced from decomposition of ammonia on nickel-alumina catalyst bed simultaneously and permeates from reaction side to shell side through thin layer of palladium-silver membrane. Also a sweep gas is used in the shell side for increasing driving force. In this way, 4588 tons/yr hydrogen is produced and environmental problem of urea plant is solved. The membrane reactor and urea wastewater treatment loop are modeled mathematically and the predicted data of the model are consistent with the experimental and plant data that show validity of the model. Also the effects of key parameters on the performance of catalytic hydrogen-permselective membrane reactor such as the temperature, pressure, thickness of Pd-Ag layer, configuration of flow and sweep gas flow ratio were examined. (author)
Bhattacharyya, Sonalee; Namakshi, Nama; Zunker, Christina; Warshauer, Hiroko K.; Warshauer, Max
2016-01-01
Making math more engaging for students is a challenge that every teacher faces on a daily basis. These authors write that they are constantly searching for rich problem-solving tasks that cover the necessary content, develop critical-thinking skills, and engage student interest. The Mystery Fraction activity provided here focuses on a key number…
Fraction Reduction through Continued Fractions
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.
Fractional Derivative as Fractional Power of Derivative
Tarasov, Vasily E.
2007-01-01
Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.
Zou, Yanping; Chang, Sam K C; Gu, Yan; Qian, Steven Y
2011-03-23
Phenolic compounds were extracted from Morton lentils using acidified aqueous acetone. The crude Morton extract (CME) was applied onto a macroresin column and desorbed by aqueous methanol to obtain a semipurified Morton extract (SPME). The SPME was further fractionated over a Sephadex LH-20 column into five main fractions (I-V). The phytochemical contents such as total phenolic content (TPC), total flavonoid content (TFC), and condensed tannin content (CTC) of the CME, SPME, and its fractions were examined by colorimetric methods. Antioxidant activity of extracts and fractions were screened by DPPH scavenging activity, Trolox equivalent antioxidant capacity (TEAC), ferric reduced antioxidant power (FRAP), and oxygen radical absorbing capacity (ORAC) methods. In addition, the compositions of active fractions were determined by HPLC-DAD and HPLC-MS methods. Results showed that the fraction enriched in condensed tannins (fraction V) exhibited significantly higher values of TPC, CTC, and antioxidant activity as compared to the crude extract, SPME, and low molecular weight fractions (I-IV). Eighteen compounds existed in those fractions, and 17 were tentatively identified by UV and MS spectra. HPLC-MS analysis revealed fraction II contained mainly kaempferol glycoside, fractions III and IV mainly contained flavonoid glycosides, and fraction V was composed of condensed tannins. The results suggested that the extract of Morton lentils is a promising source of antioxidant phenolics and may be used as a dietary supplement for health promotion.
Fractional complex transform for fractional differential equations
National Research Council Canada - National Science Library
Lİ, Zheng Biao; HE, Ji Huan
2010-01-01
Fractional complex transform is proposed to convert fractional differential equations into ordinary differential equations, so that all analytical methods devoted to advanced calculus can be easily...
Fractional vector calculus for fractional advection dispersion
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.
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.
Lavilla, I; Pena-Pereira, F; Gil, S; Costas, M; Bendicho, C
2009-08-04
In this work, we demonstrate the feasibility of applying headspace single-drop microextraction with in-drop precipitation for the quantitative determination of the acid labile sulfide fraction (H2S, HS-, and S2- (free sulfide), amorphous FeS and some metal sulfide complexes-clusters as ZnS) in aqueous samples by microvolume turbidimetry. The methodology lies in the in situ hydrogen sulfide generation and subsequent sequestration into an alkaline microdrop containing ZnO(2)(2-) and exposed to the headspace above the stirred aqueous sample. The ZnS formed in the drop was then determined by microvolume turbidimetry. The optimum experimental conditions of the proposed method were: 2 microL of a microdrop containing 750 mg L(-1) Zn(II) in 1 mol L(-1) NaOH exposed to the headspace of a 20-mL aqueous sample stirred at 1600 rpm during 80 s after derivatization with 1 mL of 6 mol L(-1) HCl. An enrichment factor of 1710 was achieved in only 80 s. The calibration graph was linear in the range of 5-100 microg L(-1) with a detection limit of 0.5 microg L(-1). The repeatability, expressed as relative standard deviation, was 5.8% (N = 9). Finally, the proposed methodology was successfully applied to the determination of the acid labile sulfide fraction in different natural water samples.
Random fractional Fourier transform.
Liu, Zhengjun; Liu, Shutian
2007-08-01
We propose a novel random fractional Fourier transform by randomizing the transform kernel function of the conventional fractional Fourier transform. The random fractional Fourier transform inherits the excellent mathematical properties from the fractional Fourier transform and can be easily implemented in optics. As a primary application the random fractional Fourier transform can be directly used in optical image encryption and decryption. The double phase encoding image encryption schemes can thus be modeled with cascaded random fractional Fourier transformers.
Zou, Yanping; Chang, Sam K.C.; Gu, Yan; Qian, Steven Y.
2011-01-01
Phenolic compounds were extracted from Morton lentils using acidified aqueous acetone. The crude Morton extract (CME) was applied onto a macroresin column and desorbed by aqueous methanol to obtain a semi-purified Morton extract (SPME). The SPME was further fractionated over Sephadex LH-20 column into five main fractions (Fr I – Fr V). The phytochemical contents such as total phenolic content (TPC), total flavonoid content (TFC), and condensed tannin content (CTC) of the CME, SPME, and its fractions were examined by colorimetric methods. Antioxidant activity of extracts and fractions were screened by DPPH scavenging activity, trolox equivalent antioxidant capacity (TEAC), ferric reduced antioxidant power (FRAP), and oxygen radical absorbing capacity (ORAC) methods. In addition, the compositions of active fractions were determined by HPLC-DAD and HPLC-MS methods. Results showed that fraction enriched in condensed tannins (Fr V) exhibited significantly higher value of TPC, CTC and higher antioxidant activity as compared to the crude extract, SPME and low-molecular-weight fractions (Fr I – IV). Eighteen compounds existed in those fractions, and seventeen were tentatively identified by UV and MS spectra. HPLC-MS analysis revealed Fr II contained mainly kaempferol glycoside, Fr III and Fr IV mainly contained flavonoid glycosides, and Fr V was composed of condensed tannins. The results suggested that extract of Morton lentils is a promising source of antioxidant phenolics, and may be used as a dietary supplement for health promotion. PMID:21332205
Energy Technology Data Exchange (ETDEWEB)
Burke, F.P.; Winschel, R.A.; Wooton, D.L.
1979-07-01
A method is described for the solvent fractionation of coal liquefaction and petroleum products which is both reproducible and considerably more rapid than many conventional solvent fractionation techniques. This method involves sequential elution of a sample injected onto an inert liquid chromatographic column. Applications of this method to coal liquefaction and petroleum products are given.
Initialized Fractional Calculus
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.
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.
MEERSCHAERT, MARK M.; SABZIKAR, FARZAD; CHEN, JINGHUA
2014-01-01
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 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. PMID:26085690
Meerschaert, Mark M; Sabzikar, Farzad; Chen, Jinghua
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 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.
FRACTIONAL INTEGRATION TOOLBOX.
Marinov, Toma M; Ramirez, Nelson; Santamaria, Fidel
2013-09-01
The problems formulated in the fractional calculus framework often require numerical fractional integration/differentiation of large data sets. Several existing fractional control toolboxes are capable of performing fractional calculus operations, however, none of them can efficiently perform numerical integration on multiple large data sequences. We developed a Fractional Integration Toolbox (FIT), which efficiently performs fractional numerical integration/differentiation of the Riemann-Liouville type on large data sequences. The toolbox allows parallelization and is designed to be deployed on both CPU and GPU platforms.
Fractionation of whey proteins with high-capacity superparamagnetic ion-exchangers
DEFF Research Database (Denmark)
Heebøll-Nielsen, Anders; Justesen, S.F.L.; Thomas, Owen R. T.
2004-01-01
In this study we describe the design, preparation and testing of superparamagnetic anion-exchangers, and their use together with cation-exchangers in the fractionation of bovine whey proteins as a model study for high-gradient magnetic fishing. Adsorbents prepared by attachment of trimethyl amine...... to 337 mg g(-1) with a dissociation constant of 0.042 muM. The latter anion-exchanger was selected for studies of whey protein fractionation. In these, crude bovine whey was treated with a superparamagnetic cation-exchanger to adsorb basic protein species, and the supernatant arising from this treatment......) was achieved with some simultaneous binding of immunoglobulins (1g). The immunoglobulins were separated from the other two proteins by desorbing with a low concentration of NaCl (less than or equal to0.4 M), whereas lactoferrin and lactoperoxidase were co-eluted in significantly purer form, e...
Fractionation of whey proteins with high-capacity superparamagnetic ion-exchangers
DEFF Research Database (Denmark)
Heebøll-Nielsen, Anders; Justesen, Sune; Thomas, Owen R. T.
2004-01-01
In this study we describe the design, preparation and testing of superparamagnetic anion-exchangers, and their use together with cation-exchangers in the fractionation of bovine whey proteins as a model study for high-gradient magnetic fishing. Adsorbents prepared by attachment of trimethyl amine...... to 337 mg g-1 with a dissociation constant of 0.042 µM. The latter anion-exchanger was selected for studies of whey protein fractionation. In these, crude bovine whey was treated with a superparamagnetic cation-exchanger to adsorb basic protein species, and the supernatant arising from this treatment......) was achieved with some simultaneous binding of immunoglobulins (Ig). The immunoglobulins were separated from the other two proteins by desorbing with a low concentration of NaCl (=0.4 M), whereas lactoferrin and lactoperoxidase were co-eluted in significantly purer form, e.g. lactoperoxidase was purified 28...
Dewi, D. A. K.; Suryadi, D.; Suratno, T.; Mulyana, E.; Kurniawan, H.
2017-02-01
Introducing fractions is identical to divide an object. Suppose we divide the apple into two parts. One divided into two parts, the question arises whether one part can be called a half or not. Based on this activity, how can students give meaning to fractions. This study aims at designing a different fractions lesson by applying Didactical Design Research. In doing so, we undertook several research phases: 1) thinking what is fractions and why students should learn this concept; 2) designing didactical situation based on identified learning obstacles; and 3) reflecting retrospectively on the lesson design and its implementation as to redesign the fractions lesson. Our analysis revealed that most students held epistemological obstacles in giving meaning of fractions because they only know fractions as numbers that have numerator and denominator. By positioning ourselves as students, we discuss the ideal design to help students in constructing the meaning of fractions.
Fractional Multidimensional System
Zhu, Xiaogang; Lu, Junguo
2017-01-01
The multidimensional ($n$-D) systems described by Roesser model are presented in this paper. These $n$-D systems consist of discrete systems and continuous fractional order systems with fractional order $\
MEERSCHAERT, MARK M.; SABZIKAR, FARZAD; 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 obs...
On continued fraction algorithms
Smeets, Ionica
2010-01-01
Is there a good continued fraction approximation between every two bad ones? What is the entropy of the natural extension for alpha-Rosen fractions? How do you find multi-dimensional continued fractions with a guaranteed quality in polynomial time? These, and many more, questions are answered in
Nonlinear fractional relaxation
Indian Academy of Sciences (India)
Nonlinear fractional equation; nonlinear fractional relaxation; -expansion. Abstract. We deﬁne a nonlinear model for fractional relaxation phenomena. We use -expansion method to analyse this model. By studying the fundamental solutions of this model we ﬁnd that when → 0 the model exhibits a fast decay rate and ...
Unfolding Fraction Multiplication
Wyberg, Terry; Whitney, Stephanie R.; Cramer, Kathleen A.; Monson, Debra S.; Leavitt, Seth
2011-01-01
Students often have difficulty understanding fractions, in general, and understanding how to multiply fractions, in particular. To move past this potential problem area, students need to develop a deeper understanding of multiplication and connect the ideas to fractions. In this article, the authors share their insights into teaching fraction…
Wooding, Madelien; Rohwer, Egmont R; Naudé, Yvette
2017-09-01
The presence of micropollutants in the aquatic environment is a worldwide environmental concern. The diversity of micropollutants and the low concentration levels at which they may occur in the aquatic environment have greatly complicated the analysis and detection of these chemicals. Two sorptive extraction samplers and two thermal desorption methods for the detection of micropollutants in water were compared. A low-cost, disposable, in-house made sorptive extraction sampler was compared to SBSE using a commercial Twister sorptive sampler. Both samplers consisted of polydimethylsiloxane (PDMS) as a sorptive medium to concentrate micropollutants. Direct thermal desorption of the disposable samplers in the inlet of a GC was compared to conventional thermal desorption using a commercial thermal desorber system (TDS). Comprehensive gas chromatography coupled to time-of-flight mass spectrometry (GC × GC-TOFMS) was used for compound separation and identification. Ten micropollutants, representing a range of heterogeneous compounds, were selected to evaluate the performance of the methods. The in-house constructed sampler, with its associated benefits of low-cost and disposability, gave results comparable to commercial SBSE. Direct thermal desorption of the disposable sampler in the inlet of a GC eliminated the need for expensive consumable cryogenics and total analysis time was greatly reduced as a lengthy desorption temperature programme was not required. Limits of detection for the methods ranged from 0.0010 ng L-1 to 0.19 ng L-1. For most compounds, the mean (n = 3) recoveries ranged from 85% to 129% and the % relative standard deviation (% RSD) ranged from 1% to 58% with the majority of the analytes having a %RSD of less than 30%. Copyright © 2017 Elsevier B.V. All rights reserved.
Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Jianping Zhao
2012-01-01
Full Text Available 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 powerful mathematical tool for solving fractional differential equations.
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.
Fractional Dynamics and Control
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...
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...
Dividing Fractions: A Pedagogical Technique
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…
FRACTIONAL PEARSON DIFFUSIONS.
Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla
2013-07-15
Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change.
1999-01-01
Javelin, a Lone Peak Engineering Inc. Company has introduced the SteamRoller(TM) System as a commercial product. The system was designed by Javelin during a Phase II NASA funded small commercial product. The purpose of the invention was to allow automated-feed of flexible ceramic tapes to the Laminated Object Manufacturing rapid prototyping equipment. The ceramic material that Javelin was working with during the Phase II project is silicon nitride. This engineered ceramic material is of interest for space-based component.
Can Kindergartners Do Fractions?
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…
Fractional and noncommutative spacetimes
Arzano, M.|info:eu-repo/dai/nl/32616443X; Calcagni, M.; Oriti, D.; Scalisi, M.
2011-01-01
We establish a mapping between fractional and noncommutative spacetimes in configuration space. Depending on the scale at which the relation is considered, there arise two possibilities. For a fractional spacetime with log-oscillatory measure, the effective measure near the fundamental scale
Directory of Open Access Journals (Sweden)
Brajesh Kumar Singh
2017-01-01
Full Text Available This paper deals with an alternative approximate analytic solution to time fractional partial differential equations (TFPDEs with proportional delay, obtained by using fractional variational iteration method, where the fractional derivative is taken in Caputo sense. The proposed series solutions are found to converge to exact solution rapidly. To confirm the efficiency and validity of FRDTM, the computation of three test problems of TFPDEs with proportional delay was presented. The scheme seems to be very reliable, effective, and efficient powerful technique for solving various types of physical models arising in science and engineering.
Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases
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Fazal Haq
2017-01-01
Full Text Available The fractional order Susceptible-Infected-Recovered (SIR epidemic model of childhood disease is considered. Laplace–Adomian Decomposition Method is used to compute an approximate solution of the system of nonlinear fractional differential equations. We obtain the solutions of fractional differential equations in the form of infinite series. The series solution of the proposed model converges rapidly to its exact value. The obtained results are compared with the classical case.
Fractions of ruminant feeds: kinetics of degradation in vitro
Azarfar, A.
2007-01-01
A widely adopted procedure to characterise the degradation in the rumen and its dynamics is the in situ incubation technique that assumes the washable fraction of feeds (W) to be equal to the soluble (S) fraction and that both are rapidly and completely degraded which may not be
Simplified fractional Fourier transforms.
Pei, S C; Ding, J J
2000-12-01
The fractional Fourier transform (FRFT) has been used for many years, and it is useful in many applications. Most applications of the FRFT are based on the design of fractional filters (such as removal of chirp noise and the fractional Hilbert transform) or on fractional correlation (such as scaled space-variant pattern recognition). In this study we introduce several types of simplified fractional Fourier transform (SFRFT). Such transforms are all special cases of a linear canonical transform (an affine Fourier transform or an ABCD transform). They have the same capabilities as the original FRFT for design of fractional filters or for fractional correlation. But they are simpler than the original FRFT in terms of digital computation, optical implementation, implementation of gradient-index media, and implementation of radar systems. Our goal is to search for the simplest transform that has the same capabilities as the original FRFT. Thus we discuss not only the formulas and properties of the SFRFT's but also their implementation. Although these SFRFT's usually have no additivity properties, they are useful for the practical applications. They have great potential for replacing the original FRFT's in many applications.
Fractional calculus in bioengineering.
Magin, Richard L
2004-01-01
Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub
Fractional finite Fourier transform.
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.
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....
Matsumiya, Hiroaki; Inoue, Hiroto; Hiraide, Masataka
2014-10-01
Gadolinium complexed with naturally occurring, negatively charged humic substances (humic and fulvic acids) was collected from 500 mL of sample solution onto a column packed with 150 mg of a strongly basic anion-exchanger (QAE-Sephadex A-25). A Gd-based magnetic resonance imaging contrast agent (diethylenetriamine-N,N,N',N″,N″-pentaacetato aquo gadolinium(III), Gd-DTPA(2-)) was simultaneously collected on the same column. The Gd-DTPA complex was desorbed by anion-exchange with 50mM tetramethylammonium sulfate, leaving the Gd-humic complexes on the column. The Gd-humic complexes were subsequently dissociated with 1M nitric acid to desorb the humic fraction of Gd. The two-step desorption with small volumes of the eluting agents allowed the 100-fold preconcentration for the fractionation analysis of Gd at low ng L(-1) levels by inductively coupled plasma-mass spectrometry (ICP-MS). On the other hand, Gd(III) neither complexed with humic substances nor DTPA, i.e., free species, was not sorbed on the column. The free Gd in the effluent was preconcentrated 100-fold by a conventional solid-phase extraction with an iminodiacetic acid-type chelating resin and determined by ICP-MS. The proposed analytical fractionation method was applied to river water samples. Copyright © 2014 Elsevier B.V. All rights reserved.
FRACTIONS: CONCEPTUAL AND DIDACTIC ASPECTS
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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.
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...
Laskin, Nick
2000-12-01
A new extension of a fractality concept in financial mathematics has been developed. We have introduced a new fractional Langevin-type stochastic differential equation that differs from the standard Langevin equation: (i) by replacing the first-order derivative with respect to time by the fractional derivative of order μ; and (ii) by replacing “white noise” Gaussian stochastic force by the generalized “shot noise”, each pulse of which has a random amplitude with the α-stable Lévy distribution. As an application of the developed fractional non-Gaussian dynamical approach the expression for the probability distribution function (pdf) of the returns has been established. It is shown that the obtained fractional pdf fits well the central part and the tails of the empirical distribution of S&P 500 returns.
Generalized Fractional Statistics
Kaniadakis, G.; A. Lavagno(Politecnico di Torino and INFN Sezione di Torino, Torino Italy); Quarati, P.
1996-01-01
We link, by means of a semiclassical approach, the fractional statistics of particles obeying the Haldane exclusion principle to the Tsallis statistics and derive a generalized quantum entropy and its associated statistics.
Competitive sorption of heavy metal by soils. Isotherms and fractional factorial experiments.
Echeverría, J C; Morera, M T; Mazkiarán, C; Garrido, J J
1998-01-01
Competing ions strongly affect heavy metal sorption onto the solid surfaces of soil. This study evaluated competitive sorption of Cd, Cu, Ni, Pb and Zn on three soils: Calcixerollic Xerochrept, Paralithic Xerorthent and Lithic Haplumbrept. Monometal and competitive sorption isotherms were obtained at 25 degrees C. The individual effect of ions on retention of the others was ascertained by a fractional factorial analysis design. Most of the sorption isotherms belonged to type L subtype 2 in the classification of Giles. In competitive sorption the initial linear part was shorter and the knee sharper when compared with monometal sorption isotherms. Parameters related to sorptive capacity, such as Point B, Langmuir monolayer and Freundlich distribution coefficient, were higher in monometal than in competitive sorption, and in basic soils than in acidic soil. Calcium desorbed at different points of the sorption isotherms indicated that cationic exchange with Ca was the main retention mechanism in calcareous soils. For Pb, the ratio Ca desorbed/Pb sorbed was close to one; for Cu, Ni and Zn the ratio ranged from 1.20 to 1.37, probably due to partial dissolution of calcium carbonates by hydrolytic processes during retention. On the other hand, Cd had a ratio around 0.6 reflecting another additional retention mechanism, probably surface complexation. Fractional factorial design confirmed that the presence of the cations investigated reduced the amount of the five metals retained, but the presence of Cu and Pb in the system depressed Ni, Cd and Zn sorption more than the inverse. Cation mobility was enhanced when equilibrium concentration increased and the effect was higher in Ca-saturated soils.
Stable Chlorine Isotope Fractionation
Sharp, Z.
2006-12-01
Chlorine isotope partitioning between different phases is not well understood. Pore fluids can have δ37Cl values as low as -8‰, with neoform sediments having strongly positive values. Most strikingly, volcanic gases have δ37Cl values that cover a range in excess of 14‰ (Barnes et al., this meeting). The large range is difficult to explain in terms of equilibrium fractionation, which, although calculated to be very large for Cl in different oxidation states, should be less than 2‰ between chloride species (Schauble et al., 2003, GCA). To address the discrepancy between Nature and theory, we have measured Cl isotope fractionation for selected equilibrium and disequilibrium experiments in order to identify mechanisms that might lead to large fractionations. 1) NaCl (s,l) NaCl (v): NaCl was sealed in an evacuated silica tube and heated at one end, causing vaporization and reprecipitation of NaCl (v) at the cool end of the tube. The fractionation is 0.2‰ at 700°C (halite-vapor) and 0.7‰ at 800°C (liquid-vapor), respectively. The larger fractionation at higher temperature may be related to equilibrium fractionation between liquid and gas vs. `stripping' of the solid in the lower T experiments. 2) Sodalite NaCl(l): Nepheline and excess NaCl were sealed in a Pt crucible at 825°C for 48 hrs producing sodalite. The measured newly-formed sodalite-NaCl fractionation is -0.2‰. 3) Volatilization of HCl: Dry inert gas was bubbled through HCl solutions and the vapor was collected in a downstream water trap. There was no fractionation for 12.4M HCl (HCl fuming) vapor at 25°C. For a 1 M boiling HCl solution, the HCl-vapor fractionation was ~9‰. The difference is probably related to the degree of dissociation in the acid, with HCl dissolved in water for the highly acidic solutions, and dissociated H3O+ and Cl- for lower concentrations. The HCl volatilization experiments are in contrast to earlier vapor-liquid experiments in NaCl-H2O system, where fractionation was
Liu, Si-Qi; Zhang, Youjin; Zhou, Chunhui
2018-02-01
The generating function of cubic Hodge integrals satisfying the local Calabi-Yau condition is conjectured to be a tau function of a new integrable system which can be regarded as a fractional generalization of the Volterra lattice hierarchy, so we name it the fractional Volterra hierarchy. In this paper, we give the definition of this integrable hierarchy in terms of Lax pair and Hamiltonian formalisms, construct its tau functions, and present its multi-soliton solutions.
Energy Technology Data Exchange (ETDEWEB)
Fernandez-Bayo, J.D. [Department of Environmental Protection, Estacion Experimental del Zaidin (CSIC), C/Profesor Albareda 1, 18008 Granada (Spain)], E-mail: jesus.bayo@eez.csic.es; Romero, E. [Department of Environmental Protection, Estacion Experimental del Zaidin (CSIC), C/Profesor Albareda 1, 18008 Granada (Spain); Schnitzler, F.; Burauel, P. [Agrosphere Institute, ICG 4, Forschungszentrum Juelich, Juelich (Germany)
2008-07-15
The influence of two vermicomposts from winery and distillery wastes on the distribution of diuron in agricultural soil was studied. Physical soil fractionations at 0, 9, 27, 49 and 77 days, allowed the quantification of pesticide residues in different particle-size fractions, coarse waste (WF), sand-sized (SF), silt-sized (SiF), clay-sized (CF) and dissolved organic matter-sized fraction (DOM). The SiF made a greater contribution to the formation of non-extractable residues in unamended soil, but when vermicomposts were added, new sorption sites in WF appeared, being higher for the more humified vermicompost V2. The dissolved organic carbon (DOC) increased with the addition of vermicompost, but the concentration of the desorbed {sup 14}C-radiochemical did not increase. Non-significant increment was observed with time for the non-extractable fraction with amendments. Diuron was transformed in all samples, although less than 0.5% was mineralized. The main effect caused by vermicomposts was a reduction in the availability of diuron in soil. - Winery vermicomposts as organic amendments to reduce pesticide pollution.
Role of foam drainage in producing protein aggregates in foam fractionation.
Li, Rui; Zhang, Yuran; Chang, Yunkang; Wu, Zhaoliang; Wang, Yanji; Chen, Xiang'e; Wang, Tao
2017-10-01
It is essential to obtain a clear understanding of the foam-induced protein aggregation to reduce the loss of protein functionality in foam fractionation. The major effort of this work is to explore the roles of foam drainage in protein aggregation in the entire process of foam fractionation with bovine serum albumin (BSA) as a model protein. The results show that enhancing foam drainage increased the desorption of BSA molecules from the gas-liquid interface and the local concentration of desorbed molecules in foam. Therefore, it intensified the aggregation of BSA in foam fractionation. Simultaneously, it also accelerated the flow of BSA aggregates from rising foam into the residual solution along with the drained liquid. Because enhancing foam drainage increased the relative content of BSA molecules adsorbed at the gas-liquid interface, it also intensified the aggregation of BSA during both the defoaming process and the storage of the foamate. Furthermore, enhancing foam drainage more readily resulted in the formation of insoluble BSA aggregates. The results are highly important for a better understanding of foam-induced protein aggregation in foam fractionation. Copyright © 2017 Elsevier B.V. All rights reserved.
A discrete fractional random transform
Liu, Zhengjun; Zhao, Haifa; Liu, Shutian
2006-01-01
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of the fractional Fourier transform along with some fantastic features of its own. As a primary application, the discrete fractional random transform has been used for image encryption and decryption.
Microbial Enzyme Activity and Carbon Cycling in Grassland Soil Fractions
Allison, S. D.; Jastrow, J. D.
2004-12-01
Extracellular enzymes are necessary to degrade complex organic compounds present in soils. Using physical fractionation procedures, we tested whether old soil carbon is spatially isolated from degradative enzymes across a prairie restoration chronosequence in Illinois, USA. We found that carbon-degrading enzymes were abundant in all soil fractions, including macroaggregates, microaggregates, and the clay fraction, which contains carbon with a mean residence time of ~200 years. The activities of two cellulose-degrading enzymes and a chitin-degrading enzyme were 2-10 times greater in organic matter fractions than in bulk soil, consistent with the rapid turnover of these fractions. Polyphenol oxidase activity was 3 times greater in the clay fraction than in the bulk soil, despite very slow carbon turnover in this fraction. Changes in enzyme activity across the restoration chronosequence were small once adjusted for increases in soil carbon concentration, although polyphenol oxidase activity per unit carbon declined by 50% in native prairie versus cultivated soil. These results are consistent with a `two-pool' model of enzyme and carbon turnover in grassland soils. In light organic matter fractions, enzyme production and carbon turnover both occur rapidly. However, in mineral-dominated fractions, both enzymes and their carbon substrates are immobilized on mineral surfaces, leading to slow turnover. Soil carbon accumulation in the clay fraction and across the prairie restoration chronosequence probably reflects increasing physical isolation of enzymes and substrates on the molecular scale, rather than the micron to millimeter scale.
New Fractional Complex Transform for Conformable Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
Çenesiz Y.
2016-12-01
Full Text Available Conformable fractional complex transform is introduced in this paper for converting fractional partial differential equations to ordinary differential equations. Hence analytical methods in advanced calculus can be used to solve these equations. Conformable fractional complex transform is implemented to fractional partial differential equations such as space fractional advection diffusion equation and space fractional telegraph equation to obtain the exact solutions of these equations.
On Efficient Method for System of Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Jamil Muhammad
2011-01-01
Full Text Available The present study introduces a new version of homotopy perturbation method for the solution of system of fractional-order differential equations. In this approach, the solution is considered as a Taylor series expansion that converges rapidly to the nonlinear problem. The systems include fractional-order stiff system, the fractional-order Genesio system, and the fractional-order matrix Riccati-type differential equation. The new approximate analytical procedure depends only on two components. Comparing the methodology with some known techniques shows that the present method is relatively easy, less computational, and highly accurate.
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...
The Local Fractional Bootstrap
DEFF Research Database (Denmark)
Bennedsen, Mikkel; Hounyo, Ulrich; Lunde, Asger
new resampling method, the local fractional bootstrap, relies on simulating an auxiliary fractional Brownian motion that mimics the fine properties of high frequency differences of the Brownian semistationary process under the null hypothesis. We prove the first order validity of the bootstrap method...... and in simulations we observe that the bootstrap-based hypothesis test provides considerable finite-sample improvements over an existing test that is based on a central limit theorem. This is important when studying the roughness properties of time series data; we illustrate this by applying the bootstrap method...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 5; Issue 1. Continued Fractions for e. Shailesh A Shirali. General Article Volume 5 Issue 1 January 2000 pp 14-28. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/005/01/0014-0028. Author Affiliations.
Brewing with fractionated barley
Donkelaar, van L.H.G.
2016-01-01
Brewing with fractionated barley Beer is a globally consumed beverage, which is produced from malted barley, water, hops and yeast. In recent years, the use of unmalted barley and exogenous enzymes have become more popular because they enable simpler processing and reduced environmental impact. Raw
Fractional Differential Equation
Directory of Open Access Journals (Sweden)
Moustafa El-Shahed
2007-01-01
where 2<α<3 is a real number and D0+α is the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.
Vinogradova, Natalya; Blaine, Larry
2013-01-01
Almost everyone loves chocolate. However, the same cannot be said about fractions, which are loved by markedly fewer. Middle school students tend to view them with wary respect, but little affection. The authors attempt to sweeten the subject by describing a type of game involving division of chocolate bars. The activity they describe provides a…
Knowledge acquisition and rapid protyping of an expert system: Dealing with real world problems
Bailey, Patrick A.; Doehr, Brett B.
1988-01-01
The knowledge engineering and rapid prototyping phases of an expert system that does fault handling for a Solid Amine, Water Desorbed CO2 removal assembly for the Environmental Control and Life Support System for space based platforms are addressed. The knowledge acquisition phase for this project was interesting because it could not follow the textbook examples. As a result of this, a variety of methods were used during the knowledge acquisition task. The use of rapid prototyping and the need for a flexible prototype suggested certain types of knowledge representation. By combining various techniques, a representative subset of faults and a method for handling those faults was achieved. The experiences should prove useful for developing future fault handling expert systems under similar constraints.
-Dimensional Fractional Lagrange's Inversion Theorem
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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.
Arbitrage with fractional Gaussian processes
Zhang, Xili; Xiao, Weilin
2017-04-01
While the arbitrage opportunity in the Black-Scholes model driven by fractional Brownian motion has a long history, the arbitrage strategy in the Black-Scholes model driven by general fractional Gaussian processes is in its infancy. The development of stochastic calculus with respect to fractional Gaussian processes allowed us to study such models. In this paper, following the idea of Shiryaev (1998), an arbitrage strategy is constructed for the Black-Scholes model driven by fractional Gaussian processes, when the stochastic integral is interpreted in the Riemann-Stieltjes sense. Arbitrage opportunities in some fractional Gaussian processes, including fractional Brownian motion, sub-fractional Brownian motion, bi-fractional Brownian motion, weighted-fractional Brownian motion and tempered fractional Brownian motion, are also investigated.
Fractional cointegration rank estimation
DEFF Research Database (Denmark)
Lasak, Katarzyna; Velasco, Carlos
We consider cointegration rank estimation for a p-dimensional Fractional Vector Error Correction Model. We propose a new two-step procedure which allows testing for further long-run equilibrium relations with possibly different persistence levels. The fi…rst step consists in estimating the parame......We consider cointegration rank estimation for a p-dimensional Fractional Vector Error Correction Model. We propose a new two-step procedure which allows testing for further long-run equilibrium relations with possibly different persistence levels. The fi…rst step consists in estimating...... to control for stochastic trend estimation effects from the first step. The critical values of the tests proposed depend only on the number of common trends under the null, p - r, and on the interval of the cointegration degrees b allowed, but not on the true cointegration degree b0. Hence, no additional...
Alternatives for plasma fractionation.
Schneider, W; Wolter, D; McCarty, L J
1976-01-01
At the present time there is an enormously increasing demand for albumin. The most common procedure for the isolation of this plasma component is the cold ethanol technique developed by Cohn. Because this process necessarily isolates other blood components for which there is less demand in relation to albumin, albumin production is expensive. Therefore, we have developed a two-step fractionation for the isolation of albumin. It is basically a heat precipitation method with the albumin yield being about 90% of the original plasma albumin. In comparison to cold ethanol methods, it is considerably less expensive. Other blood components, e.g., clotting factors, immunoglobulins, may also be isolated. A nonmodified gamma-globulin for intravenous use is obtained by removing anti-complementary activity with hydroxyethyl starch. Additional fractionation steps are required to isolate these other components, but unlike in established methods, these are not necessary for the isolation of solely albumin.
