#### Sample records for continued fractions

1. Smarandache Continued Fractions

OpenAIRE

Ibstedt, H.

2001-01-01

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

2. Fraction Reduction through Continued Fractions

Science.gov (United States)

Carley, Holly

2011-01-01

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

3. The random continued fraction transformation

Science.gov (United States)

Kalle, Charlene; Kempton, Tom; Verbitskiy, Evgeny

2017-03-01

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

4. Geodesic continued fractions and LLL

NARCIS (Netherlands)

Beukers, F

2014-01-01

We discuss a proposal for a continued fraction-like algorithm to determine simultaneous rational approximations to dd real numbers α1,…,αdα1,…,αd. It combines an algorithm of Hermite and Lagarias with ideas from LLL-reduction. We dynamically LLL-reduce a quadratic form with parameter tt as t↓0t↓0.

5. Pythagorean Approximations and Continued Fractions

Science.gov (United States)

Peralta, Javier

2008-01-01

In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers…

6. Continuous fractional distillation of petroleum

Energy Technology Data Exchange (ETDEWEB)

1921-11-05

This invention has for its object a process of distillation, fractional, and continuous, of shale oil, tar, etc., characterized by the vapors leaving the evaporation chamber being forced, before condensation, to go over a continuous circuit. The vapors traverse first a preheater then return to the vaporization chamber in which they are passed along large surfaces and by application of the counter-current principle in contact with the liquid to be distilled. They stream through the chamber in a continuous manner (the quantity of vapor emitted in the circuit being determined in a manner to advance the distillation just to completion); the excess of vapor formed being removed from the circuit and sent to a condensing apparatus for fractionation.

7. Operator continued fraction and bound states

International Nuclear Information System (INIS)

Pindor, M.

1984-01-01

The effective Hamiltonian of the model space perturbation theory (multilevel Rayleigh-Schroedinger theory) is expressed as an operator continued fraction. In the case of a nondegenerate model space the expression becomes an operator branched continued fraction. The method is applied to the harmonic oscillator with the kinetic energy treated as the perturbation and to the anharmonic oscillator

8. Stieltjes' continued fraction for the gamma function

International Nuclear Information System (INIS)

Cha, B.W.

1980-01-01

The first forty-one coefficients of a continued fraction for 1n GAMMA(z)+z-(z-1/2) 1n z-1n√2π, are given. The computation, based on Wall's algorithm for converting a function's power series representation to a continued fraction representation, was run on the algebraic manipulation system MACSYMA

9. Vector continued fractions using a generalized inverse

International Nuclear Information System (INIS)

Haydock, Roger; Nex, C M M; Wexler, Geoffrey

2004-01-01

A real vector space combined with an inverse (involution) for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse permits construction of vector analogues of the Jacobi continued fraction. These vector Jacobi fractions are related to vector and scalar-valued polynomial functions of the vectors, which satisfy recurrence relations similar to those of orthogonal polynomials. The vector Jacobi fraction has strong convergence properties which are demonstrated analytically, and illustrated numerically

10. Generalized continued fractions and ergodic theory

International Nuclear Information System (INIS)

Pustyl'nikov, L D

2003-01-01

In this paper a new theory of generalized continued fractions is constructed and applied to numbers, multidimensional vectors belonging to a real space, and infinite-dimensional vectors with integral coordinates. The theory is based on a concept generalizing the procedure for constructing the classical continued fractions and substantially using ergodic theory. One of the versions of the theory is related to differential equations. In the finite-dimensional case the constructions thus introduced are used to solve problems posed by Weyl in analysis and number theory concerning estimates of trigonometric sums and of the remainder in the distribution law for the fractional parts of the values of a polynomial, and also the problem of characterizing algebraic and transcendental numbers with the use of generalized continued fractions. Infinite-dimensional generalized continued fractions are applied to estimate sums of Legendre symbols and to obtain new results in the classical problem of the distribution of quadratic residues and non-residues modulo a prime. In the course of constructing these continued fractions, an investigation is carried out of the ergodic properties of a class of infinite-dimensional dynamical systems which are also of independent interest

11. Singular values of the Rogers-Ramanujan continued fraction

NARCIS (Netherlands)

Gee, A.C.P.; Honsbeek, M

1999-01-01

Let $z\\in\\C$ be imaginary quadratic in the upper half plane.Then the Rogers-Ramanujan continued fraction evaluated at $q=e^{2\\pi i z}$ is contained in a class field of $\\Q(z)$. Ramanujan showed that for certain values of $z$, one can write these continued fractions as nested radicals. We use the

12. Generating bessel functions in mie scattering calculations using continued fractions.

Science.gov (United States)

Lentz, W J

1976-03-01

A new method of generating the Bessel functions and ratios of Bessel functions necessary for Mie calculations is presented. Accuracy is improved while eliminating the need for extended precision word lengths or large storage capability. The algorithm uses a new technique of evaluating continued fractions that starts at the beginning rather than the tail and has a built-in error check. The continued fraction representations for both spherical Bessel functions and ratios of Bessel functions of consecutive order are presented.

13. The overlap Dirac operator as a continued fraction

International Nuclear Information System (INIS)

Wenger, U.; Deutsches Elektronen-Synchrotron

2004-03-01

We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single Krylov space method and nested conjugate gradient procedures are avoided. We point out that the five dimensional linear system can be made well conditioned using equivalence transformations on the continued fractions. (orig.)

14. Continuous Flash Suppression: Stimulus Fractionation rather than Integration.

Science.gov (United States)

Moors, Pieter; Hesselmann, Guido; Wagemans, Johan; van Ee, Raymond

2017-10-01

Recent studies using continuous flash suppression suggest that invisible stimuli are processed as integrated, semantic entities. We challenge the viability of this account, given recent findings on the neural basis of interocular suppression and replication failures of high-profile CFS studies. We conclude that CFS reveals stimulus fractionation in visual cortex. Copyright © 2017 Elsevier Ltd. All rights reserved.

15. Applications of (a,b)-continued fraction transformations

OpenAIRE

Katok, Svetlana; Ugarcovici, Ilie

2011-01-01

We describe a general method of arithmetic coding of geodesics on the modular surface based on a two parameter family of continued fraction transformations studied previously by the authors. The finite rectangular structure of the attractors of the natural extension maps and the corresponding "reduction theory" play an essential role. In special cases, when an (a,b)-expansion admits a so-called "dual", the coding sequences are obtained by juxtaposition of the boundary expansions of the fixed ...

16. Natural extensions and entropy of α-continued fractions

International Nuclear Information System (INIS)

Kraaikamp, Cor; Schmidt, Thomas A; Steiner, Wolfgang

2012-01-01

We construct a natural extension for each of Nakada's α-continued fraction transformations and show the continuity as a function of α of both the entropy and the measure of the natural extension domain with respect to the density function (1 + xy) −2 . For 0 2 /6. We show that the interval (3-√5)/2≤α≤(1+√5)/2 is a maximal interval upon which the entropy is constant. As a key step for all this, we give the explicit relationship between the α-expansion of α − 1 and of α. (paper)

17. Continuous fractional-order Zero Phase Error Tracking Control.

Science.gov (United States)

Liu, Lu; Tian, Siyuan; Xue, Dingyu; Zhang, Tao; Chen, YangQuan

2018-04-01

A continuous time fractional-order feedforward control algorithm for tracking desired time varying input signals is proposed in this paper. The presented controller cancels the phase shift caused by the zeros and poles of controlled closed-loop fractional-order system, so it is called Fractional-Order Zero Phase Tracking Controller (FZPETC). The controlled systems are divided into two categories i.e. with and without non-cancellable (non-minimum-phase) zeros which stand in unstable region or on stability boundary. Each kinds of systems has a targeted FZPETC design control strategy. The improved tracking performance has been evaluated successfully by applying the proposed controller to three different kinds of fractional-order controlled systems. Besides, a modified quasi-perfect tracking scheme is presented for those systems which may not have available future tracking trajectory information or have problem in high frequency disturbance rejection if the perfect tracking algorithm is applied. A simulation comparison and a hardware-in-the-loop thermal peltier platform are shown to validate the practicality of the proposed quasi-perfect control algorithm. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

18. Modeling discrete and continuous entities with fractions and decimals.

Science.gov (United States)

Rapp, Monica; Bassok, Miriam; DeWolf, Melissa; Holyoak, Keith J

2015-03-01

When people use mathematics to model real-life situations, their use of mathematical expressions is often mediated by semantic alignment (Bassok, Chase, & Martin, 1998): The entities in a problem situation evoke semantic relations (e.g., tulips and vases evoke the functionally asymmetric "contain" relation), which people align with analogous mathematical relations (e.g., the noncommutative division operation, tulips/vases). Here we investigate the possibility that semantic alignment is also involved in the comprehension and use of rational numbers (fractions and decimals). A textbook analysis and results from two experiments revealed that both mathematic educators and college students tend to align the discreteness versus continuity of the entities in word problems (e.g., marbles vs. distance) with distinct symbolic representations of rational numbers--fractions versus decimals, respectively. In addition, fractions and decimals tend to be used with nonmetric units and metric units, respectively. We discuss the importance of the ontological distinction between continuous and discrete entities to mathematical cognition, the role of symbolic notations, and possible implications of our findings for the teaching of rational numbers. PsycINFO Database Record (c) 2015 APA, all rights reserved.

19. On the solution of the Schroedinger equation through continued fractions

International Nuclear Information System (INIS)

Mignaco, J.A.

1979-05-01

The domain of interest for the applications of a method to solve the Schroedinger equation through continued fractions is studied. It is argued that the method applies almost equally well to quantum mechanical regimes (lower energy levels, low energy scattering) as well as to semiclassical ones simultaneously; this is illustrated by the example of the central power law potentials r sup(ν)(ν>o). The explanation of this behaviour is given in terms of the mathematical approximations involved and its relationship to physically interesting quantities. (Author) [pt

20. A continued fraction representation of the mass operator

International Nuclear Information System (INIS)

Saraswati, D.K.

1976-01-01

We explore some further possibilities of application of the projection operator method of Zwanzig to the theory of Green's functions of quantum statistical mechanics, initiated by Ichiyanagi, and present a continued fraction representation of the mass operator involving a hierarchy of the random forces. As an application of the theory, we calculate the polarization operator of the phonon Green's function of the Frohlich Hamiltonian in the first approximation which corresponds to the assumption that the electron momenta are orthogonal to the phonon momentum. (author)

1. Exact solutions of nonlinear differential equations using continued fractions

International Nuclear Information System (INIS)

Ditto, W.L.; Pickett, T.J.

1990-01-01

The continued-fraction conversion method (J. Math. Phys. (N.Y.), 29, 1761 (1988)) is used to generate a homologous family of exact solutions to the Lane-Emden equation φ(r) '' + 2φ(r)'/r + αφ(r) p = 0, for p=5. An exact solution is also obtained for a generalization of the Lane-Emden equation of the form -φ '' (r) -2φ(r)'/r + αφ(r) 2p+1 + λφ(r) 4p+1 = 0 for arbitrary α, γ and p. A condition is established for the generation of exact solutions from the method

2. A multidimensional continued fraction and some of its statistical properties

International Nuclear Information System (INIS)

Baldwin, P.R.

1992-01-01

The problem of simultaneously approximating a vector of irrational numbers with rationals is analyzed in a geometrical setting using notions of dynamical systems theory. The author discusses here a (vectorial) multidimensional continued-fraction algorithm (MCFA) of additive type, the generalized mediant algorithm (GMA), and gives a geometrical interpretation to it. He calculates the invariant measure of the GMA shift as well as its Kolmogorov-Sinai (KS) entropy for arbitrary number of irrationals. The KS entropy is related to the growth rate of denominators of the Euclidean algorithm. This is the first analytical calculation of the growth rate of denominators for any MCFA

3. Continuous blood fractionation using an array of slanted grooves

Science.gov (United States)

Bernate, Jorge A.; Chengxun, Liu; Lagae, Liesbet; Drazer, German

2011-11-01

Blood is a complex fluid having different specialized biological functions and containing a plethora of clinical information. The separation of different blood components is a crucial step in many research and clinical applications. In this work we take advantage of the flow characteristics in microfluidic devices in which the bottom surface is patterned with slanted rectangular grooves to continuously fractionate blood. We exploit the flow in the vicinity of the patterned surface when the dimensions of the grooves are much smaller than the dimensions of the main channel. In these devices, we observed that the grooves act as open channels guiding flow along them with the flow over them being in the direction of the main channel. We present experiments in which the different blood components are deflected laterally to a different extent by the flow along the grooves depending on their sedimentation velocity, which allows their continuous fractionation. In particular, the heavier red blood cells experience the largest deflection while the lighter white blood cells deflect the least, allowing their passive and minimally invasive isolation. In addition, this fluidic platform can also be used to separate magnetically labeled circulating cancer cells which can be retained in the flow along the grooves using a sufficiently strong magnetic force.

4. Explicit Formulae for the Continued Fraction Convergents of "Square Root of D"

Science.gov (United States)

Braza, Peter A.

2010-01-01

The formulae for the convergents of continued fractions are always given recursively rather than in explicit form. This article derives explicit formulae for the convergents of the continued fraction expansions for square roots.

5. Compositions, Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes

Science.gov (United States)

Orsingher, Enzo; Polito, Federico

2012-08-01

In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes N α ( t), N β ( t), t>0, we have that N_{α}(N_{β}(t)) stackrel{d}{=} sum_{j=1}^{N_{β}(t)} Xj, where the X j s are Poisson random variables. We present a series of similar cases, where the outer process is Poisson with different inner processes. We highlight generalisations of these results where the external process is infinitely divisible. A section of the paper concerns compositions of the form N_{α}(tauk^{ν}), ν∈(0,1], where tauk^{ν} is the inverse of the fractional Poisson process, and we show how these compositions can be represented as random sums. Furthermore we study compositions of the form Θ( N( t)), t>0, which can be represented as random products. The last section is devoted to studying continued fractions of Cauchy random variables with a Poisson number of levels. We evaluate the exact distribution and derive the scale parameter in terms of ratios of Fibonacci numbers.

6. 14 CFR 91.1411 - Continuous airworthiness maintenance program use by fractional ownership program manager.

Science.gov (United States)

2010-01-01

... program use by fractional ownership program manager. 91.1411 Section 91.1411 Aeronautics and Space FEDERAL... airworthiness maintenance program use by fractional ownership program manager. Fractional ownership program... through 91.1443. Any program manager who elects to maintain the program aircraft using a continuous...

7. Jacobi continued fraction and Hankel determinants of the Thue ...

African Journals Online (AJOL)

... a formal power series ϕ(x) is being discovered, having the property that the Hankel transforms of ϕ(x) and of ϕ(x2) are identical. Mathematics Subject Classification (2010): 05A15, 05A19, 11A55, 11B37, 11B50, 11B85, 11C20, 15A15. Keywords: Hankel determinant, Hankel transform, binomial transform, Jacobi continued ...

8. Parameters and Fractional Differentiation Orders Estimation for Linear Continuous-Time Non-Commensurate Fractional Order Systems

KAUST Repository

Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem

2017-01-01

This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.

9. Parameters and Fractional Differentiation Orders Estimation for Linear Continuous-Time Non-Commensurate Fractional Order Systems

KAUST Repository

Belkhatir, Zehor

2017-05-31

This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.

10. Applications of continuity and discontinuity of a fractional derivative of the wave functions to fractional quantum mechanics

International Nuclear Information System (INIS)

Dong Jianping; Xu Mingyu

2008-01-01

The space fractional Schroedinger equation with a finite square potential, periodic potential, and delta-function potential is studied in this paper. We find that the continuity or discontinuity condition of a fractional derivative of the wave functions should be considered to solve the fractional Schroedinger equation in fractional quantum mechanics. More parity states than those given by standard quantum mechanics for the finite square potential well are obtained. The corresponding energy equations are derived and then solved by graphical methods. We show the validity of Bloch's theorem and reveal the energy band structure for the periodic potential. The jump (discontinuity) condition for the fractional derivative of the wave function of the delta-function potential is given. With the help of the jump condition, we study some delta-function potential fields. For the delta-function potential well, an alternate expression of the wave function (the H function form of it was given by Dong and Xu [J. Math. Phys. 48, 072105 (2007)]) is obtained. The problems of a particle penetrating through a delta-function potential barrier and the fractional probability current density of the particle are also discussed. We study the Dirac comb and show the energy band structure at the end of the paper

11. Stability Tests of Positive Fractional Continuous-time Linear Systems with Delays

Directory of Open Access Journals (Sweden)

2013-06-01

Full Text Available Necessary and sufficient conditions for the asymptotic stability of positive fractional continuous-time linear systems with many delays are established. It is shown that: 1 the asymptotic stability of the positive fractional system is independent of their delays, 2 the checking of the asymptotic stability of the positive fractional systems with delays can be reduced to checking of the asymptotic stability of positive standard linear systems without delays.

12. A connection between the asymptotic iteration method and the continued fractions formalism

International Nuclear Information System (INIS)

Matamala, A.R.; Gutierrez, F.A.; Diaz-Valdes, J.

2007-01-01

In this work, we show that there is a connection between the asymptotic iteration method (a method to solve second order linear ordinary differential equations) and the older method of continued fractions to solve differential equations

13. Continuous Fractionation of a two-component mixture by zone electrophoresis

NARCIS (Netherlands)

Zalewski, D.R.; Gardeniers, Johannes G.E.

2009-01-01

Synchronized continuous-flow zone electrophoresis is a recently demonstrated tool for performing electrophoretic fractionation of a complex sample. The method resembles free flow electrophoresis, but unlike in that technique, no mechanical fluid pumping is required. Instead, fast electrokinetic flow

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

Directory of Open Access Journals (Sweden)

Riccardo Caponetto

2016-11-01

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

15. Rational fraction application for continuation of differential cross sections of nuclear reactions into the nonphysical region

International Nuclear Information System (INIS)

Borbely, I.; Nichitiu, F.

1975-01-01

We propose to apply rational fraction approximations instead of polynomial ones for analytic continuation of the differential cross section. On the example of p-d scattering it is demonstrated that the spectroscopic in-formation extracted in this way is more reliable

16. Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime

Science.gov (United States)

Wang, Jun; Liang, Jin-Rong; Lv, Long-Jin; Qiu, Wei-Yuan; Ren, Fu-Yao

2012-02-01

In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(Sα(t)), 0transaction costs of replicating strategies. We also give the total transaction costs.

17. On a Desert Island with Unit Sticks, Continued Fractions and Lagrange

Directory of Open Access Journals (Sweden)

Victor J. Ricchezza

2016-07-01

Full Text Available GLY 4866, Computational Geology, provides an opportunity, welcomed by our faculty, to teach quantitative literacy to geology majors at USF. The course continues to evolve although the second author has been teaching it for some 20 years. This paper describes our experiences with a new lab activity that we are developing on the core issue of measurement and units. The activity is inspired by a passage in the 2008 publication of lectures that Joseph Louis Lagrange delivered at the Ecole Normale in 1795. The activity envisions that young scientists are faced with the need to determine the dimensions of a rectangle with no measuring device other than an unruled stick of unknown length – to hundredths of a stick length. Following Lagrange, the students use the stick to measure the lengths with continued fractions, and then they reduce the continued fractions and convert them to decimal form. In the process, these student veterans of calculus instruction learn that as a group they are not very good at the arithmetic of fractions, which they thought they learned in the fifth grade. The group score on a continued fraction item improved from 44% on the pre-course test to 84% on the post-course test in the first semester in which the new lab was included (Fall 2015.

18. Soot volume fraction fields in unsteady axis-symmetric flames by continuous laser extinction technique.

Science.gov (United States)

Kashif, Muhammad; Bonnety, Jérôme; Guibert, Philippe; Morin, Céline; Legros, Guillaume

2012-12-17

A Laser Extinction Method has been set up to provide two-dimensional soot volume fraction field time history at a tunable frequency up to 70 Hz inside an axis-symmetric diffusion flame experiencing slow unsteady phenomena preserving the symmetry. The use of a continuous wave laser as the light source enables this repetition rate, which is an incremental advance in the laser extinction technique. The technique is shown to allow a fine description of the soot volume fraction field in a flickering flame exhibiting a 12.6 Hz flickering phenomenon. Within this range of repetition rate, the technique and its subsequent post-processing require neither any method for time-domain reconstruction nor any correction for energy intrusion. Possibly complemented by such a reconstruction method, the technique should support further soot volume fraction database in oscillating flames that exhibit characteristic times relevant to the current efforts in the validation of soot processes modeling.

19. Experimental research on energy circled fraction of continuous phase plates in focal spot

International Nuclear Information System (INIS)

Zhang Yuanhang; Yang Chunlin; Wen Shenglin; Shi Qikai; Wang Jian

2013-01-01

In inertial confinement fusion (ICF) research process, the form of focal spot is extremely crucial. Especially in the indirect driven implosion, energy circled fraction is higher than 95% in focal spot. Based on the offline test platform, the focusing spot of continuous phase plates with different application error is clearly imaged on CCD. By experimental analysis, it is found that the beam rotation error, caliber error, translational error and inclination error have a high tolerance in affecting focal plane of CPP. Energy circled fraction is higher than 95%, the range is less than 0.5%. Nevertheless, the waterfront aberration seriously affects the shaping ability of the CPP. Clearly, the main factor of reducing energy circled fraction to less than 90% is waterfront aberration. (authors)

International Nuclear Information System (INIS)

Turesson, I.

1990-01-01

The biological effects of continuous low dose-rate irradiation and fractionated high dose-rate irradiation in interstitial and intracavitary radiotherapy and total body irradiation are discussed in terms of dose-rate fractionation sensitivity for various tissues. A scaling between dose-rate and fraction size was established for acute and late normal-tissue effects which can serve as a guideline for local treatment in the range of dose rates between 0.02 and 0.005 Gy/min and fraction sizes between 8.5 and 2.5 Gy. This is valid provided cell-cycle progression and proliferation can be ignored. Assuming that the acute and late tissue responses are characterized by α/β values of about 10 and 3 Gy and a mono-exponential repair half-time of about 3 h, the same total doses given with either of the two methods are approximately equivalent. The equivalence for acute and late non-hemopoietic normal tissue damage is 0.02 Gy/min and 8.5 Gy per fraction; 0.01 Gy/min and 5.5 Gy per fraction; and 0.005 Gy/min and 2.5Gy per fraction. A very low dose rate, below 0.005 Gy/min, is thus necessary to simulate high dose-rate radiotherapy with fraction sizes of about 2Gy. The scaling factor is, however, dependent on the repair half-time of the tissue. A review of published data on dose-rate effects for normal tissue response showed a significantly stronger dose-rate dependence for late than for acute effects below 0.02 Gy/min. There was no significant difference in dose-rate dependence between various acute non-hemopoietic effects or between various late effects. The consistent dose-rate dependence, which justifies the use of a general scaling factor between fraction size and dose rate, contrasts with the wide range of values for repair half-time calculated for various normal-tissue effects. This indicates that the model currently used for repair kinetics is not satisfactory. There are also few experimental data in the clinical dose-rate range, below 0.02 Gy/min. It is therefore

1. The fast decoding of Reed-Solomon codes using Fermat theoretic transforms and continued fractions

Science.gov (United States)

Reed, I. S.; Scholtz, R. A.; Welch, L. R.; Truong, T. K.

1978-01-01

It is shown that Reed-Solomon (RS) codes can be decoded by using a fast Fourier transform (FFT) algorithm over finite fields GF(F sub n), where F sub n is a Fermat prime, and continued fractions. This new transform decoding method is simpler than the standard method for RS codes. The computing time of this new decoding algorithm in software can be faster than the standard decoding method for RS codes.

2. Comparison between splines and fractional polynomials for multivariable model building with continuous covariates: a simulation study with continuous response.

Science.gov (United States)

Binder, Harald; Sauerbrei, Willi; Royston, Patrick

2013-06-15

In observational studies, many continuous or categorical covariates may be related to an outcome. Various spline-based procedures or the multivariable fractional polynomial (MFP) procedure can be used to identify important variables and functional forms for continuous covariates. This is the main aim of an explanatory model, as opposed to a model only for prediction. The type of analysis often guides the complexity of the final model. Spline-based procedures and MFP have tuning parameters for choosing the required complexity. To compare model selection approaches, we perform a simulation study in the linear regression context based on a data structure intended to reflect realistic biomedical data. We vary the sample size, variance explained and complexity parameters for model selection. We consider 15 variables. A sample size of 200 (1000) and R(2)  = 0.2 (0.8) is the scenario with the smallest (largest) amount of information. For assessing performance, we consider prediction error, correct and incorrect inclusion of covariates, qualitative measures for judging selected functional forms and further novel criteria. From limited information, a suitable explanatory model cannot be obtained. Prediction performance from all types of models is similar. With a medium amount of information, MFP performs better than splines on several criteria. MFP better recovers simpler functions, whereas splines better recover more complex functions. For a large amount of information and no local structure, MFP and the spline procedures often select similar explanatory models. Copyright © 2012 John Wiley & Sons, Ltd.