Fractional Galilean symmetries
Directory of Open Access Journals (Sweden)
Ali Hosseiny
2016-09-01
Full Text Available We generalize the differential representation of the operators of the Galilean algebras to include fractional derivatives. As a result a whole new class of scale invariant Galilean algebras are obtained. The first member of this class has dynamical index z=2 similar to the Schrödinger algebra. The second member of the class has dynamical index z=3/2, which happens to be the dynamical index Kardar–Parisi–Zhang equation.
Fractional Number Operator and Associated Fractional Diffusion Equations
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.
Khonina, S N; Ustinov, A V
2017-11-01
Airy beams possess a number of properties that ensure their multifunction and high relevance in many applications. This fact stimulates scientists to search for new modifications and generalizations of classical Airy beams. Several generalizations of the Airy functions are known, on the basis of both the modification of the differential equation and the variations in the integral representation. In this paper we propose and investigate a new type of Airy beams-fractional Airy beams (FrAiB). They are based on the generalization of the integral representation and are close to the Olver functions, but we are considering a wider range of the power-law dependence of the argument, including non-integer (fractional) values of the power. A theoretical and numerical analysis of the FrAiBs, as well as their symmetrized variants, was performed. The properties of FrAiBs, such as being non-diffracting and autofocusing, were numerically investigated by means of the fractional Fourier transform, describing the beam transformations by paraxial optical systems. We believe that new beams can be useful for laser manipulation techniques and lensless laser patterning.
The Extended Fractional Subequation Method for Nonlinear Fractional Differential Equations
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...
Fractional Langevin equation and Riemann-Liouville fractional derivative.
Sau Fa, Kwok
2007-10-01
In this present work we consider a fractional Langevin equation with Riemann-Liouville fractional time derivative which modifies the classical Newtonian force, nonlocal dissipative force, and long-time correlation. We investigate the first two moments, variances and position and velocity correlation functions of this system. We also compare them with the results obtained from the same fractional Langevin equation which uses the Caputo fractional derivative.
Cosmological Models with Fractional Derivatives and Fractional Action Functional
Shchigolev, V. K.
2010-01-01
Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional order, are constructed. A number of exact solutions to those equations of fractional cosmological models in both cases is given.
Advances in robust fractional control
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...
Fractional variational principles with delay
Baleanu, Dumitru; Maaraba Abdeljawad, Thabet; Jarad, Fahd
2008-08-01
The fractional variational principles within Riemann-Liouville fractional derivatives in the presence of delay are analyzed. The corresponding Euler-Lagrange equations are obtained and one example is analyzed in detail.
Fractional variational principles with delay
Energy Technology Data Exchange (ETDEWEB)
Baleanu, Dumitru; Abdeljawad, Thabet Maaraba; Jarad, Fahd [Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara (Turkey)], E-mail: dumitru@cankaya.edu.tr, E-mail: baleanu@venus.nipne.ro
2008-08-08
The fractional variational principles within Riemann-Liouville fractional derivatives in the presence of delay are analyzed. The corresponding Euler-Lagrange equations are obtained and one example is analyzed in detail.
Fractional laser-assisted drug delivery
DEFF Research Database (Denmark)
Erlendsson, Andrés M; Doukas, Apostolos G; Farinelli, William A
2016-01-01
BACKGROUND AND OBJECTIVE: Ablative fractional laser (AFXL) is rapidly evolving as one of the foremost techniques for cutaneous drug delivery. While AFXL has effectively improved topical drug-induced clearance rates of actinic keratosis, treatment of basal cell carcinomas (BCCs) has been challenging...... deposition and delivery kinetics; (iii) biodistribution and diffusion pattern, estimated by mathematical simulation. METHODS: Franz diffusion chambers (FCs) were used to evaluate the PVP-technique, comparing passive (AFXL) and active (AFXL + PVP) channel filling. A fractional CO2-laser generated superficial...... intradermal biodistribution and diffusion at a depth of 1,000 µm. RESULTS: Active filling with application of PVP increased the number of filled laser channels. At a depth of 1,000 µm, filling increased from 44% (AFXL) to 94% with one PVP cycle (AFXL + PVP; P
Modified Homotopy Perturbation Method for Solving Fractional Differential Equations
Directory of Open Access Journals (Sweden)
A. A. Hemeda
2014-01-01
Full Text Available The modified homotopy perturbation method is extended to derive the exact solutions for linear (nonlinear ordinary (partial differential equations of fractional order in fluid mechanics. The fractional derivatives are taken in the Caputo sense. This work will present a numerical comparison between the considered method and some other methods through solving various fractional differential equations in applied fields. The obtained results reveal that this method is very effective and simple, accelerates the rapid convergence of the series solution, and reduces the size of work to only one iteration.
Fractional neutron point kinetics equations for nuclear reactor dynamics
Energy Technology Data Exchange (ETDEWEB)
Espinosa-Paredes, Gilberto, E-mail: gepe@xanum.uam.mx [Area de Ingenieria en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico, D.F. 09340 (Mexico); Polo-Labarrios, Marco-A. [Area de Ingenieria en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico, D.F. 09340 (Mexico); Espinosa-Martinez, Erick-G. [Retorno Quebec 6, Col. Burgos de Cuernavaca 62580, Temixco, Mor. (Mexico); Valle-Gallegos, Edmundo del [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Av. Instituto Politecnico Nacional s/n, Col. San Pedro Zacatenco, Mexico, D.F. 07738 (Mexico)
2011-02-15
The fractional point-neutron kinetics model for the dynamic behavior in a nuclear reactor is derived and analyzed in this paper. The fractional model retains the main dynamic characteristics of the neutron motion in which the relaxation time associated with a rapid variation in the neutron flux contains a fractional order, acting as exponent of the relaxation time, to obtain the best representation of a nuclear reactor dynamics. The physical interpretation of the fractional order is related with non-Fickian effects from the neutron diffusion equation point of view. The numerical approximation to the solution of the fractional neutron point kinetics model, which can be represented as a multi-term high-order linear fractional differential equation, is calculated by reducing the problem to a system of ordinary and fractional differential equations. The numerical stability of the fractional scheme is investigated in this work. Results for neutron dynamic behavior for both positive and negative reactivity and for different values of fractional order are shown and compared with the classic neutron point kinetic equations. Additionally, a related review with the neutron point kinetics equations is presented, which encompasses papers written in English about this research topic (as well as some books and technical reports) published since 1940 up to 2010.
How Weird Are Weird Fractions?
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.
Fractional Hopfield Neural Networks: Fractional Dynamic Associative Recurrent Neural Networks.
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.
Membrane Assisted Enzyme Fractionation
DEFF Research Database (Denmark)
Yuan, Linfeng
Purification of proteins is an increasingly important process for the biotechnology industry. Separation of the desired high value protein from other proteins produced by the cell is usually attempted using a combination of different chromatographic techniques. These techniques separate mixtures...... of proteins on the basis of their charge, degree of hydrophobicity, affinity or size. Adequate purity is often not achieved unless several purification steps are combined thereby increasing cost and reducing product yield. Conventional fractionation of proteins using ultrafiltration membranes is limited....... In this thesis, separations using crossflow elecro-membrane filtration (EMF) of amino acids, bovine serum albumin (BSA) and industrial enzymes from Novozymes were performed. The main objective of this study was to investigate the technological feasibility of EMF in the application of industrial enzyme...
Toward lattice fractional vector calculus
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.
Fractional vector calculus and fractional Maxwell’s equations
Tarasov, Vasily E.
2008-11-01
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.
Continuous and discrete fractional operators and some fractional functions
Sadjang, P. Njionou; Mboutngam, S.
2016-01-01
The classical orthogonal polynomials are usually defined by the Rodrigues' formula. This paper refers to a fractional extension of the classical Hermite, Laguerre, Jacobi, Charlier, Meixner, Krawtchouk and Hahn polynomials. By means of the Caputo operator of fractional calculus, C-Hermite, C-Laguerre, C-Legndre and the C-Jacobi functions are defined and their representation in terms of the hypergeometric functions are provided. Also, by means of the Gray and Zhang fractional difference oparat...
Fractional telegrapher's equation from fractional persistent random walks
Masoliver, Jaume, 1951-
2016-01-01
We generalize the telegrapher's equation to allow for anomalous transport. We derive the space-time fractional telegrapher's equation using the formalism of the persistent random walk in continuous time. We also obtain the characteristic function of the space-time fractional process and study some particular cases and asymptotic approximations. Similarly to the ordinary telegrapher's equation, the time-fractional equation also presents distinct behaviors for different time scales. Specificall...
Fractional telegrapher's equation from fractional persistent random walks.
Masoliver, Jaume
2016-05-01
We generalize the telegrapher's equation to allow for anomalous transport. We derive the space-time fractional telegrapher's equation using the formalism of the persistent random walk in continuous time. We also obtain the characteristic function of the space-time fractional process and study some particular cases and asymptotic approximations. Similarly to the ordinary telegrapher's equation, the time-fractional equation also presents distinct behaviors for different time scales. Specifically, transitions between different subdiffusive regimes or from superdiffusion to subdiffusion are shown by the fractional equation as time progresses.
Fractional telegrapher's equation from fractional persistent random walks
Masoliver, Jaume
2016-05-01
We generalize the telegrapher's equation to allow for anomalous transport. We derive the space-time fractional telegrapher's equation using the formalism of the persistent random walk in continuous time. We also obtain the characteristic function of the space-time fractional process and study some particular cases and asymptotic approximations. Similarly to the ordinary telegrapher's equation, the time-fractional equation also presents distinct behaviors for different time scales. Specifically, transitions between different subdiffusive regimes or from superdiffusion to subdiffusion are shown by the fractional equation as time progresses.
Certain fractional integral operators and the generalized multi-index ...
Indian Academy of Sciences (India)
Introduction. The fractional calculus is nowadays one of the most rapidly growing subject of Mathemat- ical Analysis in spite of the fact that is nearly 300 years old. Yet the giants of mathematics,. G W Leibnitz and L Euler, thought about the possibility to perform differentiation of non-integer order. The real birth and ...
The first calculation of fractional jets
Energy Technology Data Exchange (ETDEWEB)
Bertolini, Daniele [Ernest Orlando Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720 (United States); Center for Theoretical Physics, University of California, Berkeley, CA 94720 (United States); Thaler, Jesse [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Walsh, Jonathan R. [Ernest Orlando Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720 (United States); Center for Theoretical Physics, University of California, Berkeley, CA 94720 (United States)
2015-05-04
In collider physics, jet algorithms are a ubiquitous tool for clustering particles into discrete jet objects. Event shapes offer an alternative way to characterize jets, and one can define a jet multiplicity event shape, which can take on fractional values, using the framework of “jets without jets”. In this paper, we perform the first analytic studies of fractional jet multiplicity N-tilde{sub jet} in the context of e{sup +}e{sup −} collisions. We use fixed-order QCD to understand the N-tilde{sub jet} cross section at order α{sub s}{sup 2}, and we introduce a candidate factorization theorem to capture certain higher-order effects. The resulting distributions have a hybrid jet algorithm/event shape behavior which agrees with parton shower Monte Carlo generators. The N-tilde{sub jet} observable does not satisfy ordinary soft-collinear factorization, and the N-tilde{sub jet} cross section exhibits a number of unique features, including the absence of collinear logarithms and the presence of soft logarithms that are purely non-global. Additionally, we find novel divergences connected to the energy sharing between emissions, which are reminiscent of rapidity divergences encountered in other applications. Given these interesting properties of fractional jet multiplicity, we advocate for future measurements and calculations of N-tilde{sub jet} at hadron colliders like the LHC.
Fractional random walk lattice dynamics
Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.
2017-02-01
We analyze time-discrete and time-continuous ‘fractional’ random walks on undirected regular networks with special focus on cubic periodic lattices in n = 1, 2, 3,.. dimensions. The fractional random walk dynamics is governed by a master equation involving fractional powers of Laplacian matrices {{L}\\fracα{2}}} where α =2 recovers the normal walk. First we demonstrate that the interval 0<α ≤slant 2 is admissible for the fractional random walk. We derive analytical expressions for the transition matrix of the fractional random walk and closely related the average return probabilities. We further obtain the fundamental matrix {{Z}(α )} , and the mean relaxation time (Kemeny constant) for the fractional random walk. The representation for the fundamental matrix {{Z}(α )} relates fractional random walks with normal random walks. We show that the matrix elements of the transition matrix of the fractional random walk exihibit for large cubic n-dimensional lattices a power law decay of an n-dimensional infinite space Riesz fractional derivative type indicating emergence of Lévy flights. As a further footprint of Lévy flights in the n-dimensional space, the transition matrix and return probabilities of the fractional random walk are dominated for large times t by slowly relaxing long-wave modes leading to a characteristic {{t}-\\frac{n{α}} -decay. It can be concluded that, due to long range moves of fractional random walk, a small world property is emerging increasing the efficiency to explore the lattice when instead of a normal random walk a fractional random walk is chosen.
Fractions, Number Lines, Third Graders
Cramer, Kathleen; Ahrendt, Sue; Monson, Debra; Wyberg, Terry; Colum, Karen
2017-01-01
The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) outlines ambitious goals for fraction learning, starting in third grade, that include the use of the number line model. Understanding and constructing fractions on a number line are particularly complex tasks. The current work of the authors centers on ways to successfully…
Unwrapping Students' Ideas about Fractions
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…
Understanding Magnitudes to Understand Fractions
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.
Financial Planning with Fractional Goals
M.H. Goedhart; J. Spronk (Jaap)
1995-01-01
textabstractWhen solving financial planning problems with multiple goals by means of multiple objective programming, the presence of fractional goals leads to technical difficulties. In this paper we present a straightforward interactive approach for solving such linear fractional programs with
Radiating subdispersive fractional optical solitons
Energy Technology Data Exchange (ETDEWEB)
Fujioka, J., E-mail: fujioka@fisica.unam.mx; Espinosa, A.; Rodríguez, R. F. [Departamento de Física Química, Instituto de Física, Universidad Nacional Autónoma de México, Mexico, DF 04510 (Mexico); Malomed, B. A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)
2014-09-01
It was recently found [Fujioka et al., Phys. Lett. A 374, 1126 (2010)] that the propagation of solitary waves can be described by a fractional extension of the nonlinear Schrödinger (NLS) equation which involves a temporal fractional derivative (TFD) of order α > 2. In the present paper, we show that there is also another fractional extension of the NLS equation which contains a TFD with α < 2, and in this case, the new equation describes the propagation of radiating solitons. We show that the emission of the radiation (when α < 2) is explained by resonances at various frequencies between the pulses and the linear modes of the system. It is found that the new fractional NLS equation can be derived from a suitable Lagrangian density, and a fractional Noether's theorem can be applied to it, thus predicting the conservation of the Hamiltonian, momentum and energy.
A new fractional wavelet transform
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.
The foam drainage equation with time- and space-fractional derivatives solved by the Adomian method
Directory of Open Access Journals (Sweden)
Zoubir Dahmani
2008-10-01
Full Text Available In this paper, by introducing the fractional derivative in the sense of Caputo, we apply the Adomian decomposition method for the foam drainage equation with time- and space-fractional derivative. As a result, numerical solutions are obtained in a form of rapidly convergent series with easily computable components.
Ferroelectric Fractional-Order Capacitors
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.
Intelligent fractions learning system: implementation
CSIR Research Space (South Africa)
Smith, Adrew C
2011-05-01
Full Text Available surface, manipulatives, mobile phone, fractions, developing region, Montessori-inspired manipulatives. 1. Introduction A set of fraction blocks is a tool to learn about fractions, often used in schools. With large classes often in excess of 35 children... children prefer using manipulatives instead of on-screen interfaces [2]. However, with the poor teacher-to-student ratio in developing regions it is hardly possible for the teacher to take note of the children?s use of the available tools. In developing...
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.
Relationship between fractional calculus and fractional Fourier transform
Zhang, Yanshan; Zhang, Feng; Lu, Mingfeng
2015-09-01
The fractional calculus (FC) deals with integrals and derivatives of arbitrary (i.e., non-integer) order, and shares its origins with classical integral and differential calculus. The fractional Fourier transform (FRFT), which has been found having many applications in optics and other areas, is a generalization of the usual Fourier transform. The FC and the FRFT are two of the most interesting and useful fractional areas. In recent years, it appears many papers on the FC and FRFT, however, few of them discuss the connection of the two fractional areas. We study their relationship. The relational expression between them is deduced. The expectation of interdisciplinary cross fertilization is our motivation. For example, we can use the properties of the FC (non-locality, etc.) to solve the problem which is difficult to be solved by the FRFT in optical engineering; we can also through the physical meaning of the FRFT optical implementation to explain the physical meaning of the FC. The FC and FRFT approaches can be transposed each other in the two fractional areas. It makes that the success of the fractional methodology is unquestionable with a lot of applications, namely in nonlinear and complex system dynamics and image processing.
Experiments Studying Desorbed Gas and Electron Clouds in Ion Accelerators
Molvik, Arthur; Barnard, John J; Bieniosek, Frank; Celata, C M; Cohen, Ronald; Covo, Michel K; Friedman, Alex; Lund, Steven M; Seidl, Peter; Vay, Jean-Luc; Vujic, J L; Waldron, William
2005-01-01
Electron clouds and gas pressure rise limit the performance of many major accelerator rings. We are studying these issues experimentally with ~1 MeV heavy-ion beams, coordinated with significant efforts in self-consistent simulation and theory.* The experiments use multiple diagnostics, within and between quadrupole magnets, to measure the sources and accumulation of electrons and gas. In support of these studies, we have measured gas desorption and electron emission coefficients for potassium ions impinging on stainless steel targets at angles near grazing incidence.** Our goal is to measure the electron particle balance for each source - ionization of gas, emission from beam tubes, and emission from an end wall - determine the electron effects on the ion beam and apply the increased understanding to mitigation.
Numerical approaches to system of fractional partial differential equations
Directory of Open Access Journals (Sweden)
H. F. Ahmed
2017-04-01
Full Text Available In this paper, by introducing the fractional derivative in sense of Caputo, the Laplace- variational iteration method (LVIM and the Laplace-Adomian decomposition method (LADM are directly extended to study the linear and nonlinear systems of fractional partial differential equations, as a result the approximated numerical solutions are acquired in the form of rapidly convergent series with easily computable components. Numerical results show that the two approaches are easy to implement and accurate when are applied. Compassions are made between the two methods and exact solutions. Figures are used to show the efficiency as well as the accuracy of the achieved approximated results.
Federal Laboratory Consortium — The ARDEC Rapid Prototyping (RP) Laboratory was established in December 1992 to provide low cost RP capabilities to the ARDEC engineering community. The Stratasys,...
Australia's Next Top Fraction Model
Gould, Peter
2013-01-01
Peter Gould suggests Australia's next top fraction model should be a linear model rather than an area model. He provides a convincing argument and gives examples of ways to introduce a linear model in primary classrooms.
Physcicists rewarded for 'fractional electrons'
Ball, P
1998-01-01
The 1998 Nobel prize for physics has been awarded to Horst Stormer, Daniel Tsui and Robert Laughlin.Stormer and Tsui were the first to observe the fractional quantum Hall effect and Laughlin provided the theory shortly afterwards (1 page).
Fractional Transmission Line with Losses
Gómez-Aguilar, José Francisco; Dumitru, Baleanu
2014-11-01
In this manuscript, the fractional transmission line with losses is presented. The order of the Caputo derivative is considered as 0 Mittag-Leffler functions. The classic cases are recovered when β and γ are equal to 1.
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
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.
Loss-less Nano-fractionator for High Sensitivity, High Coverage Proteomics
DEFF Research Database (Denmark)
Kulak, Nils A; Geyer, Philipp E; Mann, Matthias
2017-01-01
to be particularly powerful. This first dimension is typically performed with milliliter/min flow and relatively large column inner diameters, which allow efficient pre-fractionation but typically require peptide amounts in the milligram range. Here, we describe a novel approach termed "spider fractionator" in which...... more rapid or for extremely deep measurements. We demonstrate excellent sensitivity by decreasing sample amounts from 100 μg into the sub-microgram range, without losses attributable to the spider fractionator and while quantifying close to 10,000 proteins. Finally, we apply the system to the rapid...
Parameter estimation in fractional diffusion models
Kubilius, Kęstutis; Ralchenko, Kostiantyn
2017-01-01
This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides s...
REFractions: The Representing Equivalent Fractions Game
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.
Fractional active disturbance rejection control.
Li, Dazi; Ding, Pan; Gao, Zhiqiang
2016-05-01
A fractional active disturbance rejection control (FADRC) scheme is proposed to improve the performance of commensurate linear fractional order systems (FOS) and the robust analysis shows that the controller is also applicable to incommensurate linear FOS control. In FADRC, the traditional extended states observer (ESO) is generalized to a fractional order extended states observer (FESO) by using the fractional calculus, and the tracking differentiator plus nonlinear state error feedback are replaced by a fractional proportional-derivative controller. To simplify controller tuning, the linear bandwidth-parameterization method has been adopted. The impacts of the observer bandwidth ωo and controller bandwidth ωc on system performance are then analyzed. Finally, the FADRC stability and frequency-domain characteristics for linear single-input single-output FOS are analyzed. Simulation results by FADRC and ADRC on typical FOS are compared to demonstrate the superiority and effectiveness of the proposed scheme. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
Bai, Yingchen; Wu, Fengchang; Xing, Baoshan; Meng, Wei; Shi, Guolan; Ma, Yan; Giesy, John P.
2015-01-01
XAD-8 adsorption technique coupled with stepwise elution using pyrophosphate buffers with initial pH values of 3, 5, 7, 9, and 13 was developed to isolate Chinese standard fulvic acid (FA) and then separated the FA into five sub-fractions: FApH3, FApH5, FApH7, FApH9 and FApH13, respectively. Mass percentages of FApH3-FApH13 decreased from 42% to 2.5%, and the recovery ratios ranged from 99.0% to 99.5%. Earlier eluting sub-fractions contained greater proportions of carboxylic groups with greater polarity and molecular mass, and later eluting sub-fractions had greater phenolic and aliphatic content. Protein-like components, as well as amorphous and crystalline poly(methylene)-containing components were enriched using neutral and basic buffers. Three main mechanisms likely affect stepwise elution of humic components from XAD-8 resin with pyrophosphate buffers including: 1) the carboxylic-rich sub-fractions are deprotonated at lower pH values and eluted earlier, while phenolic-rich sub-fractions are deprotonated at greater pH values and eluted later. 2) protein or protein-like components can be desorbed and eluted by use of stepwise elution as progressively greater pH values exceed their isoelectric points. 3) size exclusion affects elution of FA sub-fractions. Successful isolation of FA sub-fractions will benefit exploration of the origin, structure, evolution and the investigation of interactions with environmental contaminants. PMID:25735451
Bai, Yingchen; Wu, Fengchang; Xing, Baoshan; Meng, Wei; Shi, Guolan; Ma, Yan; Giesy, John P.
2015-03-01
XAD-8 adsorption technique coupled with stepwise elution using pyrophosphate buffers with initial pH values of 3, 5, 7, 9, and 13 was developed to isolate Chinese standard fulvic acid (FA) and then separated the FA into five sub-fractions: FApH3, FApH5, FApH7, FApH9 and FApH13, respectively. Mass percentages of FApH3-FApH13 decreased from 42% to 2.5%, and the recovery ratios ranged from 99.0% to 99.5%. Earlier eluting sub-fractions contained greater proportions of carboxylic groups with greater polarity and molecular mass, and later eluting sub-fractions had greater phenolic and aliphatic content. Protein-like components, as well as amorphous and crystalline poly(methylene)-containing components were enriched using neutral and basic buffers. Three main mechanisms likely affect stepwise elution of humic components from XAD-8 resin with pyrophosphate buffers including: 1) the carboxylic-rich sub-fractions are deprotonated at lower pH values and eluted earlier, while phenolic-rich sub-fractions are deprotonated at greater pH values and eluted later. 2) protein or protein-like components can be desorbed and eluted by use of stepwise elution as progressively greater pH values exceed their isoelectric points. 3) size exclusion affects elution of FA sub-fractions. Successful isolation of FA sub-fractions will benefit exploration of the origin, structure, evolution and the investigation of interactions with environmental contaminants.
Distribution of vanadium and vanadylporphyrines in petroleum fractions of different chemical types
Energy Technology Data Exchange (ETDEWEB)
Aleshin, G.N.; Altukhova, Z.P.; Antipenko, V.R.; Marchenko, S.P.; Kam' yanov, V.F.
Distribution of vanadium among petroleum components: tars, asphaltenes and oils from various levels of Samotlorsk fields was studied. It was shown that the predominant fraction of vanadium and vanadyl porphyrines is concentrated in petroleum tars. The highest absolute concentration of V was noted in the asphaltene fraction; however, vanadium atoms were found to be bound to heteroatomic fragments of the tarry-asphaltene compounds. Up to 98% of vanadium contained in asphaltenes and almost all V atoms in oil fractions are bound by non-porphyrinyl compounds. With increased methanization of the petroleum fractions, their V content drops rapidly. 5 references, 2 figures.
Huang, Min-Zong; Zhou, Chi-Chang; Liu, De-Lin; Jhang, Siou-Sian; Cheng, Sy-Chyi; Shiea, Jentaie
2013-10-01
Rapid characterization of thermally stable chemical compounds in solid or liquid states is achieved through thermal desorption electrospray ionization mass spectrometry (TD-ESI/MS). A feature of this technique is that sampling, desorption, ionization, and mass spectrometric detection are four separate events with respect to time and location. A metal probe was used to sample analytes in their solid or liquid states. The probe was then inserted in a preheated oven to thermally desorb the analytes on the probe. The desorbed analytes were carried by a nitrogen gas stream into an ESI plume, where analyte ions were formed via interactions with charged solvent species generated in the ESI plume. The analyte ions were subsequently detected by a mass analyzer attached to the TD-ESI source. Quantification of acetaminophen in aqueous solutions using TD-ESI/MS was also performed in which a linear response for acetaminophen was obtained between 25 and 500 ppb (R(2) = 0.9978). The standard deviation for a reproducibility test for ten liquid samples was 9.6%. Since sample preparation for TD-ESI/MS is unnecessary, a typical analysis can be completed in less than 10 s. Analytes such as the active ingredients in over-the-counter drugs were rapidly characterized regardless of the different physical properties of said drugs, which included liquid eye drops, viscous cold syrup solution, ointment cream, and a drug tablet. This approach was also used to detect trace chemical compounds in illicit drugs and explosives, in which samples were obtained from the surfaces of a cell phone, piece of luggage made from hard plastic, business card, and wooden desk.
Rapid Airplane Parametric Input Design (RAPID)
Smith, Robert E.
1995-01-01
RAPID is a methodology and software system to define a class of airplane configurations and directly evaluate surface grids, volume grids, and grid sensitivity on and about the configurations. A distinguishing characteristic which separates RAPID from other airplane surface modellers is that the output grids and grid sensitivity are directly applicable in CFD analysis. A small set of design parameters and grid control parameters govern the process which is incorporated into interactive software for 'real time' visual analysis and into batch software for the application of optimization technology. The computed surface grids and volume grids are suitable for a wide range of Computational Fluid Dynamics (CFD) simulation. The general airplane configuration has wing, fuselage, horizontal tail, and vertical tail components. The double-delta wing and tail components are manifested by solving a fourth order partial differential equation (PDE) subject to Dirichlet and Neumann boundary conditions. The design parameters are incorporated into the boundary conditions and therefore govern the shapes of the surfaces. The PDE solution yields a smooth transition between boundaries. Surface grids suitable for CFD calculation are created by establishing an H-type topology about the configuration and incorporating grid spacing functions in the PDE equation for the lifting components and the fuselage definition equations. User specified grid parameters govern the location and degree of grid concentration. A two-block volume grid about a configuration is calculated using the Control Point Form (CPF) technique. The interactive software, which runs on Silicon Graphics IRIS workstations, allows design parameters to be continuously varied and the resulting surface grid to be observed in real time. The batch software computes both the surface and volume grids and also computes the sensitivity of the output grid with respect to the input design parameters by applying the precompiler tool
Semi-infinite fractional programming
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...
On a Fractional Master Equation
Directory of Open Access Journals (Sweden)
Anitha Thomas
2011-01-01
derivative and Caputo derivative of order ,,1<ℜ(≤2 and 1<ℜ(≤2 respectively. In this paper, we derive an analytic solution for the fractional time-independent form of the wave equation or diffusion equation in two dimensions in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases, the solutions are represented also in terms of Fox's -function.
On a fractional difference operator
Directory of Open Access Journals (Sweden)
P. Baliarsingh
2016-06-01
Full Text Available In the present article, a set of new difference sequence spaces of fractional order has been introduced and subsequently, an application of these spaces, the notion of the derivatives and the integrals of a function to the case of non-integer order have been generalized. Certain results involving the unusual and non-uniform behavior of the corresponding difference operator have been investigated and also been verified by using some counter examples. We also verify these unusual and non-uniform behaviors by studying the geometry of fractional calculus.
... the smallest air passages of the lungs in children ( bronchiolitis ) Pneumonia or other lung infection Transient tachypnea of the newborn Anxiety and panic Other serious lung disease Home Care Rapid, shallow breathing should not be treated at home. It is ...
... worse than normal. Your first thoughts turn to strep throat. A rapid strep test in your doctor’s office ... your suspicions.Viruses cause most sore throats. However, strep throat is an infection caused by the Group A ...
Berthelot, J-M
2014-01-01
The RAPID3 score is the sum of three 0-10 patient self-report scores: pain, functional impairment on MDHAQ, and patient global estimate. It requires 5 seconds for scoring and can be used in all rheumatologic conditions, although it has mostly been used in rheumatoid arthritis where cutoffs for low disease activity (12/30) have been set. A RAPID3 score of ≤ 3/30 with 1 or 0 swollen joints (RAPID3 ≤ 3 + ≤ SJ1) provides remission criteria comparable to Boolean, SDAI, CDAI, and DAS28 remission criteria, in far less time than a formal joint count. RAPID3 performs as well as the DAS28 in separating active drugs from placebos in clinical trials. RAPID3 also predicts subsequent structural disease progression. RAPID3 can be determined at short intervals at home, allowing the determination of the area under the curve of disease activity between two visits and flare detection. However, RAPID3 should not be seen as a substitute for DAS28 and face to face visits in routine care. Monitoring patient status with only self-report information without a rheumatologist's advice (including joints and physical examination, and consideration of imaging and laboratory tests) may indeed be as undesirable for most patients than joint examination without a patient questionnaire. Conversely, combining the RAPID3 and the DAS28 may consist in faster or more sensitive confirmation that a medication is effective. Similarly, better enquiring of most important concerns of patients (pain, functional status and overall opinion on their disorder) should reinforces patients' confidence in their rheumatologist and treatments.
Fractional Processes and Fractional-Order Signal Processing Techniques and Applications
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...
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.
Fractional Trajectories: Decorrelation Versus Friction
2013-07-27
numerical solutions of fractional-order predator–prey and rabies models, J. Math. Anal. Appl. 325 (2007) 542–553. [6] D. West, B.J. West, On allometry...E 70 (2004) 051103. [17] E.W. Montroll, G.H. Weiss, Random walks on lattices . II, J. Math. Phys. 6 (1965) 167–181. [18] R. Metzler, J. Klafter, The
Complexity and the Fractional Calculus
2013-01-01
and H. A. A. El-Saka, “Equi- librium points, stability and numerical solutions of fractional- order predator-prey and rabies models,” Journal of...Montroll and G. H. Weiss, “Random walks on lattices . II,” Journal of Mathematical Physics, vol. 6, pp. 167–181, 1965. [35] J.-P. Bouchaud and A. Georges
Mokashi, Neelima A.
2009-01-01
This article depicts the rewarding experience of creating mathematical environments for kindergarten and elementary students by focusing on one of the most important and often difficult-to-grasp concepts (fractions) through play methods incorporated into a math fair. The basic concept of a math fair is threefold: (1) to create preplanned,…
A graph with fractional revival
Bernard, Pierre-Antoine; Chan, Ada; Loranger, Érika; Tamon, Christino; Vinet, Luc
2018-02-01
An example of a graph that admits balanced fractional revival between antipodes is presented. It is obtained by establishing the correspondence between the quantum walk on a hypercube where the opposite vertices across the diagonals of each face are connected and, the coherent transport of single excitations in the extension of the Krawtchouk spin chain with next-to-nearest neighbour interactions.
Staircase and Fractional Part Functions
Amram, Meirav; Dagan, Miriam; Ioshpe, Michael; Satianov, Pavel
2016-01-01
The staircase and fractional part functions are basic examples of real functions. They can be applied in several parts of mathematics, such as analysis, number theory, formulas for primes, and so on; in computer programming, the floor and ceiling functions are provided by a significant number of programming languages--they have some basic uses in…
Fractional ablative erbium YAG laser
DEFF Research Database (Denmark)
Taudorf, Elisabeth H; Haak, Christina S; Erlendsson, Andrés M
2014-01-01
BACKGROUND AND OBJECTIVES: Treatment of a variety of skin disorders with ablative fractional lasers (AFXL) is driving the development of portable AFXLs. This study measures micropore dimensions produced by a small 2,940 nm AFXL using a variety of stacked pulses, and determines a model correlating...