3. On the continuing relevance of Mandelbrot's non-ergodic fractional renewal models of 1963 to 1967

Science.gov (United States)

Watkins, Nicholas W.

2017-12-01

The problem of "1/f" noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, and their links to the CTRW, I present preliminary results of my research into the history of Mandelbrot's very little known work in that area from 1963 to 1967. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, "1/f" noise and LRD, concepts which are often treated as equivalent. Contribution to the "Topical Issue: Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

4. Finite-dimensional approximations of the resolvent of an infinite band matrix and continued fractions

International Nuclear Information System (INIS)

Barrios, Dolores; Lopez, Guillermo L; Martinez-Finkelshtein, A; Torrano, Emilio

1999-01-01

The approximability of the resolvent of an operator induced by a band matrix by the resolvents of its finite-dimensional sections is studied. For bounded perturbations of self-adjoint matrices a positive result is obtained. The convergence domain of the sequence of resolvents can be described in this case in terms of matrices involved in the representation. This result is applied to tridiagonal complex matrices to establish conditions for the convergence of Chebyshev continued fractions on sets in the complex domain. In the particular case of compact perturbations this result is improved and a connection between the poles of the limit function and the eigenvalues of the tridiagonal matrix is established

5. Matrix continued-fraction calculation of localization length in disordered systems

International Nuclear Information System (INIS)

Pastawski, H.M.; Weisz, J.F.

1983-01-01

A Matrix Continued-Fraction method is used to study the localization length of the states at the band center of a two dimensional crystals with disorder given by the Anderson model. It is found that exponentially localized states which scale according to the work of Mac Kinnon and Kramer, becomes weakly localized as the disorder becomes weaker, and there is some critical disorder for which the localization length does not saturate with the width of the strips, this confirms the resuts found by Pichard and Sarma. Weakly localized states are also found in one dimension for w/v [pt

6. Matrix continued-fraction calculation of localization length in disordered systems

International Nuclear Information System (INIS)

Pastawski, H.M.; Weisz, J.F.

1983-01-01

A Matrix Continued-Fraction method is used to study the localization length of the states at the band center of a two dimensional crystal with disorder given by the Anderson model. It is found that exponentially localized states, which scale according to the work of Mac Kinnon and Kramer, becomes weakly localized as the disorder becomes weaker, and there is some critical disorder for which the localization length does not saturate with the width of the strips, this confirms the results found by Pichard and Sarma. Weakly localized states are also found in one dimension for w/v [pt

7. Continued-fraction representation of the Kraus map for non-Markovian reservoir damping

Science.gov (United States)

van Wonderen, A. J.; Suttorp, L. G.

2018-04-01

Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In the lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In the lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes–Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field.

8. Effects of low-dose continuously fractionated X-ray irradiation on murine peripheral blood lymphocytes

International Nuclear Information System (INIS)

Xie Yi; Zhang Hong; Dang Bingrong; Hao Jifang; Guo Hongyun; Wang Xiaohu

2007-01-01

For estimating biological risks from low doses continual irradiation, we investigated the effects of exposure to continuously fractionated X-rays on murine immune system. The BALB/c mice were irradiated with 0.07Gy at the first day and 0.08 Gy/d in the following 12 days at a dose rate of 0.2 Gy/min. The peripheral blood lymphocyte cycle and death were determined by flow cytometry at the cumulative doses of 0, 0.07, 0.23, 0.39, 0.55, 0.71, 0.87 and 1.03 Gy respectively. The results showed that the cycle of peripheral blood lymphocyte was arrested in G 0 /G 1 at cumulative doses of 0.07, 0.23, 0.71 and 0.87 Gy, and in G 2 /M at cumulative doses of 0.39 and 1.03 Gy; the percentage of death of peripheral blood lymphocyte was ascended with dose increasing, and reached the death peak at cumulative doses of 0.71 Gy. The results suggested that low doses continual X-rays total-body irradiated could result in changes of cellular cycle and death, and some damages to immunocytes, which accorded to linear square model. (authors)

9. Semi-simple continued fractions and diophantine equations for real quadratic fields

International Nuclear Information System (INIS)

Zhang Xianke.

1994-09-01

Main theorem: the equation x 2 - my 2 = c has an integer solution if and only if c = (-1) i Q i for some semi-simple continued-fraction expansion √m = [b 0 , b 1 , b 2 , ...] and some 0 ≤ i is an element of Z, where Q i denotes the i-th complete denominator of the expansion, i.e. [b i , b i+1 ,...] = (√m + P i )/Q i (P i , Q i is an element of Z). Here by semi-simple one means b i could be negative (and positive) integers. Such expansion with minimal modul Q i are also discussed. (author). 9 refs

10. Application of the method of continued fractions for electron scattering by linear molecules

International Nuclear Information System (INIS)

Lee, M.-T.; Iga, I.; Fujimoto, M.M.; Lara, O.; Brasilia Univ., DF

1995-01-01

The method of continued fractions (MCF) of Horacek and Sasakawa is adapted for the first time to study low-energy electron scattering by linear molecules. Particularly, we have calculated the reactance K-matrices for an electron scattered by hydrogen molecule and hydrogen molecular ion as well as by a polar LiH molecule in the static-exchange level. For all the applications studied herein. the calculated physical quantities converge rapidly, even for a strongly polar molecule such as LiH, to the correct values and in most cases the convergence is monotonic. Our study suggests that the MCF could be an efficient method for studying electron-molecule scattering and also photoionization of molecules. (Author)

11. Feasibility of using pyranometers for continuous estimation of ground cover fraction in table grape vineyards

Directory of Open Access Journals (Sweden)

Antonio Martinez-Cob

2014-06-01

Full Text Available This paper evaluates the feasibility of using pyranometers for continuous estimation of ground cover fraction (GCF at remote, unattended sites. Photographical techniques were used for measuring GCF (GCFref at a table grape vineyard grown under a net. Daily pyranometer-driven GCF estimates (GCFpyr were obtained from solar radiation measurements above and below the canopy. For GCFpyr computation, solar radiation was averaged for two hours around solar noon (midday periods and for daylight periods (8:00 to 18:00 Universal Time Coordinated. GCFpyr and GCFref (daylight periods showed a good agreement: mean estimation error, 0.000; root mean square error, 0.113; index of agreement, 0.967. The high GCF attained, the large measurement range for GCF and the presence of the net above the table grape were the likely reasons for the good performance of GCFpyr in this crop despite the short number of pyranometers used. Further research is required to develop more appropriate calibration equations of GCFpyr and for a more detailed evaluation of using a short number of pyranometers to estimate GCF.

12. A New Approach to Rational Discrete-Time Approximations to Continuous-Time Fractional-Order Systems

OpenAIRE

Matos , Carlos; Ortigueira , Manuel ,

2012-01-01

Part 10: Signal Processing; International audience; In this paper a new approach to rational discrete-time approximations to continuous fractional-order systems of the form 1/(sα+p) is proposed. We will show that such fractional-order LTI system can be decomposed into sub-systems. One has the classic behavior and the other is similar to a Finite Impulse Response (FIR) system. The conversion from continuous-time to discrete-time systems will be done using the Laplace transform inversion integr...

13. Design and FPGA Implementation of Variable Cutoff Frequency Filter based on Continuously Variable Fractional Delay Structure and Interpolation Technique

Directory of Open Access Journals (Sweden)

Sumedh Dhabu

2015-09-01

Full Text Available This paper presents the design and FPGA implementation of interpolated continuously variable fractional delay structure based filter (ICVFD filter with fine control over the cutoff frequency. In the ICVFD filter, each unit delay of the prototype lowpass filter is replaced by a continuously variable fractional delay (CVFD element proposed in this paper. The CVFD element requires the same number of multiplications as that of the second-order fractional delay structure used in the existing fractional delay structure based variable filter (FDS based filter, however it provides fractional delays corresponding to the higher-order fractional delay structures. Hence, the proposed ICVFD filter provides wider cutoff frequency range compared to the FDS based filter. The ICVFD filter is also capable of providing variable bandpass and highpass responses. We use two-stage approach for the FPGA implementation of the ICVFD filter. First, we use pipelining stages to shorten the critical path and improve the operating frequency. Then, we make use of specific hardware resource, i.e. RAM-based Shift Register (SRL to further improve the operating frequency and resource usage.

14. JENDL-4.0 benchmarking for effective delayed neutron fraction with a continuous-energy Monte Carlo code MVP

International Nuclear Information System (INIS)

Nagaya, Yasunobu

2013-01-01

Benchmark calculations with a continuous-energy Monte Carlo code have been performed for delayed neutron data of JENDL-4.0. JENDL-4.0 gives good prediction for the effective delayed neutron fraction in the present benchmarks but further detailed analysis is required for some cores. (author)

15. Output Feedback Finite-Time Stabilization of Systems Subject to Hölder Disturbances via Continuous Fractional Sliding Modes

Directory of Open Access Journals (Sweden)

Aldo-Jonathan Muñoz-Vázquez

2017-01-01

Full Text Available The problem of designing a continuous control to guarantee finite-time tracking based on output feedback for a system subject to a Hölder disturbance has remained elusive. The main difficulty stems from the fact that such disturbance stands for a function that is continuous but not necessarily differentiable in any integer-order sense, yet it is fractional-order differentiable. This problem imposes a formidable challenge of practical interest in engineering because (i it is common that only partial access to the state is available and, then, output feedback is needed; (ii such disturbances are present in more realistic applications, suggesting a fractional-order controller; and (iii continuous robust control is a must in several control applications. Consequently, these stringent requirements demand a sound mathematical framework for designing a solution to this control problem. To estimate the full state in finite-time, a high-order sliding mode-based differentiator is considered. Then, a continuous fractional differintegral sliding mode is proposed to reject Hölder disturbances, as well as for uncertainties and unmodeled dynamics. Finally, a homogeneous closed-loop system is enforced by means of a continuous nominal control, assuring finite-time convergence. Numerical simulations are presented to show the reliability of the proposed method.

16. Separation of platelets from other blood cells in continuous-flow by dielectrophoresis field-flow-fractionation

OpenAIRE

Piacentini, Niccolò; Mernier, Guillaume; Tornay, Raphaël; Renaud, Philippe

2011-01-01

We present a microfluidic device capable of separating platelets from other blood cells in continuous flow using dielectrophoresis field-flow-fractionation. The use of hydrodynamic focusing in combination with the application of a dielectrophoretic force allows the separation of platelets from red blood cells due to their size difference. The theoretical cell trajectory has been calculated by numerical simulations of the electrical field and flow speed, and is in agreement with the experiment...

17. Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations

Science.gov (United States)

Jiang, Daijun; Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro

2017-05-01

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

18. Comparison of the intracoronary continuous infusion method using a microcatheter and the intravenous continuous adenosine infusion method for inducing maximal hyperemia for fractional flow reserve measurement.

Science.gov (United States)

Yoon, Myeong-Ho; Tahk, Seung-Jea; Yang, Hyoung-Mo; Park, Jin-Sun; Zheng, Mingri; Lim, Hong-Seok; Choi, Byoung-Joo; Choi, So-Yeon; Choi, Un-Jung; Hwang, Joung-Won; Kang, Soo-Jin; Hwang, Gyo-Seung; Shin, Joon-Han

2009-06-01

Inducing stable maximal coronary hyperemia is essential for measurement of fractional flow reserve (FFR). We evaluated the efficacy of the intracoronary (IC) continuous adenosine infusion method via a microcatheter for inducing maximal coronary hyperemia. In 43 patients with 44 intermediate coronary lesions, FFR was measured consecutively by IC bolus adenosine injection (48-80 microg in left coronary artery, 36-60 microg in the right coronary artery) and a standard intravenous (IV) adenosine infusion (140 microg x min(-1) x kg(-1)). After completion of the IV infusion method, the tip of an IC microcatheter (Progreat Microcatheter System, Terumo, Japan) was positioned at the coronary ostium, and FFR was measured with increasing IC continuous adenosine infusion rates from 60 to 360 microg/min via the microcatheter. Fractional flow reserve decreased with increasing IC adenosine infusion rates, and no further decrease was observed after 300 microg/min. All patients were well tolerated during the procedures. Fractional flow reserves measured by IC adenosine infusion with 180, 240, 300, and 360 microg/min were significantly lower than those by IV infusion (P < .05). Intracoronary infusion at 180, 240, 300, and 360 microg/min was able to shorten the times to induction of optimal and steady-stable hyperemia compared to IV infusion (P < .05). Functional significances were changed in 5 lesions by IC infusion at 240 to 360 microg/min but not by IV infusion. The results of this study suggest that an IC adenosine continuous infusion method via a microcatheter is safe and effective in inducing steady-state hyperemia and more potent and quicker in inducing optimal hyperemia than the standard IV infusion method.

19. Carbon and hydrogen isotope fractionation under continuous light: implications for paleoenvironmental interpretations of the High Arctic during Paleogene warming.

Science.gov (United States)

Yang, Hong; Pagani, Mark; Briggs, Derek E G; Equiza, M A; Jagels, Richard; Leng, Qin; Lepage, Ben A

2009-06-01

The effect of low intensity continuous light, e.g., in the High Arctic summer, on plant carbon and hydrogen isotope fractionations is unknown. We conducted greenhouse experiments to test the impact of light quantity and duration on both carbon and hydrogen isotope compositions of three deciduous conifers whose fossil counterparts were components of Paleogene Arctic floras: Metasequoia glyptostroboides, Taxodium distichum, and Larix laricina. We found that plant leaf bulk carbon isotopic values of the examined species were 1.75-4.63 per thousand more negative under continuous light (CL) than under diurnal light (DL). Hydrogen isotope values of leaf n-alkanes under continuous light conditions revealed a D-enriched hydrogen isotope composition of up to 40 per thousand higher than in diurnal light conditions. The isotope offsets between the two light regimes is explained by a higher ratio of intercellular to atmospheric CO(2) concentration (C (i)/C (a)) and more water loss for plants under continuous light conditions during a 24-h transpiration cycle. Apparent hydrogen isotope fractionations between source water and individual lipids (epsilon(lipid-water)) range from -62 per thousand (Metasequoia C(27) and C(29)) to -87 per thousand (Larix C(29)) in leaves under continuous light. We applied these hydrogen fractionation factors to hydrogen isotope compositions of in situ n-alkanes from well-preserved Paleogene deciduous conifer fossils from the Arctic region to estimate the deltaD value in ancient precipitation. Precipitation in the summer growing season yielded a deltaD of -186 per thousand for late Paleocene, -157 per thousand for early middle Eocene, and -182 per thousand for late middle Eocene. We propose that high-latitude summer precipitation in this region was supplemented by moisture derived from regionally recycled transpiration of the polar forests that grew during the Paleogene warming.

20. Formulation and solutions of fractional continuously variable order mass–spring–damper systems controlled by viscoelastic and viscous–viscoelastic dampers

Directory of Open Access Journals (Sweden)

S Saha Ray

2016-05-01

Full Text Available This article presents the formulation and a new approach to find analytic solutions for fractional continuously variable order dynamic models, namely, fractional continuously variable order mass–spring–damper systems. Here, we use the viscoelastic and viscous–viscoelastic dampers for describing the damping nature of the oscillating systems, where the order of fractional derivative varies continuously. Here, we handle the continuous changing nature of fractional order derivative for dynamic systems, which has not been studied yet. By successive recursive method, here we find the solution of fractional continuously variable order mass–spring–damper systems and then obtain closed-form solutions. We then present and discuss the solutions obtained in the cases with continuously variable order of damping for oscillator through graphical plots.

1. A Pressure Controlled Pinched Flow Fractionation Device for Continuous Particle Separation

DEFF Research Database (Denmark)

Christiansen, Thomas Lehrmann; Trosborg, Jacqueline; Tanzi, Simone

2012-01-01

In this work the problem of separating small particles of di↵erent sizes is solved by developing a simple microfluidic device using pinched flow fractionation (PFF), a technique originally presented by Yamada et al. in 2004 [1]. The present work takes the concept of PFF to the next level by makin...... Polymers GmbH) using a micro machined silicon master. The functionality of the device was confirmed using polymer beads, and by adjusting the pressure accordingly a complete separation of 2 μm and 4.5 μm beads was demonstrated....

2. Effects of continuous hyperfractionated accelerated and conventionally fractionated radiotherapy on the parotid and submandibular salivary glands of rhesus monkeys

International Nuclear Information System (INIS)

Price, R.E.; Ang, K.K.; Stephens, L.C.; Peters, L.J.

1995-01-01

3. Rapid Estimation Method for State of Charge of Lithium-Ion Battery Based on Fractional Continual Variable Order Model

Directory of Open Access Journals (Sweden)

Xin Lu

2018-03-01

Full Text Available In recent years, the fractional order model has been employed to state of charge (SOC estimation. The non integer differentiation order being expressed as a function of recursive factors defining the fractality of charge distribution on porous electrodes. The battery SOC affects the fractal dimension of charge distribution, therefore the order of the fractional order model varies with the SOC at the same condition. This paper proposes a new method to estimate the SOC. A fractional continuous variable order model is used to characterize the fractal morphology of charge distribution. The order identification results showed that there is a stable monotonic relationship between the fractional order and the SOC after the battery inner electrochemical reaction reaches balanced. This feature makes the proposed model particularly suitable for SOC estimation when the battery is in the resting state. Moreover, a fast iterative method based on the proposed model is introduced for SOC estimation. The experimental results showed that the proposed iterative method can quickly estimate the SOC by several iterations while maintaining high estimation accuracy.

4. Semi-continuous protein fractionating using affinity cross-flow filtration

NARCIS (Netherlands)

Borneman, Zandrie; Zhang, W.; van den Boomgaard, Anthonie; Smolders, C.A.

2002-01-01

Protein purification by means of downstream processing is increasingly important. At the University of Twente a semi-continuous process is developed for the isolation of BSA out of crude protein mixtures. For this purpose an automated Affinity Cross-Flow Filtration, ACFF, process is developed. This

5. Continuous-time random walk as a guide to fractional Schroedinger equation

International Nuclear Information System (INIS)

Lenzi, E. K.; Ribeiro, H. V.; Mukai, H.; Mendes, R. S.

2010-01-01

We argue that the continuous-time random walk approach may be a useful guide to extend the Schroedinger equation in order to incorporate nonlocal effects, avoiding the inconsistencies raised by Jeng et al. [J. Math. Phys. 51, 062102 (2010)]. As an application, we work out a free particle in a half space, obtaining the time dependent solution by considering an arbitrary initial condition.

6. Effects of continuous fertilization on bioavailability and fractionation of cadmium in soil and its uptake by rice (Oryza sativa L.).

Science.gov (United States)

Huang, Qingqing; Yu, Yao; Wan, Yanan; Wang, Qi; Luo, Zhang; Qiao, Yuhui; Su, Dechun; Li, Huafen

2018-06-01

A four-year field trial was conducted in a rice paddy in southern China to determine the effects of continuous phosphate fertilizer, pig manure, chicken manure, and sewage sludge application on soil Cd accumulation in soil and Cd uptake by rice. The results showed that continuous application of fertilizers with higher Cd levels caused Cd to accumulate and redistribute in various soil fractions. In turn, these effects influenced Cd bioavailability in rice plants. After four years of phosphate fertilizer, pig manure, chicken manure, and sewage sludge application, the annual soil Cd accumulation rates were 0.007-0.032 mg kg -1 , 0.005-0.022 mg kg -1 , 0.002-0.013 mg kg -1 , and 0.032-0.087 mg kg -1 , respectively. Relative to the control, the pig- and chicken manure treatments significantly increased soil pH and reduced DTPA-extractable Cd (DTPA-Cd) and the exchangeable Cd fraction (Exc-Cd). In contrast, sewage sludge application significantly increased DTPA-Cd and Cd in all soil fractions. Phosphate fertilization had no significant effect on soil pH, DTPA-Cd, or Exc-Cd. Pearson's correlation coefficients showed that the rice grain Cd levels varied directly with DTPA-Cd, and Exc-Cd but inversely with soil pH. Pig- or chicken manure decreased rice grain Cd content, but sewage sludge increased both soil Cd availability and rice grain Cd uptake. Application of phosphate fertilizer had no significant effect on rice grain Cd content. The continuous use of organic- or phosphate fertilizer with elevated Cd content at high application rates may induce soil Cd accumulation and influence rice grain Cd accumulation. Copyright © 2018 Elsevier Ltd. All rights reserved.

7. Low energy elastic scattering of positrons by CO: An application of continued fractions and Schwinger variational iterative methods

Energy Technology Data Exchange (ETDEWEB)

Arretche, F. [Departamento de Fisica, Universidade Federal de Santa Catarina, 88040-900, Florianopolis, Santa Catarina (Brazil)], E-mail: farretche@hotmail.com; Mazon, K.T.; Michelin, S.E. [Departamento de Fisica, Universidade Federal de Santa Catarina, 88040-900, Florianopolis, Santa Catarina (Brazil); Fujimoto, M.M. [Departamento de Fisica, Universidade Federal do Parana, 81531-990, Curitiba, Parana (Brazil); Iga, I.; Lee, M.-T. [Departamento de Quimica, Universidade Federal de Sao Carlos, 13565-905, Sao Paulo (Brazil)

2008-02-15

Iterative Schwinger variational methods and the method of continued fractions, widely used for electron-molecule scattering, are applied for the first time to investigate positron-molecule interactions. Specifically, integral and differential cross sections for elastic positron scattering by CO in the (0.5-20) eV energy range are calculated and reported. In our calculation, a static plus correlation-polarization potential is used to represent the collisional dynamics. Our calculated results are in general agreement with the theoretical and experimental data available in the literature.

8. Aerosol counterflow two-jets unit for continuous measurement of the soluble fraction of atmospheric aerosols.

Science.gov (United States)

Mikuska, Pavel; Vecera, Zbynek

2005-09-01

A new type of aerosol collector employing a liquid at laboratory temperature for continuous sampling of atmospheric particles is described. The collector operates on the principle of a Venturi scrubber. Sampled air flows at high linear velocity through two Venturi nozzles "atomizing" the liquid to form two jets of a polydisperse aerosol of fine droplets situated against each other. Counterflow jets of droplets collide, and within this process, the aerosol particles are captured into dispersed liquid. Under optimum conditions (air flow rate of 5 L/min and water flow rate of 2 mL/min), aerosol particles down to 0.3 microm in diameter are quantitatively collected in the collector into deionized water while the collection efficiency of smaller particles decreases. There is very little loss of fine aerosol within the aerosol counterflow two-jets unit (ACTJU). Coupling of the aerosol collector with an annular diffusion denuder located upstream of the collector ensures an artifact-free sampling of atmospheric aerosols. Operation of the ACTJU in combination with on-line detection devices allows in situ automated analysis of water-soluble aerosol species (e.g., NO2-, NO3-)with high time resolution (as high as 1 s). Under the optimum conditions, the limit of detection for particulate nitrite and nitrate is 28 and 77 ng/m(3), respectively. The instrument is sufficiently rugged for its application at routine monitoring of aerosol composition in the real time.

9. Observations of the first postirradiation division of HeLa cells following continuous or fractionated exposure to γ rays

International Nuclear Information System (INIS)

Mitchell, J.B.; Bedford, J.S.; Bailey, S.M.

1979-01-01

10. Hydrogen atom with a Yukawa potential: Perturbation theory and continued-fractions--Pade approximants at large order

International Nuclear Information System (INIS)

Vrscay, E.R.