Riesz potential versus fractional Laplacian
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.
Optimization in fractional aircraft ownership
Septiani, R. D.; Pasaribu, H. M.; Soewono, E.; Fayalita, R. A.
2012-05-01
Fractional Aircraft Ownership is a new concept in flight ownership management system where each individual or corporation may own a fraction of an aircraft. In this system, the owners have privilege to schedule their flight according to their needs. Fractional management companies (FMC) manages all aspects of aircraft operations, including utilization of FMC's aircraft in combination of outsourced aircrafts. This gives the owners the right to enjoy the benefits of private aviations. However, FMC may have complicated business requirements that neither commercial airlines nor charter airlines faces. Here, optimization models are constructed to minimize the number of aircrafts in order to maximize the profit and to minimize the daily operating cost. In this paper, three kinds of demand scenarios are made to represent different flight operations from different types of fractional owners. The problems are formulated as an optimization of profit and a daily operational cost to find the optimum flight assignments satisfying the weekly and daily demand respectively from the owners. Numerical results are obtained by Genetic Algorithm method.
A fast fractional difference algorithm
DEFF Research Database (Denmark)
Jensen, Andreas Noack; Nielsen, Morten Ørregaard
2014-01-01
We provide a fast algorithm for calculating the fractional difference of a time series. In standard implementations, the calculation speed (number of arithmetic operations) is of order T 2, where T is the length of the time series. Our algorithm allows calculation speed of order T log...
A Fast Fractional Difference Algorithm
DEFF Research Database (Denmark)
Jensen, Andreas Noack; Nielsen, Morten Ørregaard
We provide a fast algorithm for calculating the fractional difference of a time series. In standard implementations, the calculation speed (number of arithmetic operations) is of order T 2, where T is the length of the time series. Our algorithm allows calculation speed of order T log...
Fractional diffusion: recovering the distributed fractional derivative from overposed data
Rundell, W.; Zhang, Z.
2017-03-01
There has been considerable recent study in ‘subdiffusion’ models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one such is to realize that the order of the fractional derivative is related to the time scales of the underlying diffusion process. This raises the question of what order α of derivative should be taken and if a single value actually suffices. This has led to models that combine a finite number of these derivatives each with a different fractional exponent {αk} and different weighting value c k to better model a greater possible range of time scales. Ultimately, one wants to look at a situation that combines derivatives in a continuous way—the so-called distributional model with parameter μ ≤ft(α \\right) . However all of this begs the question of how one determines this ‘order’ of differentiation. Recovering a single fractional value has been an active part of the process from the beginning of fractional diffusion modeling and if this is the only unknown then the markers left by the fractional order derivative are relatively straightforward to determine. In the case of a finite combination of derivatives this becomes much more complex due to the more limited analytic tools available for such equations, but recent progress in this direction has been made, (Li et al 2015 Appl. Math. Comput. 257 381-97, Li and Yamamoto 2015 Appl. Anal. 94 570-9). This paper considers the full distributional model where the order is viewed as a function μ ≤ft(α \\right) on the interval (0, 1]. We show existence, uniqueness and regularity for an initial-boundary value problem including an important representation theorem in the case of a single spatial variable. This is then used in the inverse problem of recovering the distributional coefficient μ ≤ft(α \\right) from a time trace of the solution and a uniqueness result is proven.
9 CFR 113.7 - Multiple fractions.
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...
'The mother of all continued fractions'
Dajani, K.; Kraaikamp, C.
1999-01-01
In this paper we give the relationship between the regular continued fraction and the Lehner fractions using a procedure known as insertion Starting from the regular continued fraction expansion of any real irrational x when the maximal number of insertions is applied one obtains the Lehner fraction
Fractional vector calculus and fluid mechanics
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.
Energy Technology Data Exchange (ETDEWEB)
He, Ji-Huan, E-mail: hejihuan@suda.edu.cn [National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, 199 Ren-ai Road, Suzhou 215123 (China); Elagan, S.K., E-mail: sayed_khalil2000@yahoo.com [Mathematics and Statistics Department, Faculty of Science, Taif University, P.O. 888 (Saudi Arabia); Department of Mathematics, Faculty of Science, Menofiya University, Shebin Elkom (Egypt); Li, Z.B., E-mail: zhengbiaoli@l26.com [College of Mathematics and Information Science, Qujing Normal University, Qujing, Yunnan 655011 (China)
2012-01-09
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.
Evaluating fractionated space systems - Status
Cornford, S.; Jenkins, S.; Wall, S.; Cole, B.; Bairstow, B.; Rouquette, N.; Dubos, G.; Ryan, T.; Zarifian, P.; Boutwell, J.
DARPA has funded a number of teams to further refine its Fractionated Spacecraft vision. Several teams, including this team led by JPL, have been tasked to develop a tool for the evaluation of the Business case for a fractionated system architecture. This evaluation is to understand under what conditions and constraints the fractionated architecture make more sense (in a cost/benefit sense) than the traditional monolithic paradigm. Our approach to this evaluation is to generate and evaluate a variety of trade space options. These options include various sets of stimuli, various degrees of fractionation and various subsystem element properties. The stimuli include many not normally modeled such as technology obsolescence, funding profile changes and changes in mission objectives during the mission itself. The degrees of fractionation enable various traditional subsystem elements to be distributed across different free flyers which then act in concert as needed. This will enable key technologies to be updated as need dictates and availability allows. We have described our approach in a previous IEEE Aerospace conference paper but will briefly summarize here. Our approach to generate the Business Case evaluation is to explicitly model both the implementation and operation phases for the life cycle of a fractionated constellation. A variety of models are integrated into the Phoenix ModelCenter framework and are used to generate various intermediate data which is aggregated into the Present Strategic Value (PSV). The PSV is essentially the value (including the value of the embedded real options) minus the cost. These PSVs are calculated for a variety of configurations and scenarios including variations of various stimuli or uncertainties (e.g. supply chain delays, launch vehicle failures and orbital debris events). There are various decision options (e.g. delay, accelerate, cancel) which can now be exercised for each stimulus. We can compute the PSV for the various comb
Fractionation of ethylcellulose oleogels during setting.
Gravelle, Andrew J; Barbut, Shai; Marangoni, Alejandro G
2013-01-01
The use of ethylcellulose (EC) polymers as a means to structure edible oils for fat replacement is beginning to show great promise and the use of these 'oleogels' has recently been shown to be feasible in food products. These gels are very versatile, as the mechanical properties can be tailored by altering either the fatty acid profile of the oil component, or the viscosity or concentration of the polymer component. Here we report the observation that certain formulation of EC oleogels tend to separate into two distinct phases; a soft interior core surrounded by a firm exterior sheath. It was found that the extent of this effect depends on EC viscosity, and can also be induced through the addition of certain surfactants, such as sorbitan monostearate and sorbitan monooleate, though not by glycerol monooleate. Although the two visually distinct regions were shown to be chemically indistinct, the cooling rate during gel setting was found to play a large role; rapid setting of the gels reduces the fractionation effect, while slow cooling produced a completely homogeneous structure. In addition, by reheating only the soft region of the gel, a firm and soft fractionated gel could again be produced. Finally, it was observed that oleogels prepared with castor oil or mineral oil have the ability to remove or induce the gel separation, respectively. Taken together, these results indicate chemical interactions may incite the separation into two distinct phases, but the process also seems to be driven by the cooling conditions during gel setting. These findings lend insight into the EC-oleogel gelation process and should provide a stepping stone for future research into the manufacturing of these products.
Energy Technology Data Exchange (ETDEWEB)
Harrigan, R.W.
1998-05-09
The direct connection of information, captured in forms such as CAD databases, to the factory floor is enabling a revolution in manufacturing. Rapid response to very dynamic market conditions is becoming the norm rather than the exception. In order to provide economical rapid fabrication of small numbers of variable products, one must design with manufacturing constraints in mind. In addition, flexible manufacturing systems must be programmed automatically to reduce the time for product change over in the factory and eliminate human errors. Sensor based machine control is needed to adapt idealized, model based machine programs to uncontrolled variables such as the condition of raw materials and fabrication tolerances.
Diffraction and rapidity gap measurements with ATLAS
Kus, V; The ATLAS collaboration
2014-01-01
Two diffraction related measurements of proton-proton collisions in the ATLAS experiment of the Large Hadron Collider at $\\surd s$ = 7 TeV centre-of-mass energy are reviewed. First of them is a fraction of diffractive contribution to the inelastic cross section. Second measurement is dedicated to the identification of Single Diffractive interactions with large pseudo-rapidity gaps using early 2010 data sample of integrated luminosity 7.1 $\\mu b^{-1}$. Differential cross sections of largest forward areas of the ATLAS detector starting at its most forward edges $\\eta = \\pm 4.9$ without any particle activity above different transverse momentum thresholds are measured. Results are compared to several distinctive Monte Carlo models resulting in constraint of Pomeron intercept value in triple Pomeron based approach. Furthermore, proton-proton interactions in small pseudo-rapidity gap region test qualitatively a description of different hadronisation models as well as statistical fluctuations during hadronisation pr...
Poole, Justen J; Gómez-Ríos, German A; Boyaci, Ezel; Reyes-Garcés, Nathaly; Pawliszyn, Janusz
2017-11-07
The widespread use of pharmaceuticals in both human and animal populations, and the resultant contamination of surface waters from the outflow of water treatment facilities is an issue of growing concern. This has raised the need for analytical methods that can both perform rapid sample analysis and overcome the limitations of conventional analysis procedures, such as multistep workflows and tedious procedures. Coated blade spray (CBS) is a solid-phase microextraction based technique that enables the direct-to-mass-spectrometry analysis of extracted compounds via the use of limited organic solvent to desorb analytes and perform electrospray ionization. This paper documents how CBS can be applied for the concomitant tandem mass spectrometric (MS/MS) analysis of nine pharmaceuticals in treated wastewater. The total analysis times of less than 11 min provided limits of detection lower than 50 ng L-1 for all target compounds in river water. The CBS methodology was then compared to a conventional solid-phase extraction technique for the analysis of the final effluent of six wastewater treatment facilities. The experimental results strongly suggest that CBS offers scientists a viable alternative method for analyzing water samples that is both rapid and relatively solvent-free.
Complexity and the Fractional Calculus
Directory of Open Access Journals (Sweden)
Pensri Pramukkul
2013-01-01
Full Text Available We study complex processes whose evolution in time rests on the occurrence of a large and random number of events. The mean time interval between two consecutive critical events is infinite, thereby violating the ergodic condition and activating at the same time a stochastic central limit theorem that supports the hypothesis that the Mittag-Leffler function is a universal property of nature. The time evolution of these complex systems is properly generated by means of fractional differential equations, thus leading to the interpretation of fractional trajectories as the average over many random trajectories each of which satisfies the stochastic central limit theorem and the condition for the Mittag-Leffler universality.
Fractional Authorship in Nuclear Physics
Pritychenko, B
2015-01-01
Large, multi-institutional groups or collaborations of scientists are engaged in nuclear physics research projects, and the number of research facilities is dwindling. These collaborations have their own authorship rules, and they produce a large number of highly-cited papers. Multiple authorship of nuclear physics publications creates a problem with the assessment of an individual author's productivity relative to his/her colleagues and renders ineffective a performance metrics solely based on annual publication and citation counts. Many institutions are increasingly relying on the total number of first-author papers; however, this approach becomes counterproductive for large research collaborations with an alphabetical order of authors. A concept of fractional authorship (the claiming of credit for authorship by more than one individual) helps to clarify this issue by providing a more complete picture of research activities. In the present work, nuclear physics fractional and total authorships have been inv...
Rapid Cycling and Its Treatment
... Announcements Public Service Announcements Partnering with DBSA Rapid Cycling and its Treatment What is bipolar disorder? Bipolar ... to Depression and Manic Depression . What is rapid cycling? Rapid cycling is defined as four or more ...
Implementation of fractional order integrator/differentiator on field programmable gate array
Directory of Open Access Journals (Sweden)
K.P.S. Rana
2016-06-01
Full Text Available Concept of fractional order calculus is as old as the regular calculus. With the advent of high speed and cost effective computing power, now it is possible to model the real world control and signal processing problems using fractional order calculus. For the past two decades, applications of fractional order calculus, in system modeling, control and signal processing, have grown rapidly. This paper presents a systematic procedure for hardware implementation of the basic operators of fractional calculus i.e. fractional integrator and derivative, using Grünwald–Letnikov definition, on field programmable gate array (FPGA in LabVIEW environment. The simulation and hardware implementation results for fractional order integrator and derivative of sinusoid and square waveform signals for some selected fractional orders have been presented. A close agreement between the simulated and the experimental results demonstrated the suitability of FPGA device in fractional order control and signal processing applications. LabVIEW being one of the finest tools for measurement and control, and signal processing applications the fractional order operator implementation is expected to further enhance the capability of the tool to cater to the needs of advanced experimental research employing fractional order operators.
Rapid manufacturing for microfluidics
CSIR Research Space (South Africa)
Land, K
2012-10-01
Full Text Available . Microfluidics is at the forefront of developing solutions for drug discovery, diagnostics (from glucose tests to malaria and TB testing) and environmental diagnostics (E-coli monitoring of drinking water). In order to quickly implement new designs, a rapid...
Munoz, Cesar A.; Butler, Ricky (Technical Monitor)
2003-01-01
PVSio is a conservative extension to the PVS prelude library that provides basic input/output capabilities to the PVS ground evaluator. It supports rapid prototyping in PVS by enhancing the specification language with built-in constructs for string manipulation, floating point arithmetic, and input/output operations.
Rapid Prototyping Reconsidered
Desrosier, James
2011-01-01
Continuing educators need additional strategies for developing new programming that can both reduce the time to market and lower the cost of development. Rapid prototyping, a time-compression technique adapted from the high technology industry, represents one such strategy that merits renewed evaluation. Although in higher education rapid…
Fractional Sums and Differences with Binomial Coefficients
Directory of Open Access Journals (Sweden)
Thabet Abdeljawad
2013-01-01
Full Text Available In fractional calculus, there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and derivatives. The second approach is by iterating the derivative and then defining a fractional order by making use of the binomial theorem to obtain Grünwald-Letnikov fractional derivatives. In this paper we formulate the delta and nabla discrete versions for left and right fractional integrals and derivatives representing the second approach. Then, we use the discrete version of the Q-operator and some discrete fractional dual identities to prove that the presented fractional differences and sums coincide with the discrete Riemann ones describing the first approach.
Fire effects on silica fractionation
Unzué-Belmonte, Dácil; Schaller, Jörg; Vandevenne, Floor; Barao, Lúcia; Struyf, Eric; Meire, Patrick
2015-04-01
Fire events are expected to increase due to climate change, both in number and intensity Effects range from changes in soil biogeochemistry up to the whole ecosystem functioning and morphology. While N, P and C cycling have received quite some attention, little attention was paid to fire effects on the biogeochemical Si cycle and the consequences after a fire event. The Si cycle is a globally important biogeochemical cycle, with strong connections to other biogeochemical cycles, including C. Dissolved silica is taken up by plants to form protective structures called phytoliths, which become a part of the soil and contribute strongly to soil Si cycling upon litter burial. Different silica fractions are found in soils, with phytoliths among the most easily soluble, especially compared to silicate minerals. A whole set of secondary non-biogenic fractions exist, that also have a high reactivity (adsorbed Si, reactive secondary minerals…). Biogenic and other pedogenic secondary Si stocks form an important filter between weathering of mineral silicates and eventual transport of dissolved Si to rivers and the coastal zone. We used a new method to analyze the different reactive fractions of silica in the litter layer of 3 ecosystems after different fire treatments. Using a continuous extraction of Si and Al in 0.5M NaOH at 85°C, biogenic and non-biogenic alkaline reactive Si fractions can be separated based on their Si/Al ratios and their reactivity. We analyzed the silica fractionation after two burning treatments (no heating, 350°C and 550°C) from three types of litter (spruce forest, beech forest and Sphagnum peat). Reactive Si from litter of spruce and beech forest was purely biogenic, based on the observed Si/Al ratio. Beech litter (~2.2 % BSi) had two different biogenic silica pools, one reactive and one more refractory. Spruce litter (~1.5% BSi) showed only one fraction of biogenic Si. There was negligible biogenic Si present in the peat samples (<0.1%). While
2017-01-01
In this study, we couple iron isotope analysis to microscopic and mineralogical investigation of iron speciation during circumneutral Fe(II) oxidation and Fe(III) precipitation with photosynthetically produced oxygen. In the presence of the cyanobacterium Synechococcus PCC 7002, aqueous Fe(II) (Fe(II)aq) is oxidized and precipitated as amorphous Fe(III) oxyhydroxide minerals (iron precipitates, Feppt), with distinct isotopic fractionation (ε56Fe) values determined from fitting the δ56Fe(II)aq (1.79‰ and 2.15‰) and the δ56Feppt (2.44‰ and 2.98‰) data trends from two replicate experiments. Additional Fe(II) and Fe(III) phases were detected using microscopy and chemical extractions and likely represent Fe(II) and Fe(III) sorbed to minerals and cells. The iron desorbed with sodium acetate (FeNaAc) yielded heavier δ56Fe compositions than Fe(II)aq. Modeling of the fractionation during Fe(III) sorption to cells and Fe(II) sorption to Feppt, combined with equilibration of sorbed iron and with Fe(II)aq using published fractionation factors, is consistent with our resulting δ56FeNaAc. The δ56Feppt data trend is inconsistent with complete equilibrium exchange with Fe(II)aq. Because of this and our detection of microbially excreted organics (e.g., exopolysaccharides) coating Feppt in our microscopic analysis, we suggest that electron and atom exchange is partially suppressed in this system by biologically produced organics. These results indicate that cyanobacteria influence the fate and composition of iron in sunlit environments via their role in Fe(II) oxidation through O2 production, the capacity of their cell surfaces to sorb iron, and the interaction of secreted organics with Fe(III) minerals. PMID:28402123
Swanner, E D; Bayer, T; Wu, W; Hao, L; Obst, M; Sundman, A; Byrne, J M; Michel, F M; Kleinhanns, I C; Kappler, A; Schoenberg, R
2017-05-02
In this study, we couple iron isotope analysis to microscopic and mineralogical investigation of iron speciation during circumneutral Fe(II) oxidation and Fe(III) precipitation with photosynthetically produced oxygen. In the presence of the cyanobacterium Synechococcus PCC 7002, aqueous Fe(II) (Fe(II)aq) is oxidized and precipitated as amorphous Fe(III) oxyhydroxide minerals (iron precipitates, Feppt), with distinct isotopic fractionation (ε56Fe) values determined from fitting the δ56Fe(II)aq (1.79‰ and 2.15‰) and the δ56Feppt (2.44‰ and 2.98‰) data trends from two replicate experiments. Additional Fe(II) and Fe(III) phases were detected using microscopy and chemical extractions and likely represent Fe(II) and Fe(III) sorbed to minerals and cells. The iron desorbed with sodium acetate (FeNaAc) yielded heavier δ56Fe compositions than Fe(II)aq. Modeling of the fractionation during Fe(III) sorption to cells and Fe(II) sorption to Feppt, combined with equilibration of sorbed iron and with Fe(II)aq using published fractionation factors, is consistent with our resulting δ56FeNaAc. The δ56Feppt data trend is inconsistent with complete equilibrium exchange with Fe(II)aq. Because of this and our detection of microbially excreted organics (e.g., exopolysaccharides) coating Feppt in our microscopic analysis, we suggest that electron and atom exchange is partially suppressed in this system by biologically produced organics. These results indicate that cyanobacteria influence the fate and composition of iron in sunlit environments via their role in Fe(II) oxidation through O2 production, the capacity of their cell surfaces to sorb iron, and the interaction of secreted organics with Fe(III) minerals.
Conformable Fractional Nikiforov—Uvarov Method
Karayer, H.; Demirhan, D.; Büyükkılıç, F.
2016-07-01
We introduce conformable fractional Nikiforov—Uvarov (NU) method by means of conformable fractional derivative which is the most natural definition in non-integer calculus. Since, NU method gives exact eigenstate solutions of Schrödinger equation (SE) for certain potentials in quantum mechanics, this method is carried into the domain of fractional calculus to obtain the solutions of fractional SE. In order to demonstrate the applicability of the conformable fractional NU method, we solve fractional SE for harmonic oscillator potential, Woods—Saxon potential, and Hulthen potential.
On fractional Langevin equation involving two fractional orders
Baghani, Omid
2017-01-01
In numerical analysis, it is frequently needed to examine how far a numerical solution is from the exact one. To investigate this issue quantitatively, we need a tool to measure the difference between them and obviously this task is accomplished by the aid of an appropriate norm on a certain space of functions. For example, Sobolev spaces are indispensable part of theoretical analysis of partial differential equations and boundary integral equations, as well as are necessary for the analysis of some numerical methods for the solving of such equations. But most of articles that appear in this field usually use ‖.‖∞ in the space of C[a, b] which is very restrictive. In this paper, we introduce a new norm that is convenient for the fractional and singular differential equations. Using this norm, the existence and uniqueness of initial value problems for nonlinear Langevin equation with two different fractional orders are studied. In fact, the obtained results could be used for the classical cases. Finally, by two examples we show that we cannot always speak about the existence and uniqueness of solutions just by using the previous methods.
Directory of Open Access Journals (Sweden)
Yong-Ju Yang
2013-01-01
Full Text Available The local fractional variational iteration method for local fractional Laplace equation is investigated in this paper. The operators are described in the sense of local fractional operators. The obtained results reveal that the method is very effective.
Modeling equilibrium Fe isotope fractionation
Anbar, A.; Jarzecki, A.; Spiro, T.
2003-04-01
Research into the stable isotope biogeochemistry of Fe and other transition metals has been driven primarily by analytical innovations which have revealed significant isotope effects in nature and the laboratory. Further development of these new isotope systems requires complementary theoretical research to guide analytical efforts. The results of the first such studies show some discrepancies with experiments. For example, Johnson et al. (2002) report an experimentally-determined 56Fe/54Fe equilibrium fractionation factor between Fe(II) and Fe(III) aquo complexes of ˜1.0025. This effect is ˜50% smaller than predicted theoretically by Schauble et al. (2001). It is important to resolve such discrepancies. Equilibrium isotope fractionation factors can be predicted from vibrational spectroscopic data of isotopically-substituted complexes, or from theoretical predictions of some or all of these frequencies obtained using force field models. The pioneering work of Schauble et al. (2001) utilized a modified Urey-Bradley force field (MUBFF) model. This approach is limiting in at least three ways: First, it is not ab initio, requiring as input some measured vibrational frequencies. Such data are not always available, or may have significant uncertainties. Second, the MUBFF does not include potentially important effects of solvent interaction. Third, because it makes certain assumptions about molecular symmetry, the MUBFF-based approach is not able to model the spectra of mixed-ligand complexes. To address these limitations, we are evaluating the use of density functional theory (DFT) as an ab initio method to predict vibrational frequencies of isotopically-substituted complexes and, hence, equilibrium fractionation factors. In a preliminary examination of the frequency shift upon isotope substitution of the bending and asymmetric stretching modes of the tetrahedral FeCl_42- complex, we find substantial differences between MUBFF and DFT predictions. Results for other Fe
Solving Linear Fractional Multilevel Programs
Directory of Open Access Journals (Sweden)
Shifali Bhargava
2014-01-01
Full Text Available The linear fractional multilevel programming (LFMP problem has been studied and it has been proved that an optimal solution to this problem occurs at a boundary feasible extreme point. Hence the Kth-best algorithm can be proposed to solve the problem. This property can be applied to quasiconcave multilevel problems provided that the first (n - 1 level objective functions are explicitly quasimonotonic, otherwise it cannot be proved that there exists a boundary feasible extreme point that solves the LFMP problem. (original abstract
Rapid manufacturing facilitated customisation
Tuck, Christopher John; Hague, Richard; Ruffo, Massimiliano; Ransley, Michelle; Adams, Paul Russell
2008-01-01
Abstract This paper describes the production of body-fitting customised seat profiles utilising the following digital methods: three dimensional laser scanning, reverse engineering and Rapid Manufacturing (RM). The seat profiles have been manufactured in order to influence the comfort characteristics of an existing ejector seat manufactured by Martin Baker Aircraft Ltd. The seat, known as Navy Aircrew Common Ejection Seat (NACES), was originally designed with a generic profile. ...
Energy Technology Data Exchange (ETDEWEB)
David Perlin
2005-08-14
Pathogen identification is a crucial first defense against bioterrorism. A major emphasis of our national biodefense strategy is to establish fast, accurate and sensitive assays for diagnosis of infectious diseases agents. Such assays will ensure early and appropriate treatment of infected patients. Rapid diagnostics can also support infection control measures, which monitor and limit the spread of infectious diseases agents. Many select agents are highly transmissible in the early stages of disease, and it is critical to identify infected patients and limit the risk to the remainder of the population and to stem potential panic in the general population. Nucleic acid-based molecular approaches for identification overcome many of the deficiencies associated with conventional culture methods by exploiting both large- and small-scale genomic differences between organisms. PCR-based amplification of highly conserved ribosomal RNA (rRNA) genes, intergenic sequences, and specific toxin genes is currently the most reliable approach for bacterial, fungal and many viral pathogenic agents. When combined with fluorescence-based oligonucleotide detection systems, this approach provides real-time, quantitative, high fidelity analysis capable of single nucleotide allelic discrimination (4). These probe systems offer rapid turn around time (<2 h) and are suitable for high throughput, automated multiplex operations that are critical for clinical diagnostic laboratories. In this pilot program, we have used molecular beacon technology invented at the Public health Research Institute to develop a new generation of molecular probes to rapidly detect important agents of infectious diseases. We have also developed protocols to rapidly extract nucleic acids from a variety of clinical specimen including and blood and tissue to for detection in the molecular assays. This work represented a cooperative research development program between the Kramer-Tyagi/Perlin labs on probe development
Directory of Open Access Journals (Sweden)
Diego Carlo D'agostino
2011-02-01
Full Text Available The project “Tiber Personal Rapid Transit” have been presented by the author at the Rome City Vision Competition1 2010, an ideas competition, which challenges architects, engineers, designers, students and creatives individuals to develop visionary urban proposals with the intention of stimulating and supporting the contemporary city, in this case Rome. The Tiber PRT proposal tries to answer the competition questions with the definition of a provocative idea: a Personal Rapid transit System on the Tiber river banks. The project is located in the central section of the Tiber river and aims at the renewal of the river banks with the insertion of a Personal Rapid Transit infrastructure. The project area include the riverbank of Tiber from Rome Transtevere RFI station to Piazza del Popolo, an area where main touristic and leisure attractions are located. The intervention area is actually no used by the city users and residents and constitute itself a strong barrier in the heart of the historic city.
On the fractional derivatives at extrema points
Directory of Open Access Journals (Sweden)
Mohammed Al-Refai
2012-08-01
Full Text Available We correct a recent result concerning the fractional derivative at extrema points. We then establish new results for the Caputo and Riemann-Liouville fractional derivatives at extrema points.
Fractional Tarig transform and Mittag - Leffler function
Directory of Open Access Journals (Sweden)
Deshna Loonker
2017-03-01
Full Text Available In the present paper the Tarig transform of fractional order is studied by employing Mittag - Leffler function. Properties of Tarig transform are proved using the same fractional Tarig transform.
Fractional Order Element Based Impedance Matching
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.
Fractional Fourier processing of quantum light
National Research Council Canada - National Science Library
Sun, Yifan; Tao, Ran; Zhang, Xiangdong
2014-01-01
We have extended Fourier transform of quantum light to a fractional Fourier processing, and demonstrated that a classical optical fractional Fourier processor can be used for the shaping of quantum...
Fractional Transforms in Optical Information Processing
Directory of Open Access Journals (Sweden)
Maria Luisa Calvo
2005-06-01
Full Text Available We review the progress achieved in optical information processing during the last decade by applying fractional linear integral transforms. The fractional Fourier transform and its applications for phase retrieval, beam characterization, space-variant pattern recognition, adaptive filter design, encryption, watermarking, and so forth is discussed in detail. A general algorithm for the fractionalization of linear cyclic integral transforms is introduced and it is shown that they can be fractionalized in an infinite number of ways. Basic properties of fractional cyclic transforms are considered. The implementation of some fractional transforms in optics, such as fractional Hankel, sine, cosine, Hartley, and Hilbert transforms, is discussed. New horizons of the application of fractional transforms for optical information processing are underlined.
Boundary Controllability of Nonlinear Fractional Integrodifferential Systems
Directory of Open Access Journals (Sweden)
Ahmed HamdyM
2010-01-01
Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.
Fractional Levy motion through path integrals
Energy Technology Data Exchange (ETDEWEB)
Calvo, Ivan [CIEMAT, Madrid; Sanchez, Raul [ORNL; Carreras, Benjamin A [BACV Solutions, Inc., Oak Ridge
2009-01-01
Fractional Levy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we give an explicit derivation of the propagator of fLm by using path integral methods. The propagators of Brownian motion and fractional Brownian motion are recovered as particular cases. The fractional diffusion equation corresponding to fLm is also obtained.
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.
Fractional dynamics of complex networks
Turalska, Malgorzata; West, Bruce J.
2014-03-01
The relation between the behavior of a single element and the global dynamics of its host network is an open problem in the science of complex networks. Typically one attempts to infer the global dynamics by combining the behavior of single elements within the system, following a bottom-up approach. Here we address an inverse problem. We show that for a generic model within the Ising universality class it is possible to construct a description of the dynamics of an individual element, given the information about the network's global behavior. We demonstrate that the individual trajectory response to the collective motion of the network is described by a linear fractional differential equation, whose analytic solution is the Mittag-Leffler function. This solution is obtained through a subordination procedure without the necessity of linearizing the underlying dynamics, that is, the solution retains the influence of the nonlinear network dynamics on the individual. Moreover the solutions to the fractional equation of motion suggest a new direction for designing control mechanisms for complex networks. The implications of this new perspective are explored by introducing a control signal into a small number of network elements and analyzing the subsequent change in the network dynamics.
Dean flow fractionation of chromosomes
Hockin, Matt; Sant, Himanshu J.; Capecchi, Mario; Gale, Bruce K.
2016-03-01
Efforts to transfer intact mammalian chromosomes between cells have been attempted for more than 50 years with the consistent result being transfer of sub unit length pieces regardless of method. Inertial microfluidics is a new field that has shown much promise in addressing the fractionation of particles in the 2-20 μm size range (with unknown limits) and separations are based upon particles being carried by curving confined flows (within a spiral shaped, often rectangular flow chamber) and migrating to stable "equilibrium" positions of varying distance from a chamber wall depending on the balance of dean and lift forces. We fabricated spiral channels for inertial microfluidic separations using a standard soft lithography process. The concentration of chromosomes, small contaminant DNA and large cell debris in each outlets were evaluated using microscope (60X) and a flow cytometer. Using Dean Flow Fractionation, we were able to focus 4.5 times more chromosomes in outlet 2 compared to outlet 4 where most of the large debris is found. We recover 16% of the chromosomes in outlet #1- 50% in 2, 23% in 3 and 11% in 4. It should be noted that these estimates of recovery do not capture one piece of information- it actually may be that the chromosomes at each outlet are physically different and work needs to be done to verify this potential.
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...
Teaching Fractions. Educational Practices Series-22
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…
Stretching Student Teachers' Understanding of Fractions
Harvey, Roger
2012-01-01
The teaching of fractions in elementary school is known to be challenging. Literature indicates that teachers' and prospective teachers' lack of depth of fraction content knowledge and associated pedagogical knowledge is of concern. This study investigated the fraction content knowledge of prospective teachers and their ability to use that…
On Fractals, Fractional Splines and Wavelets
2005-01-07
this picture. QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. From Goldberger, Rigney and West Heart Arterial tree Dendritic...this picture. Mandelbrot meets Mondrian 27 FRACTIONAL WAVELETS Basic ingredients Constructing fractional wavelets Fractional B-spline wavelets Multi
Identifying Fractions on a Number Line
Wong, Monica
2013-01-01
Fractions are generally introduced to students using the part--whole model. Yet the number line is another important representation which can be used to build fraction concepts (Australian Curriculum Assessment and Reporting Authority [ACARA], 2012). Number lines are recognised as key in students' number development not only of fractions, but…
Chaos in discrete fractional difference equations
Indian Academy of Sciences (India)
In the present paper, the chaotic behaviour of fractional difference equations for the tent map, Gauss map and 2x(mod 1) map are studied numerically. We analyse the chaotic behaviour of these fractional difference equations and compare them with their integer counterparts. It is observed that fractional difference equations ...
On Fractional Duffin-Kemmer-Petiau Equation
Bouzid, N.; Merad, M.; Baleanu, D.
2016-04-01
In this paper we treat a fractional bosonic, scalar and vectorial, time equation namely Duffin-Kemmer-Petiau Equation. The fractional variational principle was used, the fractional Euler-Lagrange equations were presented. The wave functions were determined and expressed in terms of Mittag-Leffler function.
The Area Model of Multiplication of Fractions
Tsankova, Jenny K.; Pjanic, Karmen
2009-01-01
Teaching students how to multiply fractions is challenging, not so much from a computational point of view but from a conceptual one. The algorithm for multiplying fractions is much easier to learn than many other algorithms, such as subtraction with regrouping, long division, and certainly addition of fractions with unlike denominators. However,…
Building Understanding of Multiplication of Fractions.
Burns, Marilyn
It is not complex to teach the algorithm for multiplying fractions so that children can multiply numerators and denominators to arrive at correct answers. However, it is a challenge to teach so that students build understanding of multiplication of fractions, extending what they have already learned about fractions and about multiplication of…
Saggiomo, Silvia L A; Seymour, Jamie E
2012-09-01
An investigation into the cardiotoxic effects in human cardiomyocytes of different fractions (as produced from an FPLC) of the venom from Chironex fleckeri showed that whole venom caused cardiac cell death in minutes, measured as cell detachment using xCELLigence technology. However, only one fraction of the venom was responsible for this effect. When all extracted venoms were recombined a similar result was seen for the toxic fraction, however these effects were slower than unfractionated venom alone even though the concentrations were similar. The difference in the results between fractioned and unfractionated venom may have been caused by compounds remaining in the FPLC column, which may interact with the toxic fraction to cause rapid cell detachment or death. Copyright © 2012. Published by Elsevier Ltd.
Fractal physiology and the fractional calculus: a perspective.
West, Bruce J
2010-01-01
fractal statistical process. Control of physiologic complexity is one of the goals of medicine, in particular, understanding and controlling physiological networks in order to ensure their proper operation. We emphasize the difference between homeostatic and allometric control mechanisms. Homeostatic control has a negative feedback character, which is both local and rapid. Allometric control, on the other hand, is a relatively new concept that takes into account long-time memory, correlations that are inverse power law in time, as well as long-range interactions in complex phenomena as manifest by inverse power-law distributions in the network variable. We hypothesize that allometric control maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can often be described using the fractional calculus to capture the dynamics of complex physiologic networks.
Rapidly variable relatvistic absorption
Parker, M.; Pinto, C.; Fabian, A.; Lohfink, A.; Buisson, D.; Alston, W.; Jiang, J.
2017-10-01
I will present results from the 1.5Ms XMM-Newton observing campaign on the most X-ray variable AGN, IRAS 13224-3809. We find a series of nine absorption lines with a velocity of 0.24c from an ultra-fast outflow. For the first time, we are able to see extremely rapid variability of the UFO features, and can link this to the X-ray variability from the inner accretion disk. We find a clear flux dependence of the outflow features, suggesting that the wind is ionized by increasing X-ray emission.
Energy Technology Data Exchange (ETDEWEB)
Gregory, D.L.; Hansche, B.D.
1996-06-01
In order to support advanced manufacturing, Sandia has acquired the capability to produce plastic prototypes using stereolithography. Currently, these prototypes are used mainly to verify part geometry and ``fit and form`` checks. This project investigates methods for rapidly testing these plastic prototypes, and inferring from prototype test data actual metal part performance and behavior. Performances examined include static load/stress response, and structural dynamic (modal) and vibration behavior. The integration of advanced non-contacting measurement techniques including scanning laser velocimetry, laser holography, and thermoelasticity into testing of these prototypes is described. Photoelastic properties of the epoxy prototypes to reveal full field stress/strain fields are also explored.
Lawrence, Craig
2003-01-01
IDEO (pronounced 'eye-dee-oh') is an international design, engineering, and innovation firm that has developed thousands of products and services for clients across a wide range of industries. Its process and culture attracted the attention of academics, businesses, and journalists around the world, and are the subject of a bestselling book, The Art of Innovation by Tom Kelley. One of the keys to IDEO's success is its use of prototyping as a tool for rapid innovation. This story covers some of IDEO's projects, and gives reasons for why they were successful.
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.
Heavy-tailed fractional Pearson diffusions.
Leonenko, N N; Papić, I; Sikorskii, A; Šuvak, N
2017-11-01
We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.
Correlation Structure of Fractional Pearson Diffusions.
Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla
2013-09-01
The stochastic solution to a diffusion equations with polynomial coefficients is called a Pearson diffusion. If the first time derivative is replaced by a Caputo fractional derivative of order less than one, the stochastic solution is called a fractional Pearson diffusion. This paper develops an explicit formula for the covariance function of a fractional Pearson diffusion in steady state, in terms of Mittag-Leffler functions. That formula shows that fractional Pearson diffusions are long range dependent, with a correlation that falls off like a power law, whose exponent equals the order of the fractional derivative.
Fractional-calculus diffusion equation.
Ajlouni, Abdul-Wali Ms; Al-Rabai'ah, Hussam A
2010-05-21
Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis.
Fractional-calculus diffusion equation
2010-01-01
Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677
Working with a fractional object:
DEFF Research Database (Denmark)
Christensen, Bodil Just; Hillersdal, Line; Holm, Lotte
2017-01-01
This paper explores the productive tensions occurring in an interdisciplinary research project on weight loss after obesity surgery. The study was a bio-medical/anthropological collaboration investigating to what extent eating patterns, the subjective experience of hunger and physiological...... mechanisms are involved in appetite regulation that might determine good or poor response to the surgery. Linking biomedical and anthropological categories and definitions of central concepts about the body turned out to be a major challenge in the collaborative analysis. Notably, the conception of what...... constitutes ‘appetite’ was a key concern, as each discipline has its particular definition and operationalization of the term. In response, a material-semiotic approach was chosen which allowed for a reconceptualization of appetite as a ‘fractional object’, engaged in multiple relations and enacted...
Diffraction and rapidity gap measurements in ATLAS
Bernat, P; The ATLAS collaboration
2012-01-01
The early data recorded by the ATLAS detector during 2010 presents a great opportunity to study diffraction cross section in proton-proton collision. The differential cross section of diffractive dissociation is studied as a function of the maximum rapidity gap, up to 8 in rapidity units. Data are compared to different models of diffractive dynamics in standard event generators. A rise at large rapidity gaps is interpreted with a triple pomeron based approach, using Pythia 8 prediction (with a Donnachie-Landshoff model). A pomeron intercept of 1.058 ± 0.003(stat) +0.034-0.039 (syst) is found. A measurement of the dijet production with a jet veto on additional central activity using 2010 data is also presented. The use of a veto scale at 20 GeV allows to measure the jet activity in dijet events. As the veto scale is much larger than Lambda_s different QCD phenomena can be studied. Moreover, ATLAS data explores regions of the phase space for the first time. The main observable in this analysis is the fraction ...
Rapid mineralocorticoid receptor trafficking.
Gekle, M; Bretschneider, M; Meinel, S; Ruhs, S; Grossmann, C
2014-03-01
The mineralocorticoid receptor (MR) is a ligand-dependent transcription factor that physiologically regulates water-electrolyte homeostasis and controls blood pressure. The MR can also elicit inflammatory and remodeling processes in the cardiovascular system and the kidneys, which require the presence of additional pathological factors like for example nitrosative stress. However, the underlying molecular mechanism(s) for pathophysiological MR effects remain(s) elusive. The inactive MR is located in the cytosol associated with chaperone molecules including HSP90. After ligand binding, the MR monomer rapidly translocates into the nucleus while still being associated to HSP90 and after dissociation from HSP90 binds to hormone-response-elements called glucocorticoid response elements (GREs) as a dimer. There are indications that rapid MR trafficking is modulated in the presence of high salt, oxidative or nitrosative stress, hypothetically by induction or posttranslational modifications. Additionally, glucocorticoids and the enzyme 11beta hydroxysteroid dehydrogenase may also influence MR activation. Because MR trafficking and its modulation by micro-milieu factors influence MR cellular localization, it is not only relevant for genomic but also for nongenomic MR effects. Copyright © 2013 Elsevier Inc. All rights reserved.
Rapid response manufacturing (RRM)
Energy Technology Data Exchange (ETDEWEB)
Cain, W.D. [Lockheed Martin Energy Systems, Inc., Oak Ridge, TN (United States); Waddell, W.L. [National Centers for Manufacturing Sciences, Ann Arbor, MI (United States)
1997-02-18
US industry is fighting to maintain its competitive edge in the global market place. Today markets fluctuate rapidly. Companies, to survive, have to be able to respond with quick-to-market, improved, high quality, cost efficient products. The way products are developed and brought to market can be improved and made more efficient through the proper incorporation of emerging technologies. The RRM project was established to leverage the expertise and resources of US private industries and federal agencies to develop, integrate, and deploy new technologies that meet critical needs for effective product realization. The RRM program addressed a needed change in the US Manufacturing infrastructure that will ensure US competitiveness in world market typified by mass customization. This project provided the effort needed to define, develop and establish a customizable infrastructure for rapid response product development design and manufacturing. A major project achievement was the development of a broad-based framework for automating and integrating the product and process design and manufacturing activities involved with machined parts. This was accomplished by coordinating and extending the application of feature-based product modeling, knowledge-based systems, integrated data management, and direct manufacturing technologies in a cooperative integrated computing environment. Key technological advancements include a product model that integrates product and process data in a consistent, minimally redundant manner, an advanced computer-aided engineering environment, knowledge-based software aids for design and process planning, and new production technologies to make products directly from design application software.
On Coupled Systems of Time-Fractional Differential Problems by Using a New Fractional Derivative
Directory of Open Access Journals (Sweden)
Ahmed Alsaedi
2016-01-01
Full Text Available The existence of solutions for a coupled system of time-fractional differential equations including continuous functions and the Caputo-Fabrizio fractional derivative is examined. After that we investigated a coupled system of time-fractional differential inclusions including compact- and convex-valued L1-Caratheodory multifunctions and the Caputo-Fabrizio fractional derivative.
On Coupled Systems of Time-Fractional Differential Problems by Using a New Fractional Derivative
Alsaedi, Ahmed; Baleanu, Dumitru; Etemad, Sina; Rezapour, Shahram
2016-01-01
The existence of solutions for a coupled system of time-fractional differential equations including continuous functions and the Caputo-Fabrizio fractional derivative is examined. After that we investigated a coupled system of time-fractional differential inclusions including compact- and convex-valued L1-Caratheodory multifunctions and the Caputo-Fabrizio 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.
Directory of Open Access Journals (Sweden)
Saowaluk Chasreechai
2015-01-01
Full Text Available We study existence and uniqueness results for Caputo fractional sum-difference equations with fractional sum boundary value conditions, by using the Banach contraction principle and Schaefer’s fixed point theorem. Our problem contains different numbers of order in fractional difference and fractional sums. Finally, we present some examples to show the importance of these results.
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...
Fractional Complex Transform and exp-Function Methods for Fractional Differential Equations
Bekir, Ahmet; Güner, Özkan; Cevikel, Adem C.
2013-01-01
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 succ...
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.
Wei Li; Huizhang Yang; Bin He
2014-01-01
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.
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.
Ping Zhou; Rui Ding
2012-01-01
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.
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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.
National Oceanic and Atmospheric Administration, Department of Commerce — The Rapid Refresh (RAP) numerical weather model took the place of the Rapid Update Cycle (RUC) on May 1, 2012. Run by the National Centers for Environmental...
National Oceanic and Atmospheric Administration, Department of Commerce — The Rapid Refresh (RAP) numerical weather model took the place of the Rapid Update Cycle (RUC) on May 1, 2012. Run by the National Centers for Environmental...
Trautmann, N
1976-01-01
A survey is given on the progress of fast chemical separation procedures during the last few years. Fast, discontinuous separation techniques are illustrated by a procedure for niobium. The use of such techniques for the chemical characterization of the heaviest known elements is described. Other rapid separation methods from aqueous solutions are summarized. The application of the high speed liquid chromatography to the separation of chemically similar elements is outlined. The use of the gas jet recoil transport method for nuclear reaction products and its combination with a continuous solvent extraction technique and with a thermochromatographic separation is presented. Different separation methods in the gas phase are briefly discussed and the attachment of a thermochromatographic technique to an on-line mass separator is shown. (45 refs).
Improved tumor targeting of radiolabeled RGD peptides using rapid dose fractionation.
Janssen, M.; Frielink, C.; Dijkgraaf, I.; Oyen, W.J.G.; Edwards, D.S.; Liu, S.; Rajopadhye, M.; Massuger, L.F.A.G.; Corstens, F.H.M.; Boerman, O.C.
2004-01-01
Arginine-glycine-aspartic acid (RGD) peptides preferentially bind to alphavbeta3 integrin, an integrin expressed on newly formed endothelial cells and on various tumor cells. When labeled with beta-emitting radionuclides, these peptides can be used for peptide-receptor radionuclide therapy of
DEFF Research Database (Denmark)
Berning, J; Rokkedal Nielsen, J; Launbjerg, J
1992-01-01
variability by linear regression was r = 0.89, SEE = 7.1 with a mean difference between paired observations of -1.5 +/- 6.9 (SD). In a random sample of 18 patients (45 observations), ECHO-LVEF allowed separation between RNV-LVEF values greater than or equal to 40 and less than 40, representing low and high...
Vortex Fractionalization in a Josephson Ladder
Stroud, David; Tornes, Ivan
2006-03-01
We show numerically that in a Josephson ladder with periodic boundary conditions and subject to a suitable transverse magnetic field, a vortex excitation can break up into two or more fractional excitations. If the ladder has N plaquettes, and N is divisible by an integer q, then in an applied field of 1/q flux quanta per plaquette, the ground state is a regular lattice of one fluxon every q plaquettes. When an additional fluxon is added, it spontaneously breaks up into q fractional fluxons, each carrying 1/q units of vorticity. The fractional fluxons are basically walls between different domains of the underlying 1/q lattice. The fractional fluxons are all depinned at the same applied current and move as a unit. For certain applied fields and ladder lengths, we show that there are isolated fractional fluxons. The fractional fluxons produce a time-averaged voltage related in a characteristic way to the ac voltage frequency.
Field-flow fractionation of chromosomes
Energy Technology Data Exchange (ETDEWEB)
Giddings, J.C.
1990-09-01
Research continued on field flow fractionation of chromosomes. Progress in the past year can be organized into three main categories: (1) chromosome sample preparation; (2) preliminary chromosome fractionation; (3) fractionation of a polystyrene aggregate model which approximates the chromosome shape. We have been successful in isolating metaphase chromosomes from the Chinese hamster. We also received a human chromosome sample from Dr. Carolyn Bell-Prince of Los Alamos National Laboratory. Results are discussed. 2 figs.
Fractional Order Models of Industrial Pneumatic Controllers
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Abolhassan Razminia
2014-01-01
Full Text Available This paper addresses a new approach for modeling of versatile controllers in industrial automation and process control systems such as pneumatic controllers. Some fractional order dynamical models are developed for pressure and pneumatic systems with bellows-nozzle-flapper configuration. In the light of fractional calculus, a fractional order derivative-derivative (FrDD controller and integral-derivative (FrID are remodeled. Numerical simulations illustrate the application of the obtained theoretical results in simple examples.
Operator Fractional Brownian Motion and Martingale Differences
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Hongshuai Dai
2014-01-01
Full Text Available It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays an important role in both applications and theory. In this paper, we study the relation between them. We construct an approximation sequence of operator fractional Brownian motion based on a martingale difference sequence.
Exact Solutions for Some Fractional Differential Equations
Sonmezoglu, Abdullah
2015-01-01
The extended Jacobi elliptic function expansion method is used for solving fractional differential equations in the sense of Jumarie’s modified Riemann-Liouville derivative. By means of this approach, a few fractional differential equations are successfully solved. As a result, some new Jacobi elliptic function solutions including solitary wave solutions and trigonometric function solutions are established. The proposed method can also be applied to other fractional differential e...
Space-time fractional Zener wave equation.
Atanackovic, T M; Janev, M; Oparnica, Lj; Pilipovic, S; Zorica, D
2015-02-08
The space-time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigated and numerical examples are presented.
Space–time fractional Zener wave equation
Atanackovic, T.M.; Janev, M.; Oparnica, Lj.; Pilipovic, S.; Zorica, D.
2015-01-01
The space–time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigated and numerical examples are presented. PMID:25663807
A dynamic programming approach to adaptive fractionation.
Ramakrishnan, Jagdish; Craft, David; Bortfeld, Thomas; Tsitsiklis, John N
2012-03-07
We conduct a theoretical study of various solution methods for the adaptive fractionation problem. The two messages of this paper are as follows: (i) dynamic programming (DP) is a useful framework for adaptive radiation therapy, particularly adaptive fractionation, because it allows us to assess how close to optimal different methods are, and (ii) heuristic methods proposed in this paper are near-optimal, and therefore, can be used to evaluate the best possible benefit of using an adaptive fraction size. The essence of adaptive fractionation is to increase the fraction size when the tumor and organ-at-risk (OAR) are far apart (a 'favorable' anatomy) and to decrease the fraction size when they are close together. Given that a fixed prescribed dose must be delivered to the tumor over the course of the treatment, such an approach results in a lower cumulative dose to the OAR when compared to that resulting from standard fractionation. We first establish a benchmark by using the DP algorithm to solve the problem exactly. In this case, we characterize the structure of an optimal policy, which provides guidance for our choice of heuristics. We develop two intuitive, numerically near-optimal heuristic policies, which could be used for more complex, high-dimensional problems. Furthermore, one of the heuristics requires only a statistic of the motion probability distribution, making it a reasonable method for use in a realistic setting. Numerically, we find that the amount of decrease in dose to the OAR can vary significantly (5-85%) depending on the amount of motion in the anatomy, the number of fractions and the range of fraction sizes allowed. In general, the decrease in dose to the OAR is more pronounced when: (i) we have a high probability of large tumor-OAR distances, (ii) we use many fractions (as in a hyper-fractionated setting) and (iii) we allow large daily fraction size deviations.
Improved fast fractional-Fourier-transform algorithm.
Yang, Xingpeng; Tan, Qiaofeng; Wei, Xiaofeng; Xiang, Yong; Yan, Yingbai; Jin, Guofan
2004-09-01
Through the optimization of the main interval of the fractional order, an improved fast algorithm for numerical calculation of the fractional Fourier transforms is proposed. With this improved algorithm, the fractional Fourier transforms of a rectangular function and a Gaussian function are calculated. Its calculation errors are compared with those calculated with the previously published algorithm, and the results show that the calculation accuracy of the improved algorithm is much higher.
Rapid surface sampling and archival record system
Energy Technology Data Exchange (ETDEWEB)
Barren, E.; Penney, C.M.; Sheldon, R.B. [GE Corporate Research and Development Center, Schenectady, NY (United States)] [and others
1995-10-01
A number of contamination sites exist in this country where the area and volume of material to be remediated is very large, approaching or exceeding 10{sup 6} m{sup 2} and 10{sup 6} m{sup 3}. Typically, only a small fraction of this material is actually contaminated. In such cases there is a strong economic motivation to test the material with a sufficient density of measurements to identify which portions are uncontaminated, so extensively they be left in place or be disposed of as uncontaminated waste. Unfortunately, since contamination often varies rapidly from position to position, this procedure can involve upwards of one million measurements per site. The situation is complicated further in many cases by the difficulties of sampling porous surfaces, such as concrete. This report describes a method for sampling concretes in which an immediate distinction can be made between contaminated and uncontaminated surfaces. Sample acquisition and analysis will be automated.
Pharmacotherapy of heart failure with preserved ejection fraction.
Basaraba, Jade E; Barry, Arden R
2015-04-01
Heart failure with preserved ejection fraction (HFpEF) constitutes ~50% of all heart failure diagnoses and is associated with considerable morbidity and mortality. The treatment of HFpEF can be challenging due to a lack of evidence supporting the benefit of various drug therapies. In practice, treatment can be divided into acute and chronic management. Acute therapy for decompensated heart failure is similar for both HFpEF and heart failure with reduced ejection fraction. The mainstay of treatment is diuretics to reduce volume overload and improve dyspnea. Patients with an acute exacerbation of HFpEF and rapid atrial fibrillation (AF) should be rate controlled with negative chronotropic agents. For chronic therapy, patients with HFpEF should not be treated like patients with heart failure with reduced ejection fraction. Chronic management of HFpEF can be simplified by using three strategies based on applicability: treat precipitating conditions (e.g., hypertension, AF), control symptoms by maintaining euvolemia with diuretics, and avoid therapies that have been shown not to be beneficial unless another compelling indication exists. Nondrug interventions for HFpEF include salt and fluid restriction, regular physical activity, and referral to a heart function clinic, if appropriate. © 2015 Pharmacotherapy Publications, Inc.
Building a rapid response team.
Halvorsen, Lisa; Garolis, Salomeja; Wallace-Scroggs, Allyson; Stenstrom, Judy; Maunder, Richard
2007-01-01
The use of rapid response teams is a relatively new approach for decreasing or eliminating codes in acute care hospitals. Based on the principles of a code team for cardiac and/or respiratory arrest in non-critical care units, the rapid response teams have specially trained nursing, respiratory, and medical personnel to respond to calls from general care units to assess and manage decompensating or rapidly changing patients before their conditions escalate to a full code situation. This article describes the processes used to develop a rapid response team, clinical indicators for triggering a rapid response team call, topics addressed in an educational program for the rapid response team members, and methods for evaluating effectiveness of the rapid response team.
RHEOLOGICAL BEHAVIOUR OF PSYLLIUM GUM FRACTIONS
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Mohammad Hojjatoleslamyi
2013-10-01
Full Text Available Psyllium (Plantago psyllium is a native plant that grows widely in India, Iran and Pinjab. Studies showed psyllium gum has good rheological properties for using in wide range of food products. In this study, different fractions of psyllium gum extracted by water and alkali treatment. Rheological properties of these fractions determined by Brookfield rheometer (RV DVIII. Obtained data fitted in three temperatures 30, 60 and 80°C by Herschel-bulkly rheological model. Results showed that fractions have different behaviour during heating treatment. The most difference observed in AEG0.5 fraction.
Oxygen isotope fractionation in double carbonates.
Zheng, Yong-Fei; Böttcher, Michael E
2016-01-01
Oxygen isotope fractionations in double carbonates of different crystal structures were calculated by the increment method. Synthesis experiments were performed at 60 °C and 100 °C to determine oxygen and carbon isotope fractionations involving PbMg[CO3]2. The calculations suggest that the double carbonates of calcite structure are systematically enriched in (18)O relative to those of aragonite and mixture structures. Internally consistent oxygen isotope fractionation factors are obtained for these minerals with respect to quartz, calcite and water at a temperature range of 0-1200 °C. The calculated fractionation factors for double carbonate-water systems are generally consistent with the data available from laboratory experiments. The experimentally determined fractionation factors for PbMg[CO3]2, BaMg[CO3]2 and CaMg[CO3]2 against H2O not only fall between fractionation factors involving pure carbonate end-members but are also close to the calculated fractionation factors. In contrast, experimentally determined carbon isotope fractionation factors between PbMg[CO3]2 and CO2 are much closer to theoretical predictions for the cerussite-CO2 system than for the magnesite-CO2 system, similar to the fractionation behavior for BaMg[CO3]2. Therefore, the combined theoretical and experimental results provide insights into the effects of crystal structure and exchange kinetics on oxygen isotope partitioning in double carbonates.
Control of Initialized Fractional-Order Systems
Hartly, Tom T.; Lorenzo, Carl F.
2002-01-01
Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex Airplane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex Airplane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.
Fractional Dynamics of Computer Virus Propagation
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Carla M. A. Pinto
2014-01-01
Full Text Available We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.
Controllability of Nonlinear Fractional Delay Dynamical Systems
Nirmala, R. Joice; Balachandran, K.; Rodríguez-Germa, L.; Trujillo, J. J.
2016-02-01
This paper is concerned with controllability of nonlinear fractional delay dynamical systems with delay in state variables. The solution representations of fractional delay differential equations have been established by using the Laplace transform technique and the Mittag-Leffler function. Necessary and sufficient conditions for the controllability criteria of linear fractional delay systems are established. Further sufficient condition for the controllability of nonlinear fractional delay dynamical system are obtained by using the fixed point argument. Examples and numerical simulation are presented to illustrate the results.
DYNAMICS OF FRACTIONAL ORDER CHAOTIC SYSTEM
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M. Jana
2017-02-01
Full Text Available This paper deals with the dynamics of chaos and synchronization for fractional order chaotic system. For fractional order derivative Captuo definition is used here and numerical simulations are done using Predictor-Correctors scheme by Diethlm based on the Adams-Baseforth-Moulton algorithm. Stability analysis is discussed here for non linear fractional order chaotic system and synchronization is achieved between two non identical fractional order chaotic systems: Finance chaotic system(driving systemand Lorenz system(response systemvia active control.Numerical simulations are performed to show the effectiveness of these approaches.
Theory and applications of fractional differential equations
Kilbas, Anatoly A; Trujillo, Juan J; Van Mill, Jan
2006-01-01
This monograph provides the most recent and up-to-date developments on fractional differential and fractional integro-differential equations involving many different potentially useful operators of fractional calculus. The subject of fractional calculus and its applications (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. Some of the areas of prese
Directory of Open Access Journals (Sweden)
Min Huang
Full Text Available Generation of action potentials (APs is a crucial step in neuronal information processing. Existing biophysical models for AP generation almost universally assume that individual voltage-gated sodium channels operate statistically independently, and their avalanche-like opening that underlies AP generation is coordinated only through the transmembrane potential. However, biological ion channels of various types can exhibit strongly cooperative gating when clustered. Cooperative gating of sodium channels has been suggested to explain rapid onset dynamics and large threshold variability of APs in cortical neurons. It remains however unknown whether these characteristic properties of cortical APs can be reproduced if only a fraction of channels express cooperativity, and whether the presence of cooperative channels has an impact on encoding properties of neuronal populations. To address these questions we have constructed a conductance-based neuron model in which we continuously varied the size of a fraction [Formula: see text] of sodium channels expressing cooperativity and the strength of coupling between cooperative channels [Formula: see text]. We show that starting at a critical value of the coupling strength [Formula: see text], the activation curve of sodium channels develops a discontinuity at which opening of all coupled channels becomes an all-or-none event, leading to very rapid AP onsets. Models with a small fraction, [Formula: see text], of strongly cooperative channels generate APs with the most rapid onset dynamics. In this regime APs are triggered by simultaneous opening of the cooperative channel fraction and exhibit a pronounced biphasic waveform often observed in cortical neurons. We further show that presence of a small fraction of cooperative Na+ channels significantly improves the ability of neuronal populations to phase-lock their firing to high frequency input fluctuation. We conclude that presence of a small fraction of
Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems
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.
Rabah, Karima; Ladaci, Samir; Lashab, Mohamed
2017-09-01
In this paper, a new design of fractional-order sliding mode control scheme is proposed for the synchronization of a class of nonlinear fractional-order systems with chaotic behaviour. The considered design approach provides a set of fractional-order laws that guarantee asymptotic stability of fractional-order chaotic systems in the sense of the Lyapunov stability theorem. Two illustrative simulation examples on the fractional-order Genesio-Tesi chaotic systems and the fractional-order modified Jerk systems are provided. These examples show the effectiveness and robustness of this control solution.
Kim, T D
1980-01-01
South Korea's export-oriented development strategy has achieved a remarkable growth record, but it has also brought 2 different problems: 1) since the country's exports accounted for about 1% of total world export volume, the 1st world has become fearful about Korea's aggressive export drive; and 2) the fact that exports account for over 30% of its total gross national product (GNP) exposes the vulnerability of South Korea's economy itself. South Korea continues to be a poor nation, although it is rated as 1 of the most rapidly growing middle income economies. A World Bank 1978 report shows Korea to be 28th of 58 middle income countries in terms of per capita GNP in 1976. Of 11 newly industrializing countries (NIC), 5 in the European continent are more advanced than the others. A recent emphasis on the basic human needs approach has tended to downgrade the concept of GNP. Korea has only an abundant labor force and is without any natural resources. Consequently, Korea utilized an export-oriented development strategy. Oil requirements are met with imports, and almost all raw materials to be processed into exportable products must be imported. To pay import bills Korea must export and earn foreign exchange. It must be emphasized that foreign trade must always be 2-way traffic. In order to export more to middle income countries like Korea, the countries of the 1st world need to ease their protectionist measures against imports from developing countries.
Stolc, Viktor (Inventor); Brock, Matthew W (Inventor)
2013-01-01
Method and system for rapid and accurate determination of each of a sequence of unknown polymer components, such as nucleic acid components. A self-assembling monolayer of a selected substance is optionally provided on an interior surface of a pipette tip, and the interior surface is immersed in a selected liquid. A selected electrical field is impressed in a longitudinal direction, or in a transverse direction, in the tip region, a polymer sequence is passed through the tip region, and a change in an electrical current signal is measured as each polymer component passes through the tip region. Each of the measured changes in electrical current signals is compared with a database of reference electrical change signals, with each reference signal corresponding to an identified polymer component, to identify the unknown polymer component with a reference polymer component. The nanopore preferably has a pore inner diameter of no more than about 40 nm and is prepared by heating and pulling a very small section of a glass tubing.
Gehan, Charlotte; Mosser, Benoît; Michel, Eric
2017-10-01
Stellar oscillations give seismic information on the internal properties of stars. Red giants are targets of interest since they present mixed modes, wich behave as pressure modes in the convective envelope and as gravity modes in the radiative core. Mixed modes thus directly probe red giant cores, and allow in particular the study of their mean core rotation. The high-quality data obtained by CoRoT and Kepler satellites represent an unprecedented perspective to obtain thousands of measurements of red giant core rotation, in order to improve our understanding of stellar physics in deep stellar interiors. We developed an automated method to obtain such core rotation measurements and validated it for stars on the red giant branch. In this work, we particularly focus on the specific application of this method to red giants having a rapid core rotation. They show complex spectra where it is tricky to disentangle rotational splittings from mixed-mode period spacings. We demonstrate that the method based on the identification of mode crossings is precise and efficient. The determination of the mean core rotation directly derives from the precise measurement of the asymptotic period spacing ΔΠ1 and of the frequency at which the crossing of the rotational components is observed.
Directory of Open Access Journals (Sweden)
Yi-Fei Pu
2013-01-01
Full Text Available The traditional integer-order partial differential equation-based image denoising approaches often blur the edge and complex texture detail; thus, their denoising effects for texture image are not very good. To solve the problem, a fractional partial differential equation-based denoising model for texture image is proposed, which applies a novel mathematical method—fractional calculus to image processing from the view of system evolution. We know from previous studies that fractional-order calculus has some unique properties comparing to integer-order differential calculus that it can nonlinearly enhance complex texture detail during the digital image processing. The goal of the proposed model is to overcome the problems mentioned above by using the properties of fractional differential calculus. It extended traditional integer-order equation to a fractional order and proposed the fractional Green’s formula and the fractional Euler-Lagrange formula for two-dimensional image processing, and then a fractional partial differential equation based denoising model was proposed. The experimental results prove that the abilities of the proposed denoising model to preserve the high-frequency edge and complex texture information are obviously superior to those of traditional integral based algorithms, especially for texture detail rich images.
Rapid Cycle Amine (RCA) 3.0 System Development
Chullen, Cinda; Campbell, Colin; Papale, William; Hawes, Kevin; Wichowski, Robert
2015-01-01
The Rapid Cycle Amine (RCA) 3.0 system is currently under development by NASA, the Lyndon B. Johnson Space Center (JSC) in conjunction with United Technologies Corporation Aerospace Systems (UTAS). The RCA technology is a new carbon dioxide (CO2) and humidity removal system that has been baselined for the Advanced Extravehicular Mobility Unit (AEMU) Portable Life Support System. The evolution of the RCA development has progressed through several iterations of technology readiness levels including RCA 1.0, RCA 2.0, and RCA 3.0 test articles. The RCA is an advancement over currently technologies due to its unique regeneration capability. The RCA is capable of simultaneously removing CO2 and humidity from an influent air steam and subsequent regeneration when exposed to a vacuum source. The RCA technology uses two solid amine sorbent beds in an alternating fashion to adsorb CO2 and water (uptake mode) and desorb CO2 and water (regeneration mode) at the same time. The two beds operate in an efficient manner so that while one bed is in the uptake mode, the other is in the regeneration mode, thus continuously providing an on-service sorbent bed by which CO2 and humidity may be removed. The RCA 2.0 and 3.0 test articles were designed with a novel valve assembly which allows for switching between uptake and regeneration modes with only one moving part while minimizing gas volume losses to the vacuum source by means of an internal pressure equalization step during actuation. The RCA technology also is low power, small, and has performed extremely well in all development testing thus far. A final design was selected for the RCA 3.0, fabricated, assembled, and performance tested in 2014 with delivery to NASAJSC in January 2015. This paper will provide an overview on the RCA 3.0 system design and results of pre-delivery testing with references to the development of RCA 1.0 and RCA 2.0.
Directory of Open Access Journals (Sweden)
Hossein Aminikhah
2013-01-01
Full Text Available A new homotopy perturbation method (NHPM is applied to system of variable coefficient coupled Burgers' equation with time-fractional derivative. The fractional derivatives are described in the Caputo fractional derivative sense. The concept of new algorithm is introduced briefly, and NHPM is examined for two systems of nonlinear Burgers' equation. In this approach, the solution is considered as a power series expansion that converges rapidly to the nonlinear problem. The new approximate analytical procedure depends on two iteratives. The modified algorithm provides approximate solutions in the form of convergent series with easily computable components. Results indicate that the introduced method is promising for solving other types of systems of nonlinear fractional-order partial differential equations.