1986-01-01

A simple power-series method is developed to calculate to large order the Rayleigh-Schroedinger perturbation expansions for energy levels of a hydrogen atom with a Yukawa-type screened Coulomb potential. Perturbation series for the 1s, 2s, and 2p levels, shown not to be of the Stieltjes type, are calculated to 100th order. Nevertheless, the poles of the Pade approximants to these series generally avoid the region of the positive real axis 0 < lambda < lambda(, where lambda( represents the coupling constant threshold. As a result, the Pade sums afford accurate approximations to E(lambda) in this domain. The continued-fraction representations to these perturbation series have been accurately calculated to large (100th) order and demonstrate a curious ''quasioscillatory,'' but non-Stieltjes, behavior. Accurate values of E(lambda) as well as lambda( for the 1s, 2s, and 2p levels are reported

11. Effect of light on 2H/1H fractionation in lipids from continuous cultures of the diatom Thalassiosira pseudonana

Science.gov (United States)

Sachs, Julian P.; Maloney, Ashley E.; Gregersen, Joshua

2017-07-01

Continuous cultures of the marine diatom Thalassiosira pseudonana were grown at irradiances between 6 and 47 μmol m-2 s-1 in order to evaluate the effect of light on hydrogen isotope fractionation in lipids. δ2H values increased with irradiance in phytol by 1.1‰ (μmol m-2 s-1)-1 and by 0.3‰ (μmol m-2 s-1)-1 in the C14:0 fatty acid, but decreased by 0.8‰ (μmol m-2 s-1)-1 in the sterol 24-methyl-cholesta-5,24(28)-dien-3β-ol (C28Δ5,24(28)). The anticorrelation between δ2H values in C28Δ5,24(28) and irradiance is attributed to enhanced sterol precursor synthesis via the plastidic methylerythritol phosphate (MEP) pathway at high irradiance, relative to the cytosolic mevalonic acid (MVA) pathway, and the supposition that MEP precursors are 2H-depleted compared to MVA precursors because they incorporate a greater proportion of hydrogen from photosynthetically produced NADPH. Increasing δ2H values of phytol and C14:0 with irradiance is attributed to a greater proportion of pyruvate, the last common precursor to both lipids, being sourced from glycolysis in the mitochondria and cytosol, where enhanced incorporation of metabolic NADPH and further hydrogen exchange with cell water can enrich pyruvate with 2H relative to pyruvate from the chloroplast. Irrespective of the biosynthetic mechanisms responsible for the 2H/1H fractionation response to light, the high sensitivity of lipid δ2H values in T. pseudonana continuous cultures would result in -30‰ to +40‰ variations in δ2H over a 40 μmol m-2 s-1 range in sub-saturating irradiance if expressed in the environment, depending on the lipid.

12. Imaging water velocity and volume fraction distributions in water continuous multiphase flows using inductive flow tomography and electrical resistance tomography

International Nuclear Information System (INIS)

Meng, Yiqing; Lucas, Gary P

2017-01-01

This paper presents the design and implementation of an inductive flow tomography (IFT) system, employing a multi-electrode electromagnetic flow meter (EMFM) and novel reconstruction techniques, for measuring the local water velocity distribution in water continuous single and multiphase flows. A series of experiments were carried out in vertical-upward and upward-inclined single phase water flows and ‘water continuous’ gas–water and oil–gas–water flows in which the velocity profiles ranged from axisymmetric (single phase and vertical-upward multiphase flows) to highly asymmetric (upward-inclined multiphase flows). Using potential difference measurements obtained from the electrode array of the EMFM, local axial velocity distributions of the continuous water phase were reconstructed using two different IFT reconstruction algorithms denoted RT#1, which assumes that the overall water velocity profile comprises the sum of a series of polynomial velocity components, and RT#2, which is similar to RT#1 but which assumes that the zero’th order velocity component may be replaced by an axisymmetric ‘power law’ velocity distribution. During each experiment, measurement of the local water volume fraction distribution was also made using the well-established technique of electrical resistance tomography (ERT). By integrating the product of the local axial water velocity and the local water volume fraction in the cross section an estimate of the water volumetric flow rate was made which was compared with a reference measurement of the water volumetric flow rate. In vertical upward flows RT#2 was found to give rise to water velocity profiles which are consistent with the previous literature although the profiles obtained in the multiphase flows had relatively higher central velocity peaks than was observed for the single phase profiles. This observation was almost certainly a result of the transfer of axial momentum from the less dense dispersed phases to the

13. Imaging water velocity and volume fraction distributions in water continuous multiphase flows using inductive flow tomography and electrical resistance tomography

Science.gov (United States)

Meng, Yiqing; Lucas, Gary P.

2017-05-01

This paper presents the design and implementation of an inductive flow tomography (IFT) system, employing a multi-electrode electromagnetic flow meter (EMFM) and novel reconstruction techniques, for measuring the local water velocity distribution in water continuous single and multiphase flows. A series of experiments were carried out in vertical-upward and upward-inclined single phase water flows and ‘water continuous’ gas-water and oil-gas-water flows in which the velocity profiles ranged from axisymmetric (single phase and vertical-upward multiphase flows) to highly asymmetric (upward-inclined multiphase flows). Using potential difference measurements obtained from the electrode array of the EMFM, local axial velocity distributions of the continuous water phase were reconstructed using two different IFT reconstruction algorithms denoted RT#1, which assumes that the overall water velocity profile comprises the sum of a series of polynomial velocity components, and RT#2, which is similar to RT#1 but which assumes that the zero’th order velocity component may be replaced by an axisymmetric ‘power law’ velocity distribution. During each experiment, measurement of the local water volume fraction distribution was also made using the well-established technique of electrical resistance tomography (ERT). By integrating the product of the local axial water velocity and the local water volume fraction in the cross section an estimate of the water volumetric flow rate was made which was compared with a reference measurement of the water volumetric flow rate. In vertical upward flows RT#2 was found to give rise to water velocity profiles which are consistent with the previous literature although the profiles obtained in the multiphase flows had relatively higher central velocity peaks than was observed for the single phase profiles. This observation was almost certainly a result of the transfer of axial momentum from the less dense dispersed phases to the water

14. A Universal Ts-VI Triangle Method for the Continuous Retrieval of Evaporative Fraction From MODIS Products

Science.gov (United States)

Zhu, Wenbin; Jia, Shaofeng; Lv, Aifeng

2017-10-01

The triangle method based on the spatial relationship between remotely sensed land surface temperature (Ts) and vegetation index (VI) has been widely used for the estimates of evaporative fraction (EF). In the present study, a universal triangle method was proposed by transforming the Ts-VI feature space from a regional scale to a pixel scale. The retrieval of EF is only related to the boundary conditions at pixel scale, regardless of the Ts-VI configuration over the spatial domain. The boundary conditions of each pixel are composed of the theoretical dry edge determined by the surface energy balance principle and the wet edge determined by the average air temperature of open water. The universal triangle method was validated using the EF observations collected by the Energy Balance Bowen Ratio systems in the Southern Great Plains of the United States of America (USA). Two parameterization schemes of EF were used to demonstrate their applicability with Terra Moderate Resolution Imaging Spectroradiometer (MODIS) products over the whole year 2004. The results of this study show that the accuracy produced by both of these two parameterization schemes is comparable to that produced by the traditional triangle method, although the universal triangle method seems specifically suited to the parameterization scheme proposed in our previous research. The independence of the universal triangle method from the Ts-VI feature space makes it possible to conduct a continuous monitoring of evapotranspiration and soil moisture. That is just the ability the traditional triangle method does not possess.

15. Continuously tunable photonic fractional Hilbert transformer using a high-contrast germanium-doped silica-on-silicon microring resonator.

Science.gov (United States)

Shahoei, Hiva; Dumais, Patrick; Yao, Jianping

2014-05-01

We propose and experimentally demonstrate a continuously tunable fractional Hilbert transformer (FHT) based on a high-contrast germanium-doped silica-on-silicon (SOS) microring resonator (MRR). The propagation loss of a high-contrast germanium-doped SOS waveguide can be very small (0.02 dB/cm) while the lossless bend radius can be less than 1 mm. These characteristics lead to the fabrication of an MRR with a high Q-factor and a large free-spectral range (FSR), which is needed to implement a Hilbert transformer (HT). The SOS MRR is strongly polarization dependent. By changing the polarization direction of the input signal, the phase shift introduced at the center of the resonance spectrum is changed. The tunable phase shift at the resonance wavelength can be used to implement a tunable FHT. A germanium-doped SOS MRR with a high-index contrast of 3.8% is fabricated. The use of the fabricated MRR for the implementation of a tunable FHT with tunable orders at 1, 0.85, 0.95, 1.05, and 1.13 for a Gaussian pulse with the temporal full width at half-maximum of 80 ps is experimentally demonstrated.

16. Continuous fraction collection of gas chromatographic separations with parallel mass spectrometric detection applied to cell-based bioactivity analysis

NARCIS (Netherlands)

Jonker, Willem; Zwart, Nick; Stockl, Jan B.; de Koning, Sjaak; Schaap, Jaap; Lamoree, Marja H.; Somsen, Govert W.; Hamers, Timo; Kool, Jeroen

2017-01-01

We describe the development and evaluation of a GC-MS fractionation platform that combines high-resolution fraction collection of full chromatograms with parallel MS detection. A y-split at the column divides the effluent towards the MS detector and towards an inverted y-piece where vaporized trap

17. A comparison of anti-tumor effects of high dose rate fractionated and low dose rate continuous irradiation in multicellular spheroids

International Nuclear Information System (INIS)

Kubota, Nobuo; Omura, Motoko; Matsubara, Sho.

1997-01-01

In a clinical experience, high dose rate (HDR) fractionated interstitial radiotherapy can be an alternative to traditional low dose rate (LDR) continuous interstitial radiotherapy for head and neck cancers. To investigate biological effect of HDR, compared to LDR, comparisons have been made using spheroids of human squamous carcinoma cells. Both LDR and HDR were delivered by 137 Cs at 37degC. Dose rate of LDR was 8 Gy/day and HDR irradiations of fraction size of 4, 5 or 6 Gy were applied twice a day with an interval time of more than 6 hr. We estimated HDR fractionated dose of 31 Gy with 4 Gy/fr to give the same biological effects of 38 Gy by continuous LDR for spheroids. The ratio of HDR/LDR doses to control 50% spheroids was 0.82. (author)

18. Simulating the reactions of CO2 in aqueous monoethanolamine solution by reaction ensemble Monte Carlo using the continuous fractional component method

NARCIS (Netherlands)

Balaji, S.P.; Gangarapu, S.; Ramdin, M.; Torres-Knoop, A.; Zuilhof, H.; Goetheer, E.L.V.; Dubbeldam, D.; Vlugt, T.J.H.

2015-01-01

Molecular simulations were used to compute the equilibrium concentrations of the different species in CO2/monoethanolamine solutions for different CO2 loadings. Simulations were performed in the Reaction Ensemble using the continuous fractional component Monte Carlo method at temperatures of 293,

19. Improving snow fraction spatio-temporal continuity using a combination of MODIS and Fengyun-2 satellites over China

Science.gov (United States)

Jiang, L.; Wang, G.

2017-12-01

Snow cover is one of key elements in the investigations of weather, climatic change, water resource, and snow hazard. Satellites observations from on-board optical sensors provides the ability to snow cover mapping through the discrimination of snow from other surface features and cloud. MODIS provides maximum of snow cover data using 8-day composition data in order to reduce the cloud obscuration impacts. However, snow cover mapping is often required to obtain at the temporal scale of less than one day, especially in the case of disasters. Geostationary satellites provide much higher temporal resolution measurements (typically at 15 min or half or one hour), which has a great potential to reduce cloud cover problem and observe ground surface for identifying snow. The proposed method in this work is that how to take the advantages of polar-orbiting and geostationary optical sensors to accurately map snow cover without data gaps due to cloud. FY-2 geostationary satellites have high temporal resolution observations, however, they are lacking enough spectral bands essential for snow cover monitoring, such as the 1.6 μm band. Based on our recent work (Wang et al., 2017), we improved FY-2/VISSR fractional snow cover estimation with a linear spectral unmixing analysis method. The linear approach is applied then using the reflectance observed at the certain hourly image of FY-2 to calculate pixel-wise snow cover fraction. The composition of daily factional snow cover employs the sun zenith angle, where the snow fraction under lowest sun zenith angle is considered as the most confident result. FY-2/VISSR fractional snow cover map has less cloud due to the composition of multi-temporal snow maps in a single day. In order to get an accurate and cloud-reduced fractional snow cover map, both of MODIS and FY-2/VISSR daily snow fraction maps are blended together. With the combination of FY-2E/VISSR and MODIS, there are still some cloud existing in the daily snow fraction map

20. Production of high-brightness continuous wave proton beams with very high proton fractions (abstract)a

International Nuclear Information System (INIS)

Spence, D.; McMichael, G.; Lykke, K.R.; Schneider, J.D.; Sherman, J.; Stevens, R. Jr.; Hodgkins, D.

1996-01-01

This article demonstrates a new technique to significantly enhance the proton fraction of an ion beam extracted from a plasma ion source. We employ a magnetically confined microwave driven source, though the technique is not source specific and can probably be applied equally effectively to other plasma sources such as Penning and multicusp types. Specifically, we dope the plasma with about 1% H 2 O, which increases the proton fraction of a 45 keV 45 mA beam from 75% to 90% with 375 W 2.45 GHz power to the source and from 84% to 92% for 500 W when the source is operated under nonresonant conditions. Much of the remaining fraction of the beam comprises a heavy mass ion we believe to be N + impurity ions resulting from the conditions under which the experiments were performed. If so, this impurity can easily be removed and much higher proton fractions could be expected. Preliminary measurements show the additive has no adverse effect on the emittance of the extracted beam, and source stability is greatly improved

1. Calculation of controllability and observability matrices for special case of continuous-time multi-order fractional systems.

Science.gov (United States)

2017-03-28

In this paper, controllability and observability matrices for pseudo upper or lower triangular multi-order fractional systems are derived. It is demonstrated that these systems are controllable and observable if and only if their controllability and observability matrices are full rank. In other words, the rank of these matrices should be equal to the inner dimension of their corresponding state space realizations. To reduce the computational complexities, these matrices are converted to simplified matrices with smaller dimensions. Numerical examples are provided to show the usefulness of the mentioned matrices for controllability and observability analysis of this case of multi-order fractional systems. These examples clarify that the duality concept is not necessarily true for these special systems. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

2. Modeling of gas condensates properties using continuous distribution functions for the characterization of the plus fraction; Modelisation des proprietes thermodynamiques des gaz a condensat par representation de la fraction lourde a laide de fonctions de distribution

Energy Technology Data Exchange (ETDEWEB)

Sportisse, M.

1996-12-20

The modeling of thermodynamic behaviour for gas condensates is not yet satisfactory and it involves an adjustment of thermodynamic models. We propose here a fitting based on the characterization of the plus fraction using three continuous distribution functions associated to the following families: n-alkanes, n-alkylbenzenes and poly-aromatics. No continuous thermodynamic model is used and PVT calculations are made with the Peng-Robinson equation of state. For poly-aromatics, a simple correlation of {l_brace} T{sub c}, P{sub c}, {omega} {r_brace} is given. The parameters of the distributions are fitted in order to improve the accuracy of the liquid deposit curve calculation. A continuous minimization by simulated annealing has been used to avoid local minima. Good results on fitting PVT properties have been obtained with more than twenty gas condensates from different areas. Moreover, the prediction of tank liquid and heavy-plus fraction densities are given with an average deviation of 1.2 % and 3.6 %. Tests on temperature extrapolation show that our modeling yields a good representation of pressure and temperature influence on gas condensates behaviour. (author) 89 refs.

3. Operational strategies for thermophilic anaerobic digestion of organic fraction of municipal solid waste in continuously stirred tank reactors

DEFF Research Database (Denmark)

Angelidaki, Irini; Cui, J.; Chen, X.

2006-01-01

Three operational strategies to reduce inhibition due to ammonia during thermophilic anaerobic digestion of source-sorted organic fraction of municipal solid waste (SS-OFMSW) rich in proteins were investigated. Feed was prepared by diluting SS-OFMSW (ratio of 1:4) with tap water or reactor process...... ammonium bicarbonate additions. Dilution of SS-OFMSW with fresh water showed a stable performance with volatile fatty acids of solids (VS). Use of recirculated process water after stripping ammonia showed even better performance with a methane yield...... of 0.43 m(3) kg(-1)VS. Recirculation of process water alone on the other hand, resulted in process inhibition at both TAN levels of 3.5 and 5.5 g-N l(-1). However, after a short period, the process recovered and adapted to the tested TAN levels. Thus, use of recirculated process water after stripping...

4. Carbon and Nitrogen Mineralization in Relation to Soil Particle-Size Fractions after 32 Years of Chemical and Manure Application in a Continuous Maize Cropping System

Science.gov (United States)

Shao, Xingfang; Zhu, Ping; Zhang, Wenju; Xu, Minggang; Murphy, Daniel V.

2016-01-01

Long-term manure application is recognized as an efficient management practice to enhance soil organic carbon (SOC) accumulation and nitrogen (N) mineralization capacity. A field study was established in 1979 to understand the impact of long-term manure and/or chemical fertilizer application on soil fertility in a continuous maize cropping system. Soil samples were collected from field plots in 2012 from 9 fertilization treatments (M0CK, M0N, M0NPK, M30CK, M30N, M30NPK, M60CK, M60N, and M60NPK) where M0, M30, and M60 refer to manure applied at rates of 0, 30, and 60 t ha−1 yr−1, respectively; CK indicates no fertilizer; N and NPK refer to chemical fertilizer in the forms of either N or N plus phosphorus (P) and potassium (K). Soils were separated into three particle-size fractions (2000–250, 250–53, and fertilization application, on the accumulation and mineralization of SOC and total N in each fraction. Results showed that long-term manure application significantly increased SOC and total N content and enhanced C and N mineralization in the three particle-size fractions. The content of SOC and total N followed the order 2000–250 μm > 250–53μm > 53 μm fraction, whereas the amount of C and N mineralization followed the reverse order. In the fertilizers, resulted in increased soil microbial biomass C and N, and a decreased microbial metabolic quotient. Consequently, long-term manure fertilization was beneficial to both soil C and N turnover and microbial activity, and had significant effect on the microbial metabolic quotient. PMID:27031697

5. Carbon and Nitrogen Mineralization in Relation to Soil Particle-Size Fractions after 32 Years of Chemical and Manure Application in a Continuous Maize Cropping System.

Directory of Open Access Journals (Sweden)

Andong Cai

Full Text Available Long-term manure application is recognized as an efficient management practice to enhance soil organic carbon (SOC accumulation and nitrogen (N mineralization capacity. A field study was established in 1979 to understand the impact of long-term manure and/or chemical fertilizer application on soil fertility in a continuous maize cropping system. Soil samples were collected from field plots in 2012 from 9 fertilization treatments (M0CK, M0N, M0NPK, M30CK, M30N, M30NPK, M60CK, M60N, and M60NPK where M0, M30, and M60 refer to manure applied at rates of 0, 30, and 60 t ha(-1 yr(-1, respectively; CK indicates no fertilizer; N and NPK refer to chemical fertilizer in the forms of either N or N plus phosphorus (P and potassium (K. Soils were separated into three particle-size fractions (2000-250, 250-53, and 250-53 μm > 53 μm fraction, whereas the amount of C and N mineralization followed the reverse order. In the <53 μm fraction, the M60NPK treatment significantly increased the amount of C and N mineralized (7.0 and 10.1 times, respectively compared to the M0CK treatment. Long-term manure application, especially when combined with chemical fertilizers, resulted in increased soil microbial biomass C and N, and a decreased microbial metabolic quotient. Consequently, long-term manure fertilization was beneficial to both soil C and N turnover and microbial activity, and had significant effect on the microbial metabolic quotient.

6. The Influence of Growth Rate on 2H/1H Fractionation in Continuous Cultures of the Coccolithophorid Emiliania huxleyi and the Diatom Thalassiosira pseudonana.

Science.gov (United States)

Sachs, Julian P; Kawka, Orest E

2015-01-01

The hydrogen isotope (2H/1H) ratio of lipids from phytoplankton is a powerful new tool for reconstructing hydroclimate variations in the geologic past from marine and lacustrine sediments. Water 2H/1H changes are reflected in lipid 2H/1H changes with R2 > 0.99, and salinity variations have been shown to cause about a 1‰ change in lipid δ2H values per unit (ppt) change in salinity. Less understood are the effects of growth rate, nutrient limitation and light on 2H/1H fractionation in phytoplankton. Here we present the first published study of growth rate effects on 2H/1H fractionation in the lipids of coccolithophorids grown in continuous cultures. Emiliania huxleyi was cultivated in steady state at four growth rates and the δ2H value of individual alkenones (C37:2, C37:3, C38:2, C38:3), fatty acids (C14:0, C16:0, C18:0), and 24-methyl cholest-5,22-dien-3β-ol (brassicasterol) were measured. 2H/1H fractionation increased in all lipids as growth rate increased by 24‰ to 79‰ (div d-1)-1. We attribute this response to a proportional increase in the fraction of NADPH from Photosystem I (PS1) of photosynthesis relative to NADPH from the cytosolic oxidative pentose phosphate (OPP) pathway in the synthesis of lipids as growth rate increases. A 3-endmember model is presented in which lipid hydrogen comes from NADPH produced in PS1, NADPH produced by OPP, and intracellular water. With published values or best estimates of the fractionation factors for these sources (αPS1 = 0.4, αOPP = 0.75, and αH2O = 0) and half of the hydrogen in a lipid derived from water the model indicates αlipid = 0.79. This value is within the range measured for alkenones (αalkenone = 0.77 to 0.81) and fatty acids (αFA = 0.75 to 0.82) in the chemostat cultures, but is greater than the range for brassicasterol (αbrassicasterol = 0.68 to 0.72). The latter is attributed to a greater proportion of hydrogen from NADPH relative to water in isoprenoid lipids. The model successfully explains

7. Spirals, Spots and Continued Fractions

Science.gov (United States)

Dixon, Robert

2012-01-01

This is mathematics in action, in context, in real life, and in detail. Begin the journey with Archimedes, and travel alongside the likes of Fermat, Fibonacci, Coxeter, and Adler. There is much to consider and opportunities to make links to things that might be "known", but maybe not well appreciated. On the way you will come across an angular…

8. Multistage-multiorifice flow fractionation (MS-MOFF): continuous size-based separation of microspheres using multiple series of contraction/expansion microchannels.

Science.gov (United States)

Sim, Tae Seok; Kwon, Kiho; Park, Jae Chan; Lee, Jeong-Gun; Jung, Hyo-Il

2011-01-07

Previously we introduced a novel hydrodynamic method using a multi-orifice microchannel for size-based particle separation, which is called a multi-orifice flow fractionation (MOFF). The MOFF has several advantages such as continuous, non-intrusive, and minimal power consumption. However, it has a limitation that the recovery yield is relatively low. Although the recovery may be increased by adjusting parameters such as the Reynolds number and central collecting region, poor purity inevitably followed. We newly designed and fabricated a microfluidic channel for multi-stage multi-orifice flow fractionation (MS-MOFF), which is made by combining three multi-orifice segments, and consists of 3 inlets, 3 filters, 3 multi-orifice segments and 5 outlets. The structure and dimensions of the MS-MOFF were determined by the hydrodynamic principles to have constant Reynolds numbers at each multi-orifice segment. Polystyrene microspheres of two different sizes (7 μm and 15 μm) were tested. With this device, we made an attempt to improve recovery and minimize loss of purity by collecting and re-separating non-selected particles of the first separation. The final recovery successfully increased from 73.2% to 88.7% while the final purity slightly decreased from 91.4% to 89.1% (for 15 μm). These values were never achievable with the single-stage MOFF (SS-MOFF) having only one multi-orifice segment in our previous work. The MS-MOFF channel will be useful for clinical applications, such as separation of circulating tumor cells (CTC) or rare cells from human blood samples.

9. Effect of continuous gamma-ray exposure on performance of learned tasks and effect of subsequent fractionated exposures on blood-forming tissue

Science.gov (United States)

Spalding, J. F.; Holland, L. M.; Prine, J. R.; Farrer, D. N.; Braun, R. G.

1972-01-01

Sixteen monkeys trained to perform continuous and discrete-avoidance and fixed-ratio tasks with visual and auditory cues were performance-tested before, during, and after 10-day gamma-ray exposures totaling 0, 500, 750, and 1000 rads. Approximately 14 months after the performance-test exposures, surviving animals were exposed to 100-rad gamma-ray fractions at 56-day intervals to observe injury and recovery patterns of blood-forming tissues. The fixed-ratio, food-reward task performance showed a transient decline in all dose groups within 24 hours of the start of gamma-ray exposure, followed by recovery to normal food-consumption levels within 48 to 72 hours. Avoidance tasks were performed successfully by all groups during the 10-day exposure, but reaction times of the two higher dose-rate groups in which animals received 3 and 4 rads per hour or total doses of 750 and 1000 rads, respectively, were somewhat slower.