Aminikhah, Hossein; Malekzadeh, Nasrin
2013-01-01
A new homotopy perturbation method (NHPM) is applied to system of variable coefficient coupled Burgers' equation with time-fractional derivative. The fractional derivatives are described in the Caputo fractional derivative sense. The concept of new algorithm is introduced briefly, and NHPM is examined for two systems of nonlinear Burgers' equation. In this approach, the solution is considered as a power series expansion that converges rapidly to the nonlinear problem. The new approximate analytical procedure depends on two iteratives. The modified algorithm provides approximate solutions in the form of convergent series with easily computable components. Results indicate that the introduced method is promising for solving other types of systems of nonlinear fractional-order partial differential equations.
Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher
2015-07-01
Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.
Rapid mixing kinetic techniques.
Martin, Stephen R; Schilstra, Maria J
2013-01-01
Almost all of the elementary steps in a biochemical reaction scheme are either unimolecular or bimolecular processes that frequently occur on sub-second, often sub-millisecond, time scales. The traditional approach in kinetic studies is to mix two or more reagents and monitor the changes in concentrations with time. Conventional spectrophotometers cannot generally be used to study reactions that are complete within less than about 20 s, as it takes that amount of time to manually mix the reagents and activate the instrument. Rapid mixing techniques, which generally achieve mixing in less than 2 ms, overcome this limitation. This chapter is concerned with the use of these techniques in the study of reactions which reach equilibrium; the application of these methods to the study of enzyme kinetics is described in several excellent texts (Cornish-Bowden, Fundamentals of enzyme kinetics. Portland Press, 1995; Gutfreund, Kinetics for the life sciences. Receptors, transmitters and catalysis. Cambridge University Press, 1995).There are various ways to monitor changes in concentration of reactants, intermediates and products after mixing, but the most common way is to use changes in optical signals (absorbance or fluorescence) which often accompany reactions. Although absorbance can sometimes be used, fluorescence is often preferred because of its greater sensitivity, particularly in monitoring conformational changes. Such methods are continuous with good time resolution but they seldom permit the direct determination of the concentrations of individual species. Alternatively, samples may be taken from the reaction volume, mixed with a chemical quenching agent to stop the reaction, and their contents assessed by techniques such as HPLC. These methods can directly determine the concentrations of different species, but are discontinuous and have a limited time resolution.
Is the exchangeable fraction determining the activity of mineral associated carbon?
Schrumpf, Marion; Mayer, Allegra; Kaiser, Klaus; Trumbore, Susan
2017-04-01
Sorption of organic molecules to mineral surfaces is assumed to be playing an important role for the long-term persistence of organic carbon (OC) in soils. Possibly due to the different mechanisms by which organic matter can be associated with minerals, not all carbon is equally strong bound to mineral surfaces. Therefore, it was observed that despite old average ages of mineral associated carbon, a portion is typically active. Assuming that active carbon has to be desorbed from mineral surfaces before mineralization, we hypothesize that (1) exchangeable OC will be younger than the residue, and that the portion of exchangeable carbon will (2) depend on the amount of pedogenic oxides and (3) decline with soil depth due to increasing ages of mineral associated OC with depth. To test these hypotheses, we treated the heavy fraction (d > 1.6 g cm-3) of five different soils and from three soil depths (0-5 cm, 10-20 cm, 30-40 cm) with NaF as a strong anion exchanger. Carbon and radiocarbon (14C) content were determined in both, extracts and residues. In order to test, if the extraction was able to remove all active carbon from mineral surfaces, and to get an idea about maximum ages of mineral associated carbon, we additionally treated the heavy fraction with heated (60°C) H2O2, and analyzed OC and 14C content in the residue. The NaF treatment removed on average 60±10% of total carbon from mineral surfaces. Following our expectation, the age of removed carbon was younger, and the residue older than the bulk HF fraction across soils and soil depths with an average 14C difference of 91‰. There was, however, no detectable influence of soil mineralogy or soil depth on the portion of exchangeable OC. Exchangeable OC was rather correlated to total OC in mineral associated fractions across sites and depths and proportional to OC in the residue. Only at the agricultural site studied with overall smallest OC contents, exchangeable OC was 25% less than at the other sites
Nickel and zinc isotope fractionation in hyperaccumulating and nonaccumulating plants.
Deng, Teng-Hao-Bo; Cloquet, Christophe; Tang, Ye-Tao; Sterckeman, Thibault; Echevarria, Guillaume; Estrade, Nicolas; Morel, Jean-Louis; Qiu, Rong-Liang
2014-10-21
Until now, there has been little data on the isotope fractionation of nickel (Ni) in higher plants and how this can be affected by plant Ni and zinc (Zn) homeostasis. A hydroponic cultivation was conducted to investigate the isotope fractionation of Ni and Zn during plant uptake and translocation processes. The nonaccumulator Thlaspi arvense, the Ni hyperaccumulator Alyssum murale and the Ni and Zn hyperaccumulator Noccaea caerulescens were grown in low (2 μM) and high (50 μM) Ni and Zn solutions. Results showed that plants were inclined to absorb light Ni isotopes, presumably due to the functioning of low-affinity transport systems across root cell membrane. The Ni isotope fractionation between plant and solution was greater in the hyperaccumulators grown in low Zn treatments (Δ(60)Ni(plant-solution) = -0.90 to -0.63‰) than that in the nonaccumulator T. arvense (Δ(60)Ni(plant-solution) = -0.21‰), thus indicating a greater permeability of the low-affinity transport system in hyperaccumulators. Light isotope enrichment of Zn was observed in most of the plants (Δ(66)Zn(plant-solution) = -0.23 to -0.10‰), but to a lesser extent than for Ni. The rapid uptake of Zn on the root surfaces caused concentration gradients, which induced ion diffusion in the rhizosphere and could result in light Zn isotope enrichment in the hyperaccumulator N. caerulescens. In high Zn treatment, Zn could compete with Ni during the uptake process, which reduced Ni concentration in plants and decreased the extent of Ni isotope fractionation (Δ(60)Ni(plant-solution) = -0.11 to -0.07‰), indicating that plants might take up Ni through a low-affinity transport system of Zn. We propose that isotope composition analysis for transition elements could become an empirical tool to study plant physiological processes.
Isotope fractionation of cadmium in lunar material
Schediwy, S.; Rosman, K. J. R.; de Laeter, J. R.
2006-03-01
The double spike technique has been used to measure the isotope fractionation and elemental abundance of Cd in nine lunar samples, the Brownfield meteorite and the Columbia River Basalt BCR-1, by thermal ionisation mass spectrometry. Lunar soil samples give a tightly grouped set of positive isotope fractionation values of between + 0.42% and + 0.50% per mass unit. Positive isotope fractionation implies that the heavy isotopes are enhanced with respect to those of the Laboratory Standard. A vesicular mare basalt gave zero isotope fractionation, indicating that the Cd isotopic composition of the Moon is identical to that of the Earth. A sample of orange glass from the Taurus-Littrow region gave a negative isotope fractionation of - 0.23 ± 0.06% per mass unit, presumably as a result of redeposition of Cd from the Cd-rich vapour cloud associated with volcanism. Cadmium is by far the heaviest element to show isotope fractionation effects in lunar samples. The volatile nature of Cd is of importance in explaining these isotope fractionation results. Although a number of mechanisms have been postulated to be the cause of isotope fractionation of certain elements in lunar soils, we believe that the most likely mechanisms are ion and particle bombardment of the lunar surface.
Tin isotope fractionation in terrestrial cassiterites
Energy Technology Data Exchange (ETDEWEB)
McNaughton, N.J. (Univ. of Western Australia, Nedlands (Australia)); Rosman, K.J.R. (Curtin Univ. of Technology, Bentley (Australia))
1991-02-01
The isotopic composition of tin has been measured in a range of cassiterites and pure reagents to assess the extent to which this element is isotopically fractionated in natural processes. Only two samples showed evidence of isotopic fractionation, and it is concluded that natural Sn isotope fractionation is small and uncommon. This feature reflects the world dominance of Sn-oxide ores Sn-sulfide ores, and the highly efficient processes of Sn dissolution and precipitation which negate equilibrium and kinetic fractionation of Sn isotopes, respectively. The two samples which show slight fractionation are a highly purified and cassiterite from the Archaean Greenbushes pegmatite, Western Australia. The latter Sn is 0.15{per thousand} per mass unit heavier than the authors laboratory standard, whereas the former is 0.12{per thousand} per mass unit lighter. Although the cassiterite fractionation is considered to result from natural geological processes, the fractionation of purified Sn may be either natural or relate to the purification process, the fractionation of this magnitude has a negligible effect on the current best estimate of the atomic weight of Sn, but it does place a lower limit on its associated accuracy.
Forced splitting of fractions in CE
Zalewski, D.R.; Schlautmann, Stefan; Gardeniers, Johannes G.E.
2008-01-01
In order to increase the electrophoretic separation between fractions of analytes on a microfluidic chip, without the need for a longer separation channel, we propose and demonstrate a preparative electrokinetic procedure by which overlapping or closely spaced fractions are automatically split. The
Fractions Learning in Children with Mathematics Difficulties
Tian, Jing; Siegler, Robert S.
2017-01-01
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…
Estimation's Role in Calculations with Fractions
Johanning, Debra I.
2011-01-01
Estimation is more than a skill or an isolated topic. It is a thinking tool that needs to be emphasized during instruction so that students will learn to develop algorithmic procedures and meaning for fraction operations. For students to realize when fractions should be added, subtracted, multiplied, or divided, they need to develop a sense of…
Engaging Students with Multiple Models of Fractions
Zhang, Xiaofen; Clements, M. A.; Ellerton, Nerida F.
2015-01-01
An understanding of unit fractions, and especially of one-half, one-third, and one-fourth, is crucially important for elementary school children's development of number sense (CCSSI 2010). We describe multimodal activities designed to assist elementary school students in gaining a rich understanding of unit fractions. Research has shown (Zhang,…
Paper Plate Fractions: The Counting Connection
McCoy, Ann; Barnett, Joann; Stine, Tammy
2016-01-01
Without a doubt, fractions prove to be a stumbling block for many children. Researchers have suggested a variety of explanations for why this is the case. The introduction of symbolization and operations before the development of conceptual understanding of fractions, a lack of understanding of the role of the numerator and denominator, and an…
Modular polynomial arithmetic in partial fraction decomposition
Abdali, S. K.; Caviness, B. F.; Pridor, A.
1977-01-01
Algorithms for general partial fraction decomposition are obtained by using modular polynomial arithmetic. An algorithm is presented to compute inverses modulo a power of a polynomial in terms of inverses modulo that polynomial. This algorithm is used to make an improvement in the Kung-Tong partial fraction decomposition algorithm.
Phytotoxic characterization of various fractions of Launaea ...
African Journals Online (AJOL)
Allelopathic screening of various fractions of Launaea procumbens, collected from Wah Cantt (Punjab) Pakistan, was conceded to identify potent allelopathic fraction for future phytochemical analyses. For this purpose, radish root inhibition method was used to test allelopathic potential. Two different concentrations of 100 ...
Cell fractionation of parasitic protozoa: a review
Directory of Open Access Journals (Sweden)
Souza Wanderley de
2003-01-01
Full Text Available Cell fractionation, a methodological strategy for obtaining purified organelle preparations, has been applied successfully to parasitic protozoa by a number of investigators. Here we present and discuss the work of several groups that have obtained highly purified subcellular fractions from trypanosomatids, Apicomplexa and trichomonads, and whose work have added substantially to our knowledge of the cell biology of these parasites.
psychrometry: from partial pressures to mole fractions
African Journals Online (AJOL)
ES Obe
1980-03-01
Mar 1, 1980 ... ABSTRACT. This study uses the viria1 and interaction coefficients of the normal air components in deriving compressibility factors and thereafter a simple iterative formulation for mole fractions. Conversion from partial pressures to mole fractions now becomes tractable by means of determinate multipliers.
Unpacking Referent Units in Fraction Operations
Philipp, Randolph A.; Hawthorne, Casey
2015-01-01
Although fraction operations are procedurally straightforward, they are complex, because they require learners to conceptualize different units and view quantities in multiple ways. Prospective secondary school teachers sometimes provide an algebraic explanation for inverting and multiplying when dividing fractions. That authors of this article…
Chaos in discrete fractional difference equations
Indian Academy of Sciences (India)
2016-09-07
Sep 7, 2016 ... Abstract. Recently, the discrete fractional calculus (DFC) is receiving attention due to its potential applica- tions in the mathematical modelling of real-world phenomena with memory effects. In the present paper, the chaotic behaviour of fractional difference equations for the tent map, Gauss map and 2x(mod ...
Fractional dynamics pharmacokinetics–pharmacodynamic models
2010-01-01
While an increasing number of fractional order integrals and differential equations applications have been reported in the physics, signal processing, engineering and bioengineering literatures, little attention has been paid to this class of models in the pharmacokinetics–pharmacodynamic (PKPD) literature. One of the reasons is computational: while the analytical solution of fractional differential equations is available in special cases, it this turns out that even the simplest PKPD models that can be constructed using fractional calculus do not allow an analytical solution. In this paper, we first introduce new families of PKPD models incorporating fractional order integrals and differential equations, and, second, exemplify and investigate their qualitative behavior. The families represent extensions of frequently used PK link and PD direct and indirect action models, using the tools of fractional calculus. In addition the PD models can be a function of a variable, the active drug, which can smoothly transition from concentration to exposure, to hyper-exposure, according to a fractional integral transformation. To investigate the behavior of the models we propose, we implement numerical algorithms for fractional integration and for the numerical solution of a system of fractional differential equations. For simplicity, in our investigation we concentrate on the pharmacodynamic side of the models, assuming standard (integer order) pharmacokinetics. PMID:20455076
Antidiarrhoeal Activity of Chromatographic Fractions of ...
African Journals Online (AJOL)
Purpose: The present study was undertaken in order to evaluate the antidiarrhoeal activity of three chromatographic fractions (L, S and Y) of Stereospermum kunthianum stem bark in mice. Methods: Vacuum liquid/column chromatography (VLC/ CC) were used to obtain three fractions (L,S and Y) of Stereospermum ...
Assessing Students' Understanding of Fraction Multiplication
Rumsey, Chepina; Guarino, Jody; Beltramini, Jennie; Cole, Shelbi; Farmer, Alicia; Gray, Kristin; Saxby, Morgan
2016-01-01
In this article the authors describe a project during which they unpacked fraction standards, created rigorous tasks and lesson plans, and developed formative and summative assessments to analyze students' thinking about fraction multiplication. The purpose of this article is to (1) illustrate a process that can be replicated by educators…
Phytotoxic characterization of various fractions of Launaea ...
African Journals Online (AJOL)
Administrator
2011-06-15
Jun 15, 2011 ... Allelopathic screening of various fractions of Launaea procumbens, collected from Wah Cantt (Punjab). Pakistan, was conceded to identify potent allelopathic fraction for future phytochemical analyses. For this purpose, radish root inhibition method was used to test allelopathic potential. Two different.
Quantitative metric theory of continued fractions
Indian Academy of Sciences (India)
Quantitative versions of the central results of the metric theory of contin- ued fractions were given primarily by C. ... Continued fractions; ergodic averages; metric theory of numbers. Mathematics Subject ... of subsets of X, a probability measure μ on the measurable space (X, β) and a measurable self-map T of X that is also ...
Protein-contg. fraction from mussel feet
Van der Leeden, M.C.; Groen, B.W.
1997-01-01
Abstract of NL 1000732 (C1) A protein-contg. fraction suitable for use as an adhesive that can provide an adhesive bond with a strength of more than 15 N/cm2 is claimed. The fraction comprises one or more proteins contg. 3,4-dihydroxyphenylalanine (Dopa) and is obtd. by a process comprising treating
Synchronization of Fractional-Order Hyperchaotic Systems via Fractional-Order Controllers
National Research Council Canada - National Science Library
Tianzeng Li; Yu Wang; Yong Yang
2014-01-01
In this paper, the synchronization of fractional-order chaotic systems is studied and a new fractional-order controller for hyperchaos synchronization is presented based on the Lyapunov stability theory...
Research on inter-fraction and intra-fraction motion of crystalline lens in radiotherapy
Directory of Open Access Journals (Sweden)
Shu-ming YANG
2013-03-01
Full Text Available Objective To investigate the range of inter-fraction and intra-fraction motion of crystalline lens in radiotherapy. Methods The CT and MRI images of 17 patients were registered, and the profile of crystalline lens was delineated to determine the respective center coordinates, thus simulating and analyzing inter-fraction and intra-fraction motion of lens in radiotherapy. Results Both left and right lens moved in different degree during both inter-or intra-fraction phase. The range of lens movement was larger in inter-fraction than in intra-fraction phase in all directions. Conclusion When radiotherapy is given in the free state, considering the distance of lens movement alone in inter-and intra-fraction and without considering the setup error, the lens planning organs at risk should increase 1.5mm outside the lens boundary.
Reply to "Comment on 'Fractional quantum mechanics' and 'Fractional Schrödinger equation' ".
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.
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.
National Research Council Canada - National Science Library
Banu Ünalmis Uzun
2017-01-01
We state the fractional Fourier transform and the continuous fractional wave packet transform as ways for analyzing persistent signals such as almost periodic functions and strong limit power signals...
Variable-order fuzzy fractional PID controller.
Liu, Lu; Pan, Feng; Xue, Dingyu
2015-03-01
In this paper, a new tuning method of variable-order fractional fuzzy PID controller (VOFFLC) is proposed for a class of fractional-order and integer-order control plants. Fuzzy logic control (FLC) could easily deal with parameter variations of control system, but the fractional-order parameters are unable to change through this way and it has confined the effectiveness of FLC. Therefore, an attempt is made in this paper to allow all the five parameters of fractional-order PID controller vary along with the transformation of system structure as the outputs of FLC, and the influence of fractional orders λ and μ on control systems has been investigated to make the fuzzy rules for VOFFLC. Four simulation results of different plants are shown to verify the availability of the proposed control strategy. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Fractional Vortices in Multi-Gap Superconductors
Loh, Yen Lee; Kim, Monica; Kim, Ju H.
2014-03-01
Novel topological defects, known as fractional vortices, can occur in thin films of multi-gap superconductors. We study two-gap and three-gap superconducting films within a classical Ginzburg-Landau description, using numerical simulations and analytic approximations. In two-gap superconducting films, we find that the interband Josephson coupling J12 leads to an effective attraction between half-vortices, whereas the permeability parameter μ leads to an effective repulsion between half-vortices. We locate the phase boundary in (J12 , μ) space that marks the onset of spontaneous vortex fractionalization. We describe how the size of a fractional vortex increases as one goes deeper into the fractionalized phase. Our results suggest that coating a multi-gap superconducting film with a paramagnetic overlayer will enhance the tendency towards vortex fractionalization.
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.
Neutron Imaging Calibration to Measure Void Fraction
Energy Technology Data Exchange (ETDEWEB)
Geoghegan, Patrick J [ORNL; Bilheux, Hassina Z [ORNL; Sharma, Vishaldeep [ORNL; Fricke, Brian A [ORNL
2015-01-01
Void fraction is an intuitive parameter that describes the fraction of vapor in a two-phase flow. It appears as a key variable in most heat transfer and pressure drop correlations used to design evaporating and condensing heat exchangers, as well as determining charge inventory in refrigeration systems. Void fraction measurement is not straightforward, however, and assumptions on the invasiveness of the measuring technique must be made. Neutron radiography or neutron imaging has the potential to be a truly non-invasive void fraction measuring technique but has until recently only offered qualitative descriptions of two-phase flow, in terms of flow maldistributions, for example. This paper describes the calibration approach necessary to employ neutron imaging to measure steady-state void fraction. Experiments were conducted at the High Flux Isotope Reactor (HFIR) Cold Guide 1D neutron imaging facility at Oak Ridge National Laboratory (ORNL), Oak Ridge, TN, USA.
Maximum likelihood estimation of fractionally cointegrated systems
DEFF Research Database (Denmark)
Lasak, Katarzyna
In this paper we consider a fractionally cointegrated error correction model and investigate asymptotic properties of the maximum likelihood (ML) estimators of the matrix of the cointe- gration relations, the degree of fractional cointegration, the matrix of the speed of adjustment to the equilib......In this paper we consider a fractionally cointegrated error correction model and investigate asymptotic properties of the maximum likelihood (ML) estimators of the matrix of the cointe- gration relations, the degree of fractional cointegration, the matrix of the speed of adjustment...... to the equilibrium parameters and the variance-covariance matrix of the error term. We show that using ML principles to estimate jointly all parameters of the fractionally cointegrated system we obtain consistent estimates and provide their asymptotic distributions. The cointegration matrix is asymptotically mixed...
Directory of Open Access Journals (Sweden)
Sajewski Łukasz
2017-03-01
Full Text Available Reachability and minimum energy control of descriptor fractional discrete-time linear systems with different fractional orders are addressed. Using the Weierstrass–Kronecker decomposition theorem of the regular pencil, a solution to the state equation of descriptor fractional discrete-time linear systems with different fractional orders is given. The reachability condition of this class of systems is presented and used for solving the minimum energy control problem. The discussion is illustrated with numerical examples.
Keshtkar, F.; Erjaee, G.; Boutefnouchet, M.
2014-01-01
In this article, a brief stability analysis of equilibrium points in nonlinear fractional order dynamical systems is given. Then, based on the first integral concept, a definition of planar Hamiltonian systems with fractional order introduced. Some interesting properties of these fractional Hamiltonian systems are also presented. Finally, we illustrate two examples to see the differences between fractional Hamiltonian systems with their classical order counterparts. NPRP . Grant Number: NP...
Directory of Open Access Journals (Sweden)
Fanwei Meng
2013-01-01
Full Text Available A new fractional subequation method is proposed for finding exact solutions for fractional partial differential equations (FPDEs. The fractional derivative is defined in the sense of modified Riemann-Liouville derivative. As applications, abundant exact solutions including solitary wave solutions as well as periodic wave solutions for the space-time fractional generalized Hirota-Satsuma coupled KdV equations are obtained by using this method.
Zayed, Elsayed M.E.; Amer, Yasser A.; Shohib, Reham M.A.
2016-01-01
In this article, the modified extended tanh-function method is employed to solve fractional partial differential equations in the sense of the modified Riemann–Liouville derivative. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into nonlinear ordinary differential equations of integer orders. For illustrating the validity of this method, we apply it to four nonlinear equations namely, the space–time fractional generaliz...
Directory of Open Access Journals (Sweden)
Yong-Ju Yang
2015-01-01
Full Text Available We apply the local fractional Fourier series method for solving nonlinear equation with local fractional operators. This method is the coupling of the local fractional Fourier series expansion method with other methods, such as the Yang-Laplace transformation method and the local fractional power series method, which effectively separates the variables of partial differential equation. Some testing nonlinear equations and equation systems are given to demonstrate the accuracy and applicability of the proposed approach.
Yong-Ju Yang; Shun-Qin Wang
2015-01-01
We apply the local fractional Fourier series method for solving nonlinear equation with local fractional operators. This method is the coupling of the local fractional Fourier series expansion method with other methods, such as the Yang-Laplace transformation method and the local fractional power series method, which effectively separates the variables of partial differential equation. Some testing nonlinear equations and equation systems are given to demonstrate the accuracy and applicabilit...
Synchronization of Fractional-Order Hyperchaotic Systems via Fractional-Order Controllers
Tianzeng Li; Yu Wang; Yong Yang
2014-01-01
In this paper, the synchronization of fractional-order chaotic systems is studied and a new fractional-order controller for hyperchaos synchronization is presented based on the Lyapunov stability theory. The proposed synchronized method can be applied to an arbitrary four-dimensional fractional hyperchaotic system. And we give the optimal value of control parameters to achieve synchronization of fractional hyperchaotic system. This approach is universal, simple, and theoretically rigorous. Nu...
Chen, Wen; Fang, Jun; Pang, Guofei; Holm, Sverre
2017-01-01
This paper proposes a fractional biharmonic operator equation model in the time-space domain to describe scattering attenuation of acoustic waves in heterogeneous media. Compared with the existing models, the proposed fractional model is able to describe arbitrary frequency-dependent scattering attenuation, which typically obeys an empirical power law with an exponent ranging from 0 to 4. In stark contrast to an extensive and rapidly increasing application of the fractional derivative models for wave absorption attenuation in the literature, little has been reported on frequency-dependent scattering attenuation. This is largely because the order of the fractional Laplacian is from 0 to 2 and is infeasible for scattering attenuation. In this study, the definition of the fractional biharmonic operator in space with an order varying from 0 to 4 is proposed, as well as a fractional biharmonic operator equation model of scattering attenuation which is consistent with arbitrary frequency power-law dependency and obeys the causal relation under the smallness approximation. Finally, the correlation between the fractional order and the ratio of wavelength to the diameter of the scattering heterogeneity is investigated and an expression on exponential form is also provided.
Opposing effects of different soil organic matter fractions on crop yields.
Wood, Stephen A; Sokol, Noah; Bell, Colin W; Bradford, Mark A; Naeem, Shahid; Wallenstein, Matthew D; Palm, Cheryl A
2016-10-01
Soil organic matter is critical to sustainable agriculture because it provides nutrients to crops as it decomposes and increases nutrient- and water-holding capacity when built up. Fast- and slow-cycling fractions of soil organic matter can have different impacts on crop production because fast-cycling fractions rapidly release nutrients for short-term plant growth and slow-cycling fractions bind nutrients that mineralize slowly and build up water-holding capacity. We explored the controls on these fractions in a tropical agroecosystem and their relationship to crop yields. We performed physical fractionation of soil organic matter from 48 farms and plots in western Kenya. We found that fast-cycling, particulate organic matter was positively related to crop yields, but did not have a strong effect, while slower-cycling, mineral-associated organic matter was negatively related to yields. Our finding that slower-cycling organic matter was negatively related to yield points to a need to revise the view that stabilization of organic matter positively impacts food security. Our results support a new paradigm that different soil organic matter fractions are controlled by different mechanisms, potentially leading to different relationships with management outcomes, like crop yield. Effectively managing soils for sustainable agriculture requires quantifying the effects of specific organic matter fractions on these outcomes. © 2016 by the Ecological Society of America.
Peters, Gregory
2010-01-01
A field-deployable, battery-powered Rapid Active Sampling Package (RASP), originally designed for sampling strong materials during lunar and planetary missions, shows strong utility for terrestrial geological use. The technology is proving to be simple and effective for sampling and processing materials of strength. Although this originally was intended for planetary and lunar applications, the RASP is very useful as a powered hand tool for geologists and the mining industry to quickly sample and process rocks in the field on Earth. The RASP allows geologists to surgically acquire samples of rock for later laboratory analysis. This tool, roughly the size of a wrench, allows the user to cut away swaths of weathering rinds, revealing pristine rock surfaces for observation and subsequent sampling with the same tool. RASPing deeper (.3.5 cm) exposes single rock strata in-situ. Where a geologist fs hammer can only expose unweathered layers of rock, the RASP can do the same, and then has the added ability to capture and process samples into powder with particle sizes less than 150 microns, making it easier for XRD/XRF (x-ray diffraction/x-ray fluorescence). The tool uses a rotating rasp bit (or two counter-rotating bits) that resides inside or above the catch container. The container has an open slot to allow the bit to extend outside the container and to allow cuttings to enter and be caught. When the slot and rasp bit are in contact with a substrate, the bit is plunged into it in a matter of seconds to reach pristine rock. A user in the field may sample a rock multiple times at multiple depths in minutes, instead of having to cut out huge, heavy rock samples for transport back to a lab for analysis. Because of the speed and accuracy of the RASP, hundreds of samples can be taken in one day. RASP-acquired samples are small and easily carried. A user can characterize more area in less time than by using conventional methods. The field-deployable RASP used a Ni
Rapid Robot Design Validation Project
National Aeronautics and Space Administration — Energid Technologies will create a comprehensive software infrastructure for rapid validation of robotic designs. The software will support push-button validation...
Rapid Robot Design Validation Project
National Aeronautics and Space Administration — Energid Technologies will create a comprehensive software infrastructure for rapid validation of robot designs. The software will support push-button validation...
Directory of Open Access Journals (Sweden)
Wang Huan-Huan
2017-01-01
Full Text Available In this paper, the Adomian decomposition method and the fractional complex transform are adopted to solve a fractional Bratu-type equations based on He’s fractional derivative. The solution process is elucidated and analytical results can be directly used in practical applications.
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.
Directory of Open Access Journals (Sweden)
Ahmad Neirameh
2018-07-01
Full Text Available In this study, we propose a new algorithm to find exact solitary wave solutions of nonlinear time- fractional order of extended biological population model. The new algorithm basically illustrates how two powerful algorithms, conformable fractional derivative and the homogeneous balance method can be combined and used to get exact solutions of fractional partial differential equations.
Directory of Open Access Journals (Sweden)
Banu Ünalmış Uzun
2017-06-01
Full Text Available Abstract We state the fractional Fourier transform and the continuous fractional wave packet transform as ways for analyzing persistent signals such as almost periodic functions and strong limit power signals. We construct frame decompositions for almost periodic functions using these two transforms. Also a norm equality of this signal is given using the continuous fractional wave packet transform.
Uzun, Banu Ünalmış
2017-01-01
We state the fractional Fourier transform and the continuous fractional wave packet transform as ways for analyzing persistent signals such as almost periodic functions and strong limit power signals. We construct frame decompositions for almost periodic functions using these two transforms. Also a norm equality of this signal is given using the continuous fractional wave packet transform.
Uzun, Banu ?nalm??
2017-01-01
We state the fractional Fourier transform and the continuous fractional wave packet transform as ways for analyzing persistent signals such as almost periodic functions and strong limit power signals. We construct frame decompositions for almost periodic functions using these two transforms. Also a norm equality of this signal is given using the continuous fractional wave packet transform.
Banu Ünalmış Uzun
2017-01-01
Abstract We state the fractional Fourier transform and the continuous fractional wave packet transform as ways for analyzing persistent signals such as almost periodic functions and strong limit power signals. We construct frame decompositions for almost periodic functions using these two transforms. Also a norm equality of this signal is given using the continuous fractional wave packet transform.
Directory of Open Access Journals (Sweden)
D. Vivek
2016-11-01
Full Text Available In this paper, the improved Euler method is used for solving hybrid fuzzy fractional differential equations (HFFDE of order $q \\in (0, 1 $ under Caputo-type fuzzy fractional derivatives. This method is based on the fractional Euler method and generalized Taylor's formula. The accuracy and efficiency of the proposed method is demonstrated by solving numerical examples.
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.
Xu, Lisa Y; Kilmer, Suzanne L; Ross, E Victor; Avram, Mathew M
2015-02-01
Non-ablative fractional laser procedures have become increasingly popular since their introduction in 2004. The fractional 1,927 nm thulium laser is a non-ablative device that penetrates up to 300 μm in the skin and the 1,550 nm erbium:glass laser penetrates up to 1,400 μm. These procedures are considered minimally invasive with a high safety profile; therefore, infectious complications are exceedingly rare. However, we report five recent cases of bacterial infection with both gram-positive and gram-negative organisms following treatment with the fractional 1550/1927 nm laser approximately 1 day to 1 week post-procedure. One patient had a rapidly progressing pustular eruption with symptoms of sepsis. These patients were seen immediately, cultures were obtained and empiric antibiotic therapy was initiated. They recovered without long-term complications. Rapid-onset bacterial infections following non-ablative laser resurfacing with the 1550/1927 nm laser have not been previously reported in the literature. The infections can progress quickly and lead to serious sequelae, including systemic illness and severe scarring, if not identified and appropriately treated. We present these cases to highlight the importance of close surveillance and when appropriate, rapid intervention, following non-ablative fractional procedures, especially when patients present with atypical symptoms and signs. © 2015 Wiley Periodicals, Inc.
CCII based fractional filters of different orders
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Ahmed Soltan
2014-03-01
Full Text Available This paper aims to generalize the design of continuous-time filters to the fractional domain with different orders and validates the theoretical results with two different CCII based filters. In particular, the proposed study introduces the generalized formulas for the previous fractional-order analysis of equal orders. The fractional-order filters enhance the design flexibility and prove that the integer-order performance is a very narrow subset from the fractional-order behavior due to the extra degrees of freedom. The general fundamentals of these filters are presented by calculating the maximum and minimum frequencies, the half power frequency and the right phase frequency which are considered a critical issue for the filter design. Different numerical solutions for the generalized fractional order low pass filters with two different fractional order elements are introduced and verified by the circuit simulations of two fractional-order filters: Kerwin–Huelsman–Newcomb (KHN and Tow-Tomas CCII-based filters, showing great matching.
Antibacterial Curcuma xanthorrhiza Extract and Fractions
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Hartiwi Diastuti
2014-12-01
Full Text Available An acetone extract of Curcuma xanthorrhiza rhizomes and the nhexane and chloroform fractions obtained from it were tested on eight pathogenic bacteria. The results showed that the acetone extract and the nhexane fraction exhibited significant activities against Bacillus subtilis, Pseudomonas aeruginosa, and Staphylococcus aureus, and weak activities against Shigella dysenteriae and Vibrio cholerae. They were inactive against Escherichia coli, Enterobacter aerogenes and Salmonella thypi, while the chloroform fraction was devoid of activities. NMR analysis disclosed the presence of α-curcumene, xanthorrhizol and an unknown monoterpene in the nhexane fraction. In the chloroform fraction, curcumin was found to be the main compound, together with xanthorrhizol as a minor compound. These results suggest that the antibacterial potency of acetone extract of C. xanthorrhiza is contained in the n-hexane fraction, in which the active constituents are terpenoid compounds. This is the first report of the use of NMR analysis for compound identification contained in an extract or fractions of C. xanthorrhiza.