10. SU-G-JeP4-13: Continuous Intra-Fractional Monitoring of the Prostate Using Dynamic KV Collimation and Tube Current Modulation

Energy Technology Data Exchange (ETDEWEB)

Parsons, D [Dalhousie Unviersity, Halifax, Nova Scotia (Canada); Robar, J [Dalhousie Unviersity, Halifax, Nova Scotia (Canada); Nova Scotia Health Authority, Halifax, NS (Canada)

2016-06-15

Purpose: The focus of this work is to improve the available kV image quality for continuous intra-fraction monitoring of the prostate. This is investigated using a novel blade collimation system enabling modulated volume-of-interest (VOI) imaging of prostate fiducial markers. Methods: A four-blade dynamic kV collimator was used to track a VOI during gantry rotation. Planar image quality was investigated as a function of collimator dimension, while maintaining the same dose to isocenter, for a 22.2 cm diameter cylindrical water phantom with a 9 mm diameter bone insert. A sample prostate anatomy was defined in the planning system, including three fiducial markers within the CTV. The VOI margin around each marker was set to be 2σ of the population covariance matrix characterizing prostate motion. DRRs were used to calculate the kV attenuation for each VOI as a function of angle. The optimal marker and tube current were determined using kV attenuation. Monte Carlo simulations were used to calculate the imaging dose to the phantom and MV scatter dose to the imaging panel. Results: Preliminary measurements show an increase in CNR by a factor of 1.3 with the VOI method, when decreasing from an 6×6 to 2×2 cm{sup 2} field. Attenuation calculations show a change in kV fluence at the detector by a factor of 21.6 with fiducial optimization; resultant tube current modulation increases maximum dose by a factor of 1.4 compared to no modulation. MV scatter contribution to the kV detector changes by approximately a factor of two over a complete gantry rotation. Conclusion: The dynamic collimation system allows single fiducial marker tracking at a very low dose, with reduction of scatter and improvement of image quality, compared to imaging the entire prostate. The approach is compatible with tube current modulation, which enables consistent image quality throughout the range of gantry rotation. This project was funded by Varian Medical Systems.

11. Anaerobic co-digestion of cheese whey and the screened liquid fraction of dairy manure in a single continuously stirred tank reactor process: Limits in co-substrate ratios and organic loading rate.

Science.gov (United States)

Rico, Carlos; Muñoz, Noelia; Rico, José Luis

2015-01-01

Mesophilic anaerobic co-digestion of cheese whey and the screened liquid fraction of dairy manure was investigated with the aim of determining the treatment limits in terms of the cheese whey fraction in feed and the organic loading rate. The results of a continuous stirred tank reactor that was operated with a hydraulic retention time of 15.6 days showed that the co-digestion process was possible with a cheese whey fraction as high as 85% in the feed. The efficiency of the process was similar within the range of the 15-85% cheese whey fraction. To study the effect of the increasing loading rate, the HRT was progressively shortened with the 65% cheese whey fraction in the feed. The reactor efficiency dropped as the HRT decreased but enabled a stable operation over 8.7 days of HRT. At these operating conditions, a volumetric methane production rate of 1.37 m(3) CH4 m(-3) d(-1) was achieved. Copyright © 2015 Elsevier Ltd. All rights reserved.

12. On a connection between the limit set of the Moebius-Klein transformation, periodic continued fractions, El Naschie's topological theory of high energy particle physics and the possibility of a new axion-like particle

International Nuclear Information System (INIS)

Marek-Crnjac, L.

2004-01-01

In the present work we first give a general representation of the derivatives of the irrational number phi, for instance ((1)/(phi)), ((1)/(phi 2 )), ((1)/(phi 3 )) etc., as periodic continued fractions. Any irrational number can then be expanded in an infinite continued fraction. The limit set of the Kleinian transformation acting on the E-infinity Cantorian spacetime turned out to be this set of periodic continued fractions, consequently the vacuum of the E-infinity is described by this limit set. As discussed by El Naschie, every particle can be interpreted geometrically as a scaling of another. This is done using the topology of hyperbolic Kleinian space of VAK, which is nothing but our limit set. Here we will present the ratios of the theoretical masses of certain elementary particles to that of some chosen particles in term of phi. Many of these masses are quite close to integer multiples of the mass of a chosen particle. Finally we discuss the possibility of new transfinite, axion-like particles as discussed recently by Krauss and El Naschie [Quintessence, Vintage, London, 1999

13. FRACTIONAL BANKING

OpenAIRE

Maria Klimikova

2010-01-01

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

14. Dose-rate effects in synchronous mammalian cells in culture. II. A comparison of the life cycle of HeLa cells during continuous irradiation or multiple-dose fractionation

International Nuclear Information System (INIS)

Mitchell, J.B.; Bedford, J.S.

1977-01-01

The life cycle of synchronized S3 HeLa cells was examined during continuous irradiation at a dose rate of approximately 37 rad/hr and during multiple dose fractionation schedules of the same average dose rate (total dose / overall time = average dose rate). For all regimes given at this dose rate the effects on the life cyclee were similar. Cells progressed through G1 and S without appreciable delay and experienced a minimum G2 delay of about 10 hr. Cells eventually entered mitosis but virtually none were able to complete a successful division

15. Fractional thermoelasticity

CERN Document Server

Povstenko, Yuriy

2015-01-01

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

16. SARAD EQF 3020 - A new microsystem based monitoring system for the continuous measurement of radon and the attached and unattached fraction of the radon progeny

International Nuclear Information System (INIS)

Streil, T.; Holfeld, G.; Oeser, V.; Feddersen, C.; Schoenefeld, K.

1996-01-01

Due to the large differences in the dose factors for radon and radon daughters it's recommended to measure both, but monitors for the continuous and simultaneous measurement of radon and radon progeny concentrations are too expensive to be widely used if they are built from individual components. Integrating detector, readout electronics, memory and an A/D converter on a single chip offers far lower prices at least if this silicon microsystem can be produced in large quantities. It is known that dRAM cells of commercial available memories are sensitive to alpha particles, but even if one accepts unstable operating conditions (Ucc 2 . Further development with special PMOS-transistors in a floating n-well as sensor cells has resulted in an alpha particle spectrometric microsystem with an effective sensor array of 40 mm 2 . Alternative for higher resolution we developed PiN -structures with more than 100 mm 2 sensor area with integrated preamplification

17. Radiation-Free Weekend Rescued! Continuous Accelerated Irradiation of 7-Days per Week Is Equal to Accelerated Fractionation With Concomitant Boost of 7 Fractions in 5-Days per Week: Report on Phase 3 Clinical Trial in Head-and-Neck Cancer Patients

Energy Technology Data Exchange (ETDEWEB)

Skladowski, Krzysztof, E-mail: skladowski@io.gliwice.pl [Maria Sklodowska-Curie Memorial Cancer Center and the Institute of Oncology, Branch in Gliwice (Poland); Hutnik, Marcin; Wygoda, Andrzej; Golen, Maria; Pilecki, Boleslaw; Przeorek, Wieslawa; Rutkowski, Tomasz; Lukaszczyk-Widel, Beata; Heyda, Alicja; Suwinski, Rafal; Tarnawski, Rafal; Maciejewski, Boguslaw [Maria Sklodowska-Curie Memorial Cancer Center and the Institute of Oncology, Branch in Gliwice (Poland)

2013-03-01

Purpose: To report long-term results of randomized trial comparing 2 accelerated fractionations of definitive radiation therapy assessing the need to irradiate during weekend in patients with head and neck squamous cell carcinoma. Methods and Materials: A total of 345 patients with SCC of the oral cavity, larynx, and oro- or hypo-pharynx, stage T2-4N0-1M0, were randomized to receive continuous accelerated irradiation (CAIR: once per day, 7 days per week) or concomitant accelerated boost (CB: once per day, 3 days per week, and twice per day, 2 days per week). Total dose ranged from 66.6-72 Gy, dose per fraction was 1.8 Gy, number of fractions ranged from 37-40 fractions, and overall treatment time ranged from 37-40 days. Results: No differences for all trial end-points were noted. At 5 and 10 years, the actuarial rates of local-regional control were 63% and 60% for CAIR vs 65% and 60% for CB, and the corresponding overall survival were 40% and 25% vs 44% and 25%, respectively. Confluent mucositis was the main acute toxicity, with an incidence of 89% in CAIR and 86% in CB patients. The 5-year rate of grade 3-4 late radiation morbidity was 6% for both regimens. Conclusions: Results of this trial indicate that the effects of accelerated fractionation can be achieve by delivering twice-per-day irradiation on weekday(s). This trial has also confirmed that an accelerated, 6-weeks schedule is a reasonable option for patients with intermediate-stage head-and-neck squamous cell carcinoma because of the associated high cure rate and minimal severe late toxicity.

18. Regional cerebral blood flow measurements by a noninvasive microsphere method using 123I-IMP. Comparison with the modified fractional uptake method and the continuous arterial blood sampling method

International Nuclear Information System (INIS)

Nakano, Seigo; Matsuda, Hiroshi; Tanizaki, Hiroshi; Ogawa, Masafumi; Miyazaki, Yoshiharu; Yonekura, Yoshiharu

1998-01-01

A noninvasive microsphere method using N-isopropyl-p-( 123 I)iodoamphetamine ( 123 I-IMP), developed by Yonekura et al., was performed in 10 patients with neurological diseases to quantify regional cerebral blood flow (rCBF). Regional CBF values by this method were compared with rCBF values simultaneously estimated from both the modified fractional uptake (FU) method using cardiac output developed by Miyazaki et al. and the conventional method with continuous arterial blood sampling. In comparison, we designated the factor which converted raw SPECT voxel counts to rCBF values as a CBF factor. A highly significant correlation (r=0.962, p<0.001) was obtained in the CBF factors between the present method and the continuous arterial blood sampling method. The CBF factors by the present method were only 2.7% higher on the average than those by the continuous arterial blood sampling method. There were significant correlation (r=0.811 and r=O.798, p<0.001) in the CBF factor between modified FU method (threshold for estimating total brain SPECT counts; 10% and 30% respectively) and the continuous arterial blood sampling method. However, the CBF factors of the modified FU method showed 31.4% and 62.3% higher on the average (threshold; 10% and 30% respectively) than those by the continuous arterial blood sampling method. In conclusion, this newly developed method for rCBF measurements was considered to be useful for routine clinical studies without any blood sampling. (author)

19. Fractional charges

International Nuclear Information System (INIS)

2001-01-01

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

20. Fractional fermions

International Nuclear Information System (INIS)

Jackiw, R.; Massachusetts Inst. of Tech., Cambridge; Massachusetts Inst. of Tech., Cambridge

1984-01-01

The theory of fermion fractionization due to topologically generated fermion ground states is presented. Applications to one-dimensional conductors, to the MIT bag, and to the Hall effect are reviewed. (author)

1. Handbook of continued fractions for special functions

CERN Document Server

Cuyt, Annie

2008-01-01

Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, the Handbook of mathematical functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 00

2. Fractional hydrodynamic equations for fractal media

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2005-01-01

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

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

OpenAIRE

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

2017-01-01

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

4. Some comparison of two fractional oscillators

International Nuclear Information System (INIS)

Kang Yonggang; Zhang Xiu'e

2010-01-01

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

5. Mystery Fractions

Science.gov (United States)

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…

6. Toward lattice fractional vector calculus

Science.gov (United States)

Tarasov, Vasily E.

2014-09-01

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

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

Directory of Open Access Journals (Sweden)

M. L. Kavvas

2017-10-01

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

8. Estimation of the bio-accessible fraction of Cr, As, Cd and Pb in locally available bread using on-line continuous leaching method coupled to inductively coupled plasma mass spectrometry.

Science.gov (United States)

Lamsal, Ram P; Beauchemin, Diane

2015-03-31

9. A Fractionally Integrated Wishart Stochastic Volatility Model

NARCIS (Netherlands)

M. Asai (Manabu); M.J. McAleer (Michael)

2013-01-01

textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of

10. Fractional vector calculus for fractional advection dispersion

Science.gov (United States)

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

2006-07-01

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

11. Fractional Schroedinger equation

International Nuclear Information System (INIS)

2002-01-01

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

OpenAIRE

Bergstra, Jan A.

2015-01-01

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

13. Impact of early, late, and no ST-segment resolution measured by continuous ST Holter monitoring on left ventricular ejection fraction and infarct size as determined by cardiovascular magnetic resonance imaging

NARCIS (Netherlands)

Haeck, Joost D. E.; Verouden, Niels J. W.; Kuijt, Wichert J.; Koch, Karel T.; Majidi, Mohamed; Hirsch, Alexander; Tijssen, Jan G. P.; Krucoff, Mitchell W.; de Winter, Robbert J.

2011-01-01

Background: The goal of this study is to determine the predictive value of ST-segment resolution (STR) early after percutaneous coronary intervention (PCI), late STR, and no STR for left ventricular ejection fraction (LVEF) and infarct size (IS) by cardiovascular magnetic resonance (CMR) at

14. Fractional Vector Calculus and Fractional Special Function

OpenAIRE

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

2010-01-01

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

15. Toward lattice fractional vector calculus

International Nuclear Information System (INIS)

Tarasov, Vasily E

2014-01-01

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

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

KAUST Repository

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

2015-01-01

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

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

KAUST Repository

N'Doye, Ibrahima

2015-07-01

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

18. Fractional quantum mechanics

CERN Document Server

2018-01-01

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

19. Fractional vector calculus and fractional Maxwell's equations

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2008-01-01

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

20. Fractional statistics and fractional quantized Hall effect

International Nuclear Information System (INIS)

Tao, R.; Wu, Y.S.

1985-01-01

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

1. 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.

2. Fractional Charge Definitions and Conditions

International Nuclear Information System (INIS)

Goldhaber, A.S.

2004-01-01

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

3. Initialized Fractional Calculus

Science.gov (United States)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

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

4. On the Conformable Fractional Quantum Mechanics

Science.gov (United States)

Mozaffari, F. S.; Hassanabadi, H.; Sobhani, H.; Chung, W. S.

2018-05-01

In this paper, a conformable fractional quantum mechanic has been introduced using three postulates. Then in such a formalism, Schr¨odinger equation, probability density, probability flux and continuity equation have been derived. As an application of considered formalism, a fractional-radial harmonic oscillator has been considered. After obtaining its wave function and energy spectrum, effects of the conformable fractional parameter on some quantities have been investigated and plotted for different excited states.

5. Tempered fractional calculus

Energy Technology Data Exchange (ETDEWEB)

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

2015-07-15

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

6. Tempered fractional calculus

Science.gov (United States)

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

2015-07-01

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

7. Tempered fractional calculus

International Nuclear Information System (INIS)

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

2015-01-01

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

8. Higher fractions theory of fractional hall effect

International Nuclear Information System (INIS)

1985-07-01

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

9. Continuous auditing & continuous monitoring : Continuous value?

NARCIS (Netherlands)

van Hillo, Rutger; Weigand, Hans; Espana, S; Ralyte, J; Souveyet, C

2016-01-01

Advancements in information technology, new laws and regulations and rapidly changing business conditions have led to a need for more timely and ongoing assurance with effectively working controls. Continuous Auditing (CA) and Continuous Monitoring (CM) technologies have made this possible by

10. 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.

11. Hidratación oral continua o a dosis fraccionadas en niños deshidratados por diarrea aguda Oral rehydration in continuous administration or in fractionated doses in dehydrated children with acute diarrhea

Directory of Open Access Journals (Sweden)

Felipe Mota-Hernández

2002-01-01

12. Fractional charge definitions and conditions

International Nuclear Information System (INIS)

Goldhaber, Alfred Scharff

2003-01-01

The phenomenon of fractional charge has come to prominence in recent decades through theoretical and experimental discoveries of isolable objects which carry fractions of familiar charge units--electric charge Q, spin S, baryon number B and lepton number L. It is shown here on the basis of a few simple assumptions that all these effects may be described using a generalized version of charge renormalization for locally conserved charges, in which many-body correlations can produce familiar adiabatic, continuous renormalization, and in some circumstances nonadiabatic, discrete renormalization. The fractional charges may be carried either by fundamental particles or by fundamental solitons. This excludes nontopological solitons and also skyrmions: The only known fundamental solitons in three or fewer space dimensions d are the kink (d=1), the vortex (d=2), and the magnetic monopole (d=3). Further, for a charge which is not intrinsically coupled to the topological charge of a soliton, only the kink and the monopole may carry fractional values. The same reasoning enforces fractional local values of B-L for electrically charged elementary particles

13. Asphalt chemical fractionation

International Nuclear Information System (INIS)

Obando P, Klever N.

1998-01-01

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

14. Fractional smith chart theory

KAUST Repository

Shamim, Atif

2011-03-01

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

15. The Initial Conditions of Fractional Calculus

International Nuclear Information System (INIS)

Trigeassou, J. C.; Maamri, N.

2011-01-01

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

16. Fractional factorial plans

CERN Document Server

Dey, Aloke

2009-01-01

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

17. Fractional Dynamics and Control

CERN Document Server

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...

18. Simultaneous measurement of cerebral blood flow and oxygen extraction fraction by positron emission tomography: theoretical study and experimental evidence of cerebral blood flow measurement with the C15O2 continuous inhalation technique

International Nuclear Information System (INIS)

Steinling, M.

1983-01-01

The method of the continuous inhalation technique of oxygen-15 labelled CO 2 coupled with positron emission tomography for the measurement of cerebral blood flow (C.B.F.) is described. An indirect experimental verification that this technique allowed the measurement of C.B.F. has been carried out in baboons by showing the expected change in the measured parameter with variations in the PaCO 2 . A critical investigation of the C 15 O 2 model was performed. The amount of tracer present in the cerebral vascular pool has a negligible effect on C.B.F. value. The use of a mean brain-blood partition coefficient of water instead of that specific to gray or to white matter is commented upon, and its influence on the final C.B.F. value is studied. Lastly, the problem of the limited diffusion of water across the blood-brain-barrier is discussed. The study of the combined effects of gray-white mixing and limited wates extraction of the C.B.F. value shows that the C 15 O 2 technique tends to understimate real C.B.F., and that this error is more severe with high flows and even gray white mixing. These limitations do not depart from the possibility to estimate in the same brain locus not only C.B.F. but oxygen utilization as well by the consecutive inhalation of C 15 O 2 and 15 O 2 . The advantages of this possibility has already been shown in a number of clinical studies [fr

19. Continuous Problem of Function Continuity

Science.gov (United States)

Jayakody, Gaya; Zazkis, Rina

2015-01-01

We examine different definitions presented in textbooks and other mathematical sources for "continuity of a function at a point" and "continuous function" in the context of introductory level Calculus. We then identify problematic issues related to definitions of continuity and discontinuity: inconsistency and absence of…

20. Dividing Fractions: A Pedagogical Technique

Science.gov (United States)

Lewis, Robert

2016-01-01

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

1. What next in fractionated radiotherapy

International Nuclear Information System (INIS)

Fowler, J.F.

1984-01-01

Trends in models for predicting the total dose required to produce tolerable normal-tissue injury can be seen by the progression from the ''cube root law'', through Strandqvist's slope of 0.22, to NSD, TDF and CRE which have separate time and fraction number exponents, to even better approximations now available. The dose-response formulae that can be used to define the effect of fraction size (and number) include (1) the linear quadratic (LQ) model (2) the two-component (TC) multi-target model and (3) repair-misrepair models. The LQ model offers considerable convenience, requires only two parameters to be determined, and emphasizes the difference between late and early normal-tissue dependence on dose per fraction first shown by exponents greater than the NSD slope of 0.24. Exponents of overall time, e.g. Tsup(0.11), yield the wrong shape of time curve, suggesting that most proliferating occurs early, although it really occurs after a delay depending on the turnover time of the tissue. Improved clinical results are being sought by hyperfractionation, accelerated fractionation, or continuous low dose rate irradiation as in interstitial implants. (U.K.)

2. 40 CFR 1065.365 - Nonmethane cutter penetration fractions.

Science.gov (United States)

2010-07-01

... fractions. 1065.365 Section 1065.365 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED... Measurements § 1065.365 Nonmethane cutter penetration fractions. (a) Scope and frequency. If you use a FID... penetration fractions of methane, PFCH4, and ethane, PF C2H6. As detailed in this section, these penetration...

3. 19 CFR 159.3 - Rounding of fractions.

Science.gov (United States)

2010-04-01

... 19 Customs Duties 2 2010-04-01 2010-04-01 false Rounding of fractions. 159.3 Section 159.3 Customs... (CONTINUED) LIQUIDATION OF DUTIES General Provisions § 159.3 Rounding of fractions. (a) Value. In the... cents or more, the lower fractions shall be dropped, and if it is necessary to take up as whole dollars...

4. 7 CFR 1405.2 - Basic rule of fractions.

Science.gov (United States)

2010-01-01

... 7 Agriculture 10 2010-01-01 2010-01-01 false Basic rule of fractions. 1405.2 Section 1405.2 Agriculture Regulations of the Department of Agriculture (Continued) COMMODITY CREDIT CORPORATION, DEPARTMENT... rule of fractions. Fractions shall be rounded in accordance with the provisions of 7 CFR part 718. ...

5. 7 CFR 718.5 - Rule of fractions.

Science.gov (United States)

2010-01-01

... 7 Agriculture 7 2010-01-01 2010-01-01 false Rule of fractions. 718.5 Section 718.5 Agriculture Regulations of the Department of Agriculture (Continued) FARM SERVICE AGENCY, DEPARTMENT OF AGRICULTURE FARM... General Provisions § 718.5 Rule of fractions. (a) Fractions shall be rounded after completion of the...

6. Fractional distillation of oil

Energy Technology Data Exchange (ETDEWEB)

Jones, L D

1931-10-31

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

7. 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....

8. Fractional Poisson process (II)

International Nuclear Information System (INIS)

Wang Xiaotian; Wen Zhixiong; Zhang Shiying

2006-01-01

In this paper, we propose a stochastic process W H (t)(H-bar (12,1)) which we call fractional Poisson process. The process W H (t) is self-similar in wide sense, displays long range dependence, and has more fatter tail than Gaussian process. In addition, it converges to fractional Brownian motion in distribution

9. An Appetite for Fractions

Science.gov (United States)

Wilkerson, Trena L.; Bryan, Tommy; Curry, Jane

2012-01-01

This article describes how using candy bars as models gives sixth-grade students a taste for learning to represent fractions whose denominators are factors of twelve. Using paper models of the candy bars, students explored and compared fractions. They noticed fewer different representations for one-third than for one-half. The authors conclude…

10. Can Kindergartners Do Fractions?

Science.gov (United States)

Cwikla, Julie

2014-01-01

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

International Nuclear Information System (INIS)

Breunhoelder, Gert

2002-01-01

This presentation deals with the following keypoints: Information Technology (IT) Business Continuity and Recovery essential for any business; lessons learned after Sept. 11 event; Detailed planning, redundancy and testing being the key elements for probability estimation of disasters

12. Fractional bosonic strings

Science.gov (United States)

Diaz, Victor Alfonzo; Giusti, Andrea

2018-03-01

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

13. Continuous tokamaks

International Nuclear Information System (INIS)

Peng, Y.K.M.

1978-04-01

A tokamak configuration is proposed that permits the rapid replacement of a plasma discharge in a ''burn'' chamber by another one in a time scale much shorter than the elementary thermal time constant of the chamber first wall. With respect to the chamber, the effective duty cycle factor can thus be made arbitrarily close to unity minimizing the cyclic thermal stress in the first wall. At least one plasma discharge always exists in the new tokamak configuration, hence, a continuous tokamak. By incorporating adiabatic toroidal compression, configurations of continuous tokamak compressors are introduced. To operate continuous tokamaks, it is necessary to introduce the concept of mixed poloidal field coils, which spatially groups all the poloidal field coils into three sets, all contributing simultaneously to inducing the plasma current and maintaining the proper plasma shape and position. Preliminary numerical calculations of axisymmetric MHD equilibria in continuous tokamaks indicate the feasibility of their continued plasma operation. Advanced concepts of continuous tokamaks to reduce the topological complexity and to allow the burn plasma aspect ratio to decrease for increased beta are then suggested

14. Convergence criterion for branched contіnued fractions of the special form with positive elements

Directory of Open Access Journals (Sweden)

D. I. Bodnar

2017-07-01

Full Text Available In this paper the problem of convergence of the important type of a multidimensional generalization of continued fractions, the branched continued fractions with independent variables, is considered. This fractions are an efficient apparatus for the approximation of multivariable functions, which are represented by multiple power series. When variables are fixed these fractions are called the branched continued fractions of the special form. Their structure is much simpler then the structure of general branched continued fractions. It has given a possibility to establish the necessary and sufficient conditions of convergence of branched continued fractions of the special form with the positive elements. The received result is the multidimensional analog of Seidel's criterion for the continued fractions. The condition of convergence of investigated fractions is the divergence of series, whose elements are continued fractions. Therefore, the sufficient condition of the convergence of this fraction which has been formulated by the divergence of series composed of partial denominators of this fraction, is established. Using the established criterion and Stieltjes-Vitali Theorem the parabolic theorems of branched continued fractions of the special form with complex elements convergence, is investigated. The sufficient conditions gave a possibility to make the condition of convergence of the branched continued fractions of the special form, whose elements lie in parabolic domains.

15. Continuous Dropout.

Science.gov (United States)

Shen, Xu; Tian, Xinmei; Liu, Tongliang; Xu, Fang; Tao, Dacheng

2017-10-03

Dropout has been proven to be an effective algorithm for training robust deep networks because of its ability to prevent overfitting by avoiding the co-adaptation of feature detectors. Current explanations of dropout include bagging, naive Bayes, regularization, and sex in evolution. According to the activation patterns of neurons in the human brain, when faced with different situations, the firing rates of neurons are random and continuous, not binary as current dropout does. Inspired by this phenomenon, we extend the traditional binary dropout to continuous dropout. On the one hand, continuous dropout is considerably closer to the activation characteristics of neurons in the human brain than traditional binary dropout. On the other hand, we demonstrate that continuous dropout has the property of avoiding the co-adaptation of feature detectors, which suggests that we can extract more independent feature detectors for model averaging in the test stage. We introduce the proposed continuous dropout to a feedforward neural network and comprehensively compare it with binary dropout, adaptive dropout, and DropConnect on Modified National Institute of Standards and Technology, Canadian Institute for Advanced Research-10, Street View House Numbers, NORB, and ImageNet large scale visual recognition competition-12. Thorough experiments demonstrate that our method performs better in preventing the co-adaptation of feature detectors and improves test performance.

16. Fractional Order Generalized Information

Directory of Open Access Journals (Sweden)

2014-04-01

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

17. Fractional finite Fourier transform.

Science.gov (United States)

Khare, Kedar; George, Nicholas

2004-07-01

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

18. 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....

19. Continuity theory

CERN Document Server

Nel, Louis

2016-01-01

This book presents a detailed, self-contained theory of continuous mappings. It is mainly addressed to students who have already studied these mappings in the setting of metric spaces, as well as multidimensional differential calculus. The needed background facts about sets, metric spaces and linear algebra are developed in detail, so as to provide a seamless transition between students' previous studies and new material. In view of its many novel features, this book will be of interest also to mature readers who have studied continuous mappings from the subject's classical texts and wish to become acquainted with a new approach. The theory of continuous mappings serves as infrastructure for more specialized mathematical theories like differential equations, integral equations, operator theory, dynamical systems, global analysis, topological groups, topological rings and many more. In light of the centrality of the topic, a book of this kind fits a variety of applications, especially those that contribute to ...

20. FRACTIONS: CONCEPTUAL AND DIDACTIC ASPECTS

Directory of Open Access Journals (Sweden)

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.

1. Fractional Stochastic Field Theory

Science.gov (United States)

Honkonen, Juha

2018-02-01

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

2. Discrete fractional calculus

CERN Document Server

Goodrich, Christopher

2015-01-01

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

3. Fractional smith chart theory

KAUST Repository

Shamim, Atif; Radwan, Ahmed Gomaa; Salama, Khaled N.

2011-01-01

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.

4. Continuation calculus

NARCIS (Netherlands)

Geron, B.; Geuvers, J.H.; de'Liguoro, U.; Saurin, A.

2013-01-01

Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic model of computation that is evaluated using only head

Science.gov (United States)

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

2011-12-01

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

6. Fractional laser skin resurfacing.

Science.gov (United States)

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

2012-11-01

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

7. Continuation calculus

Directory of Open Access Journals (Sweden)

Bram Geron

2013-09-01

Full Text Available Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic model of computation that is evaluated using only head reduction, and argue that it is suitable for modeling programs with control. It is demonstrated how to define programs, specify them, and prove them correct. This is shown in detail by presenting in CC a list multiplication program that prematurely returns when it encounters a zero. The correctness proof includes termination of the program. In continuation calculus we can model both call-by-name and call-by-value. In addition, call-by-name functions can be applied to call-by-value results, and conversely.

8. Series expansion in fractional calculus and fractional differential equations

OpenAIRE

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

2009-01-01

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

9. The Fractional Orthogonal Difference with Applications

Directory of Open Access Journals (Sweden)

Enno Diekema

2015-06-01

Full Text Available This paper is a follow-up of a previous paper of the author published in Mathematics journal in 2015, which treats the so-called continuous fractional orthogonal derivative. In this paper, we treat the discrete case using the fractional orthogonal difference. The theory is illustrated with an application of a fractional differentiating filter. In particular, graphs are presented of the absolutel value of the modulus of the frequency response. These make clear that for a good insight into the behavior of a fractional differentiating filter, one has to look for the modulus of its frequency response in a log-log plot, rather than for plots in the time domain.

International Nuclear Information System (INIS)

1996-01-01

Patients with advanced lung cancers have bad prognosis and, many times, are submitted to prolonged and not always efficient treatments. We present a study where 51 patients were treated with hypo fractionated radiotherapy, based on two distinct schemes, according to the performance status and social conditions of each patient: continuous treatment: 30 Gy, 10 fractions of 3 Gy, 5 days/week (37 cases); weekly treatment: 30 Gy, 6 fractions of 5 Gy, once a week (14 cases). Symptoms relief and impact in survival were evaluated. In both groups, we observed improvement of symptoms in about 70% of the occurrences with a medium survival of three months. We conclude that hypo fractionation is an effective palliative treatment for lung cancers, in patients with short life-expectancy and must be considered as a option in advanced cases, in patients with short life-expectancy that deserve some kind of treatment. (author). 37 refs., 2 tabs

11. Software quality assurance plan for void fraction instrument

International Nuclear Information System (INIS)

Gimera, M.

1994-01-01

Waste Tank SY-101 has been the focus of extensive characterization work over the past few years. The waste continually generates gases, most notably hydrogen, which are periodically released from the waste. Gas can be trapped in tank waste in three forms: as void gas (bubbles), dissolved gas, or absorbed gas. Void fraction is the volume percentage of a given sample that is comprised of void gas. The void fraction instrument (VFI) acquires the data necessary to calculate void fraction. This document covers the product, Void Fraction Data Acquisition Software. The void fraction software being developed will have the ability to control the void fraction instrument hardware and acquire data necessary to calculate the void fraction in samples. This document provides the software quality assurance plan, verification and validation plan, and configuration management plan for developing the software for the instrumentation that will be used to obtain void fraction data from Tank SY-101

12. Multiparticle quantum mechanics obeying fractional statistics

International Nuclear Information System (INIS)

Wu, Y.

1984-01-01

We obtain the rule governing many-body wave functions for particles obeying fractional statistics in two (space) dimensions. It generalizes and continuously interpolates the usual symmetrization and antisymmetrization. Quantum mechanics of more than two particles is discussed and some new features are found

13. FRACTIONS: CONCEPTUAL AND DIDACTIC ASPECTS

OpenAIRE

Sead Rešić; Ismet Botonjić; Maid Omerović

2016-01-01

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

14. Fractional-order devices

CERN Document Server

Biswas, Karabi; Caponetto, Riccardo; Mendes Lopes, António; Tenreiro Machado, José António

2017-01-01

This book focuses on two specific areas related to fractional order systems – the realization of physical devices characterized by non-integer order impedance, usually called fractional-order elements (FOEs); and the characterization of vegetable tissues via electrical impedance spectroscopy (EIS) – and provides readers with new tools for designing new types of integrated circuits. The majority of the book addresses FOEs. The interest in these topics is related to the need to produce “analogue” electronic devices characterized by non-integer order impedance, and to the characterization of natural phenomena, which are systems with memory or aftereffects and for which the fractional-order calculus tool is the ideal choice for analysis. FOEs represent the building blocks for designing and realizing analogue integrated electronic circuits, which the authors believe hold the potential for a wealth of mass-market applications. The freedom to choose either an integer- or non-integer-order analogue integrator...

OpenAIRE

D'Ovidio, M.; Garra, R.

2013-01-01

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

16. Sweet Work with Fractions

Science.gov (United States)

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…

17. Fermion Number Fractionization

Srimath

1 . In tro d u ctio n. T he N obel P rize in C hem istry for the year 2000 w as aw arded to A lan J H ... soliton, the ground state of the ferm ion-soliton system can have ..... probability density,in a heuristic w ay that a fractional ferm ion num ber m ay ...

18. Momentum fractionation on superstrata

International Nuclear Information System (INIS)

Bena, Iosif; Martinec, Emil; Turton, David; Warner, Nicholas P.

2016-01-01

Superstrata are bound states in string theory that carry D1, D5, and momentum charges, and whose supergravity descriptions are parameterized by arbitrary functions of (at least) two variables. In the D1-D5 CFT, typical three-charge states reside in high-degree twisted sectors, and their momentum charge is carried by modes that individually have fractional momentum. Understanding this momentum fractionation holographically is crucial for understanding typical black-hole microstates in this system. We use solution-generating techniques to add momentum to a multi-wound supertube and thereby construct the first examples of asymptotically-flat superstrata. The resulting supergravity solutions are horizonless and smooth up to well-understood orbifold singularities. Upon taking the AdS_3 decoupling limit, our solutions are dual to CFT states with momentum fractionation. We give a precise proposal for these dual CFT states. Our construction establishes the very nontrivial fact that large classes of CFT states with momentum fractionation can be realized in the bulk as smooth horizonless supergravity solutions.

19. 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.

20. Vapor liquid fraction determination

International Nuclear Information System (INIS)

1980-01-01

This invention describes a method of measuring liquid and vapor fractions in a non-homogeneous fluid flowing through an elongate conduit, such as may be required with boiling water, non-boiling turbulent flows, fluidized bed experiments, water-gas mixing analysis, and nuclear plant cooling. (UK)

1. Brewing with fractionated barley

NARCIS (Netherlands)

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

2. Fractionation and rectification apparatus

Energy Technology Data Exchange (ETDEWEB)

Sauerwald, A

1932-05-25

Fractionation and rectifying apparatus with a distillation vessel and a stirring tube, drainage tubes leading from its coils to a central collecting tube, the drainage tubes being somewhat parallel and attached to the outer half of the stirring tube and partly on the inner half of the central collecting tube, whereby distillation and rectification can be effected in a single apparatus.

3. Fractional charge search

International Nuclear Information System (INIS)

Innes, W.; Klein, S.; Perl, M.; Price, J.C.

1982-06-01

A device to search for fractional charge in matter is described. The sample is coupled to a low-noise amplifier by a periodically varying capacitor and the resulting signal is synchronously detected. The varying capacitor is constructed as a rapidly spinning wheel. Samples of any material in volumes of up to 0.05 ml may be searched in less than an hour

4. Alternative Forms of Compound Fractional Poisson Processes

Directory of Open Access Journals (Sweden)

Luisa Beghin

2012-01-01

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

5. Fractional Fick's law: the direct way

International Nuclear Information System (INIS)

Neel, M C; Abdennadher, A; Joelson, M

2007-01-01

Levy flights, which are Markovian continuous time random walks possibly accounting for extreme events, serve frequently as small-scale models for the spreading of matter in heterogeneous media. Among them, Brownian motion is a particular case where Fick's law holds: for a cloud of walkers, the flux is proportional to the gradient of the probability density of finding a particle at some place. Levy flights resemble Brownian motion, except that jump lengths are distributed according to an α-stable Levy law, possibly showing heavy tails and skewness. For α between 1 and 2, a fractional form of Fick's law is known to hold in infinite media: that the flux is proportional to a combination of fractional derivatives or the order of α - 1 of the density of walkers was obtained as a consequence of a fractional dispersion equation. We present a direct and natural proof of this result, based upon a novel definition of usual fractional derivatives, involving a convolution and a limiting process. Taking account of the thus obtained fractional Fick's law yields fractional dispersion equation for smooth densities. The method adapts to domains, limited by boundaries possibly implying non-trivial modifications to this equation

6. -Dimensional Fractional Lagrange's Inversion Theorem

Directory of Open Access Journals (Sweden)

F. A. Abd El-Salam

2013-01-01

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

7. Gauge invariant fractional electromagnetic fields

International Nuclear Information System (INIS)

Lazo, Matheus Jatkoske

2011-01-01

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

8. Gauge invariant fractional electromagnetic fields

Energy Technology Data Exchange (ETDEWEB)

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

2011-09-26

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

9. On matrix fractional differential equations

Directory of Open Access Journals (Sweden)

2017-01-01

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

10. On stability of fixed points and chaos in fractional systems

Science.gov (United States)

Edelman, Mark

2018-02-01

In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0 logistic maps. Based on our analysis, we make a conjecture that chaos is impossible in the corresponding continuous fractional systems.

11. The fundamental solutions for fractional evolution equations of parabolic type

Directory of Open Access Journals (Sweden)

Mahmoud M. El-Borai

2004-01-01

Full Text Available The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is given as an application.

12. On stability of fixed points and chaos in fractional systems.

Science.gov (United States)

Edelman, Mark

2018-02-01

In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0chaos is impossible in the corresponding continuous fractional systems.

13. The Local Fractional Bootstrap

DEFF Research Database (Denmark)

Bennedsen, Mikkel; Hounyo, Ulrich; Lunde, Asger

We introduce a bootstrap procedure for high-frequency statistics of Brownian semistationary processes. More specifically, we focus on a hypothesis test on the roughness of sample paths of Brownian semistationary processes, which uses an estimator based on a ratio of realized power variations. Our...... 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...

14. Fractionalization and Entrepreneurial Activities

OpenAIRE

Awaworyi Churchill, Sefa

2015-01-01

The vast majority of the literature on ethnicity and entrepreneurship focuses on the construct of ethnic entrepreneurship. However, very little is known about how ethnic heterogeneity affects entrepreneurship. This study attempts to fill the gap, and thus examines the effect of ethnic heterogeneity on entrepreneurial activities in a cross-section of 90 countries. Using indices of ethnic and linguistic fractionalization, we show that ethnic heterogeneity negatively influences entrepreneurship....

15. Fractional Number Operator and Associated Fractional Diffusion Equations

Science.gov (United States)

Rguigui, Hafedh

2018-03-01

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

16. Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries.

Science.gov (United States)

Jeon, Jae-Hyung; Metzler, Ralf

2010-02-01

Motivated by subdiffusive motion of biomolecules observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time-averaged mean-squared displacement and displacement correlation) are affected by spatial confinement and dimensionality. In particular, we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain. The general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality. We define the displacement correlation function and find that this quantity shows distinct features for fractional Brownian motion, fractional Langevin equation, and continuous time subdiffusion, such that it appears an efficient measure to distinguish these different processes based on single-particle trajectory data.

17. Gauge invariant fractional electromagnetic fields

Science.gov (United States)

Lazo, Matheus Jatkoske

2011-09-01

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

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

OpenAIRE

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

2012-01-01

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

19. Content knowledge of prospective elementary school teacher for fractional concepts

Science.gov (United States)

Pattimukay, N.; Juniati, D.; Budiarto, M. T.

2018-03-01

The aim of this study was to describe the content knowledge especially the concept of fraction of prospective elementary school teacher. The purpose of this study is to describe the content knowledge, especially the concept of fraction of prospective elementary school teacher. The subject of the study was one of prospective elementary school teacher of Pattimura University. This research is qualitative research. Data were collected through the provision of tests to explore the knowledge content of primary school teacher candidates about fractional concepts. Then continued with qualitative data analysis. The results of this study are as follows: that the prospective primary school teacher defines fractions as part of the whole if an object is divided into equal parts, so that the part that has been divided is part of the whole. Furthermore, the prospective elementary school teacher understood the fractions as division shown in two ways, namely the prospective elementary school teacher understood the fraction as a division operation, the primary school teacher candidate interpreted the fraction as a division when an object is divided be part of the same. Meanwhile, the fraction as a ratio is interpreted as the relationship between a pair of numbers. Then, the denominations are interpreted as a ratio between the numerator and the denominator of the same value. The prospective elementary school teacher also understands fractions of value when simplifying fractions. Primary school teacher candidates understand the concept of fractional operations.

20. Functional Fractional Calculus

CERN Document Server

Das, Shantanu

2011-01-01

When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with 'ordinary' differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematic

1. Fractional Reserve Banking

OpenAIRE

Andreasen, Niels; Bjerregaard, Mads; Lund, Jonas; Olsen, Ove Bitsch; Rasmussen, Andreas Dalgas

2012-01-01

Projektet er bygget op omkring kritisk realisme, som er det gennemgående videnskabelige fundament til undersøgelsen af hvilke strukturelle grunde der er til finansiel ustabilitet i Danmark. Projektet går i dybden med Fractional Reserve Banking og incitamentsstrukturen i banksystemet. Vi bevæger os både på det makro- og mikroøkonomiske niveau i analysen. På makro niveau bruger vi den østrigske skole om konjunktur teori (The Positive Theory of the Cycle). På mikro niveau arbejder vi med princip...

2. Plasma fractionation issues.

Science.gov (United States)

Farrugia, Albert; Evers, Theo; Falcou, Pierre-Francois; Burnouf, Thierry; Amorim, Luiz; Thomas, Sylvia

2009-04-01

Procurement and processing of human plasma for fractionation of therapeutic proteins or biological medicines used in clinical practice is a multi-billion dollar international trade. Together the private sector and public sector (non-profit) provide large amounts of safe and effective therapeutic plasma proteins needed worldwide. The principal therapeutic proteins produced by the dichotomous industry include gamma globulins or immunoglobulins (including pathogen-specific hyperimmune globulins, such as hepatitis B immune globulins) albumin, factor VIII and Factor IX concentrates. Viral inactivation, principally by solvent detergent and other processes, has proven highly effective in preventing transmission of enveloped viruses, viz. HBV, HIV, and HCV.

3. Continuous monitoring of gaseous effluents

International Nuclear Information System (INIS)

Velasco, A.; Giraut, H.; Prado, M.; Bonino, A.D.

1990-01-01

The system allows to continuously determine the radioactive materials discharge (iodine, noble gases and aerosols) to the environment. It consists in compelling, by a pump, a known and fixed fraction of the total flow and preserving the aerosols by a filter. The gas -now free from aerosols- traverses an activated carbon filter which keeps the iodine; after being free from aerosols and iodine, the effluent traverses a measurement chambers for noble gases which has a scintillator. (Author) [es

4. On some generalization of fractional Brownian motions

International Nuclear Information System (INIS)

Wang Xiaotian; Liang Xiangqian; Ren Fuyao; Zhang Shiying

2006-01-01

The multifractional Brownian motion (mBm) is a continuous Gaussian process that extends the classical fractional Brownian motion (fBm) defined by Barton and Vincent Poor [Barton RJ, Vincent Poor H. IEEE Trans Inform 1988;34(5):943] and Decreusefond and Ustuenel [Decreusefond L, Ustuenel AS. Potential Anal 1999;10:177]. In addition, an innovational representation of fBm is given

5. Advances in robust fractional control

CERN Document Server

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...

6. Search for fractional charge

International Nuclear Information System (INIS)

Turner, R.E.

1984-01-01

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

7. Fractional Reserve in Banking System

OpenAIRE

Valkonen, Maria

2016-01-01

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

8. On matrix fractional differential equations

OpenAIRE

2017-01-01

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

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

Science.gov (United States)

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

2017-10-01

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

10. How Weird Are Weird Fractions?

Science.gov (United States)

Stuffelbeam, Ryan

2013-01-01

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

11. Do Children Understand Fraction Addition?

Science.gov (United States)

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

2017-01-01

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

12. On fractional Fourier transform moments

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.

2000-01-01

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

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

CERN Document Server

Georgiev, Svetlin G

2018-01-01

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

14. Implementation of quantum and classical discrete fractional Fourier transforms

Science.gov (United States)

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

2016-01-01

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089

15. Implementation of quantum and classical discrete fractional Fourier transforms.

Science.gov (United States)

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander

2016-03-23

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

16. Electronic realization of the fractional-order systems

Directory of Open Access Journals (Sweden)

Františka Dorčáková

2007-10-01

Full Text Available This article is devoted to the electronic (analogue realization of the fractional-order systems – controllers or controlled objects whose we earlier used, identified, and analyzed as a mathematical models only ��� namely a fractional-order differential equation, and solved numerically using a method based on the truncated version of the Grunwald - Letnikov formula for fractional derivative. The electronic realization of the fractional derivative is based on the continued fraction expansion of the rational approximation of the fractional differentiator from which we obtained the values of the resistors and capacitors of the electronic circuit. Along with the mathematical description are presented also simulation and measurement results.

17. Nonhomogeneous fractional Poisson processes

Energy Technology Data Exchange (ETDEWEB)

Wang Xiaotian [School of Management, Tianjin University, Tianjin 300072 (China)]. E-mail: swa001@126.com; Zhang Shiying [School of Management, Tianjin University, Tianjin 300072 (China); Fan Shen [Computer and Information School, Zhejiang Wanli University, Ningbo 315100 (China)

2007-01-15

In this paper, we propose a class of non-Gaussian stationary increment processes, named nonhomogeneous fractional Poisson processes W{sub H}{sup (j)}(t), which permit the study of the effects of long-range dependance in a large number of fields including quantum physics and finance. The processes W{sub H}{sup (j)}(t) are self-similar in a wide sense, exhibit more fatter tail than Gaussian processes, and converge to the Gaussian processes in distribution in some cases. In addition, we also show that the intensity function {lambda}(t) strongly influences the existence of the highest finite moment of W{sub H}{sup (j)}(t) and the behaviour of the tail probability of W{sub H}{sup (j)}(t)

18. Nonhomogeneous fractional Poisson processes

International Nuclear Information System (INIS)

Wang Xiaotian; Zhang Shiying; Fan Shen

2007-01-01

In this paper, we propose a class of non-Gaussian stationary increment processes, named nonhomogeneous fractional Poisson processes W H (j) (t), which permit the study of the effects of long-range dependance in a large number of fields including quantum physics and finance. The processes W H (j) (t) are self-similar in a wide sense, exhibit more fatter tail than Gaussian processes, and converge to the Gaussian processes in distribution in some cases. In addition, we also show that the intensity function λ(t) strongly influences the existence of the highest finite moment of W H (j) (t) and the behaviour of the tail probability of W H (j) (t)

19. Membrane Assisted Enzyme Fractionation

DEFF Research Database (Denmark)

Yuan, Linfeng

to the variation in size of the proteins and a reasonable separation factor can be observed only when the size difference is in the order of 10 or more. This is partly caused by concentration polarization and membrane fouling which hinders an effective separation of the proteins. Application of an electric field...... across the porous membrane has been demonstrated to be an effective way to reduce concentration polarization and membrane fouling. In addition, this technique can also be used to separate the proteins based on difference in charge, which to some extent overcome the limitations of size difference...... 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...

20. Fraction Reduction in Membrane Systems

Directory of Open Access Journals (Sweden)

Ping Guo

2014-01-01

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

1. Thermochemical transformations of anthracite fractions

Energy Technology Data Exchange (ETDEWEB)

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

1979-08-01

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

2. Efeitos de diferentes frações inspiradas de oxigênio no índice biespectral em cães submetidos à infusão contínua de propofol Effects of several inspired oxygen fractions on the bispectral index in dogs submitted to continuous infusion of propofol

Directory of Open Access Journals (Sweden)

P.C.F. Lopes

2008-04-01

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

International Nuclear Information System (INIS)

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

1980-01-01

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

4. Continuous limit of discrete systems with long-range interaction

International Nuclear Information System (INIS)

Tarasov, Vasily E

2006-01-01

Discrete systems with long-range interactions are considered. Continuous medium models as continuous limit of discrete chain system are defined. Long-range interactions of chain elements that give the fractional equations for the medium model are discussed. The chain equations of motion with long-range interaction are mapped into the continuum equation with the Riesz fractional derivative. We formulate the consistent definition of continuous limit for the systems with long-range interactions. In this paper, we consider a wide class of long-range interactions that give fractional medium equations in the continuous limit. The power-law interaction is a special case of this class

5. Fractional statistics and fractional quantized Hall effect. Revision

International Nuclear Information System (INIS)

Tao, R.; Wu, Y.S.

1984-01-01

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

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

Science.gov (United States)

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

2017-11-01

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

7. Fractional variational calculus in terms of Riesz fractional derivatives

International Nuclear Information System (INIS)

Agrawal, O P

2007-01-01

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

8. Modelling altered fractionation schedules

International Nuclear Information System (INIS)

Fowler, J.F.

1993-01-01

The author discusses the conflicting requirements of hyperfractionation and accelerated fractionation used in radiotherapy, and the development of computer modelling to predict how to obtain an optimum of tumour cell kill without exceeding normal-tissue tolerance. The present trend is to shorten hyperfractionated schedules from 6 or 7 weeks to give overall times of 4 or 5 weeks as in new schedules by Herskovic et al (1992) and Harari (1992). Very high doses are given, much higher than can be given when ultrashort schedules such as CHART (12 days) are used. Computer modelling has suggested that optimum overall times, to yield maximum cell kill in tumours ((α/β = 10 Gy) for a constant level of late complications (α/β = 3 Gy) would be X or X-1 weeks, where X is the doubling time of the tumour cells in days (Fowler 1990). For median doubling times of about 5 days, overall times of 4 or 5 weeks should be ideal. (U.K.)