Synchronization of Fractional-Order Hyperchaotic Systems via Fractional-Order Controllers
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Tianzeng Li
2014-01-01
Full Text Available In this paper, the synchronization of fractional-order chaotic systems is studied and a new fractional-order controller for hyperchaos synchronization is presented based on the Lyapunov stability theory. The proposed synchronized method can be applied to an arbitrary four-dimensional fractional hyperchaotic system. And we give the optimal value of control parameters to achieve synchronization of fractional hyperchaotic system. This approach is universal, simple, and theoretically rigorous. Numerical simulations of several fractional-order hyperchaotic systems demonstrate the universality and the effectiveness of the proposed method.
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Bhausaheb R. Sontakke
2016-11-01
Full Text Available In this paper, fractional complex transform with new iterative method (NIM is used to obtain approximate solutions for the nonlinear time fractional Kawahara and modified Kawahara equations based on He's fractional derivative. Fractional complex transform is proposed to convert time fractional Kawahara and modified Kawahara equations to the nonlinear ordinary differential equations and then NIM is applied to the new obtained equations. The obtained approximate solutions are compared with the exact solutions to verify the applicability, efficiency and accuracy of the method.
Rapid prototyping in medical sciences
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Ákos Márk Horváth
2015-09-01
Full Text Available Even if it sound a bit incredible rapid prototyping (RPT as production method has been used for decades in other professions. Nevertheless medical science just started discover the possibilities of this technology and use the offered benefits of 3D printing. In this paper authors have investigated the pharmaceutical usage of rapid prototyping.
Stable iron isotope fractionation between aqueous Fe(II) and hydrous ferric oxide.
Wu, Lingling; Beard, Brian L; Roden, Eric E; Johnson, Clark M
2011-03-01
Despite the ubiquity of poorly crystalline ferric hydrous oxides (HFO, or ferrihydrite) in natural environments, stable Fe isotopic fractionation between HFO and other Fe phases remains unclear. In particular, it has been difficult to determine equilibrium Fe isotope fractionation between aqueous Fe(II) and HFO due to fast transformation of the latter to more stable minerals. Here we used HFO stabilized by the presence of dissolved silica (2.14 mM), or a Si-HFO coprecipitate, to determine an equilibrium Fe(II)-HFO fractionation factor using a three-isotope method. Iron isotope exchange between Fe(II) and HFO was rapid and near complete with the Si-HFO coprecipitate, and rapid but incomplete for HFO in the presence of dissolved silica, the latter case likely reflecting blockage of oxide surface sites by sorbed silica. Equilibrium Fe(II)-HFO (56)Fe/(54)Fe fractionation factors of -3.17 ± 0.08 (2σ)‰ and -2.58 ± 0.14 (2σ)‰ were obtained for HFO plus silica and the Si-HFO coprecipitate, respectively. Structural similarity between ferrihydrite and hematite, as suggested by spectroscopic studies, combined with the minor isotopic effect of dissolved silica, imply that the true equilibrium Fe(II)-HFO (56)Fe/(54)Fe fractionation factor in the absence of silica may be ∼-3.2‰. These results provide a critical interpretive context for inferring the stable isotope effects of Fe redox cycling in nature.
The Fractions SNARC Revisited: Processing Fractions on a Consistent Mental Number Line.
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.
Sabeena Farvin, K H; Andersen, Lisa Lystbæk; Otte, Jeanette; Nielsen, Henrik Hauch; Jessen, Flemming; Jacobsen, Charlotte
2016-08-01
This study aimed to characterise peptide fractions (>5kDa, 3-5kDa and <3kDa) with antioxidative activity obtained from a cod protein hydrolysate. The free amino acids in all fractions were dominated by Ala, Gly, Glu and Ser. The total amino acid composition had high proportions of Lys, Ala and Glu. The 3-5kDa and <3kDa fractions were further fractionated by size exclusion chromatography. All sub-fractions showed high Fe(2+) chelating activity. The DPPH radical-scavenging activity of the 3-5kDa fraction was exerted mainly by one sub-fraction dominated by peptides with masses below 600Da. The DPPH radical-scavenging activity of the <3kDa 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 to the antioxidative activity of the peptide fractions, and Tyr seemed to play a major role in the antioxidant activity. Copyright © 2016. Published by Elsevier Ltd.
Characteristic ratio assignment in fractional order systems.
Tabatabaei, Mohammad; Haeri, Mohammad
2010-10-01
In this paper the characteristic ratios and generalized time constant are defined for all-pole commensurate fractional order systems. The sufficient condition for stability of these systems in terms of their characteristic ratios is obtained. Also an analytical approach for characteristic ratio assignment (CRA) to have a non-overshooting fast closed loop step response is introduced. The proposed CRA method is then employed to design a fractional order controller. Computer simulation results are presented to illustrate the performance of the CRA based designed fractional order controllers. Copyright © 2010 ISA. Published by Elsevier Ltd. All rights reserved.
Applications of fractional calculus in physics
2000-01-01
Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and co
Fractional calculus in bioengineering, part 3.
Magin, Richard L
2004-01-01
Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub
Directory of Open Access Journals (Sweden)
Elsayed M.E. Zayed
2016-02-01
Full Text Available In this article, the modified extended tanh-function method is employed to solve fractional partial differential equations in the sense of the modified Riemann–Liouville derivative. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into nonlinear ordinary differential equations of integer orders. For illustrating the validity of this method, we apply it to four nonlinear equations namely, the space–time fractional generalized nonlinear Hirota–Satsuma coupled KdV equations, the space–time fractional nonlinear Whitham–Broer–Kaup equations, the space–time fractional nonlinear coupled Burgers equations and the space–time fractional nonlinear coupled mKdV equations.
Bio-oil fractionation and condensation
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.
Antioxidant Enriched Fractions from Zingiber Officinale Roscoe
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Ismail Rahath Kubra
2011-01-01
Full Text Available Ginger rhizome (Zingiber officinale Roscoe has many diverse properties and medicinal values such as antioxidant potential combined with the properties of a spice. Dried ginger (DG were extracted with aqueous ethanol and freeze-dried. The extract was evaluated for antioxidant potential, using 1,1'-diphenyl-2-picryl-hydrazyl radical scavenging, antioxidant capacity and reducing power assays. DG extract was further fractionated into methanol (Mfr and water-soluble (Wfr fractions. The Mfr exhibited higher antioxidant capacity when compared to DG extract. Higher antioxidant potential of the methanol fraction may be due to the presence higher polyphenols and [6]-gingerol content. This suggests that alcoholic soluble fraction possess enormous scope to enhance the antioxidant potential when used as a supplement in various food as well as pharmaceutical formulations / products.
Symmetric, discrete fractional splines and Gabor systems
DEFF Research Database (Denmark)
Søndergaard, Peter Lempel
2006-01-01
In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing the continu......In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing...... the continuous splines, and one is a truly finite, discrete construction. We discuss the properties of these splines and their usefulness as windows for Gabor frames and Wilson bases....
Likelihood based testing for no fractional cointegration
DEFF Research Database (Denmark)
Lasak, Katarzyna
We consider two likelihood ratio tests, so-called maximum eigenvalue and trace tests, for the null of no cointegration when fractional cointegration is allowed under the alternative, which is a first step to generalize the so-called Johansen's procedure to the fractional cointegration case....... The standard cointegration analysis only considers the assumption that deviations from equilibrium can be integrated of order zero, which is very restrictive in many cases and may imply an important loss of power in the fractional case. We consider the alternative hypotheses with equilibrium deviations...... that can be mean reverting with order of integration possibly greater than zero. Moreover, the degree of fractional cointegration is not assumed to be known, and the asymptotic null distribution of both tests is found when considering an interval of possible values. The power of the proposed tests under...
Fractional diffusion equations and anomalous diffusion
Evangelista, Luiz Roberto
2018-01-01
Anomalous diffusion has been detected in a wide variety of scenarios, from fractal media, systems with memory, transport processes in porous media, to fluctuations of financial markets, tumour growth, and complex fluids. Providing a contemporary treatment of this process, this book examines the recent literature on anomalous diffusion and covers a rich class of problems in which surface effects are important, offering detailed mathematical tools of usual and fractional calculus for a wide audience of scientists and graduate students in physics, mathematics, chemistry and engineering. Including the basic mathematical tools needed to understand the rules for operating with the fractional derivatives and fractional differential equations, this self-contained text presents the possibility of using fractional diffusion equations with anomalous diffusion phenomena to propose powerful mathematical models for a large variety of fundamental and practical problems in a fast-growing field of research.
Early Predictors of Middle School Fraction Knowledge
Bailey, Drew H.; Siegler, Robert S.; Geary, David C.
2014-01-01
Recent findings that earlier fraction knowledge predicts later mathematics achievement raise the question of what predicts later fraction knowledge. Analyses of longitudinal data indicated that whole number magnitude knowledge in first grade predicted knowledge of fraction magnitudes in middle school, controlling for whole number arithmetic proficiency, domain general cognitive abilities, parental income and education, race, and gender. Similarly, knowledge of whole number arithmetic in first grade predicted knowledge of fraction arithmetic in middle school, controlling for whole number magnitude knowledge in first grade and the other control variables. In contrast, neither type of early whole number knowledge uniquely predicted middle school reading achievement. We discuss the implications of these findings for theories of numerical development and for improving mathematics learning. PMID:24576209
Tunneling time in space fractional quantum mechanics
Hasan, Mohammad; Mandal, Bhabani Prasad
2018-02-01
We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantum mechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width b of the barrier for b → ∞ and therefore Hartman effect doesn't exist in space fractional quantum mechanics. Interestingly we found that the tunneling time monotonically reduces with increasing b. The tunneling time is smaller in space fractional quantum mechanics as compared to the case of standard quantum mechanics. We recover the Hartman effect of standard quantum mechanics as a special case of space fractional quantum mechanics.
Exact solution to fractional logistic equation
West, Bruce J.
2015-07-01
The logistic equation is one of the most familiar nonlinear differential equations in the biological and social sciences. Herein we provide an exact solution to an extension of this equation to incorporate memory through the use of fractional derivatives in time. The solution to the fractional logistic equation (FLE) is obtained using the Carleman embedding technique that allows the nonlinear equation to be replaced by an infinite-order set of linear equations, which we then solve exactly. The formal series expansion for the initial value solution of the FLE is shown to be expressed in terms of a series of weighted Mittag-Leffler functions that reduces to the well known analytic solution in the limit where the fractional index for the derivative approaches unity. The numerical integration to the FLE provides an excellent fit to the analytic solution. We propose this approach as a general technique for solving a class of nonlinear fractional differential equations.
The fractional Fourier transform and applications
Bailey, David H.; Swarztrauber, Paul N.
1991-01-01
This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.
The Fractional Orthogonal Difference with Applications
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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.
Thermomechanical Fractional Model of Two Immiscible TEMHD
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F. Hamza
2015-01-01
Full Text Available We introduce a mathematical model of unsteady thermoelectric MHD flow and heat transfer of two immiscible fractional second-grade fluids, with thermal fractional parameters αi and mechanical fractional parameters βi, i=1,2. The Laplace transform with respect to time is used to obtain the solution in the transformed domain. The inversion of Laplace transform is obtained by using numerical method based on a Fourier-series expansion. The numerical results for temperature, velocity, and the stress distributions are represented graphically for different values of αi and βi. The graphs describe the fractional thermomechanical parameters effect on the case of two immiscible fluids and the case of a single fluid.
Bio-oil fractionation and condensation
Brown, Robert C.; Jones, Samuel T.; Pollard, Anthony
2017-04-04
The present invention relates to a method of fractionating bio-oil vapors which involves providing bio-oil vapors comprising bio-oil constituents. 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 disclosed are steps for subsequently recovering further liquid fractions of liquefied bio-oil constituents. Particular compositions of bio-oil condensation products are also described.
Ca isotope fractionation on the moon
Russell, W. A.; Papanastassiou, D. A.; Tombrello, T. A.; Epstein, S.
1977-01-01
Ca has been measured in a lunar soil in order to establish the presence of isotopically mass-fractionated components. Ca was extracted by a series of water leaches after the soils were 'activated' by brief exposures to fluorine gas. The O2 obtained by this fluorination is found to have delta (O-18) of +21 per mil and to be, therefore, significantly mass-fractionated. Ca obtained in the leaches was analyzed using the double-spike technique. Very small Ca isotope fractionation is found in the leaches of this soil of up to 1 per mil per mass unit difference. The small Ca effects are in marked contrast to the measured delta (O-18) for the same sample and to large effects observed in many soils for oxygen, silicon, sulfur, and potassium. The data on Ca provide stringent constraints on models which attempt to explain the isotope mass-fractionation effects in lunar soils.
Fractional Diffusion in Gaussian Noisy Environment
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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.
Fractional Langevin equation to describe anomalous diffusion
Kobelev, V
1999-01-01
A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle, with the power exponent being noninteger. More general equation containing fractional time differential operators instead of usual ones is also proposed to describe anomalous diffusion processes. Such equation can be regarded as corresponding to systems with incomplete Hamiltonian chaos, and depending on the type of the relationship between the speed and coordinate of a particle yields either usual or fractional long-time behavior of diffusion. Correlations with the fractional Fokker-Planck equation are analyzed. Possible applications of the proposed equation beside anomalous diffusion itself are discussed.
Fractional calculus in bioengineering, part 2.
Magin, Richard L
2004-01-01
Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub
How Rapid is Rapid Prototyping? Analysis of ESPADON Programme Results
Directory of Open Access Journals (Sweden)
Ian D. Alston
2003-05-01
Full Text Available New methodologies, engineering processes, and support environments are beginning to emerge for embedded signal processing systems. The main objectives are to enable defence industry to field state-of-the-art products in less time and with lower costs, including retrofits and upgrades, based predominately on commercial off the shelf (COTS components and the model-year concept. One of the cornerstones of the new methodologies is the concept of rapid prototyping. This is the ability to rapidly and seamlessly move from functional design to the architectural design to the implementation, through automatic code generation tools, onto real-time COTS test beds. In this paper, we try to quantify the term Ã¢Â€ÂœrapidÃ¢Â€Â and provide results, the metrics, from two independent benchmarks, a radar and sonar beamforming application subset. The metrics show that the rapid prototyping process may be sixteen times faster than a conventional process.
Deformable fractional derivative and its applications
Ahuja, Priyanka; Zulfeqarr, Fahed; Ujlayan, Amit
2017-10-01
In this paper, we introduce an application of recently proposed deformable derivative which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach as ordinary derivative. Thus it could also be regarded as fractional derivative. The simple nature of this definition allows us for the extension of some classical theorems in calculus like the Rolles, Mean Value and Extended Mean Value theorems. As a theoritical application some fractional differentiable equations are solved.
The Vertical Linear Fractional Initialization Problem
Lorenzo, Carl F.; Hartley, Tom T.
1999-01-01
This paper presents a solution to the initialization problem for a system of linear fractional-order differential equations. The scalar problem is considered first, and solutions are obtained both generally and for a specific initialization. Next the vector fractional order differential equation is considered. In this case, the solution is obtained in the form of matrix F-functions. Some control implications of the vector case are discussed. The suggested method of problem solution is shown via an example.
Fractional Differential and Integral Inequalities with Applications
2016-02-14
method has been extended to the Caputo fractional differential equation of order q (where 0<qə) with an initial condition as well as the existence of... coupled minimal and maximal solutions for such an equation and a numerical example is provided as an application of the theoretical results. The...linear sub hyperbolic fractional partial differential equation in one dimensional space, that is the qth time order 1. REPORT DATE (DD-MM-YYYY) 4
On linear and nonlinear fractional PDEs
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Ahmad Jamshad
2013-01-01
Full Text Available In this study, Variational Iteration Method (VIM has been applied to obtain the analytical solutions of fractional order nonlinear partial differential equations. The iteration procedure is based on a relatively new approach which is called Jumarie’s fractional derivative. Several examples have been solved to elucidate effectiveness of the proposed method and the results are compared with the exact solution, revealing high accuracy and efficiency of the method.
Stability of fractional positive nonlinear systems
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Kaczorek Tadeusz
2015-12-01
Full Text Available The conditions for positivity and stability of a class of fractional nonlinear continuous-time systems are established. It is assumed that the nonlinear vector function is continuous, satisfies the Lipschitz condition and the linear part is described by a Metzler matrix. The stability conditions are established by the use of an extension of the Lyapunov method to fractional positive nonlinear systems.
Isotope fractionation of benzene during partitioning - Revisited.
Kopinke, F-D; Georgi, A; Imfeld, G; Richnow, H-H
2017-02-01
Isotope fractionation between benzene-D0 and benzene-D6 caused by multi-step partitioning of the benzenes between water and two organic solvents, n-octane and 1-octanol, as well as between water and the gas phase, was measured. The obtained fractionation factors αH = KH/KD are αH = 1.080 ± 0.015 and αH = 1.074 ± 0.015 for extraction into n-octane and 1-octanol, respectively, and αH = 1.049 ± 0.010 for evaporation from aqueous solution. The comparison of solvent- and gas-phase partitioning reveals that about 2/3 of the driving force of fractionation is due to different interactions in the aqueous phase, whereas 1/3 is due to different interactions in the organic phase. The heavy benzene isotopologue behaves more 'hydrophilically' and the light one more 'hydrophobically'. This synergistic alignment gives rise to relatively large fractionation effects in partitioning between water and non-polar organic matter. In contrast to a previous study, there is no indication of strong fractionation by specific interactions between benzene and octanol. Partitioning under non-equilibrium conditions yields smaller apparent fractionation effects due to opposite trends of thermodynamic and kinetic fractionation parameters, i.e. partition and diffusion coefficients of the isotopologues. This may have consequences which should be taken into account when considering isotope fractionation due to sorption in environmental compartments. Copyright © 2016 Elsevier Ltd. All rights reserved.
Chaos synchronization of a fractional nonautonomous system
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Hammouch Zakia
2014-01-01
Full Text Available In this paper we investigate the dynamic behavior of a nonautonomous fractional-order biological system.With the stability criterion of active nonlinear fractional systems, the synchronization of the studied chaotic system is obtained. On the other hand, using a Phase-Locked-Loop (PLL analogy we synchronize the same system. The numerical results demonstrate the efiectiveness of the proposed methods
Fractional Dynamics in Calcium Oscillation Model
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Yoothana Suansook
2015-01-01
Full Text Available The calcium oscillations have many important roles to perform many specific functions ranging from fertilization to cell death. The oscillation mechanisms have been observed in many cell types including cardiac cells, oocytes, and hepatocytes. There are many mathematical models proposed to describe the oscillatory changes of cytosolic calcium concentration in cytosol. Many experiments were observed in various kinds of living cells. Most of the experimental data show simple periodic oscillations. In certain type of cell, there exists the complex periodic bursting behavior. In this paper, we have studied further the fractional chaotic behavior in calcium oscillations model based on experimental study of hepatocytes proposed by Kummer et al. Our aim is to explore fractional-order chaotic pattern in this oscillation model. Numerical calculation of bifurcation parameters is carried out using modified trapezoidal rule for fractional integral. Fractional-order phase space and time series at fractional order are present. Numerical results are characterizing the dynamical behavior at different fractional order. Chaotic behavior of the model can be analyzed from the bifurcation pattern.
Generalized continued fractions and ergodic theory
Pustyl'nikov, L. D.
2003-02-01
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.
Alternative Forms of Compound Fractional Poisson Processes
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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.
Isotopic fractionation of tritium in biological systems.
Le Goff, Pierre; Fromm, Michel; Vichot, Laurent; Badot, Pierre-Marie; Guétat, Philippe
2014-04-01
Isotopic fractionation of tritium is a highly relevant issue in radiation protection and requires certain radioecological considerations. Sound evaluation of this factor is indeed necessary to determine whether environmental compartments are enriched/depleted in tritium or if tritium is, on the contrary, isotopically well-distributed in a given system. The ubiquity of tritium and the standard analytical methods used to assay it may induce biases in both the measurement and the signification that is accorded to the so-called fractionation: based on an exhaustive review of the literature, we show how, sometimes large deviations may appear. It is shown that when comparing the non-exchangeable fraction of organically bound tritium (neOBT) to another fraction of tritium (e.g. tritiated water) the preparation of samples and the measurement of neOBT reported frequently led to underestimation of the ratio of tritium to hydrogen (T/H) in the non-exchangeable compartment by a factor of 5% to 50%. In the present study, corrections are proposed for most of the biological matrices studied so far. Nevertheless, the values of isotopic fractionation reported in the literature remain difficult to compare with each other, especially since the physical quantities and units often vary between authors. Some improvements are proposed to better define what should encompass the concepts of exchangeable and non-exchangeable fractions. Copyright © 2014 Elsevier Ltd. All rights reserved.
Maximizing Tumor Immunity With Fractionated Radiation
Energy Technology Data Exchange (ETDEWEB)
Schaue, Doerthe, E-mail: dschaue@mednet.ucla.edu [Department of Radiation Oncology, David Geffen School of Medicine at UCLA, Los Angeles, CA (United States); Ratikan, Josephine A.; Iwamoto, Keisuke S.; McBride, William H. [Department of Radiation Oncology, David Geffen School of Medicine at UCLA, Los Angeles, CA (United States)
2012-07-15
Purpose: Technologic advances have led to increased clinical use of higher-sized fractions of radiation dose and higher total doses. How these modify the pathways involved in tumor cell death, normal tissue response, and signaling to the immune system has been inadequately explored. Here we ask how radiation dose and fraction size affect antitumor immunity, the suppression thereof, and how this might relate to tumor control. Methods and Materials: Mice bearing B16-OVA murine melanoma were treated with up to 15 Gy radiation given in various-size fractions, and tumor growth followed. The tumor-specific immune response in the spleen was assessed by interferon-{gamma} enzyme-linked immunospot (ELISPOT) assay with ovalbumin (OVA) as the surrogate tumor antigen and the contribution of regulatory T cells (Tregs) determined by the proportion of CD4{sup +}CD25{sup hi}Foxp3{sup +} T cells. Results: After single doses, tumor control increased with the size of radiation dose, as did the number of tumor-reactive T cells. This was offset at the highest dose by an increase in Treg representation. Fractionated treatment with medium-size radiation doses of 7.5 Gy/fraction gave the best tumor control and tumor immunity while maintaining low Treg numbers. Conclusions: Radiation can be an immune adjuvant, but the response varies with the size of dose per fraction. The ultimate challenge is to optimally integrate cancer immunotherapy into radiation therapy.
Fractionation behavior of chromium isotopes during coprecipitation with calcium carbonate
DEFF Research Database (Denmark)
Rodler, Alexandra; Sánchez-Pastor, Nuria; Fernández-Díaz, Lurdes
2015-01-01
Interest in chromium (Cr) isotope incorporation into carbonates arises from the observation that Cr isotopic composition of carbonates could be used as a paleoclimate proxy to elucidate past fluctuations of oxygen contents in atmosphere and hydrosphere. The use of Cr isotopes to track....... The fractionation of Cr isotopes during calcium carbonate coprecipitation was assumed to be small, based on previously published data of modern seawater and modern non-skeletal marine carbonates. However, results from this study for rapidly precipitated calcium carbonate in the presence of chromate show a tendency...... showed the presence of vaterite. Calcium carbonate crystals were also precipitated in a double diffusion silica hydrogel over a longer period of time resulting in samples consisting of micrometric-millimetric calcite crystals, which were again significantly enriched in heavy Cr isotopes compared...
Halevy, I.; Wing, B. A.; Wenk, C.; Guimond, C.
2015-12-01
Microbial S isotope fractionations close to the thermodynamic fractionation between sulfate and sulfide (~70‰) are encountered only at the slowest rates of sulfate reduction in laboratory cultures. In turn, the slowest laboratory reduction rates overlap with only the highest values of cell-specific sulfate reduction rates measured in marine sediments. This chain-of-logic implies that sulfate-reducing microbes in the marine sedimentary biosphere fractionate S isotopes at magnitudes close to the thermodynamic limit. Recent observations from sulfate-poor environments indicate that fractionations are large even at micromolar sulfate concentrations, in agreement with model predictions of near-thermodynamic S isotope fractionation at these sulfate concentrations as long as cell-specific sulfate reduction rates are low. Despite the expectation of large microbial fractionations, pyrite in both modern marine sediments and Phanerozoic sedimentary rocks records apparent fractionations ranging from 0 to more than 70‰. We suggest that the observed range of modern marine and geologic apparent fractionations recorded in pyrite does not reflect variability in intrinsic microbial behavior, but an early diagenetic modulation of large microbial fractionations, which are pinned to the thermodynamic limit by the low natural rates of sulfate reduction. With a diagenetic model developed in this study, we show that the entire range of apparent fractionations is possible with microbial fractionations at the thermodynamic limit. Apparent fractionations depend on a variety of physical parameters of the sedimentary environment like sedimentation rate, porosity, and organic matter content, most of which correlate with water depth. These findings, in combination with knowledge about the preservation potential of sediments deposited at different depths, make predictions for the observed geologic range of apparent fractionations, and ways in which it differs from the range in modern marine
Characterization of Coconut Oil Fractions Obtained from Solvent Fractionation Using Acetone.
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.
Directory of Open Access Journals (Sweden)
Olaniyi Samuel Iyiola
2014-09-01
Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.
The fractional - order controllers: Methods for their synthesis and application
Petras, I.
2000-01-01
This paper deals with fractional-order controllers. We outline mathematical description of fractional controllers and methods of their synthesis and application. Synthesis method is a modified root locus method for fractional-order systems and fractional-order controllers. In the next section we describe how to apply the fractional controller on control systems.
Continued Fractions of Order Six and New Eisenstein Series Identities
Chandrashekar Adiga; A. Vanitha; M. S. Surekha
2014-01-01
We prove two identities for Ramanujan’s cubic continued fraction and a continued fraction of Ramanujan, which are analogues of Ramanujan’s identities for the Rogers-Ramanujan continued fraction. We further derive Eisenstein series identities associated with Ramanujan’s cubic continued fraction and Ramanujan’s continued fraction of order six.
Polysome Fractionation to Analyze mRNA Distribution Profiles.
Panda, Amaresh C; Martindale, Jennifer L; Gorospe, Myriam
2017-02-05
Eukaryotic cells adapt to changes in external or internal signals by precisely modulating the expression of specific gene products. The expression of protein-coding genes is controlled at the transcriptional and post-transcriptional levels. Among the latter steps, the regulation of translation is particularly important in cellular processes that require rapid changes in protein expression patterns. The translational efficiency of mRNAs is altered by RNA-binding proteins (RBPs) and noncoding (nc)RNAs such as microRNAs (Panda et al., 2014a and 2014b; Abdelmohsen et al., 2014). The impact of factors that regulate selective mRNA translation is a critical question in RNA biology. Polyribosome (polysome) fractionation analysis is a powerful method to assess the association of ribosomes with a given mRNA. It provides valuable information about the translational status of that mRNA, depending on the number of ribosomes with which they are associated, and identifies mRNAs that are not translated (Panda et al., 2016). mRNAs associated with many ribosomes form large polysomes that are predicted to be actively translated, while mRNAs associated with few or no ribosomes are expected to be translated poorly if at all. In sum, polysome fractionation analysis allows the direct determination of translation efficiencies at the level of the whole transcriptome as well as individual mRNAs.
Reactive transport modeling of chromium isotope fractionation during Cr(VI) reduction.
Jamieson-Hanes, Julia H; Amos, Richard T; Blowes, David W
2012-12-18
Chromium isotope fractionation is indicative of mass-transfer processes, such as reduction of Cr(VI) to Cr(III) during groundwater remediation. Laboratory experiments comparing batch and column treatment of Cr(VI) using organic carbon suggest that the associated isotope fractionation may be influenced by solute-transport mechanisms. These batch and column experiments were simulated using the reactive transport model MIN3P to further evaluate the effects of Cr reduction and transport on isotope fractionation under saturated flow conditions. Simulation of the batch experiment provided a good fit to the experimental data, where a fractionation factor (α₅₃) of 0.9965 was attributed to a single, dominant Cr(VI) removal mechanism. Calibration of the column simulations to the experimental results suggested the presence of a second, more rapid Cr(VI) removal mechanism with α₅₃ = 0.9992. Results from this study demonstrate that the interpretation of Cr isotope fractionation during reduction can be complex, particularly where multiple removal mechanisms are evident. Reactive transport modeling of Cr isotope fractionation can provide a quantitative assessment of the contaminant removal mechanisms, thus improving the application of Cr isotope measurements as a tool to track Cr(VI) migration and attenuation in groundwater.
Xu, Kaixuan; Wang, Jun
2017-02-01
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.
Fractional order differentiation by integration: An application to fractional linear systems
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.
A Rapid Coliform Detector Project
National Aeronautics and Space Administration — ORBITEC, in collaboration with Lucigen, proposes a rapid genetic detector for spaceflight water systems to enable real-time detection of E-coli with minimal...
Rapid Multiplex Microbial Detector Project
National Aeronautics and Space Administration — ORBITEC, in collaboration with Lucigen, proposes a rapid nucleic acid-based detector for spaceflight water systems to enable simultaneous quantification of multiple...
Synchronization of Fractional Chaotic Systems via Fractional-Order Adaptive Controller
Hosseinnia, S. H.; Ghaderi, R.; N., A. Ranjbar; Sadati, J.; Momani, S.
2012-01-01
In this paper, an adaptive fractional controller has been designed to control chaotic systems. In fact, this controller is a fractional PID controller, which the coefficients will be tuned according to a proper adaptation mechanism. The adaptation law will be constructed from a sliding surface via gradient method. The adaptive fractional controller is implemented on a gyro system to signify the performance of the proposed technique.
Fractional boundary value problems with multiple orders of fractional derivatives and integrals
Directory of Open Access Journals (Sweden)
Sotiris K. Ntouyas
2017-04-01
Full Text Available In this article we study a new class of boundary value problems for fractional differential equations and inclusions with multiple orders of fractional derivatives and integrals, in both fractional differential equation and boundary conditions. The Sadovski's fixed point theorem is applied in the single-valued case while, in multi-valued case, the nonlinear alternative for contractive maps is used. Some illustrative examples are also included.
Fractional diffusion models of nonlocal transport
Energy Technology Data Exchange (ETDEWEB)
Del-Castillo-Negrete, Diego B [ORNL
2006-08-01
A class of nonlocal models based on the use of fractional derivatives (FDs) is proposed to describe nondiffusive transport in magnetically confined plasmas. FDs are integro-differential operators that incorporate in a unified framework asymmetric non-Fickian transport, non-Markovian ('memory') effects, and nondiffusive scaling. To overcome the limitations of fractional models in unbounded domains, we use regularized FDs that allow the incorporation of finite-size domain effects, boundary conditions, and variable diffusivities. We present an alpha-weighted explicit/implicit numerical integration scheme based on the Grunwald-Letnikov representation of the regularized fractional diffusion operator in flux conserving form. In sharp contrast with the standard diffusive model, the strong nonlocality of fractional diffusion leads to a linear in time response for a decaying pulse at short times. In addition, an anomalous fractional pinch is observed, accompanied by the development of an uphill transport region where the 'effective' diffusivity becomes negative. The fractional flux is in general asymmetric and, for steady states, it has a negative (toward the core) component that enhances confinement and a positive component that increases toward the edge and leads to poor confinement. The model exhibits the characteristic anomalous scaling of the confinement time, {tau}, with the system's size, L, {tau}{approx}L{sup {alpha}}, of low-confinement mode plasma where 1<{alpha}<2 is the order of the FD operator. Numerical solutions of the model with an off-axis source show that the fractional inward transport gives rise to profile peaking reminiscent of what is observed in tokamak discharges with auxiliary off-axis heating. Also, cold-pulse perturbations to steady states in the model exhibit fast, nondiffusive propagation phenomena that resemble perturbative experiments.
Fractional diffusion models of nonlocal transport
del-Castillo-Negrete, D.
2006-08-01
A class of nonlocal models based on the use of fractional derivatives (FDs) is proposed to describe nondiffusive transport in magnetically confined plasmas. FDs are integro-differential operators that incorporate in a unified framework asymmetric non-Fickian transport, non-Markovian ("memory") effects, and nondiffusive scaling. To overcome the limitations of fractional models in unbounded domains, we use regularized FDs that allow the incorporation of finite-size domain effects, boundary conditions, and variable diffusivities. We present an α-weighted explicit/implicit numerical integration scheme based on the Grunwald-Letnikov representation of the regularized fractional diffusion operator in flux conserving form. In sharp contrast with the standard diffusive model, the strong nonlocality of fractional diffusion leads to a linear in time response for a decaying pulse at short times. In addition, an anomalous fractional pinch is observed, accompanied by the development of an uphill transport region where the "effective" diffusivity becomes negative. The fractional flux is in general asymmetric and, for steady states, it has a negative (toward the core) component that enhances confinement and a positive component that increases toward the edge and leads to poor confinement. The model exhibits the characteristic anomalous scaling of the confinement time, τ, with the system's size, L, τ ˜Lα, of low-confinement mode plasma where 1<α<2 is the order of the FD operator. Numerical solutions of the model with an off-axis source show that the fractional inward transport gives rise to profile peaking reminiscent of what is observed in tokamak discharges with auxiliary off-axis heating. Also, cold-pulse perturbations to steady sates in the model exhibit fast, nondiffusive propagation phenomena that resemble perturbative experiments.