9. Between strong continuity and almost continuity

Directory of Open Access Journals (Sweden)

J.K. Kohli

2010-04-01

Full Text Available As embodied in the title of the paper strong and weak variants of continuity that lie strictly between strong continuity of Levine and almost continuity due to Singal and Singal are considered. Basic properties of almost completely continuous functions (≡ R-maps and δ-continuous functions are studied. Direct and inverse transfer of topological properties under almost completely continuous functions and δ-continuous functions are investigated and their place in the hier- archy of variants of continuity that already exist in the literature is out- lined. The class of almost completely continuous functions lies strictly between the class of completely continuous functions studied by Arya and Gupta (Kyungpook Math. J. 14 (1974, 131-143 and δ-continuous functions defined by Noiri (J. Korean Math. Soc. 16, (1980, 161-166. The class of almost completely continuous functions properly contains each of the classes of (1 completely continuous functions, and (2 al- most perfectly continuous (≡ regular set connected functions defined by Dontchev, Ganster and Reilly (Indian J. Math. 41 (1999, 139-146 and further studied by Singh (Quaestiones Mathematicae 33(2(2010, 1–11 which in turn include all δ-perfectly continuous functions initi- ated by Kohli and Singh (Demonstratio Math. 42(1, (2009, 221-231 and so include all perfectly continuous functions introduced by Noiri (Indian J. Pure Appl. Math. 15(3 (1984, 241-250.

10. 29 CFR 4211.4 - Contributions for purposes of the numerator and denominator of the allocation fractions.

Science.gov (United States)

2010-07-01

... of the allocation fractions. 4211.4 Section 4211.4 Labor Regulations Relating to Labor (Continued... denominator of the allocation fractions. Each of the allocation fractions used in the presumptive, modified... five-year period. (a) The numerator of the allocation fraction, with respect to a withdrawing employer...

11. Accessible solitons of fractional dimension

Energy Technology Data Exchange (ETDEWEB)

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

2016-05-15

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

12. Fractional Calculus and Shannon Wavelet

Directory of Open Access Journals (Sweden)

Carlo Cattani

2012-01-01

Full Text Available An explicit analytical formula for the any order fractional derivative of Shannon wavelet is given as wavelet series based on connection coefficients. So that for any 2(ℝ function, reconstructed by Shannon wavelets, we can easily define its fractional derivative. The approximation error is explicitly computed, and the wavelet series is compared with Grünwald fractional derivative by focusing on the many advantages of the wavelet method, in terms of rate of convergence.

13. Fractional variational principles in action

Energy Technology Data Exchange (ETDEWEB)

Baleanu, Dumitru [Department of Mathematics and Computer Science, Faculty of Art and Sciences, Cankaya University, 06530 Ankara (Turkey); Institute of Space Sciences, PO Box MG-23, R 76900, Magurele-Bucharest (Romania)], E-mail: dumitru@cankaya.edu.tr

2009-10-15

The fractional calculus has gained considerable importance in various fields of science and engineering, especially during the last few decades. An open issue in this emerging field is represented by the fractional variational principles area. Therefore, the fractional Euler-Lagrange and Hamilton equations started to be examined intensely during the last decade. In this paper, we review some new trends in this field and we discuss some of their potential applications.

14. Fractional quiver W-algebras

Science.gov (United States)

Kimura, Taro; Pestun, Vasily

2018-04-01

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

15. On the Fractional Mean Value

OpenAIRE

2014-01-01

This work, dealt with the classical mean value theorem and took advantage of it in the fractional calculus. The concept of a fractional critical point is introduced. Some sufficient conditions for the existence of a critical point is studied and an illustrative example rele- vant to the concept of the time dilation effect is given. The present paper also includes, some connections between convexity (and monotonicity) with fractional derivative in the Riemann-Liouville sense.

16. Continuous spinal anesthesia.

Science.gov (United States)

Moore, James M

2009-01-01

Continuous spinal anesthesia (CSA) is an underutilized technique in modern anesthesia practice. Compared with other techniques of neuraxial anesthesia, CSA allows incremental dosing of an intrathecal local anesthetic for an indefinite duration, whereas traditional single-shot spinal anesthesia usually involves larger doses, a finite, unpredictable duration, and greater potential for detrimental hemodynamic effects including hypotension, and epidural anesthesia via a catheter may produce lesser motor block and suboptimal anesthesia in sacral nerve root distributions. This review compares CSA with other anesthetic techniques and also describes the history of CSA, its clinical applications, concerns regarding neurotoxicity, and other pharmacologic implications of its use. CSA has seen a waxing and waning of its popularity in clinical practice since its initial description in 1907. After case reports of cauda equina syndrome were reported with the use of spinal microcatheters for CSA, these microcatheters were withdrawn from clinical practice in the United States but continued to be used in Europe with no further neurologic sequelae. Because only large-bore catheters may be used in the United States, CSA is usually reserved for elderly patients out of concern for the risk of postdural puncture headache in younger patients. However, even in younger patients, sometimes the unique clinical benefits and hemodynamic stability involved in CSA outweigh concerns regarding postdural puncture headache. Clinical scenarios in which CSA may be of particular benefit include patients with severe aortic stenosis undergoing lower extremity surgery and obstetric patients with complex heart disease. CSA is an underutilized technique in modern anesthesia practice. Perhaps more accurately termed fractional spinal anesthesia, CSA involves intermittent dosing of local anesthetic solution via an intrathecal catheter. Where traditional spinal anesthesia involves a single injection with a

17. Fractionated Spacecraft Architectures Seeding Study

National Research Council Canada - National Science Library

Mathieu, Charlotte; Weigel, Annalisa

2006-01-01

.... Models were developed from a customer-centric perspective to assess different fractionated spacecraft architectures relative to traditional spacecraft architectures using multi-attribute analysis...

18. Methods And Apparatus For Acoustic Fiber Fractionation

Science.gov (United States)

Brodeur, Pierre

1999-11-09

Methods and apparatus for acoustic fiber fractionation using a plane ultrasonic wave field interacting with water suspended fibers circulating in a channel flow using acoustic radiation forces to separate fibers into two or more fractions based on fiber radius, with applications of the separation concept in the pulp and paper industry. The continuous process relies on the use of a wall-mounted, rectangular cross-section piezoelectric ceramic transducer to selectively deflect flowing fibers as they penetrate the ultrasonic field. The described embodiment uses a transducer frequency of approximately 150 kHz. Depending upon the amount of dissolved gas in water, separation is obtained using a standing or a traveling wave field.

19. Fractional calculus and morphogen gradient formation

Science.gov (United States)

Yuste, Santos Bravo; Abad, Enrique; Lindenberg, Katja

2012-12-01

Some microscopic models for reactive systems where the reaction kinetics is limited by subdiffusion are described by means of reaction-subdiffusion equations where fractional derivatives play a key role. In particular, we consider subdiffusive particles described by means of a Continuous Time Random Walk (CTRW) model subject to a linear (first-order) death process. The resulting fractional equation is employed to study the developmental biology key problem of morphogen gradient formation for the case in which the morphogens are subdiffusive. If the morphogen degradation rate (reactivity) is constant, we find exponentially decreasing stationary concentration profiles, which are similar to the profiles found when the morphogens diffuse normally. However, for the case in which the degradation rate decays exponentially with the distance to the morphogen source, we find that the morphogen profiles are qualitatively different from the profiles obtained when the morphogens diffuse normally.

20. Fractional order differentiation by integration with Jacobi polynomials

KAUST Repository

Liu, Dayan

2012-12-01

The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.

1. Fractional order differentiation by integration with Jacobi polynomials

KAUST Repository

Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid; Laleg-Kirati, Taous-Meriem

2012-01-01

The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.

2. COMMERCIAL SNF ACCIDENT RELEASE FRACTIONS

Energy Technology Data Exchange (ETDEWEB)

1999-10-18

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

3. COMMERCIAL SNF ACCIDENT RELEASE FRACTIONS

International Nuclear Information System (INIS)

1999-01-01

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

4. Fractions, Number Lines, Third Graders

Science.gov (United States)

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…

5. Unwrapping Students' Ideas about Fractions

Science.gov (United States)

Lewis, Rebecca M.; Gibbons, Lynsey K.; Kazemi, Elham; Lind, Teresa

2015-01-01

Supporting students to develop an understanding of the meaning of fractions is an important goal of elementary school mathematics. This involves developing partitioning strategies, creating representations, naming fractional quantities, and using symbolic notation. This article describes how teachers can use a formative assessment problem to…

6. Understanding Magnitudes to Understand Fractions

Science.gov (United States)

Gabriel, Florence

2016-01-01

Fractions are known to be difficult to learn and difficult to teach, yet they are vital for students to have access to further mathematical concepts. This article uses evidence to support teachers employing teaching methods that focus on the conceptual understanding of the magnitude of fractions.

7. Financial Planning with Fractional Goals

OpenAIRE

Goedhart, Marc; 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 multiple goal variables. The approach is illustrated by means of an example in financial planning.

8. Deterministic ratchets for suspension fractionation

NARCIS (Netherlands)

Kulrattanarak, T.

2010-01-01

Driven by the current insights in sustainability and technological development in
biorefining natural renewable resources, the food industry has taken an interest in
fractionation of agrofood materials, like milk and cereal crops. The purpose of fractionation
is to split the raw

9. Fermion fractionization and index theorem

International Nuclear Information System (INIS)

Hirayama, Minoru; Torii, Tatsuo

1982-01-01

The relation between the fermion fractionization and the Callias-Bott-Seeley index theorem for the Dirac operator in the open space of odd dimension is clarified. Only the case of one spatial dimension is discussed in detail. Sum rules for the expectation values of various quantities in fermion-fractionized configurations are derived. (author)

10. A new fractional wavelet transform

Science.gov (United States)

Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

2017-03-01

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

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

International Nuclear Information System (INIS)

Wang Shaowei; Xu Mingyu

2007-01-01

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

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

International Nuclear Information System (INIS)

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

2008-01-01

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

13. Continuous carbon nanotube reinforced composites.

Science.gov (United States)

Ci, L; Suhr, J; Pushparaj, V; Zhang, X; Ajayan, P M

2008-09-01

Carbon nanotubes are considered short fibers, and polymer composites with nanotube fillers are always analogues of random, short fiber composites. The real structural carbon fiber composites, on the other hand, always contain carbon fiber reinforcements where fibers run continuously through the composite matrix. With the recent optimization in aligned nanotube growth, samples of nanotubes in macroscopic lengths have become available, and this allows the creation of composites that are similar to the continuous fiber composites with individual nanotubes running continuously through the composite body. This allows the proper utilization of the extreme high modulus and strength predicted for nanotubes in structural composites. Here, we fabricate such continuous nanotube polymer composites with continuous nanotube reinforcements and report that under compressive loadings, the nanotube composites can generate more than an order of magnitude improvement in the longitudinal modulus (up to 3,300%) as well as damping capability (up to 2,100%). It is also observed that composites with a random distribution of nanotubes of same length and similar filler fraction provide three times less effective reinforcement in composites.

14. The Fractionation and Enrichment of La Content by Precipitation

International Nuclear Information System (INIS)

Suyanti; Purwani, MV

2007-01-01

The fractionation and enrichment of La content by precipitation have been done. The feed was La hydroxide by product of monazite sand. La hydroxide was diluted in HNO 3 and was precipitated with ammonia. For to obtain La, diluent was precipitated at pH 8 and the filtrate was precipitated with oxalic acid. The precipitant of La concentrated was more rich than the feed. This process was done continue and fractionally. The best yield of enrichment of La was obtained at dilution of 25 gram La Hydroxide in 20 ml HNO 3 . The efficient degree of fractionation was XV. The average weight of La concentrate was obtained at every fraction was 1 gram. The total sum weight from fraction I until fraction XV 13.5 grams. The average of La content was 48%, average fractionation efficiency of La for every step of fractionation was 48 %. Total efficiency all process was 100%. The average ratio of La/Nd was 2 and the ratio of La/Ce almost infinite. Before processed La/Ce was 7.86, and after process increase to 26.92 - to approach ∞. Before processed ratio of La/Nd was 2.79, after processed increased to 4.4 - to approach ∞. (author)

15. Ferroelectric Fractional-Order Capacitors

KAUST Repository

Agambayev, Agamyrat

2017-07-25

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

16. Ferroelectric Fractional-Order Capacitors

KAUST Repository

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

2017-01-01

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

17. 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.

18. Fractional Solitons in Excitonic Josephson Junctions

Science.gov (United States)

Su, Jung-Jung; Hsu, Ya-Fen

The Josephson effect is especially appealing because it reveals macroscopically the quantum order and phase. Here we study this effect in an excitonic Josephson junction: a conjunct of two exciton condensates with a relative phase ϕ0 applied. Such a junction is proposed to take place in the quantum Hall bilayer (QHB) that makes it subtler than in superconductor because of the counterflow of excitonic supercurrent and the interlayer tunneling in QHB. We treat the system theoretically by first mapping it into a pseudospin ferromagnet then describing it by the Landau-Lifshitz-Gilbert equation. In the presence of interlayer tunneling, the excitonic Josephson junction can possess a family of fractional sine-Gordon solitons that resemble the static fractional Josephson vortices in the extended superconducting Josephson junctions. Interestingly, each fractional soliton carries a topological charge Q which is not necessarily a half/full integer but can vary continuously. The resultant current-phase relation (CPR) shows that solitons with Q =ϕ0 / 2 π are the lowest energy states for small ϕ0. When ϕ0 > π , solitons with Q =ϕ0 / 2 π - 1 take place - the polarity of CPR is then switched.

19. On generalized fractional vibration equation

International Nuclear Information System (INIS)

Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

2017-01-01

Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

20. Physcicists rewarded for 'fractional electrons'

CERN Multimedia

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).

1. Ultracentrifugation for ultrafine nanodiamond fractionation

Science.gov (United States)

Koniakhin, S. V.; Besedina, N. A.; Kirilenko, D. A.; Shvidchenko, A. V.; Eidelman, E. D.

2018-01-01

In this paper we propose a method for ultrafine fractionation of nanodiamonds using the differential centrifugation in the fields up to 215000g. The developed protocols yield 4-6 nm fraction giving main contribution to the light scattering intensity. The desired 4-6 nm fraction can be obtained from various types of initial nanodiamonds: three types of detonation nanodiamonds differing in purifying methods, laser synthesis nanodiamonds and nanodiamonds made by milling. The characterization of the obtained hydrosols was conducted with Dynamic Light Scattering, Zeta potential measurements, powder XRD and TEM. According to powder XRD and TEM data ultracentrifugation also leads to a further fractionation of the primary diamond nanocrystallites in the hydrosols from 4 to 2 nm.

2. 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

3. Commercial SNF Accident Release Fractions

International Nuclear Information System (INIS)

Schulz, J.

2004-01-01

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

4. Fractional Reserve Banking: Some Quibbles

OpenAIRE

Bagus, Philipp; Howden, David

2010-01-01

We explore several unaddressed issues in George Selgin’s (1988) claim that the best monetary system to maintain monetary equilibrium is a fractional reserve free banking one. The claim that adverse clearing balances would limit credit expansion in a fractional reserve free banking system is more troublesome than previously reckoned. Both lengthened clearing periods and interbank agreements render credit expansion unrestrained. “The theory of free banking” confuses increases in money held with...

5. Intelligent fractions learning system: implementation

CSIR Research Space (South Africa)

Smith, Andrew C

2011-05-01

Full Text Available Conference Proceedings Paul Cunningham and Miriam Cunningham (Eds) IIMC International Information Management Corporation, 2011 ISBN: 978-1-905824-24-3 An Intelligent Fractions Learning System: Implementation Andrew Cyrus SMITH1, Teemu H. LAINE2 1CSIR... to fractions. Our aim with the current research project is to extend the existing UFractions learning system to incorporate automatic data capturing. ?Intelligent UFractions? allows a teacher to remotely monitor the children?s progress during...

6. Xenon fractionation in porous planetesimals

Science.gov (United States)

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

1990-01-01

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

7. Xenon fractionation in porous planetesimals

International Nuclear Information System (INIS)

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

1990-01-01

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

8. Red light photodynamic therapy for actinic keratosis using 37 J/cm2 : Fractionated irradiation with 12.3 mW/cm2 after 30 minutes incubation time compared to standard continuous irradiation with 75 mW/cm2 after 3 hours incubation time using a mathematical modeling.

Science.gov (United States)

Vignion-Dewalle, Anne-Sophie; Baert, Gregory; Devos, Laura; Thecua, Elise; Vicentini, Claire; Mortier, Laurent; Mordon, Serge

2017-09-01

Photodynamic therapy (PDT) is an emerging treatment modality for various diseases, especially for dermatological conditions. Although, the standard PDT protocol for the treatment of actinic keratoses in Europe has shown to be effective, treatment-associated pain is often observed in patients. Different modifications to this protocol attempted to decrease pain have been investigated. The decrease in fluence rate seems to be a promising solution. Moreover, it has been suggested that light fractionation significantly increases the efficacy of PDT. Based on a flexible light-emitting textile, the FLEXITHERALIGHT device specifically provides a fractionated illumination at a fluence rate more than six times lower than that of the standard protocol. In a recently completed clinical trial of PDT for the treatment of actinic keratosis, the non-inferiority of a protocol involving illumination with the FLEXITHERALIGHT device after a short incubation time and referred to as the FLEXITHERALIGHT protocol has been assessed compared to the standard protocol. In this paper, we propose a comparison of the two above mentioned 635 nm red light protocols with 37 J/cm 2 in the PDT treatment of actinic keratosis: the standard protocol and the FLEXITHERALIGHT one through a mathematical modeling. This mathematical modeling, which slightly differs from the one we have already published, enables the local damage induced by the therapy to be estimated. The comparison performed in terms of the local damage induced by the therapy demonstrates that the FLEXITHERALIGHT protocol with lower fluence rate, light fractionation and shorter incubation time is somewhat less efficient than the standard protocol. Nevertheless, from the clinical trial results, the FLEXITHERALIGHT protocol results in non-inferior response rates compared to the standard protocol. This finding raises the question of whether the PDT local damage achieved by the FLEXITHERALIGHT protocol (respectively, the standard protocol

9. Governing equations of transient soil water flow and soil water flux in multi-dimensional fractional anisotropic media and fractional time

OpenAIRE

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

2017-01-01

In this study dimensionally consistent governing equations of continuity and motion for transient soil water flow and soil water flux in fractional time and in fractional multiple space dimensions in anisotropic media are developed. Due to the anisotropy in the hydraulic conductivities of natural soils, the soil medium within which the soil water flow occurs is essentially anisotropic. Accordingly, in this study the fractional dimensions in two horizontal and one vertical di...

10. Fractionation schedules for cancers of the head and neck

International Nuclear Information System (INIS)

Harari, Paul M.

1995-01-01

11. Completely continuous and weakly completely continuous abstract ...

An algebra A is called right completely continuous (right weakly completely continuous) ... Moreover, some applications of these results in group algebras are .... A linear subspace S(G) of L1(G) is said to be a Segal algebra, if it satisfies the.

12. Fractional Diffusion Equations and Anomalous Diffusion

Science.gov (United States)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

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

13. Conformable Fractional Bessel Equation and Bessel Functions

OpenAIRE

Gökdoğan, Ahmet; Ünal, Emrah; Çelik, Ercan

2015-01-01

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

14. Discrete fractional solutions of a Legendre equation

Science.gov (United States)

Yılmazer, Resat

2018-01-01

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

15. Fractional and multivariable calculus model building and optimization problems

CERN Document Server

Mathai, A M

2017-01-01

This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable ...

16. Boundary value problemfor multidimensional fractional advection-dispersion equation

Directory of Open Access Journals (Sweden)

2015-05-01

Full Text Available In recent time there is a very great interest in the study of differential equations of fractional order, in which the unknown function is under the symbol of fractional derivative. It is due to the development of the theory of fractional integro-differential theory and application of it in different fields.The fractional integrals and derivatives of fractional integro-differential equations are widely used in modern investigations of theoretical physics, mechanics, and applied mathematics. The fractional calculus is a very powerful tool for describing physical systems, which have a memory and are non-local. Many processes in complex systems have nonlocality and long-time memory. Fractional integral operators and fractional differential operators allow describing some of these properties. The use of the fractional calculus will be helpful for obtaining the dynamical models, in which integro-differential operators describe power long-time memory by time and coordinates, and three-dimensional nonlocality for complex medium and processes.Differential equations of fractional order appear when we use fractal conception in physics of the condensed medium. The transfer, described by the operator with fractional derivatives at a long distance from the sources, leads to other behavior of relatively small concentrations as compared with classic diffusion. This fact redefines the existing ideas about safety, based on the ideas on exponential velocity of damping. Fractional calculus in the fractal theory and the systems with memory have the same importance as the classic analysis in mechanics of continuous medium.In recent years, the application of fractional derivatives for describing and studying the physical processes of stochastic transfer is very popular too. Many problems of filtration of liquids in fractal (high porous medium lead to the need to study boundary value problems for partial differential equations in fractional order.In this paper the

17. On the discretization of linear fractional representations of LPV systems

NARCIS (Netherlands)

Toth, R.; Lovera, M.; Heuberger, P.S.C.; Corno, M.; Hof, Van den P.M.J.

2012-01-01

Commonly, controllers for linear parameter-varying (LPV) systems are designed in continuous time using a linear fractional representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a

18. 40 CFR 53.64 - Test procedure: Static fractionator test.

Science.gov (United States)

2010-07-01

... 40 Protection of Environment 5 2010-07-01 2010-07-01 false Test procedure: Static fractionator test. 53.64 Section 53.64 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR... Performance Characteristics of Class II Equivalent Methods for PM2.5 § 53.64 Test procedure: Static...

19. REFractions: The Representing Equivalent Fractions Game

Science.gov (United States)

Tucker, Stephen I.

2014-01-01

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

20. dimensional generalised time-fractional Hirota equation

Youwei Zhang

2018-02-09

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

1. Providing Continuous Assurance

NARCIS (Netherlands)

Kocken, Jonne; Hulstijn, Joris

2017-01-01

It has been claimed that continuous assurance can be attained by combining continuous monitoring by management, with continuous auditing of data streams and the effectiveness of internal controls by an external auditor. However, we find that in existing literature the final step to continuous

2. Silica fractionation and reactivity in soils

Science.gov (United States)

Unzué Belmonte, Dácil; Barão, Lúcia; Vandevenne, Floor; Schoelynck, Jonas; Struyf, Eric; Meire, Patrick

2014-05-01

The Si cycle is a globally important biogeochemical cycle, with strong connections to other biogeochemical cycles, including C. 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…). A good characterization of the different fractions of reactive silica is crucial to move forward knowledge on ecosystem Si cycling, which has been recognized in the last decade as crucial for terrestrial Si fluxes. A new method to analyze the different fractions of silica in soils has been described by Koning et al. (2002) and adapted by our research team (Barão et al. 2013). Using a continuous extraction of Si and aluminum in 0.5M NaOH, biogenic and non-biogenic reactive fractions are separated based on their Si/Al ratios and their reactivity in NaOH. Applying this new method I will investigate three emerging ideas on how humans can affect directly terrestrial Si fluxes. -Land use. I expect strong silica fractionation and reactivity differences in different land uses. These effects due to agricultural and forestry management have already been shown earlier in temperate soils (Vandevenne et al. 2012). Now we will test this hypothesis in recently deforested soils, in the south of Brazil. 'Pristine' forest, managed forest and tobacco field soils (with and without rotation crops) will be studied. This research belongs to an interdisciplinary project on soils and global change. -Fire. According to the IPCC report, extreme events such as fires (number and intensity) would increase due to climate change. We analyzed litter from spruce forest, beech forest and peat soils at two burning levels, after 350°C and

3. Generalized Multiparameters Fractional Variational Calculus

Directory of Open Access Journals (Sweden)

Om Prakash Agrawal

2012-01-01

Full Text Available This paper builds upon our recent paper on generalized fractional variational calculus (FVC. Here, we briefly review some of the fractional derivatives (FDs that we considered in the past to develop FVC. We first introduce new one parameter generalized fractional derivatives (GFDs which depend on two functions, and show that many of the one-parameter FDs considered in the past are special cases of the proposed GFDs. We develop several parts of FVC in terms of one parameter GFDs. We point out how many other parts could be developed using the properties of the one-parameter GFDs. Subsequently, we introduce two new two- and three-parameter GFDs. We introduce some of their properties, and discuss how they can be used to develop FVC. In addition, we indicate how these formulations could be used in various fields, and how the generalizations presented here can be further extended.