Particle Simulation of Fractional Diffusion Equations
Allouch, Samer
2017-07-12
This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the fractional diffusion term. The first method is based on direct differentiation of the particle representation, it follows the Riesz definition of the fractional derivative and results in a non-conservative scheme. The other three methods follow the particle strength exchange (PSE) methodology and are by construction conservative, in the sense that the total particle strength is time invariant. The first PSE algorithm is based on using direct differentiation to estimate the fractional diffusion flux, and exploiting the resulting estimates in an integral representation of the divergence operator. Meanwhile, the second one relies on the regularized Riesz representation of the fractional diffusion term to derive a suitable interaction formula acting directly on the particle representation of the diffusing field. A third PSE construction is considered that exploits the Green\\'s function of the fractional diffusion equation. The performance of all four approaches is assessed for the case of a one-dimensional diffusion equation with constant diffusivity. This enables us to take advantage of known analytical solutions, and consequently conduct a detailed analysis of the performance of the methods. This includes a quantitative study of the various sources of error, namely filtering, quadrature, domain truncation, and time integration, as well as a space and time self-convergence analysis. These analyses are conducted for different values of the order of the fractional derivatives, and computational experiences are used to gain insight that can be used for generalization of the present constructions.
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.
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.
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.
Zayernouri, Mohsen; Matzavinos, Anastasios
2016-07-01
We first formulate a fractional class of explicit Adams-Bashforth (A-B) and implicit Adams-Moulton (A-M) methods of first- and second-order accuracy for the time-integration of t τ 0 CD u (x , t) = g (t ; u), τ ∈ (0 , 1 ], where t τ 0 CD #x03c4; 0 C denotes the fractional derivative in the Caputo sense. In this fractional setting and in contrast to the standard Adams methods, an extra history load term emerges and the associated weight coefficients are τ-dependent. However when τ = 1, the developed schemes reduce to the well-known A-B and A-M methods with standard coefficients. Hence, in terms of scientific computing, our approach constitutes a minimal modification of the existing Adams libraries. Next, we develop an implicit-explicit (IMEX) splitting scheme for linear and nonlinear fractional PDEs of a general advection-reaction-diffusion type, and we apply our scheme to the time-space fractional Keller-Segel chemotaxis system. In this context, we evaluate the nonlinear advection term explicitly, employing the fractional A-B method in the prediction step, and we treat the corresponding diffusion term implicitly in the correction step using the fractional A-M scheme. Moreover, we perform the corresponding spatial discretization by employing an efficient and spectrally-accurate fractional spectral collocation method. Our numerical experiments exhibit the efficiency of the proposed IMEX scheme in solving nonlinear fractional PDEs.
A New fractional derivative for differential equation of fractional order under interval uncertainty
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Soheil Salahshour
2015-12-01
Full Text Available In this article, we develop a new definition of fractional derivative under interval uncertainty. This fractional derivative, which is called conformable fractional derivative, inherits some interesting properties from the integer differentiability which is more convenient to work with the mathematical models of the real-world phenomena. The interest for this new approach was born from the notion that makes a dependency just on the basic limit definition of the derivative. We will introduce and prove the main features of this well-behaved simple fractional derivative under interval arithmetic uncertainty. The actualization and usefulness of this approach are validated by solving two practical models.
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.
Liu, Jian; Zhu, Yaohui; He, Peisong; Chen, Xiaosong; Bao, Jing-Dong
2017-04-01
Anomalous diffusion is researched within the framework of the coupled continuous time random walk model, in which the space-time coupling is considered through the correlated function g(t) tγ, 0 ≤ γfractional generalized master equation is derived analytically which can be applied to describe the transient bi-fractional diffusion phenomenon which is induced by the space-time coupling and the asymptotic behavior of ω(t). Numerical results show that for the transient bi-fractional diffusion, there is a transition from one fractional diffusion to another one in the diffusive process.
Directory of Open Access Journals (Sweden)
Emad A.-B. Abdel-Salam
2013-01-01
Full Text Available The fractional Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, space-time fractional Korteweg-de Vries equation, regularized long-wave equation, Boussinesq equation, and Klein-Gordon equation are considered. As a result, abundant types of exact analytical solutions are obtained. These solutions include generalized trigonometric and hyperbolic functions solutions which may be useful for further understanding of the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The periodic and kink solutions are founded as special case.
Fractional diffusion equation with a generalized Riemann-Liouville time fractional derivative
Energy Technology Data Exchange (ETDEWEB)
Sandev, Trifce [Radiation Safety Directorate, Partizanski odredi 143, PO Box 22, 1020 Skopje (Macedonia, The Former Yugoslav Republic of); Metzler, Ralf [Department of Physics, Technical University of Munich, James Franck Strasse, 85747 Garching (Germany); Tomovski, Zivorad, E-mail: trifce.sandev@drs.gov.mk, E-mail: metz@ph.tum.de, E-mail: tomovski@pmf.ukim.mk [Faculty of Natural Sciences and Mathematics, Institute of Mathematics, Saints Cyril and Methodius University, 1000 Skopje (Macedonia, The Former Yugoslav Republic of)
2011-06-24
In this paper, the solution of a fractional diffusion equation with a Hilfer-generalized Riemann-Liouville time fractional derivative is obtained in terms of Mittag-Leffler-type functions and Fox's H-function. The considered equation represents a quite general extension of the classical diffusion (heat conduction) equation. The methods of separation of variables, Laplace transform, and analysis of the Sturm-Liouville problem are used to solve the fractional diffusion equation defined in a bounded domain. By using the Fourier-Laplace transform method, it is shown that the fundamental solution of the fractional diffusion equation with a generalized Riemann-Liouville time fractional derivative defined in the infinite domain can be expressed via Fox's H-function. It is shown that the corresponding solutions of the diffusion equations with time fractional derivative in the Caputo and Riemann-Liouville sense are special cases of those diffusion equations with the Hilfer-generalized Riemann-Liouville time fractional derivative. The asymptotic behaviour of the solutions are found for large values of the spatial variable. The fractional moments of the fundamental solution of the fractional diffusion equation are obtained. The obtained results are relevant in the context of glass relaxation and aquifer problems.
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Ya-Ning Li
2014-08-01
Full Text Available As an extension of the fact that a sectorial operator can determine an analytic semigroup, we first show that a sectorial operator can determine a real analytic alpha-order fractional resolvent which is defined in terms of Mittag-Leffler function and the curve integral. Then we give some properties of real analytic alpha-order fractional resolvent. Finally, based on these properties, we discuss the regularity of mild solution of a class of fractional abstract Cauchy problems with Riemann-Liouville fractional derivative.
On sampling fractions and electron shower shapes
Energy Technology Data Exchange (ETDEWEB)
Peryshkin, Alexander; Raja, Rajendran; /Fermilab
2011-12-01
We study the usage of various definitions of sampling fractions in understanding electron shower shapes in a sampling multilayer electromagnetic calorimeter. We show that the sampling fractions obtained by the conventional definition (I) of (average observed energy in layer)/(average deposited energy in layer) will not give the best energy resolution for the calorimeter. The reason for this is shown to be the presence of layer by layer correlations in an electromagnetic shower. The best resolution is obtained by minimizing the deviation from the total input energy using a least squares algorithm. The 'sampling fractions' obtained by this method (II) are shown to give the best resolution for overall energy. We further show that the method (II) sampling fractions are obtained by summing the columns of a non-local {lambda} tensor that incorporates the correlations. We establish that the sampling fractions (II) cannot be used to predict the layer by layer energies and that one needs to employ the full {lambda} tensor for this purpose. This effect is again a result of the correlations.
Oscillation results for certain fractional difference equations
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Zhiyun WANG
2017-08-01
Full Text Available Fractional calculus is a theory that studies the properties and application of arbitrary order differentiation and integration. It can describe the physical properties of some systems more accurately, and better adapt to changes in the system, playing an important role in many fields. For example, it can describe the process of tumor growth (growth stimulation and growth inhibition in biomedical science. The oscillation of solutions of two kinds of fractional difference equations is studied, mainly using the proof by contradiction, that is, assuming the equation has a nonstationary solution. For the first kind of equation, the function symbol is firstly determined, and by constructing the Riccati function, the difference is calculated. Then the condition of the function is used to satisfy the contradiction, that is, the assumption is false, which verifies the oscillation of the solution. For the second kind of equation with initial condition, the equivalent fractional sum form of the fractional difference equation are firstly proved. With considering 0<α≤1 and α>1, respectively, by using the properties of Stirling formula and factorial function, the contradictory is got through enhanced processing, namely the assuming is not established, and the sufficient condition for the bounded solutions of the fractional difference equation is obtained. The above results will optimize the relevant conclusions and enrich the relevant results. The results are applied to the specific equations, and the oscillation of the solutions of equations is proved.
Directory of Open Access Journals (Sweden)
J. Prakash
2016-03-01
Full Text Available In this paper, a numerical algorithm based on a modified He-Laplace method (MHLM is proposed to solve space and time nonlinear fractional differential-difference equations (NFDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. The modified He-Laplace method is a combined form of the fractional homotopy perturbation method and Laplace transforms method. The nonlinear terms can be easily decomposed by the use of He’s polynomials. This algorithm has been tested against time-fractional differential-difference equations such as the modified Lotka Volterra and discrete (modified KdV equations. The proposed scheme grants the solution in the form of a rapidly convergent series. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed method. The achieved results expose that the MHLM is very accurate, efficient, simple and can be applied to other nonlinear FDDEs.
Postmenopausal breast cancer in Iran; risk factors and their population attributable fractions
Ghiasvand, Reza; Bahmanyar, Shahram; Zendehdel, Kazem; Tahmasebi, Sedigheh; Talei, Abdolrasoul; Adami, Hans-Olov; Cnattingius, Sven
2012-01-01
Abstract Background Causes of the rapidly increasing incidence of breast cancer in Middle East and Asian countries are incompletely understood. We evaluated risk factors for postmenopausal breast cancer and estimated their attributable fraction in Iran. Methods We performed a hospital-based case–control study, including 493 women, diagnosed with breast cancer at 50 years or later between 2005–2008, and 493 controls. We used logistic regression models to estimate multivariable odds ratios (OR)...
Jacob, Mascha; Viedenz, Karin; Polle, Andrea; Thomas, Frank M
2010-12-01
We hypothesised that the decomposition rates of leaf litter will increase along a gradient of decreasing fraction of the European beech (Fagus sylvatica) and increasing tree species diversity in the generally beech-dominated Central European temperate deciduous forests due to an increase in litter quality. We studied the decomposition of leaf litter including its lignin fraction in monospecific (pure beech) stands and in stands with up to five tree genera (Acer spp., Carpinus betulus, Fagus sylvatica, Fraxinus excelsior, Tilia spp.) using a litterbag approach. Litter and lignin decomposition was more rapid in stand-representative litter from multispecific stands than in litter from pure beech stands. Except for beech litter, the decomposition rates of species-specific tree litter did not differ significantly among the stand types, but were most rapid in Fraxinus excelsior and slowest in beech in an interspecific comparison. Pairwise comparisons of the decomposition of beech litter with litter of the other tree species (except for Acer platanoides) revealed a "home field advantage" of up to 20% (more rapid litter decomposition in stands with a high fraction of its own species than in stands with a different tree species composition). Decomposition of stand-representative litter mixtures displayed additive characteristics, not significantly more rapid than predicted by the decomposition of litter from the individual tree species. Leaf litter decomposition rates were positively correlated with the initial N and Ca concentrations of the litter, and negatively with the initial C:N, C:P and lignin:N ratios. The results support our hypothesis that the overall decomposition rates are mainly influenced by the chemical composition of the individual litter species. Thus, the fraction of individual tree species in the species composition seems to be more important for the litter decomposition rates than tree species diversity itself.
Continued fractions: Yet another tool to overcome the curse of dimensionality
Energy Technology Data Exchange (ETDEWEB)
Zardecki, A.
1998-12-31
The authors provide a rapid prediction method, in which a larger number of antecedents than currently considered is accounted for. To this end, they encode the successive (possibly rescaled) values of a time series, as the partial quotients of a continued fraction, resulting in a number from the unit interval. The accuracy of a ruled-based system utilizing this coding is investigated to some extent. Qualitative criteria for the applicability of the algorithm are formulated.
Fractional Fokker-Planck equation for fractal media.
Tarasov, Vasily E
2005-06-01
We consider the fractional generalizations of equation that defines the medium mass. We prove that the fractional integrals can be used to describe the media with noninteger mass dimensions. Using fractional integrals, we derive the fractional generalization of the Chapman-Kolmogorov equation (Smolukhovski equation). In this paper fractional Fokker-Planck equation for fractal media is derived from the fractional Chapman-Kolmogorov equation. Using the Fourier transform, we get the Fokker-Planck-Zaslavsky equations that have fractional coordinate derivatives. The Fokker-Planck equation for the fractal media is an equation with fractional derivatives in the dual space.
Modelling of lossy coils using fractional derivatives
Schäfer, Ingo; Krüger, Klaus
2008-02-01
Coils exposed to eddy current and hysteresis losses are conventionally described by an inductance with equivalent core-loss resistance connected in parallel. The value of the equivalent core-loss resistance depends on the working frequency and the external wiring. Thus the model is less than satisfactory. The authors propose to describe loss inductance using fractional derivatives containing both a loss term and a storage term. After introducing the theory of fractional derivatives, the operating mode of the fractional coil model is explained by the example of an RLC oscillating circuit. Subsequent measurements of a series resonant circuit with a lossy coil impressively confirm the theoretical model with regard to both the frequency and time domains.
Isotope Fractionation in the Interstellar Medium
Charnley, Steven
2011-01-01
Anomalously fractionated isotopic material is found in many primitive Solar System objects, such as meteorites and comets. It is thought, in some cases, to trace interstellar matter that was incorporated into the Solar Nebula without undergoing significant processing. We will present the results of models of the nitrogen, oxygen, and carbon fractionation chemistry in dense molecular clouds, particularly in cores where substantial freeze-out of molecules on to dust has occurred. The range of fractionation ratios expected in different interstellar molecules will be discussed and compared to the ratios measured in molecular clouds, comets and meteoritic material. These models make several predictions that can be tested in the near future by molecular line observations, particularly with ALMA.
Measurement of Tau Lepton Branching Fractions
Energy Technology Data Exchange (ETDEWEB)
Nicol, N.
2003-12-19
We present {tau}{sup -} lepton branching fraction measurements based on data from the TPC/Two-Gamma detector at PEP. Using a sample of {tau}{sup -} {yields} {nu}{sub {tau}}K{sup -}{pi}{sup +}{pi}{sup -} events, we examine the resonance structure of the K{sup -}{pi}{sup +}{pi}{sup -} system and obtain the first measurements of branching fractions for {tau}{sup -} {yields} {nu}{sub {tau}}K{sub 1}{sup -}(1270) and {tau}{sup -} {yields} {nu}{sub {tau}}K{sub 1}{sup -}(1400). We also describe a complete set of branching fraction measurements in which all the decays of the {tau}{sup -} lepton are separated into classes defined by the identities of the charged particles and an estimate of the number of neutrals. This is the first such global measurement with decay classes defined by the four possible charged particle species, e, {mu}, {pi}, and K.
Topological bootstrap: Fractionalization from Kondo coupling.
Hsieh, Timothy H; Lu, Yuan-Ming; Ludwig, Andreas W W
2017-10-01
Topologically ordered phases of matter can host fractionalized excitations known as "anyons," which obey neither Bose nor Fermi statistics. Despite forming the basis for topological quantum computation, experimental access to these exotic phases has been very limited. We present a new route toward realizing fractionalized topological phases by literally building on unfractionalized phases, which are much more easily realized experimentally. Our approach involves a Kondo lattice model in which a gapped electronic system of noninteracting fermions is coupled to local moments via the exchange interaction. Using general entanglement-based arguments and explicit lattice models, we show that gapped spin liquids can be induced in the spin system, and we demonstrate the power of this "topological bootstrap" by realizing chiral and Z2 spin liquids. This technique enables the realization of many long sought-after fractionalized phases of matter.
Catalyzed modified clean fractionation of switchgrass.
Cybulska, Iwona; Brudecki, Grzegorz P; Hankerson, Brett R; Julson, James L; Lei, Hanwu
2013-01-01
Switchgrass was used as a lignocellulosic feedstock for second generation ethanol production, after pretreatment using sulfuric acid-catalyzed modified clean fractionation based on NREL's (National Renewable Energy Laboratory) original procedure. Optimization of temperature, catalyst concentration and solvent composition was performed using Response Surface Methodology, and 59.03 ± 7.01% lignin recovery, 84.85 ± 1.34% glucose, and 44.11 ± 3.44% aqueous fraction xylose yields were obtained at 140.00 °C, 0.46% w/w catalyst concentration, 36.71% w/w ethyl acetate concentration, and 25.00% w/w ethanol concentration. The cellulose fraction did not inhibit the fermentation performance of Saccharomyces cerevisiae and resulted in an ethanol yield of 89.60 ± 2.1%. Copyright © 2012 Elsevier Ltd. All rights reserved.
Fractional Fourier processing of quantum light.
Sun, Yifan; Tao, Ran; Zhang, Xiangdong
2014-01-13
We have extended Fourier transform of quantum light to a fractional Fourier processing, and demonstrated that a classical optical fractional Fourier processor can be used for the shaping of quantum correlations between two or more photons. Comparing the present method with that of Fourier processing, we find that fractional Fourier processing for quantum light possesses many advantages. Based on such a method, not only quantum correlations can be shaped more rich, but also the initial states can be easily identified. Moreover, the twisted phase information can be recovered and quantum states are easily controlled in performing quantum information experiments. Our findings open up new avenues for the manipulation of correlations between photons in optical quantum information processing.
Laser systems for ablative fractional resurfacing
DEFF Research Database (Denmark)
Paasch, Uwe; Haedersdal, Merete
2011-01-01
Ablative fractional resurfacing (AFR) creates microscopic vertical ablated channels that are surrounded by a thin layer of coagulated tissue, constituting the microscopic treatment zones (MTZs). AFR induces epidermal and dermal remodeling, which raises new possibilities for the treatment of a var......Ablative fractional resurfacing (AFR) creates microscopic vertical ablated channels that are surrounded by a thin layer of coagulated tissue, constituting the microscopic treatment zones (MTZs). AFR induces epidermal and dermal remodeling, which raises new possibilities for the treatment...... ablative laser systems. Fractionated CO(2) (10,600-nm), erbium yttrium aluminum garnet, 2940-nm and yttrium scandium gallium garnet, 2790-nm lasers are available. In this article, we present an overview of AFR technology, devices and histopathology, and we summarize the current clinical possibilities...
Chromium isotope fractionation in ferruginous sediments
Bauer, Kohen W.; Gueguen, Bleuenn; Cole, Devon B.; Francois, Roger; Kallmeyer, Jens; Planavsky, Noah; Crowe, Sean A.
2018-02-01
Ferrous Fe is a potent reductant of Cr(VI), and while a number of laboratory studies have characterized Cr isotope fractionation associated with Cr(VI) reduction by ferrous iron, the expression of this fractionation in real-world ferrous Fe-rich environments remains unconstrained. Here we determine the isotope fractionation associated with Cr(VI) reduction in modern ferrous Fe-rich sediments obtained from the previously well studied Lake Matano, Indonesia. Whole core incubations demonstrate that reduction of Cr(VI) within ferruginous sediments provides a sink for Cr(VI) leading to Cr(VI) concentration gradients and diffusive Cr(VI) fluxes across the sediment water interface. As reduction proceeded, Cr(VI) remaining in the overlying lake water became progressively enriched in the heavy isotope (53Cr), increasing δ53Cr by 2.0 ± 0.1‰ at the end of the incubation. Rayleigh distillation modelling of the evolution of Cr isotope ratios and Cr(VI) concentrations in the overlying water yields an effective isotope fractionation of εeff = 1.1 ± 0.2‰ (53Cr/52Cr), whereas more detailed diagenetic modelling implies an intrinsic isotope fractionation of εint = 1.80 ± 0.04‰. Parallel slurry experiments performed using anoxic ferruginous sediment yield an intrinsic isotope fractionation of εint = 2.2 ± 0.1‰. These modelled isotope fractionations are corroborated by direct measurement of the δ53Cr composition on the upper 0.5 cm of Lake Matano sediment, revealing an isotopic offset from the lake water of Δ53Cr = 0.21-1.81‰. The data and models reveal that effective isotope fractionations depend on the depth at which Cr(VI) reduction takes place below the sediment water interface-the deeper the oxic non-reactive zone, the smaller the effective fractionation relative to the intrinsic fractionation. Based on the geochemistry of the sediment we suggest the electron donors responsible for reduction are a combination of dissolved Fe(II) and 0.5 M HCl extractable (solid
Fractionalized Z_{2} Classical Heisenberg Spin Liquids.
Rehn, J; Sen, Arnab; Moessner, R
2017-01-27
Quantum spin systems are by now known to exhibit a large number of different classes of spin liquid phases. By contrast, for classical Heisenberg models, only one kind of fractionalized spin liquid phase, the so-called Coulomb or U(1) spin liquid, has until recently been identified: This exhibits algebraic spin correlations and impurity moments, "orphan spins," whose size is a fraction of that of the underlying microscopic degrees of freedom. Here, we present two Heisenberg models exhibiting fractionalization in combination with exponentially decaying correlations. These can be thought of as a classical continuous spin version of a Z_{2} spin liquid. Our work suggests a systematic search and classification of classical spin liquids as a worthwhile endeavor.
Topological bootstrap: Fractionalization from Kondo coupling
Hsieh, Timothy H.; Lu, Yuan-Ming; Ludwig, Andreas W. W.
2017-01-01
Topologically ordered phases of matter can host fractionalized excitations known as “anyons,” which obey neither Bose nor Fermi statistics. Despite forming the basis for topological quantum computation, experimental access to these exotic phases has been very limited. We present a new route toward realizing fractionalized topological phases by literally building on unfractionalized phases, which are much more easily realized experimentally. Our approach involves a Kondo lattice model in which a gapped electronic system of noninteracting fermions is coupled to local moments via the exchange interaction. Using general entanglement-based arguments and explicit lattice models, we show that gapped spin liquids can be induced in the spin system, and we demonstrate the power of this “topological bootstrap” by realizing chiral and Z2 spin liquids. This technique enables the realization of many long sought-after fractionalized phases of matter. PMID:28989961
Fractional observer to estimate periodical forces.
Coronel-Escamilla, A; Gómez-Aguilar, J F; Torres, L; Escobar-Jimnez, R F; Olivares-Peregrino, V H
2017-11-14
In the present work we propose a fractional state observer with constant gain to estimate the periodical force exerted on a mechanical system by measuring only its displacement. The state observer is designed from both the Fourier series that approximates the periodical force and the equations of the damped harmonic oscillator that represents the behavior of the system. Specifically, the reconstruction of the force is carried out from the estimates of the series coefficients, which in fact are part of the dynamical system that composes the observer. Adams-Bashforth-Moulton method is used to compute the fractional derivatives of the observer in the Liouville-Caputo sense. Experiments based on real data are presented to show the advantages of using a fractional observer in the reconstruction of forces. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Fractional-order RC and RL circuits
Radwan, Ahmed Gomaa
2012-05-30
This paper is a step forward to generalize the fundamentals of the conventional RC and RL circuits in fractional-order sense. The effect of fractional orders is the key factor for extra freedom, more flexibility, and novelty. The conditions for RC and RL circuits to act as pure imaginary impedances are derived, which are unrealizable in the conventional case. In addition, the sensitivity analyses of the magnitude and phase response with respect to all parameters showing the locations of these critical values are discussed. A qualitative revision for the fractional RC and RL circuits in the frequency domain is provided. Numerical and PSpice simulations are included to validate this study. © Springer Science+Business Media, LLC 2012.
The use of fractional accumulated precipitation for the evaluation of the annual cycle of monsoons
Sperber, Kenneth R.; Annamalai, H.
2014-12-01
Using pentad rainfall data we demonstrate the benefits of using accumulated rainfall and fractional accumulated rainfall for the evaluation of the annual cycle of rainfall over various monsoon domains. Our approach circumvents issues related to using threshold-based analysis techniques for investigating the life-cycle of monsoon rainfall. In the Coupled Model Intercomparison Project-5 models we find systematic errors in the phase of the annual cycle of rainfall. The models are delayed in the onset of summer rainfall over India, the Gulf of Guinea, and the South American Monsoon, with early onset prevalent for the Sahel and the North American Monsoon. This, in combination with the rapid fractional accumulation rate, impacts the ability of the models to simulate the fractional accumulation observed during summer. The rapid fractional accumulation rate and the time at which the accumulation begins are metrics that indicate how well the models concentrate the monsoon rainfall over the peak rainfall season, and the extent to which there is a phase error in the annual cycle. The lack of consistency in the phase error across all domains suggests that a "global" approach to the study of monsoons may not be sufficient to rectify the regional differences. Rather, regional process studies are necessary for diagnosing the underlying causes of the regionally-specific systematic model biases over the different monsoon domains. Despite the afore-mentioned biases, most models simulate well the interannual variability in the date of monsoon onset, the exceptions being models with the most pronounced dry biases. Two methods for estimating monsoon duration are presented, one of which includes nonlinear aspects of the fractional accumulation. The summer fractional accumulation of rainfall provides an objective way to estimate the extent of the monsoon domain, even in models with substantial dry biases for which monsoon is not defined using threshold-based techniques.
The quark fraction of the proton spin
Mandula, Jeffrey E.
We report on a lattice QCD estimate of the fraction of the proton spin that the quark spin is responsible for. The estimate is arrived at by means of a lattice QCD simulation of the polarized proton matrix element of the anomaly, F μνoverlineFμν. The preliminary result of the simulation is that this fraction is rather small. This is in accord with the interpretation of the EMC experiment that the quark spins are responsible for very little, if any, of the proton spin.
Hyperchaotic Chameleon: Fractional Order FPGA Implementation
Directory of Open Access Journals (Sweden)
Karthikeyan Rajagopal
2017-01-01
Full Text Available There are many recent investigations on chaotic hidden attractors although hyperchaotic hidden attractor systems and their relationships have been less investigated. In this paper, we introduce a hyperchaotic system which can change between hidden attractor and self-excited attractor depending on the values of parameters. Dynamic properties of these systems are investigated. Fractional order models of these systems are derived and their bifurcation with fractional orders is discussed. Field programmable gate array (FPGA implementations of the systems with their power and resource utilization are presented.
Fractional diffusion equations coupled by reaction terms
Lenzi, E. K.; Menechini Neto, R.; Tateishi, A. A.; Lenzi, M. K.; Ribeiro, H. V.
2016-09-01
We investigate the behavior for a set of fractional reaction-diffusion equations that extend the usual ones by the presence of spatial fractional derivatives of distributed order in the diffusive term. These equations are coupled via the reaction terms which may represent reversible or irreversible processes. For these equations, we find exact solutions and show that the spreading of the distributions is asymptotically governed by the same the long-tailed distribution. Furthermore, we observe that the coupling introduced by reaction terms creates an interplay between different diffusive regimes leading us to a rich class of behaviors related to anomalous diffusion.
Numerical study of fractional nonlinear Schrodinger equations
Klein, Christian
2014-10-08
Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödinger-type equations involving a fractional Laplacian in an one-dimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub- and supercritical regimes can be identified. This allows us to study the possibility of finite time blow-up versus global existence, the nature of the blow-up, the stability and instability of nonlinear ground states and the long-time dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation.
Conformable fractional Dirac system on time scales.
Gulsen, Tuba; Yilmaz, Emrah; Goktas, Sertac
2017-01-01
We study the conformable fractional (CF) Dirac system with separated boundary conditions on an arbitrary time scale [Formula: see text]. Then we extend some basic spectral properties of the classical Dirac system to the CF case. Eventually, some asymptotic estimates for the eigenfunction of the CF Dirac eigenvalue problem are obtained on [Formula: see text]. So, we provide a constructive procedure for the solution of this problem. These results are important steps to consolidate the link between fractional calculus and time scale calculus in spectral theory.
Fractional laser photothermolysis using Bessel beams.
Mignon, Charles; Rodriguez, Aura Higuera; Palero, Jonathan A; Varghese, Babu; Jurna, Martin
2016-12-01
Fractional photothermolysis uses lasers to generate a pattern of microscopic columnar thermal lesions within the skin stimulating collagen remodeling. In this paper we investigate the use of Bessel beams as an alternative to conventional Gaussian beams in creating laser photothermal lesions of different aspect ratios in skin. We show for the first time the improved photothermal lesion depth-to-diameter aspect ratio using Bessel beams in ex vivo human skin as well as in numerical simulations using electric field Monte Carlo photon transport, finite difference methods and Arrhenius model. Bessel beams allow the creation of deep and narrow thermal lesions necessary for improved efficacy in fractional photothermolysis.
Limited Intervention at Sub Concept of Fractions in the Object Conversion into Fractions
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…
A study of fractional Schrödinger equation composed of Jumarie fractional derivative
Banerjee, Joydip; Ghosh, Uttam; Sarkar, Susmita; Das, Shantanu
2017-04-01
In this paper we have derived the fractional-order Schrödinger equation composed of Jumarie fractional derivative. The solution of this fractional-order Schrödinger equation is obtained in terms of Mittag-Leffler function with complex arguments, and fractional trigonometric functions. A few important properties of the fractional Schrödinger equation are then described for the case of particles in one-dimensional infinite potential well. One of the motivations for using fractional calculus in physical systems is that the space and time variables, which we often deal with, exhibit coarse-grained phenomena. This means infinitesimal quantities cannot be arbitrarily taken to zero - rather they are non-zero with a minimum spread. This type of non-zero spread arises in the microscopic to mesoscopic levels of system dynamics, which means that, if we denote x as the point in space and t as the point in time, then limit of the differentials d x (and d t) cannot be taken as zero. To take the concept of coarse graining into account, use the infinitesimal quantities as (Δ x) α (and (Δ t) α ) with 0 Δ x and (Δ t) α > Δ t. This way of defining the fractional differentials helps us to use fractional derivatives in the study of dynamic systems.
Boeriu, C.G.; Fitigau, F.; Gosselink, R.J.A.; Frissen, A.E.; Stoutjesdijk, J.H.; Peter, F.
2014-01-01
Lignins from softwood, hardwood, grass and wheat straw were fractionated by selective extraction at ambient temperature using green solvents like acetone/water solutions of 10, 30, 50, 70 and 90% (v/v) acetone and ethyl acetate. A comparison between the isolated fractions and unfractionated lignins
Directory of Open Access Journals (Sweden)
Suphawat Asawasamrit
2014-01-01
Full Text Available We study a class of fractional q-integrodifference equations with nonlocal fractional q-integral boundary conditions which have different quantum numbers. By applying the Banach contraction principle, Krasnoselskii’s fixed point theorem, and Leray-Schauder nonlinear alternative, the existence and uniqueness of solutions are obtained. In addition, some examples to illustrate our results are given.
Directory of Open Access Journals (Sweden)
Emad A-B. Abdel-Salam
2015-06-01
Full Text Available In this paper, the improved fractional Riccati expansion method is proposed to solve fractional differential equations. The method is applied to solve space–time fractional modified Korteweg–de Vries equation, space–time fractional modified regularized long-wave equation, time fractional biological population model, and space–time fractional Klein–Gordon equation. The obtained solutions include generalized trigonometric and hyperbolic functions solutions. Among these solutions, some are found for the first time.
He, Shaobo; Sun, Kehui; Mei, Xiaoyong; Yan, Bo; Xu, Siwei
2017-01-01
In this paper, the numerical solutions of conformable fractional-order linear and nonlinear equations are obtained by employing the constructed conformable Adomian decomposition method (CADM). We found that CADM is an effective method for numerical solution of conformable fractional-order differential equations. Taking the conformable fractional-order simplified Lorenz system as an example, the numerical solution and chaotic behaviors of the conformable fractional-order simplified Lorenz system are investigated. It is found that rich dynamics exist in the conformable fractional-order simplified Lorenz system, and the minimum order for chaos is even less than 2. The results are validated by means of bifurcation diagram, Lyapunov characteristic exponents and phase portraits.
Composites by rapid prototyping technology
CSIR Research Space (South Africa)
Kumar, S
2010-02-01
Full Text Available powder is a fiber, problems of manufacturing occur. The method has also been used to make Metal Matrix Composite (MMC), e.g Fe and graphite [17], WC-Co [18,19], WC-Co and Cu [20,21], Fe, Ni and TiC [22] etc and Ceramic Matrix Composite (CMC) e.g. Si... of various materials used. Key words: : Rapid Prototyping (RP), Laser, Composites 1 Introduction Rapid Prototyping (RP) initially focussed on polymers. These were later re- placed/supplemented by ceramics, metals and composites. Composites are used in RP...
Antidiarrhoeal Activity of Chromatographic Fractions of ...
African Journals Online (AJOL)
Erah
Methods: Vacuum liquid/column chromatography (VLC/ CC) were used to obtain three fractions (L,S and Y) of Stereospermum kunthianum stem ... The extract (80 g) was subjected to vacuum liquid chromatography (VCC) over silica gel ... light and dark cycles , temperature (28 ± 1. oC), and free access to standard chow.