4. Semi-infinite fractional programming

CERN Document Server

Verma, Ram U

2017-01-01

This book presents a smooth and unified transitional framework from generalised fractional programming, with a finite number of variables and a finite number of constraints, to semi-infinite fractional programming, where a number of variables are finite but with infinite constraints. It focuses on empowering graduate students, faculty and other research enthusiasts to pursue more accelerated research advances with significant interdisciplinary applications without borders. In terms of developing general frameworks for theoretical foundations and real-world applications, it discusses a number of new classes of generalised second-order invex functions and second-order univex functions, new sets of second-order necessary optimality conditions, second-order sufficient optimality conditions, and second-order duality models for establishing numerous duality theorems for discrete minmax (or maxmin) semi-infinite fractional programming problems.   In the current interdisciplinary supercomputer-oriented research envi...

5. 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.

6. On a Fractional Binomial Process

Science.gov (United States)

Cahoy, Dexter O.; Polito, Federico

2012-02-01

The classical binomial process has been studied by Jakeman (J. Phys. A 23:2815-2825, 1990) (and the references therein) and has been used to characterize a series of radiation states in quantum optics. In particular, he studied a classical birth-death process where the chance of birth is proportional to the difference between a larger fixed number and the number of individuals present. It is shown that at large times, an equilibrium is reached which follows a binomial process. In this paper, the classical binomial process is generalized using the techniques of fractional calculus and is called the fractional binomial process. The fractional binomial process is shown to preserve the binomial limit at large times while expanding the class of models that include non-binomial fluctuations (non-Markovian) at regular and small times. As a direct consequence, the generality of the fractional binomial model makes the proposed model more desirable than its classical counterpart in describing real physical processes. More statistical properties are also derived.

7. Riesz potential versus fractional Laplacian

KAUST Repository

Ortigueira, Manuel Duarte

2014-09-01

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

8. 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...

9. 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...

10. A graph with fractional revival

Science.gov (United States)

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.

11. Riesz potential versus fractional Laplacian

KAUST Repository

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

2014-01-01

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

12. Fractional Laplace Transforms - A Perspective

Directory of Open Access Journals (Sweden)

Rudolf A. Treumann

2014-06-01

Full Text Available A new form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral equations or problems in non-extensive statistical mechanics.

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

CERN Document Server

Sheng, Hu; Qiu, TianShuang

2012-01-01

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

14. Cerebral blood volume alterations during fractional pneumoencephalography

International Nuclear Information System (INIS)

Voigt, K.; Greitz, T.

1976-01-01

Simultaneous and continuous measurements of the cerebral blood volume (CBV), cerebrospinal fluid (CSF) and blood pressure were carried out in six patients during fractional pneumoencephalography in order to examine intracranial volumetric interactions. Three patients (Group A) showed normal encephalographic findings, and in three patients (Group B) communicating hydrocephalus with convexity block was found encephalographically. In all patients the injection of air was followed by an immediate increase of CSF pressure and blood pressure and a concomitant decrease of CBV. The initial CSF pressure was invariably re-established within 3 to 3.5 min. During this time interval the CBV of the patients of Group B decreased significantly and 30 percent more than that of Group A. Furthermore, after restoration of the original CSF pressure, CBV returned to its initial level in all patients of Group A, whereas it remained unchanged or showed a further decrease in the patients of Group B. Removal of an amount of CSF corresponding to half of the amount of injected air was followed by a significant reactive hyperemic response in two normal patients. The intracranial volumetric alterations during fractional pneumoencephalography are discussed in detail with respect to the underlying physiologic mechanisms and are suggested as a model for acute and low pressure hydrocephalus

15. Aboriginal fractions: enumerating identity in Taiwan.

Science.gov (United States)

Liu, Jennifer A

2012-01-01

Notions of identity in Taiwan are configured in relation to numbers. I examine the polyvalent capacities of enumerative technologies in both the production of ethnic identities and claims to political representation and justice. By critically historicizing the manner in which Aborigines in Taiwan have been, and continue to be, constructed as objects and subjects of scientific knowledge production through technologies of measuring, I examine the genetic claim made by some Taiwanese to be "fractionally" Aboriginal. Numbers and techniques of measuring are used ostensibly to know the Aborigines, but they are also used to construct a genetically unique Taiwanese identity and to incorporate the Aborigines within projects of democratic governance. Technologies of enumeration thus serve within multiple, and sometimes contradictory, projects of representation and knowledge production.

Science.gov (United States)

2014-12-01

NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA MBA PROFESSIONAL REPORT BUSINESS CONTINUITY MANAGEMENT PLAN December 2014......maximum 200 words) Navy Supply Systems Command (NAVSUP) lacks a business process framework for the development of Business Continuity Management

17. Generalized time fractional IHCP with Caputo fractional derivatives

International Nuclear Information System (INIS)

Murio, D A; MejIa, C E

2008-01-01

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

18. On the noble gas isotopic fractionation in naturally occurring gases

International Nuclear Information System (INIS)

Marty, B.

1984-01-01

The isotopic composition of neon in the mantle is an important geochemical constraint on the formation of the earth and subsequent degassing. Some deviation of neon isotopic composition in natural gas and rock samples from the atmospheric value which can not be accounted for by the known nuclear process has been reported, and Nagao et al. interpreted the deviation as the result of mass fractionation in natural gas in Japan. The possible cause of such fractionation was investigated. Gaseous diffusion, such as (a) free-molecule diffusion, (b) mutual diffusion and (c) thermal diffusion, is able to cause isotopic fractionation. After the detailed consideration on these three diffusion processes, conclusion that free-molecule diffusion occurs only in very particular condition, and it is questionable that thermal diffusion occurs in nature, were obtained. (b) which means the interaction of two or more gases, is supposed to occur in nature, and is able to confirm experimentally. In mutual diffusion only, gas transfer is concerned, but other form of fractionation should not be neglected. In solid diffusion, gas is trapped by fine grained sedimentary rocks, and may be fractionated by adsorption and communication to exterior through minute channels. Underground water also works as noble gas reservoir. For example, when gas stream is in contact with water, continuous exchange is possible to take place at the interface of gas and liquid, which contributes to the fractionation. (Ishimitsu, A.)

19. A fractional calculus approach to investigate the alpha decay processes

International Nuclear Information System (INIS)

Calik, A.E.; Ertik, H.; Oder, B.; Sirin, H.

2013-01-01

In this study, the nuclear decay equation is taken under consideration by making use of fractional calculus. In this context, the first-order time derivative is changed to a Caputo fractional derivative hence, the resulting equation is the time fractional nuclear decay equation. The solution of this equation is obtained in terms of Mittag–Leffler function which plays an important role to study the non-Markovian feature of physical processes. As an application of this time fractional formalism, alpha decay half-life values have been calculated for Pb, Po, Rn, Ra, Th and U isotopes. Consequently, the theoretical half-life values have been obtained in consistent with the experimental data. The dependence of the order of fractional derivative μ being a measure of fractality of time, on the nuclear structure has been established. In the investigations carried out, we have arrived to the conclusion that for the μ values which are closed to one, where time becomes homogenous and continuous, the shell closure effects are predominant and that the fractional derivative order μ (i.e., fractality of time) and nuclear structure are closely related to each other. (author)

20. TECHNOLOGICAL FEATURES OF MILLING AND FRACTIONATION OF FLAXSEEDS

Directory of Open Access Journals (Sweden)

A. Feskova

2015-01-01

Full Text Available Summary. The optimal parameters of milling and fractionation of flaxseeds were substantiated. It was found that the hull fraction with the highest content of lignan secoisolariciresinol diglucoside SDG was obtained when flaxseeds were grinded using a rotatory impact continuous operation mill at the rotation 1380-1640 rpm. Studies have shown that with the increasing of the rotor speed the number of unbriken seeds decreased. However, due to the fact that the shells are crushed more, they become more difficult to separate from the cotyledons. For identification and quantification of SDG the HPLC-MS method was used. It is found that the optimum separation membranes and cotyledon fraction occurs at sifting milled seeds sequentially through the sieves having meshes of 1 and 0.5 mm. The technology of industrial production of lignans-containing fraction and flour on the basis of flaxseeds processing were proposed. This technology includes milling flaxseeds at the rotation 1380-1640 rpm, with subsequent 2% silicon dioxide addition and stepwise sieving using sieves with the mesh size 2 mm. To use a fraction membranes high in lignans as raw material for biologically active additives to food it needed additional enforcement-ground to a size not more than 0.4 mm (technological features of capsulation. The developed technology allowed getting with maximum yields of lignans-containing fraction (10% yield and flaxseed flour (80% yield.

1. 9 CFR 113.7 - Multiple fractions.

Science.gov (United States)

2010-01-01

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

2. A fractional Dirac equation and its solution

International Nuclear Information System (INIS)

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

2010-01-01

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

3. On the fractional calculus of Besicovitch function

International Nuclear Information System (INIS)

Liang Yongshun

2009-01-01

Relationship between fractional calculus and fractal functions has been explored. Based on prior investigations dealing with certain fractal functions, fractal dimensions including Hausdorff dimension, Box dimension, K-dimension and Packing dimension is shown to be a linear function of order of fractional calculus. Both Riemann-Liouville fractional calculus and Weyl-Marchaud fractional derivative of Besicovitch function have been discussed.

4. 12 CFR 5.67 - Fractional shares.

Science.gov (United States)

2010-01-01

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

5. Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach

Directory of Open Access Journals (Sweden)

Zhi-Yong Chen

2014-01-01

Full Text Available From the signal processing point of view, the nondifferentiable data defined on the Cantor sets are investigated in this paper. The local fractional Fourier series is used to process the signals, which are the local fractional continuous functions. Our results can be observed as significant extensions of the previously known results for the Fourier series in the framework of the local fractional calculus. Some examples are given to illustrate the efficiency and implementation of the present method.

6. Plants under continuous light

NARCIS (Netherlands)

Velez Ramirez, A.I.; Ieperen, van W.; Vreugdenhill, D.; Millenaar, F.F.

2011-01-01

Continuous light is an essential tool for understanding the plant circadian clock. Additionally, continuous light might increase greenhouse food production. However, using continuous light in research and practice has its challenges. For instance, most of the circadian clock-oriented experiments

7. Comment on "Fractional quantum mechanics" and "Fractional Schrödinger equation".

Science.gov (United States)

Wei, Yuchuan

2016-06-01

In this Comment we point out some shortcomings in two papers [N. Laskin, Phys. Rev. E 62, 3135 (2000)10.1103/PhysRevE.62.3135; N. Laskin, Phys. Rev. E 66, 056108 (2002)10.1103/PhysRevE.66.056108]. We prove that the fractional uncertainty relation does not hold generally. The probability continuity equation in fractional quantum mechanics has a missing source term, which leads to particle teleportation, i.e., a particle can teleport from a place to another. Since the relativistic kinetic energy can be viewed as an approximate realization of the fractional kinetic energy, the particle teleportation should be an observable relativistic effect in quantum mechanics. With the help of this concept, superconductivity could be viewed as the teleportation of electrons from one side of a superconductor to another and superfluidity could be viewed as the teleportation of helium atoms from one end of a capillary tube to the other. We also point out how to teleport a particle to an arbitrary destination.

8. Fractionation of Java Citronella Oil and Citronellal Purification by Batch Vacuum Fractional Distillation

Science.gov (United States)

Eden, W. T.; Alighiri, D.; Cahyono, E.; Supardi, K. I.; Wijayati, N.

2018-04-01

The aim of this work was to assess the performance of a vacuum fractionating column for the fractionation of Java Citronella Oil (Cymbopogon winterianus) and citronellal purification during batch mode operation at vacuum -76 cmHg and reflux ratios 5:1. Based on GC-MS analysis of Java Citronella Oil is known that citronellal, citronellol, and geraniol has yielded 21,59%; 7,43%; and 34,27%, respectively. Fractional distillation under reduced pressure and continued redistilled are needed to isolate the component of Java Citronella Oil. Redistilled can improve the purity, then distillate collected while the temperature changed. In the first distillate yielded citronellal with a purity of 75.67%. The first distillate obtained residue rhodinol product will then be carried back to separation into citronellol and geraniol. The purity of citronellol reached 80,65% purity, whereas geraniol reached 76.63% purity. Citronellal Purification resulting citronellal to 95.10% purity and p-menthane-3,8-diol reached 75.95% purity.

9. Fractional vector calculus and fluid mechanics

Science.gov (United States)

Lazopoulos, Konstantinos A.; Lazopoulos, Anastasios K.

2017-04-01

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

10. FRACTIONATION AND CHARACTERISATION OF TECHNICAL AMMONIUM LIGNOSULPHONATE

Directory of Open Access Journals (Sweden)

Cheryl Ann Leger

2010-08-01

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

11. IMRT dose fractionation for head and neck cancer: Variation in current approaches will make standardisation difficult

Energy Technology Data Exchange (ETDEWEB)

Ho, Kean F. (Academic Dept. of Radiation Oncology, Univ. of Manchester, Manchester (United Kingdom)); Fowler, Jack F. (Dept. of Human Oncology and Medical Physics, Univ. of Wisconsin, Wisconsin (United States)); Sykes, Andrew J.; Yap, Beng K.; Lee, Lip W.; Slevin, Nick J. (Dept. of Clinical Oncology, Christie Hospital NHS Foundation Trust, Manchester (United Kingdom))

2009-04-15

Introduction. Altered fractionation has demonstrated clinical benefits compared to the conventional 2 Gy/day standard of 70 Gy. When using synchronous chemotherapy, there is uncertainty about optimum fractionation. IMRT with its potential for Simultaneous Integrated Boost (SIB) adds further to this uncertainty. This survey will examine international practice of IMRT fractionation and suggest possible reasons for diversity in approach. Material and methods. Fourteen international cancer centres were surveyed for IMRT dose/fractionation practised in each centre. Results. Twelve different types of dose fractionation were reported. Conventional 70-72 Gy (daily 2 Gy/fraction) was used in 3/14 centres with concurrent chemotherapy while 11/14 centres used altered fractionation. Two centres used >1 schedule. Reported schedules and number of centres included 6 fractions/week DAHANCA regime (3), modest hypofractionation (=2.2 Gy/fraction) (3), dose-escalated hypofractionation (=2.3 Gy/fraction) (4), hyperfractionation (1), continuous acceleration (1) and concomitant boost (1). Reasons for dose fractionation variability include (i) dose escalation; (ii) total irradiated volume; (iii) number of target volumes; (iv) synchronous systemic treatment; (v) shorter overall treatment time; (vi) resources availability; (vii) longer time on treatment couch; (viii) variable GTV margins; (ix) confidence in treatment setup; (x) late tissue toxicity and (xi) use of lower neck anterior fields. Conclusions. This variability in IMRT fractionation makes any meaningful comparison of treatment results difficult. Some standardization is needed particularly for design of multi-centre randomized clinical trials.

12. A Reexamination of Deuterium Fractionation on Mars

Science.gov (United States)

Pathare, A.; Paige, D. A.

1997-07-01

The ratio of deuterium to hydrogen in the Martian atmosphere is enhanced by a factor of 5 with respect to the terrestrial value, probably due to fractionation associated with thermal Jeans escape from the top of the atmosphere. Theoretical analyses of the relative efficiency of H and D escape have suggested that the deuterium enrichment implies Mars has outgassed the vast majority of its H2O and that the Martian atmosphere is presently not exchanging water with a juvenile reservoir. However, measurements of high and variable D/H values within hydrous minerals in SNC meteorites strongly suggest that mixing between the atmosphere and juvenile water has taken place. Furthermore, the lack of any observed enrichment of atmospheric (18) O with respect to (16) O, in spite of fractionating nonthermal escape mechanisms, indicates buffering by some juvenile source of oxygen, most probably in the form of a surface or subsurface reservoir of water. We propose that this apparent paradox in the interpretation of isotopic hydrogen and oxygen fractionation --or lack thereof-- can be resolved by re-examining the standard model of deuterium fractionation efficiency on Mars. Specifically, we demonstrate the importance of using upper atmospheric temperatures more representative of the range experienced by the Martian exosphere over the course of the solar cycle. Preliminary calculations involving changes in effusion velocity and diffusive separation as a function of exospheric temperature indicate that incorporating these more representative lower exospheric temperatures will reduce the relative efficiency of D escape, in which case the observed enrichment of deuterium can indeed result from exchange with a juvenile source of water. We are in the process of confirming these computations with a one-dimensional upper atmospheric photochemical model that considers the effects of changing solar activity and exospheric temperature on ionospheric composition. If our initial calculations are

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

International Nuclear Information System (INIS)

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

2012-01-01

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

14. The characteristics of polysaccharides fractions of sunflower obtained in dynamic mode

International Nuclear Information System (INIS)

Makhkamov, Kh.K.; Gorshkova, R.M.; Khalikova, S.

2013-01-01

Present article describes characteristics of polysaccharides fractions of sunflower obtained in dynamic mode. The decomposition of sunflower pectin was studied by means of continuous fractionation method in dynamic regime. It was found that the process is of extreme nature due to heterogeneity of its macromolecule structure. The additional information on macromolecule structure of sunflower pectin was obtained.

15. An Investigation of Fraction Models in Early Elementary Grades: A Mixed-Methods Approach

Science.gov (United States)

Wilkerson, Trena L.; Cooper, Susan; Gupta, Dittika; Montgomery, Mark; Mechell, Sara; Arterbury, Kristin; Moore, Sherrie; Baker, Betty Ruth; Sharp, Pat T.

2015-01-01

This study examines the effect varying models have on student understanding of fractions. The study addressed the question of what students know and understand about fractional concepts through the use of discrete and continuous models. A sample of 54 students in kindergarten and 3rd grade were given an interview pretest, participated in…

16. Mixed integer (0-1) fractional programming for decision support in paper production industry

NARCIS (Netherlands)

Claassen, G.D.H.

2014-01-01

This paper presents an effective and efficient method for solving a special class of mixed integer fractional programming (FP) problems. We take a classical reformulation approach for continuous FP as a starting point and extend it for solving a more general class of mixed integer (0–1) fractional

International Nuclear Information System (INIS)

Heilig, S.J.

1985-01-01

Recent results of searches for free fractional charge have been null with the exception of the experiment at Stanford under the leadership of W. Fairbank. His experiment, while claiming the observation of free fractional charge, has yet to show that this observation was not spurious. The need for a confirming experiment with a different physical system is the motivation for the current work. A torsional pendulum has been constructed of a fused silica fiber with an attached fused silica crossbar. A transverse electric field is applied to the end of the crossbar, and the resulting deflection of the crossbar is used to measure the torque applied by the field. To date the limit of measurement for the charge on the crossbar (without sample) is 0 +/- 24 electronic charges. The history of this experiment is discussed, along with plans for pushing the limits of measurement to below the single-charge level

18. Measuring condensate fraction in superconductors

International Nuclear Information System (INIS)

Chakravarty, Sudip; Kee, Hae-Young

2000-01-01

An analysis of off-diagonal long-range order in superconductors shows that the spin-spin correlation function is significantly influenced by the order if the order parameter is anisotropic on a microscopic scale. Thus, magnetic neutron scattering can provide a direct measurement of the condensate fraction of a superconductor. It is also argued that recent measurements in high-temperature superconductors come very close to achieving this goal. (c) 2000 The American Physical Society

19. Microfluidic Devices for Blood Fractionation

OpenAIRE

Hou, Han Wei; Bhagat, Ali Asgar S.; Lee, Wong Cheng J.; Huang, Sha; Han, Jongyoon; Lim, Chwee Teck

2011-01-01

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. ...

20. Surfaces allowing for fractional statistics

International Nuclear Information System (INIS)

Aneziris, Charilaos.

1992-07-01

In this paper we give a necessary condition in order for a geometrical surface to allow for Abelian fractional statistics. In particular, we show that such statistics is possible only for two-dimentional oriented surfaces of genus zero, namely the sphere S 2 , the plane R 2 and the cylindrical surface R 1 *S 1 , and in general the connected sum of n planes R 2 -R 2 -R 2 -...-R 2 . (Author)

1. Electrochemically controlled iron isotope fractionation

Science.gov (United States)

Black, Jay R.; Young, Edward D.; Kavner, Abby

2010-02-01

Variations in the stable isotope abundances of transition metals have been observed in the geologic record and trying to understand and reconstruct the physical/environmental conditions that produced these signatures is an area of active research. It is clear that changes in oxidation state lead to large fractionations of the stable isotopes of many transition metals such as iron, suggesting that transition metal stable isotope signatures could be used as a paleo-redox proxy. However, the factors contributing to these observed stable isotope variations are poorly understood. Here we investigate how the kinetics of iron redox electrochemistry generates isotope fractionation. Through a combination of electrodeposition experiments and modeling of electrochemical processes including mass-transport, we show that electron transfer reactions are the cause of a large isotope separation, while mass transport-limited supply of reactant to the electrode attenuates the observed isotopic fractionation. Furthermore, the stable isotope composition of electroplated transition metals can be tuned in the laboratory by controlling parameters such as solution chemistry, reaction overpotential, and solution convection. These methods are potentially useful for generating isotopically-marked metal surfaces for tracking and forensic purposes. In addition, our studies will help interpret stable isotope data in terms of identifying underlying electron transfer processes in laboratory and natural samples.

2. Size fractionation of waste-to-energy boiler ash enables separation of a coarse fraction with low dioxin concentrations.

Science.gov (United States)

Weidemann, E; Allegrini, E; Fruergaard Astrup, T; Hulgaard, T; Riber, C; Jansson, S

2016-03-01

Polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/F) formed in modern Waste-to-Energy plants are primarily found in the generated ashes and air pollution control residues, which are usually disposed of as hazardous waste. The objective of this study was to explore the occurrence of PCDD/F in different grain size fractions in the boiler ash, i.e. ash originating from the convection pass of the boiler. If a correlation between particle size and dioxin concentrations could be found, size fractionation of the ashes could reduce the total amount of hazardous waste. Boiler ash samples from ten sections of a boiler's convective part were collected over three sampling days, sieved into three different size fractions - 0.355 mm - and analysed for PCDD/F. The coarse fraction (>0.355 mm) in the first sections of the horizontal convection pass appeared to be of low toxicity with respect to dioxin content. While the total mass of the coarse fraction in this boiler was relatively small, sieving could reduce the amount of ash containing toxic PCDD/F by around 0.5 kg per tonne input waste or around 15% of the collected boiler ash from the convection pass. The mid-size fraction in this study covered a wide size range (0.09-0.355 mm) and possibly a low toxicity fraction could be identified by splitting this fraction into more narrow size ranges. The ashes exhibited uniform PCDD/F homologue patterns which suggests a stable and continuous generation of PCDD/F. Copyright © 2016 Elsevier Ltd. All rights reserved.

3. Self-similar continued root approximants

International Nuclear Information System (INIS)

Gluzman, S.; Yukalov, V.I.

2012-01-01

A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various applied problems. The method is based on the self-similar approximation theory involving self-similar root approximants. The constructed self-similar continued roots extrapolate asymptotic series to finite values of the expansion parameter. The self-similar continued roots contain, as a particular case, continued fractions and Padé approximants. A theorem on the convergence of the self-similar continued roots is proved. The method is illustrated by several examples from condensed-matter physics.

4. Cutting Out Continuations

DEFF Research Database (Denmark)

Bahr, Patrick; Hutton, Graham

2016-01-01

In the field of program transformation, one often transforms programs into continuation-passing style to make their flow of control explicit, and then immediately removes the resulting continuations using defunctionalisation to make the programs first-order. In this article, we show how these two...... transformations can be fused together into a single transformation step that cuts out the need to first introduce and then eliminate continuations. Our approach is calculational, uses standard equational reasoning techniques, and is widely applicable....

5. Calcium Isotope Geochemistry: Research Horizons and Nanoscale Fractionation Processes

Science.gov (United States)

Watkins, J. M.; Depaolo, D. J.; Richter, F. M.; Fantle, M. S.; Simon, J. I.; Ryerson, F. J.; Ewing, S. A.; Turchyn, A. V.; Yang, W.; Owens, T. L.