Fractional behaviour at cyclic stretch-bending
Emmens, W.C.; van den Boogaard, Antonius H.; Kazantzis, A.V.; de Hosson, J.Th.M.; Kolleck, R
2010-01-01
The fractional behaviour at cyclic stretch-bending has been studied by performing tensile tests at long specimens that are cyclically bent at the same time, on mild steel, dual-phase steel, stainless steel, aluminium and brass. Several types of fracture are observed, these are discussed, as are the
The quark fraction of the proton spin
Energy Technology Data Exchange (ETDEWEB)
Mandula, J.E. (Department of Energy, Washington, DC (United States). Div. of High Energy Physics)
1992-05-01
We report on a lattice QCD estimate of the fraction of the proton spin that the quark spin is responsible for. The estimate is arrived at by means of a lattice QCD simulation of the polarized proton matrix element of the anomaly, F[sub [mu][nu
Fraction against Human Cancer Cell Lines
African Journals Online (AJOL)
Purpose: To investigate the anti-proliferative and apoptotic activity of crude and dichloromethane fraction of A. sieberi against seven cancer cell lines (Colo20, HCT116, DLD, MCF7, Jurkat, HepG2 and. L929). Methods: A. sieberi was extracted with methanol and further purification was carried out using liquid-.
Laser systems for ablative fractional resurfacing
DEFF Research Database (Denmark)
Paasch, Uwe; Haedersdal, Merete
2011-01-01
of a variety of skin conditions, primarily chronically photodamaged skin, but also acne and burn scars. In addition, it is anticipated that AFR can be utilized in the laser-assisted delivery of topical drugs. Clinical efficacy coupled with minimal downtime has driven the development of various fractional...
Observability of Nonlinear Fractional Dynamical Systems
Directory of Open Access Journals (Sweden)
K. Balachandran
2013-01-01
Full Text Available We study the observability of linear and nonlinear fractional differential systems of order 0<α<1 by using the Mittag-Leffler matrix function and the application of Banach’s contraction mapping theorem. Several examples illustrate the concepts.
A Statistical Treatment of Bioassay Pour Fractions
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.
Generalized Functions for the Fractional Calculus
Lorenzo, Carl F.; Hartley, Tom T.
1999-01-01
Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.
A new algorithm for generalized fractional programs
J.B.G. Frenk (Hans); A.I. Barros (Ana); S. Schaible; S. Zhang (Shuzhong)
1996-01-01
textabstractA new dual problem for convex generalized fractional programs with no duality gap is presented and it is shown how this dual problem can be efficiently solved using a parametric approach. The resulting algorithm can be seen as “dual” to the Dinkelbach-type algorithm for generalized
Analyse structurale des fractions polysaccharidiques extraites de ...
African Journals Online (AJOL)
In Morocco, the industry of carrageenans (gelling and thickening) polysaccharides is not yet developed and the activity is reduced to the harvest and to the export in the raw state of some species of. Gigartinaceae. Polysaccharides fractions of the cell wall of the carrageenophyte Hypnea musciformis extracted according to ...
Higher Order and Fractional Diffusive Equations
Directory of Open Access Journals (Sweden)
D. Assante
2015-07-01
Full Text Available We discuss the solution of various generalized forms of the Heat Equation, by means of different tools ranging from the use of Hermite-Kampé de Fériet polynomials of higher and fractional order to operational techniques. We show that these methods are useful to obtain either numerical or analytical solutions.
On Touchard's continued fraction and extensions: combinatorices ...
African Journals Online (AJOL)
We give a direct and simple proof of Touchard's continued fraction, provide an extension of it, and transform it into similar expansions related to Motzkin and Schroder numbers. Another proof is then given that uses only induction. We use this machinery on two examples that appear in recent papers of Josuat-Verges; with an ...
Remarks for one-dimensional fractional equations
Directory of Open Access Journals (Sweden)
Massimiliano Ferrara
2014-01-01
Full Text Available In this paper we study a class of one-dimensional Dirichlet boundary value problems involving the Caputo fractional derivatives. The existence of infinitely many solutions for this equations is obtained by exploiting a recent abstract result. Concrete examples of applications are presented.
Antioxidative potential of polysaccharide fractions produced from ...
African Journals Online (AJOL)
Cordyceps jiangxiensis, also called 'CaoMuWang', is a medicinal entomopathogenic macrofungus native to eastern China. Polysaccharide fractions from cultured C. jiangxiensis exhibited potent antitumor activity via the induction of cell cycle arrest and apoptotic pathway. Antioxidant pathway is also one action of ...
Initial value problem of fractional order
Directory of Open Access Journals (Sweden)
A. Guezane-Lakoud
2015-12-01
Full Text Available In this work, we discuss the existence of positive solutions for a class of fractional initial value problems. For this, we rewrite the posed problem as a Volterra integral equation, then, using Guo–Krasnoselskii theorem, positivity of solutions is established under some conditions. An example is given to illustrate the obtained results.
q-fractional calculus and equations
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 ...
Methanol fractionations of Catha edulis frosk (Celastraceae ...
African Journals Online (AJOL)
The study investigated the effect of methanol extract and its fractionations obtained from Yemeni khat on the smooth muscle isometric tension in Lewis rat aortal ring preparations and compared the effects of the crimson and green leaves. Khat leaves were sorted into green (khat Light; KL) and crimson (khat Dark; KD) leaves ...
FLUORESCENCE IN DISSOLVED FRACTIONS OF HUMAN ENAMEL
HAFSTROMBJORKMAN, U; SUNDSTROM, F; TENBOSCH, JJ
Fluorescence induced by laser light is useful in early detection of enamel caries. The present work studied the fluorescence emission pattern in dissolved human enamel and in different molecular weight fractions obtained after gel chromatography or dialysis followed by ultrafiltration. For
Identities for generalized fractional integral operators associated ...
African Journals Online (AJOL)
In this present work an attempt has been made to define two generalized fractional integral operators associated with products of analogues to Dirichlet averages and special functions. Discussions on the different aspects of the obtained results have been followed by utilization in finding out the images of multivariate ...
Ultraviolet spectroscopic evaluation of bioactive saponin fraction ...
African Journals Online (AJOL)
Ultraviolet spectroscopic evaluation of bioactive saponin fraction from the aqueous extract of Vernonia amygdalina [Esteraeceae] leaf. Paul Chukwuemeka ADIUKWU 1*, Martina BONSU 1, Inemesit OKON-BEN 1,. Paul PEPRAH 1, Paapa MENSAH-KANE 1, Jonathan JATO 1 and Grace NAMBATYA 2. 1School of Pharmacy ...
Fractional superLie algebras and groups
Energy Technology Data Exchange (ETDEWEB)
Ahmedov, H. [Feza Gursey Institute, Cengelkoy, Istanbul (Turkey)]. E-mail: hagi@gursey.gov.tr; Yildiz, A. [ Feza Gursey Institute, Cengelkoy, Istanbul (Turkey); Ucan, Y. [Yildiz Technical University, Department of Mathematics, Besiktas, Istanbul (Turkey)
2001-08-24
The nth root of a Lie algebra and its dual (that is the fractional supergroup) based on the permutation group S{sub n} invariant forms is formulated in the Hopf algebra formalism. Detailed discussion of S{sub 3}-graded sl(2) algebras is performed. (author)
A series expansion of fractional Brownian motion
K.O. Dzhaparidze (Kacha); J.H. van Zanten (Harry)
2002-01-01
textabstractLet $B$ be a fractional Brownian motion with Hurst index $H in (0,1)$. Denote by $x_1 < x_2 < cdots$ the positive, real zeros of the Bessel function $J_{-H$ of the first kind of order $-H$, and let $y_1 < y_2 < cdots$ be the positive zeros of $J_{1-H$. We prove the series
Functionality-driven fractionation of lupin seeds
Berghout, J.A.M.
2015-01-01
Classical versus complex fractional Fourier transformation.
Dragoman, D
2009-02-01
The quantum optical complex fractional Fourier transform (FRFT) has been related to the classical FRFT using both classical and quantum formalisms. In particular, it was shown that the kernel of the complex FRFT can be classically produced with rotated astigmatic optical systems that mimic the quantum entanglement property.
Particle separation and fractionation by microfiltration
Kromkamp, J.
2005-01-01
cum laude graduation (with distinction) For the production of present-day dairy products, raw milk is often considered an entity. However, a large quality improvement could be reached if selected constituents were available. In order to achieve this, milk will have to be fractionated prior to use in
Monotone iterative method for fractional differential equations
Directory of Open Access Journals (Sweden)
Zhanbing Bai
2016-01-01
Full Text Available In this article, by using the lower and upper solution method, we prove the existence of iterative solutions for a class of fractional initial value problem with non-monotone term $$\\displaylines{ D_{0+}^\\alpha u(t=f(t, u(t, \\quad t \\in (0, h, \\cr t^{1-\\alpha}u(t\\big|_{t=0} = u_0 \
Some aspects of generalized T-fractions
De Bruin, M.G.
1990-01-01
The purpose of this paper is to generalize the concept of a T-fraction into the direction of simultaneous approximation with rational functions having a common denominator. The generalization includes aspects of correspondence with formal power series in z and 1/z, the notion of orthogonality w.r.t.
Characterization of carbohydrate fractions and fermentation quality ...
African Journals Online (AJOL)
Jane
2011-08-29
Aug 29, 2011 ... This experiment was carried out to evaluate the effects of adding fast-sile (FS), previous fermented juice (PFJ), sucrose (S) or fast-sile + sucrose (FS + S) on the fermentation characteristics and carbohydrates fractions of alfalfa silages by the Cornell net carbohydrates and proteins systems. (CNCPS).
Characterization of carbohydrate fractions and fermentation quality ...
African Journals Online (AJOL)
This experiment was carried out to evaluate the effects of adding fast-sile (FS), previous fermented juice (PFJ), sucrose (S) or fast-sile + sucrose (FS + S) on the fermentation characteristics and carbohydrates fractions of alfalfa silages by the Cornell net carbohydrates and proteins systems (CNCPS). Silages quality were well ...
Intelligent fractions learning system: conceptual design
CSIR Research Space (South Africa)
Laine, TH
2010-01-01
Full Text Available UFractions is a ubiquitous learning environment which combines mobile technology, tangible fraction blocks and a story-based game into a mathematical learning experience. In this paper the authors present a novel concept for monitoring a user’s...
The Fractional Ornstein-Uhlenbeck Process
DEFF Research Database (Denmark)
Høg, Esben; Frederiksen, Per H.
The paper revisits dynamic term structure models (DTSMs) and proposes a new way in dealing with the limitation of the classical affine models. In particular, this paper expands the flexibility of the DTSMs by applying a fractional Brownian motion as the governing force of the state variable instead...
Statistical properties of the seasonal fractionally integrated ...
African Journals Online (AJOL)
In this paper we introduce a new model called Fractionally Integrated Separable Spatial Autoregressive processes with Seasonality and denoted Seasonal FISSAR. We focus on the class of separable spatial models whose correlation structure can be expressed as a product of correlations. This new modelling allows taking ...
Persistently increased intestinal fraction of alkaline phosphatase
DEFF Research Database (Denmark)
Nathan, E; Baatrup, G; Berg, H
1984-01-01
Persistent elevation of the intestinal fraction of the alkaline phosphatase (API) as an isolated finding has to our knowledge not been reported previously. It was found in a boy followed during a period of 5.5 years. The only symptom was transient periodic fatigue observed at home, but not apparent...
Inequalities for α-fractional differentiable functions
Directory of Open Access Journals (Sweden)
Yu-Ming Chu
2017-04-01
Full Text Available Abstract In this article, we present an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals. As applications, we establish some inequalities for certain special means of two positive real numbers and give the error estimations for the trapezoidal formula.
Thoracic fraction of inhaled fiber aerosol.
Cheng, Yung Sung; Su, Wei-Chung
2013-01-01
Size-selective sampling is a health-related method to collect airborne particles based on penetration of inhaled particles into different regions of the human respiratory tract; thus, it is the most relevant sampling method to correlate health risks with occupational exposure. The current practice of sampling asbestos and other fibers is not a size-selective method. The thoracic size fraction, defined as the portion of inhaled particles that can penetrate through the larynx, has been suggested as the most relevant size-selective sampling method for fiber aerosol. The thoracic fraction is based on 1-deposition of inhaled spherical particles in the human extrathoracic airways for mouth breathing and corrected for the particle inhalability. There is no comparable information for fiber aerosols; therefore, there is no technical basis to ascertain whether the current thoracic fraction definition is suitable for fiber aerosols. No human data are available from controlled experiments of inhaled fiber aerosols for the obvious reason that most fiber materials are potentially hazardous when inhaled. Our approach was to measure penetration of fiber aerosol in realistic human oropharyngeal airway replicas and to compare that with data from spherical particles. We showed that realistic human oral airway replicas (including the oral cavity, pharynx, and larynx regions) provided useful spherical and fiber particle deposition in the human head airway. These data could be used to test the thoracic fraction curves. The spherical penetration is in agreement with human in vivo data used to establish the thoracic fraction curve. Fiber penetrations through the larynx of two human oral airway replicas were higher than those for spherical particles for the same aerodynamic diameter using the same replicas. The thoracic curve as defined for spherical particles, therefore, may not include some fibers that could penetrate to the thoracic region.
Pelagic Biocarbonates: Assessing the "Forgotten" Fine Fraction
Brummer, G. J. A.
2016-02-01
Biocarbonates play an important role in the global carbon cycle and cover over half of the ocean floor. Biocarbonates in the open ocean are best known from planktonic foraminifera, which are relatively large (>150µm), heavy and few and coccoliths, which are very small (<32µm), light and abundant. Both of these components are relatively well studied. The size fraction in between adult foraminifera and coccoliths (32-150µm: the so-called fine fraction) consists of a large but poorly known mixture of particles, which is genarlly assumed to consist primarily of "juvenile" planktonic foraminifera, with minor amounts of calcareous dinoflagellates and various others less well-known microfossils. Abundance, diversity, mass and composition within the fine fraction are poorly constrained, as is the response to acidification/dissolution. This lack of knowledge primarily reflects the gap in size fraction studied by the different disciplinary approaches and techniques, which are not suited for identifying and quantifying these intermediate groups. Comparative ontogeny of planktonic foraminifera now shows that this fine fraction in sediments does not consist of "juveniles" as in the living plankton, but is dominated by mature specimens of small-sized species. First estimates indicate that these small species not only account for about one third of the number of species of planktonic foraminifera but also form about one third of their shell flux and global carbonate production in weight. Still, we hardly know anything on seasonality, depth habitat, shell composition (isotopes, trace metal incorporation), potential autotrophic symbionts, molecular genetics and geological range of these clearly very important species. Estimates from well-preserved sediments, show that the important role of these minute foraminiferal planktonic species may hold for much of the 180Ma long fossil record, opening a new research field pertaining to both modern and past pelagic ecosystems and the role
Developmental evolution facilitates rapid adaptation.
Lin, Hui; Kazlauskas, Romas J; Travisano, Michael
2017-11-21
Developmental evolution has frequently been identified as a mode for rapid adaptation, but direct observations of the selective benefits and associated mechanisms of developmental evolution are necessarily challenging to obtain. Here we show rapid evolution of greatly increased rates of dispersal by developmental changes when populations experience stringent selection. Replicate populations of the filamentous fungus Trichoderma citrinoviride underwent 85 serial transfers, under conditions initially favoring growth but not dispersal. T. citrinoviride populations shifted away from multicellular growth toward increased dispersal by producing one thousand times more single-celled asexual conidial spores, three times sooner than the ancestral genotype. Conidia of selected lines also germinated fifty percent faster. Gene expression changed substantially between the ancestral and selected fungi, especially for spore production and growth, demonstrating rapid evolution of tight regulatory control for down-regulation of growth and up-regulation of conidia production between 18 and 24 hours of growth. These changes involved both developmentally fixed and plastic changes in gene expression, showing that complex developmental changes can serve as a mechanism for rapid adaptation.
Multigrade Teaching Rapid Appraisal Procedure.
Nielsen, Dean
Multigrade classes have been recognized as part of elementary education for many years, but their special needs have been largely ignored. This manual focuses on the survey research that should predate the design of instructional management strategies in multigrade classrooms. It describes rapid and reliable ways to collect information about the…
Rapid thermal processing of semiconductors
Borisenko, Victor E
1997-01-01
Rapid thermal processing has contributed to the development of single wafer cluster processing tools and other innovations in integrated circuit manufacturing environments Borisenko and Hesketh review theoretical and experimental progress in the field, discussing a wide range of materials, processes, and conditions They thoroughly cover the work of international investigators in the field
Furnace for rapid thermal processing
Roozeboom, F.; Duine, P.A.; Sluis, P. van der
2001-01-01
A Method (1) for Rapid Thermal Processing of a wafer (7), wherein the wafer (7) is heated by lamps (9), and the heat radiation is reflected by an optical switching device (15,17) which is in the reflecting state during the heating stage. During the cooling stage of the wafer (7), the heat is
Rapid Energy Modeling Workflow Demonstration
2013-10-31
BIM Building Information Modeling BPA Building Performance Analysis BTU British Thermal Unit CBECS Commercial Building ...geometry, orientation, weather, and materials, generates 3D Building Information Models ( BIM ) guided by satellite views of building footprints and...Rapid Energy Modeling (REM) workflows that employed building information modeling ( BIM ) approaches and conceptual energy analysis.
Portable Diagnostics and Rapid Germination
Energy Technology Data Exchange (ETDEWEB)
Dunn, Zachary Spencer [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-12-01
In the Bioenergy and Defense Department of Sandia National Laboratories, characterization of the BaDx (Bacillus anthracis diagnostic cartridge) was performed and rapid germination chemistry was investigated. BaDx was tested with complex sample matrixes inoculated with Bacillus anthracis, and the trials proved that BaDx will detect Bacillus anthracis in a variety of the medium, such as dirt, serum, blood, milk, and horse fluids. The dimensions of the device were altered to accommodate an E. coli or Listeria lateral flow immunoassay, and using a laser printer, BaDx devices were manufactured to identify E. coli and Listeria. Initial testing with E. coli versions of BaDx indicate that the device will be viable as a portable diagnostic cartridge. The device would be more effective with faster bacteria germination; hence studies were performed the use of rapid germination chemistry. Trials with calcium dipicolinic acid displayed increased cell germination, as shown by control studies using a microplate reader. Upon lyophilization the rapid germination chemistry failed to change growth patterns, indicating that the calcium dipicolinic acid was not solubilized under the conditions tested. Although incompatible with the portable diagnostic device, the experiments proved that the rapid germination chemistry was effective in increasing cell germination.
A Study of Fractional Schrodinger Equation-composed via Jumarie fractional derivative
Banerjee, Joydip; Sarkar, Susmita; Das, Shantanu
2016-01-01
One of the motivations for using fractional calculus in physical systems is due to fact that many times, in the space and time variables we are dealing which exhibit coarse-grained phenomena, meaning that infinitesimal quantities cannot be placed arbitrarily to zero-rather they are non-zero with a minimum length. Especially when we are dealing in microscopic to mesoscopic level of systems. Meaning if we denote x the point in space and t as point in time; then the differentials dx (and dt) cannot be taken to limit zero, rather it has spread. A way to take this into account is to use infinitesimal quantities as (\\Deltax)^\\alpha (and (\\Deltat)^\\alpha) with 0\\Deltax. This way defining the differentials-or rather fractional differentials makes us to use fractional derivatives in the study of dynamic systems. In fractional calculus the fractional order trigonometric functions play important role. The Mittag-Leffler function which plays important role in the field of fractional calculus; and the fractional order tri...
Fractional solutions of Bessel equation with N-method.
Bas, Erdal; Yilmazer, Resat; Panakhov, Etibar
2013-01-01
This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the N-fractional calculus operator N(ν) method, we derive the fractional solutions of the equation.
Second-order fractional Fourier transform with incoherent radiation.
Cai, Yangjian; Zhu, Shi-Yao
2005-02-15
Based on the coherent optical theory, we extend the fractional Fourier transform of first-order correlation to a fractional Fourier transform of second-order correlation. An optical system for implementing a second-order fractional Fourier transform was designed. As a numerical example, we investigate the second-order fractional Fourier transform for a single slit.
Anamorphic fractional Fourier transform: optical implementation and applications.
Mendlovic, D; Bitran, Y; Dorsch, R G; Ferreira, C; Garcia, J; Ozaktaz, H M
1995-11-10
An additional degree of freedom is introduced to fractional-Fourier-transform systems by use of anamorphic optics. A different fractional Fourier order along the orthogonal principal directions is performed. Alaboratory experimental system shows preliminary results that demonstrate the proposed theory. Applications such as anamorphic fractional correlation and multiplexing in fractional domains are briefly suggested.
Development of Fraction Comparison Strategies: A Latent Transition Analysis
Rinne, Luke F.; Ye, Ai; Jordan, Nancy C.
2017-01-01
The present study investigated the development of fraction comparison strategies through a longitudinal analysis of children's responses to a fraction comparison task in 4th through 6th grades (N = 394). Participants were asked to choose the larger value for 24 fraction pairs blocked by fraction type. Latent class analysis of performance over item…
Variable Order Fractional Variational Calculus for Double Integrals
Odzijewicz, Tatiana; Malinowska, Agnieszka B.; Torres, Delfim F. M.
2012-01-01
We introduce three types of partial fractional operators of variable order. An integration by parts formula for partial fractional integrals of variable order and an extension of Green's theorem are proved. These results allow us to obtain a fractional Euler-Lagrange necessary optimality condition for variable order two-dimensional fractional variational problems.
Effect of fractionated extracts and isolated pure compounds of ...
African Journals Online (AJOL)
Open column chromatographic fractionation of the ethylacetate fraction yielded seven sub-fractions, out of which the pure coumaroyl, quercetine and gallic acid derivatives were obtained after purification on Sephadex LH 20. The ethanolic extract, butanolic fractions, ethylacetate subfractions and pure isolates of the ...
Chemical composition of material fractions in Danish household waste
DEFF Research Database (Denmark)
Riber, Christian; Petersen, Claus; Christensen, Thomas Højlund
2009-01-01
like paper, cardboard anti organic fractions. The single fraction contributing most to the total energy content is the non-recyclable plastic fraction, contributing 21% of the energy content and 60% of the chlorine content, although this fraction comprises less than 7% by weight. Heavy metals originate...
Integrable coupling system of fractional soliton equation hierarchy
Energy Technology Data Exchange (ETDEWEB)
Yu Fajun, E-mail: yfajun@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)
2009-10-05
In this Letter, we consider the derivatives and integrals of fractional order and present a class of the integrable coupling system of the fractional order soliton equations. The fractional order coupled Boussinesq and KdV equations are the special cases of this class. Furthermore, the fractional AKNS soliton equation hierarchy is obtained.
Some fractional and multifractional Gaussian processes: A brief introduction
Lim, S. C.; Eab, C. H.
2015-01-01
This paper gives a brief introduction to some important fractional and multifractional Gaussian processes commonly used in modelling natural phenomena and man-made systems. The processes include fractional Brownian motion (both standard and the Riemann-Liouville type), multifractional Brownian motion, fractional and multifractional Ornstein-Uhlenbeck processes, fractional and mutifractional Reisz-Bessel motion. Possible applications of these processes are briefly mentioned.
Are Melt Migration Rates Through the Mantle Universally Rapid?
Reagan, M. K.; Sims, K. W.
2001-12-01
Significant enrichments in 226Ra over 230Th have been observed in basalts erupted in nearly all tectonic settings. These enrichments generally are greatest in lavas with low concentrations of U, Th and other incompatible elements, including those from mid-ocean ridges and "depleted" volcanic arcs. Excesses of 226Ra over 230Th in mid-ocean ridge settings are commonly attributed to smaller bulk partition coefficients for Ra with respect to Th during mantle melting, and extraction of ingrown Ra into melts slowly migrating through interconnected pore space. In contrast, 226Ra excesses in basalts from volcanic arcs have been attributed to fluid additions from subducting slabs to the sources of the basalt and rapid (102 - 103y) melt migration to the surface (e.g. Turner et al., 2001). Such rapid melt velocities imply channeled flow rather than diffuse porous flow, and suggest that basalts from other tectonic settings migrate similarly rapidly. Here, we show that the compositions of basalts from both arc and mid-ocean ridge settings indeed can be explained by melting models involving rapid transit times to the surface. Simple fluxed melting models and rapid transfer of melt to the surface explain the U-Th-Ra systematics and incompatible trace element compositions of arc basalts. The U-Th-Ra and trace element data for young MORB from the East Pacific Rise (Sims et al. 2001) and the Siqueiros transform (Lundstrom et al. 1999) are modeled using simple 2-d polybaric melting based on Braun et al. (2000) and rapid melt migration rates. Successful models mix small-degree fractional melts derived from a broad cross-sectional area of mantle at depth with high-degree melts derived from a small cross-sectional area of shallow mantle that is the aged residue of the small degree melt.
The Use of Fractional B-Splines Wavelets in Multiterms Fractional Ordinary Differential Equations
Directory of Open Access Journals (Sweden)
X. Huang
2010-01-01
Full Text Available We discuss the existence and uniqueness of the solutions of the nonhomogeneous linear differential equations of arbitrary positive real order by using the fractional B-Splines wavelets and the Mittag-Leffler function. The differential operators are taken in the Riemann-Liouville sense and the initial values are zeros. The scheme of solving the fractional differential equations and the explicit expression of the solution is given in this paper. At last, we show the asymptotic solution of the differential equations of fractional order and corresponding truncated error in theory.
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.
Impedance matching through a single passive fractional element
Radwan, Ahmed Gomaa
2012-07-01
For the first time, a generalized admittance Smith chart theory is introduced to represent fractional order circuit elements. The principles of fractional order matching circuits are described. We show that for fractional order α < 1, a single parallel fractional element can match a wider range of load impedances as compared to its series counterpart. Several matching examples demonstrate the versatility of fractional order series and parallel element matching as compared to the conventional approach. © 2012 IEEE.
Some new properties and applications of a fractional Fourier transform
Rodrigues, M. Manuela; Luchko, Yuri
2017-01-01
In this paper, we deal with the fractional Fourier transform in the form introduced a little while ago by the first named author and his coauthors. This transform is closely connected with the Fractional Calculus operators and has been already employed for solving of both the fractional diffusion equation and the fractional Schrödinger equation. In this paper, we continue the investigation of the fractional Fourier transform, and in particular prove some new operational relations for...
Semianalytic Solution of Space-Time Fractional Diffusion Equation
Directory of Open Access Journals (Sweden)
A. Elsaid
2016-01-01
Full Text Available We study the space-time fractional diffusion equation with spatial Riesz-Feller fractional derivative and Caputo fractional time derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution of this problem is obtained via the optimal homotopy analysis method (OHAM. Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameters on the solution behavior.
Three algorithms for Egyptian fractions | Izevbizua | Journal of the ...
African Journals Online (AJOL)
The ancient Egyptians used a number system based on unit fractions, i.e. fractions with one in the numerator. This idea let them represent any fraction a/b as the sum of unit fractions e.g 27 = 14 + 128. Further, the same fraction could not be used twice (so 27 = 17 + 17 is not allowed). In this work we examine a number of ...
Stability analysis of distributed order fractional chen system.
Aminikhah, H; Refahi Sheikhani, A; Rezazadeh, H
2013-01-01
We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results.
Toufik, Mekkaoui; Atangana, Abdon
2017-10-01
Recently a new concept of fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. A new numerical scheme has been developed, in this paper, for the newly established fractional differentiation. We present in general the error analysis. The new numerical scheme was applied to solve linear and non-linear fractional differential equations. We do not need a predictor-corrector to have an efficient algorithm, in this method. The comparison of approximate and exact solutions leaves no doubt believing that, the new numerical scheme is very efficient and converges toward exact solution very rapidly.
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 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
Directory of Open Access Journals (Sweden)
Chao Yue
2013-01-01
Full Text Available A fractional quadratic-form identity is derived from a general isospectral problem of fractional order, which is devoted to constructing the Hamiltonian structure of an integrable coupling of the fractional BK hierarchy. The method can be generalized to other fractional integrable couplings.
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
Fractional diffusion models of transport in magnetically confined plasmas
Energy Technology Data Exchange (ETDEWEB)
Castillo-Negrete, D. del; Carreras, B. A.; Lynch, V. E.
2005-07-01
Experimental and theoretical evidence suggests that transport in magnetically confined fusion plasmas deviates from the standard diffusion paradigm. Some examples include the confinement time scaling in L-mode plasmas, rapid pulse propagation phenomena, and inward transport in off-axis fueling experiments. The limitations of the diffusion paradigm can be traced back to the restrictive assumptions in which it is based. In particular, Fick's law, one of the cornerstones of diffusive transport, assumes that the fluxes only depend on local quantities, i. e. the spatial gradient of the field (s). another key issue is the Markovian assumption that neglects memory effects. Also, at a microscopic level, standard diffusion assumes and underlying Gaussian, uncorrelated stochastic process (i. e. a Brownian random walk) with well defined characteristic spatio-temporal scales. Motivated by the need to develop models of non-diffusive transport, we discuss here a class of transport models base on the use of fractional derivative operators. The models incorporates in a unified way non-Fickian transport, non-Markovian processes or memory effects, and non-diffusive scaling. At a microscopic level, the models describe an underlying stochastic process without characteristic spatio-temporal scales that generalizes the Brownian random walk. As a concrete case study to motivate and test the model, we consider transport of tracers in three-dimensional, pressure-gradient-driven turbulence. We show that in this system transport is non-diffusive and cannot be described in the context of the standard diffusion parading. In particular, the probability density function (pdf) of the radial displacements of tracers is strongly non-Gaussian with algebraic decaying tails, and the moments of the tracer displacements exhibit super-diffusive scaling. there is quantitative agreement between the turbulence transport calculations and the proposed fractional diffusion model. In particular, the model
Evidence for equilibrium iron isotope fractionation by nitrate-reducing iron(II)-oxidizing bacteria
Kappler, A.; Johnson, C.M.; Crosby, H.A.; Beard, B.L.; Newman, D.K.
2010-01-01
Iron isotope fractionations produced during chemical and biological Fe(II) oxidation are sensitive to the proportions and nature of dissolved and solid-phase Fe species present, as well as the extent of isotopic exchange between precipitates and aqueous Fe. Iron isotopes therefore potentially constrain the mechanisms and pathways of Fe redox transformations in modern and ancient environments. In the present study, we followed in batch experiments Fe isotope fractionations between Fe(II)aq and Fe(III) oxide/hydroxide precipitates produced by the Fe(III) mineral encrusting, nitrate-reducing, Fe(II)-oxidizing Acidovorax sp. strain BoFeN1. Isotopic fractionation in 56Fe/54Fe approached that expected for equilibrium conditions, assuming an equilibrium Δ56FeFe(OH)3 – Fe(II)aq fractionation factor of +3.0 ‰. Previous studies have shown that Fe(II) oxidation by this Acidovorax strain occurs in the periplasm, and we propose that Fe isotope equilibrium is maintained through redox cycling via coupled electron and atom exchange between Fe(II)aq and Fe(III) precipitates in the contained environment of the periplasm. In addition to the apparent equilibrium isotopic fractionation, these experiments also record the kinetic effects of initial rapid oxidation, and possible phase transformations of the Fe(III) precipitates. Attainment of Fe isotope equilibrium between Fe(III) oxide/hydroxide precipitates and Fe(II)aq by neutrophilic, Fe(II)-oxidizing bacteria or through abiologic Fe(II)aq oxidation is generally not expected or observed, because the poor solubility of their metabolic product, i.e. Fe(III), usually leads to rapid precipitation of Fe(III) minerals, and hence expression of a kinetic fractionation upon precipitation; in the absence of redox cycling between Fe(II)aq and precipitate, kinetic isotope fractionations are likely to be retained. These results highlight the distinct Fe isotope fractionations that are produced by different pathways of biological and
Throop, H. L.; Lajtha, K.; Sollins, P.; Monger, H. C.
2008-12-01
Stabilization of organic matter on mineral surfaces strongly affects rates of soil organic matter (SOM) accumulation and turnover. Controls over SOM are of particular interest in arid and semi-arid systems where the abundance of woody plants has increased globally over the past century. This proliferation of woody plants may lead to significant soil organic carbon (SOC) accumulation, although a large degree of uncertainty exists in the direction and magnitude of SOC pool responses to woody encroachment. We hypothesized that SOC accumulation from woody encroachment would be primarily due to increased light fraction C pools and also that soil parent material would strongly influence SOC stabilization. Previous studies at mesic sites have used sequential density fractionation to separate soil particles based on mineralology and to explore C stabilization via organo-mineral complexes that might affect particle density. We explored mechanisms of SOM stabilization in arid soils by density fractionating four Chihuahuan Desert soils. The soils differed in parent material (igneous vs. limestone alluvium), landscape position (bajada vs. basin floor), and dominant vegetative cover (intact grassland vs. shrubland in former grassland). We used sodium polytungstate to separate soils into seven fractions with density cutoffs of 1.68, 1.87, 1.98, 2.18, 2.47, 2.66, and >2.66 g cm-3 (hereafter F1-F7, respectively). Concentrations of C and N generally decreased with increasing particle density. Similar to findings from mesic sites, C:N decreased with increasing particle density. While F1 accounted for a small proportion of total mass (0.29-2.61%), a large proportion of total C was present in this fraction (25.3-39.2% of total) due to the high [C] (21-38%C). Carbon in these light fractions is likely to be primarily recently-derived plant material that turns over rapidly and is not stabilized on mineral surfaces. The basin floor sites contained a large proportion of the total C in F5