2008-12-01

Interest in studies of calcium isotope variations in nature continues to increase. Investigations span human biology, plants and soils, oceanography and paleoclimate, early solar system processes, aqueous geochemistry, and silicate liquid structure. Variations in the 44Ca/40Ca ratio are generally small, about 5 ‰, but gradual small improvements in analytical capability now yield 0.05 to 0.1 ‰ resolution. The field is still plagued by a lack of universal standards for isotope ratios and data representation, but these are secondary issues. Traditional isotopic systems have been based in equilibrium thermodynamics, which can explain the magnitude and sign of observed mass-dependent fractionation behavior. For Ca isotopes this is not the case. There is still no reliable way to estimate the equilibrium free energy associated with isotopic exchange between most phases of interest. Experiments are difficult to interpret because it is almost impossible to precipitate minerals from aqueous solution at equilibrium at low temperature. Some studies suggest that, for example, there is no equilibrium isotopic fractionation between calcite and dissolved aqueous Ca. There is good evidence that most Ca isotopic fractionation is caused by kinetic effects. The details of the controlling processes are still missing, and without this mechanistic understanding it is difficult to fully understand the implications of natural isotopic variations. Recent work on dissolved Ca, calcite, and sulfates in both laboratory and natural settings is shedding light on where the fractionation may arise. There is emerging evidence for mass dependent fractionation associated with aqueous diffusion, but probably the primary source of the effects is in the details of precipitation of minerals from solution. This makes the fractionation potentially dependent on a number of factors, including solution composition and mineral growth rate. The next challenge is to develop appropriate experimental tests and

International Nuclear Information System (INIS)

Lamb, D.S.; Spry, N.A.; Gray, A.J.; Johnson, A.D.; Alexander, S.R.; Dally, M.J.

1990-01-01

Between 1981 and 1986, 89 patients with advanced head and neck squamous cancer were treated with a continuous accelerated fractionation radiotherapy (AFRT) regimen. Three fractions of 1.80 Gy, 4 h apart, were given on three treatment days per week, and the tumour dose was taken to 59.40 Gy in 33 fractions in 24-25 days. Acute mucosal reactions were generally quite severe, but a split was avoided by providing the patient with intensive support, often as an in-patient, until the reactions settled. Late radiation effects have been comparable to those obtained with conventional fractionation. The probability of local-regional control was 47% at 3 years for 69 previously untreated patients, whereas it was only 12% at one year for 20 patients treated for recurrence after radical surgery. Fifty-eight previously untreated patients with tumours arising in the upper aero-digestive tract were analysed in greated detail. The probability of local-regional control at 3 years was 78% for 17 Stage III patients and 15% for 31 Stage IV patients. This schedule of continuous AFRT is feasible and merits further investigation. (author). 31 refs.; 4 figs.; 6 tabs

7. Effective moduli of high volume fraction particulate composites

International Nuclear Information System (INIS)

Kwon, P.; Dharan, C.K.H.

1995-01-01

Predictions using current micromechanics theories for the effective moduli of particulate-reinforced composites tend to break down at high volume fractions of the reinforcing phase. The predictions are usually well below experimentally measured values of the Young's modulus for volume fractions exceeding about 0.6. In this paper, the concept of contiguity, which is a measure of phase continuity, is applied to Mori-Tanaka micromechanics theory. It is shown that contiguity of the second phase increases with volume fraction, leading eventually to a reversal in the roles of the inclusion and matrix. In powder metallurgy practice, it is well known that at high volume fractions, sintering and consolidation of the reinforcement make it increasingly continuous and more like the matrix phase, while the former matrix tends to become more like the inclusion phase. The concept of contiguity applied to micromechanics theory results in very good agreement between the predicted Young's modulus and experimental data on tungsten carbide particulate-reinforced cobalt

8. The fractional quantum Hall effect

International Nuclear Information System (INIS)

Stormer, H.L.

1988-01-01

The fractional quantum Hall effect (FQHE), is the manifestation of a new, highly correlated, many-particle ground state that forms in a two-dimensional electron system at low temperatures and in high magnetic fields. It is an example of the new physics that has grown out of the tremendous recent advances in semiconductor material science, which has provided us with high-quality, lower-dimensional carrier systems. The novel electronic state exposes itself in transport experiments through quantization of the Hall resistance to an exact rational fraction of h/e, and concomitantly vanishing longitudinal resistivity. Its relevant energy scale is only a few degrees kelvin. The quantization is a consequence of the spontaneous formation of an energy gap separating the condensed ground state from its rather elusive quasiparticle excitations. The theoretical understanding of the novel quantum liquids which underlie the FQHE has predominantly emerged from an ingenious many-particle wave function strongly supported by numerous few-particle simulations. Theory has now constructed a complex model for ideal two-dimensional electron systems in the presence of high magnetic fields and makes definitive, often fascinating predictions. Experiments have successively uncovered odd-denominator fractional states reaching presently to 7/13. The application of new experimental tools to the FQHE, such as optics, microwaves, and phonon techniques promises the direct observation of such parameters as the gap energy and possibly even some of the more elusive quantities in the future. While theory and experiment in the FQHE appear to be converging, there remains considerable room for challenging surprises. This paper provides a concise overview of the FQHE. It focuses on the experimental aspects and states, but does not expand on the theoretical advances. 70 refs., 11 figs

9. Cultivating yeast in fractions of light oil from black coal resin. [Candida tropicalis

Energy Technology Data Exchange (ETDEWEB)

Kucher, R.V.; Pavlyuk, M.I.; Dzumedzei, N.V.; Turovskii, A.A.

1982-11-01

Feasibility of using a light fraction of black coal oil from the Avdeevskii coking plant as a substrate for growing microorganisms was studied. Candida tropicalis was adapted to the light oil in multiple stages and in continually changing conditions. Maximum growth of the yeast occurred in fractions of the oil with boiling points of 363, 373-293 K. It was demonstrated that low temperature fractions of the hard coal oil are a source of hydrocarbons and energy in microbiological processes. Surface-active materials, such as sodium lauryl sulfate and syntanol-15, stimulate the growth of the yeast in light oil fractions from hard coal resin. (5 refs.) (In Russian)

10. Low power constant fraction discriminator

International Nuclear Information System (INIS)

Krishnan, Shanti; Raut, S.M.; Mukhopadhyay, P.K.

2001-01-01

This paper describes the design of a low power ultrafast constant fraction discriminator, which significantly reduces the power consumption. A conventional fast discriminator consumes about 1250 MW of power whereas this low power version consumes about 440 MW. In a multi detector system, where the number of discriminators is very large, reduction of power is of utmost importance. This low power discriminator is being designed for GRACE (Gamma Ray Atmospheric Cerenkov Experiments) telescope where 1000 channels of discriminators are required. A novel method of decreasing power consumption has been described. (author)

11. Natural fractionation of uranium isotopes

International Nuclear Information System (INIS)

Noordmann, Janine

2015-01-01

The topic of this thesis was the investigation of U (n( 238 U) / n( 235 U)) isotope variations in nature with a focus on samples (1) that represent the continental crust and its weathering products (i.e. granites, shales and river water) (2) that represent products of hydrothermal alteration on mid-ocean ridges (i.e. altered basalts, carbonate veins and hydrothermal water) and (3) from restricted euxinic basins (i.e. from the water column and respective sediments). The overall goal was to explore the environmental conditions and unravel the mechanisms that fractionate the two most abundant U isotopes, n( 238 U) and n( 235 U), on Earth.

12. Fractional separation of hydrocarbon vapours

Energy Technology Data Exchange (ETDEWEB)

1937-07-10

A process is described for converting higher boiling hydrocarbons to lower boiling hydrocarbons by subjecting them at elevated temperatures to a conversion operation, then separating the higher and lower boiling fractions. The separation takes place while the reaction products are maintained in the vapor phase by contact with a mass of solid porous material which has little or no catalytic activity but does have a preferential absorption property for higher boiling hydrocarbons so that the lower boiling part of the reaction products pass through the separation zone while the heavier hydrocarbons are retained. The separation is accomplished without substantial loss of heat of these reaction products.

13. Archives: Continuing Medical Education

African Journals Online (AJOL)

14. Generalized analytic continuation

CERN Document Server

Ross, William T

2002-01-01

The theory of generalized analytic continuation studies continuations of meromorphic functions in situations where traditional theory says there is a natural boundary. This broader theory touches on a remarkable array of topics in classical analysis, as described in the book. This book addresses the following questions: (1) When can we say, in some reasonable way, that component functions of a meromorphic function on a disconnected domain, are "continuations" of each other? (2) What role do such "continuations" play in certain aspects of approximation theory and operator theory? The authors use the strong analogy with the summability of divergent series to motivate the subject. In this vein, for instance, theorems can be described as being "Abelian" or "Tauberian". The introductory overview carefully explains the history and context of the theory. The authors begin with a review of the works of Poincaré, Borel, Wolff, Walsh, and Gončar, on continuation properties of "Borel series" and other meromorphic func...

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

International Nuclear Information System (INIS)

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

2011-01-01

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

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

OpenAIRE

Çenesiz, Yücel; Kurt, Ali

2015-01-01

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

17. Chemical study of ethyl Acetate fraction of Picrasma Javanica Bl.

Directory of Open Access Journals (Sweden)

Sri Hainil

2015-12-01

Full Text Available N-1 main compound from ethyl acetate fraction of kayu pahit bark (Picrasma Javanica B1 has been isolated and characterized with colom chromatography and continued with preparative chromatography. According to analized from spectrum data used ultraviolet (UV spectroscopy, infra red (IR, 1H RMI (Resonansi Magnet Inti, 13 C RMI, Massa , COSY (Correlated Spectroscopy, HSQC (Heteronuclear Single Quantum Correlation, HMBC ( Heteronuclear Multiple Bond Correlation and literature study showed that the compound of isolation was javanicin A.

18. Nonlinear dynamics of fractional order Duffing system

International Nuclear Information System (INIS)

Li, Zengshan; Chen, Diyi; Zhu, Jianwei; Liu, Yongjian

2015-01-01

In this paper, we analyze the nonlinear dynamics of fractional order Duffing system. First, we present the fractional order Duffing system and the numerical algorithm. Second, nonlinear dynamic behaviors of Duffing system with a fixed fractional order is studied by using bifurcation diagrams, phase portraits, Poincare maps and time domain waveforms. The fractional order Duffing system shows some interesting dynamical behaviors. Third, a series of Duffing systems with different fractional orders are analyzed by using bifurcation diagrams. The impacts of fractional orders on the tendency of dynamical motion, the periodic windows in chaos, the bifurcation points and the distance between the first and the last bifurcation points are respectively studied, in which some basic laws are discovered and summarized. This paper reflects that the integer order system and the fractional order one have close relationship and an integer order system is a special case of fractional order ones.

19. A fractional model for dye removal

Directory of Open Access Journals (Sweden)

Ji-Huan He

2016-01-01

Full Text Available The adsorption process has a fractional property, and a fractional model is suggested to study a transport model of direct textile industry wastewater. An approximate solution of the concentration is obtained by the variational iteration method.

20. 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.

1. Fractional Order Element Based Impedance Matching

KAUST Repository

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.

2. Chaos in discrete fractional difference equations

2016-09-07

Sep 7, 2016 ... chaotic behaviour of fractional difference equations for the tent map, Gauss map and 2x(mod 1) map are studied ..... (4) No significant change is observed by changing .... (3) In fractional case, the rational initial condition.

3. Fractional Order Element Based Impedance Matching

KAUST Repository

Radwan, Ahmed Gomaa; Salama, Khaled N.; Shamim, Atif

2014-01-01

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

4. Fractionated stereotactic radiotherapy for craniopharyngiomas

International Nuclear Information System (INIS)

Schulz-Ertner, Daniela; Frank, Claudia; Herfarth, Klaus K.; Rhein, Bernhard; Wannenmacher, Michael; Debus, Juergen

2002-01-01

Purpose: To investigate outcome and toxicity after fractionated stereotactic radiation therapy (FSRT) in patients with craniopharyngiomas. Methods and Materials: Twenty-six patients with craniopharyngiomas were treated with FSRT between May 1989 and February 2001. Median age was 33.5 years (range: 5-57 years). Nine patients received FSRT after surgery as primary treatment, and 17 patients were irradiated for recurrent tumor or progressive growth after initial surgery. Median target dose was 52.2 Gy (range: 50.0-57.6 Gy) with conventional fractionation. Follow-up included MRI and neurologic, ophthalmologic, and endocrinologic examinations. Results: The median follow-up was 43 months (range: 7-143 months). The actuarial local control rate and actuarial overall survival rates were 100% and 100%, respectively, at 5 years and 100% and 83%, respectively, at 10 years. Four patients showed complete response, 14 patients showed partial response, and 8 patients remained stable. In 5 patients, vision improved after radiation therapy. Acute toxicity was mild. One patient required cyst drainage 3 months after radiotherapy. Late toxicity after radiotherapy included impairment of hormone function in 3 out of 18 patients at risk. We did not observe any vision impairment, radionecrosis, or secondary malignancies. Conclusions: FSRT is effective and safe in the treatment of cystic craniopharyngiomas. Toxicity is extremely low using this conformal technique

5. 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.

6. The synchronization of three fractional differential systems

International Nuclear Information System (INIS)

Li Changpin; Yan Jianping

2007-01-01

In this paper, a new method is proposed and applied to the synchronization of fractional differential systems (or 'differential systems with fractional orders'), where both drive and response systems have the same dimensionality and are coupled by the driving signal. The present technique is based on the stability criterion of linear fractional systems. This method is implemented in (chaos) synchronization of the fractional Lorenz system, Chen system and Chua circuit. Numerical simulations show the present synchronization method works well

7. Multivariate fractional Poisson processes and compound sums

OpenAIRE

Beghin, Luisa; Macci, Claudio

2015-01-01

In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also consider compound processes. We obtain some equations in terms of some suitable fractional derivatives and fractional difference operators, which provides the extension of known equations for the univariate processes.

8. Interactions among different fractions in the thermoplastic state of Goonyella coking coal

Energy Technology Data Exchange (ETDEWEB)

Takahiro Yoshida; Toshimasa Takanohashi; Masashi Iino; Haruo Kumagai; Kenji Kato [National Institute of Advanced Industrial Science and Technology, Tsukuba (Japan)

2004-04-01

Goonyella coking-coal was extracted with a 1:1 (v/v) carbon disulfide/N-methyl-2-pyrrolidinone (CS{sub 2}/NMP) mixed solvent and then fractionated into four with pyridine and chloroform. High-temperature {sup 1}H NMR analysis conducted on each fraction and their mixtures in-situ showed that the lightest, the chloroform-soluble fraction (CS), was rich in mobile hydrogen, H{sub m}, the variation of which with temperature corresponded to that of a thermoplastic parameter tan {delta} determined by in-situ viscoelastic measurement. In contrast, chloroform-insoluble and pyridine-soluble (CIPS) and pyridine-insoluble (PIMS) fractions showed scant change in H{sub m} with temperature, although the intermediate hydrogen, H{sub int}, increased upon heating. These results allow the different fractions to be characterized qualitatively on the basis of differences in hydrogen mobility. In mixtures of the continuous fractions, positive interactions occurred that enhanced the value of tan {delta} as well as the overall hydrogen mobility. A single maximum was observed in the tan {delta} response of these mixtures, which indicated that the heavier fractions were solvated through the action of the lighter ones. In a discontinuous mixture of the fractions, molecular interaction was slight compared to continuous mixtures; only the light fraction started to soften at low temperature and, as a result, a bimodal response occurred in tan {delta}. The thermoplastic response of coking coal can be modeled on a self-dissolution basis involving the {approximately}50% of solvent-soluble components that are present in whole coking coals and which possess a continuous fraction distribution from light to heavy. The mobility of the system develops continuously upon heating as a result of the progressive solvating action of the lighter components facilitating dissolution and/or dispersion of the heavier components. 25 refs., 7 figs., 2 tabs.

9. Early Predictors of Middle School Fraction Knowledge

Science.gov (United States)

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…

10. 16 CFR 500.17 - Fractions.

Science.gov (United States)

2010-01-01

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

11. Teaching Fractions. Educational Practices Series-22

Science.gov (United States)

Fazio, Lisa; Siegler, Robert

2011-01-01

Students around the world have difficulties in learning about fractions. In many countries, the average student never gains a conceptual knowledge of fractions. This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on a…

12. On varitional iteration method for fractional calculus

Directory of Open Access Journals (Sweden)

Wu Hai-Gen

2017-01-01

Full Text Available Modification of the Das’ variational iteration method for fractional differential equations is discussed, and its main shortcoming involved in the solution process is pointed out and overcome by using fractional power series. The suggested computational procedure is simple and reliable for fractional calculus.

13. An Alternative Starting Point for Fraction Instruction

Science.gov (United States)

Cortina, José Luis; Višnovská, Jana; Zúñiga, Claudia

2015-01-01

We analyze the results of a study conducted for the purpose of assessing the viability of an alternative starting point for teaching fractions. The alternative is based on Freudenthal's insights about fraction as comparison. It involves portraying the entities that unit fractions quantify as always being apart from the reference unit, instead of…

14. Fractional Euler Limits and Their Applications

OpenAIRE

MacNamara, Shev; Henry, Bruce I; McLean, William

2016-01-01

Generalisations of the classical Euler formula to the setting of fractional calculus are discussed. Compound interest and fractional compound interest serve as motivation. Connections to fractional master equations are highlighted. An application to the Schlogl reactions with Mittag-Leffler waiting times is described.

15. Chemical fractionation of heavy metals in a soil amended with repeated sewage sludge application

International Nuclear Information System (INIS)

Walter, I.; Cuevas, G.

1999-01-01

A sequential extraction method (KNO 3 , NaOH, Na 2 -EDTA, HNO 3 ) was used to determine the soil fraction of Zn, Cd, Cu, Ni, Pb, and Cr in different plots treated with sewage sludges. The sludges were applied to cropland from 1983 to 1991. Soil samples were collected after the 1st and 5th-year of the last sludge application. Sludge applications increased the INOR-fraction for Zn, Cd, and Cu. Cu was the only element found in the EXCH-fraction. Pb and Cr were found mainly in the RES-fraction. Ni was found in the INOR and OM-fractions. All the metals increased in the more resistant fractions. Sewage sludge applications changed the metals distribution of the soil and this effect has continued for at least 5 years. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

16. Trieste will continue

International Nuclear Information System (INIS)

1968-01-01

Trieste will continue to be the home of the International Centre for Theoretical Physics for the foreseeable future. An agreement signed in Vienna during December between the Italian Government and the Agency brought this assurance. (author)

17. Nocturnal continuous glucose monitoring

DEFF Research Database (Denmark)

Bay, Christiane; Kristensen, Peter Lommer; Pedersen-Bjergaard, Ulrik

2013-01-01

Abstract Background: A reliable method to detect biochemical nocturnal hypoglycemia is highly needed, especially in patients with recurrent severe hypoglycemia. We evaluated reliability of nocturnal continuous glucose monitoring (CGM) in patients with type 1 diabetes at high risk of severe...

18. Continual improvement plan

Science.gov (United States)

1994-01-01

NASA's approach to continual improvement (CI) is a systems-oriented, agency-wide approach that builds on the past accomplishments of NASA Headquarters and its field installations and helps achieve NASA's vision, mission, and values. The NASA of the future will fully use the principles of continual improvement in every aspect of its operations. This NASA CI plan defines a systematic approach and a model for continual improvement throughout NASA, stressing systems integration and optimization. It demonstrates NASA's constancy of purpose for improvement - a consistent vision of NASA as a worldwide leader in top-quality science, technology, and management practices. The CI plan provides the rationale, structures, methods, and steps, and it defines NASA's short term (1-year) objectives for improvement. The CI plan presents the deployment strategies necessary for cascading the goals and objectives throughout the agency. It also provides guidance on implementing continual improvement with participation from top leadership and all levels of employees.

19. Continuing Medical Education

African Journals Online (AJOL)

20. Branching trajectory continual integral

International Nuclear Information System (INIS)

Maslov, V.P.; Chebotarev, A.M.

1980-01-01

Heuristic definition of the Feynman continual integral over branching trajectories is suggested which makes it possible to obtain in the closed form the solution of the Cauchy problem for the model Hartree equation. A number of properties of the solution is derived from an integral representation. In particular, the quasiclassical asymptotics, exact solution in the gaussian case and perturbation theory series are described. The existence theorem for the simpliest continual integral over branching trajectories is proved [ru

1. Natural fractionation of uranium isotopes

Energy Technology Data Exchange (ETDEWEB)

Noordmann, Janine

2015-01-24

The topic of this thesis was the investigation of U (n({sup 238}U) / n({sup 235}U)) isotope variations in nature with a focus on samples (1) that represent the continental crust and its weathering products (i.e. granites, shales and river water) (2) that represent products of hydrothermal alteration on mid-ocean ridges (i.e. altered basalts, carbonate veins and hydrothermal water) and (3) from restricted euxinic basins (i.e. from the water column and respective sediments). The overall goal was to explore the environmental conditions and unravel the mechanisms that fractionate the two most abundant U isotopes, n({sup 238}U) and n({sup 235}U), on Earth.

2. 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.

3. Hamiltonian Chaos and Fractional Dynamics

International Nuclear Information System (INIS)

Combescure, M

2005-01-01

This book provides an introduction and discussion of the main issues in the current understanding of classical Hamiltonian chaos, and of its fractional space-time structure. It also develops the most complex and open problems in this context, and provides a set of possible applications of these notions to some fundamental questions of dynamics: complexity and entropy of systems, foundation of classical statistical physics on the basis of chaos theory, and so on. Starting with an introduction of the basic principles of the Hamiltonian theory of chaos, the book covers many topics that can be found elsewhere in the literature, but which are collected here for the readers' convenience. In the last three parts, the author develops topics which are not typically included in the standard textbooks; among them are: - the failure of the traditional description of chaotic dynamics in terms of diffusion equations; - he fractional kinematics, its foundation and renormalization group analysis; - 'pseudo-chaos', i.e. kinetics of systems with weak mixing and zero Lyapunov exponents; - directional complexity and entropy. The purpose of this book is to provide researchers and students in physics, mathematics and engineering with an overview of many aspects of chaos and fractality in Hamiltonian dynamical systems. In my opinion it achieves this aim, at least provided researchers and students (mainly those involved in mathematical physics) can complement this reading with comprehensive material from more specialized sources which are provided as references and 'further reading'. Each section contains introductory pedagogical material, often illustrated by figures coming from several numerical simulations which give the feeling of what's going on, and thus is very useful to the reader who is not very familiar with the topics presented. Some problems are included at the end of most sections to help the reader to go deeper into the subject. My one regret is that the book does not

4. Utilization of Different Corn Fractions by Broilers

Directory of Open Access Journals (Sweden)

SIFR Costa

2015-09-01

Full Text Available ABSTRACTThis study was conducted to evaluate the nutritional values of fractions of damaged corn. One hundred and eighty 22-d-old Cobb 500 male broilers were distributed in batteries according to a completely randomized design with six treatments of six replicates each. The treatments consisted of diets containing five corn fractions, classified as sound, fermented, insect-damaged, mold-damaged, or reference corn. The test diets consisted of 60% of reference diet + 40% of each corn fraction. Only the reference corn fraction included all the fractions at different proportions (0.8% fermented, 0.05% insect-damaged, 3.3% mold-damaged, and 95.85% sound grains. The method of total excreta collection was used to determine AMEn values and metabolizability coefficients of dry matter (MDM, crude protein (MCP, ether extract (MEE, and gross energy (MGE of the reference corn and its fractions. The density values of the corn fractions were used to calculate the correlations among the evaluated parameters. The evaluated corn fractions presented different compositions values. The insect-damaged and mold-damaged grains presented higher CP level, lower density, and MDM and MCP coefficients compared with the other fractions. However, calculated AMEn values were not significantly different (p>0.05 among corn fractions. A low correlation between density and AMEn content (r0.8 were calculated. Although the evaluated corn fractions presented different nutritional values, there were no marked differences in their utilization by broilers.

5. The fractional dynamics of quantum systems

Science.gov (United States)

Lu, Longzhao; Yu, Xiangyang

2018-05-01

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

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

Directory of Open Access Journals (Sweden)

Ai-Min Yang

2014-01-01

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

7. Feasibility study on Ashuganj NGL Fractionation Plant

Energy Technology Data Exchange (ETDEWEB)

NONE

2001-03-01

A feasibility study has been performed on Ashuganj NGL Fractionation Plant being planned in the People's Republic of Bangladesh. The present study has discussed a plant to manufacture liquefied oil gas, automotive fuel, and diesel fuel from liquefied natural gas. The plan calls for the plant life of 20 years, liquefied natural gas as the raw material to be supplied continuously and stably from the gas reservoir areas via the existing pipelines, the storage tank to have a size of 10-day production, and the product to be transported by barges on Meghna River. As a result of the discussions, the liquefied oil gas produced annually will correspond to crude oil of 44,690 tons, and to 858,048 tons of crude oil cumulatively for 20 years of the plant life. This is an energy derived from unutilized natural gas, which is creation of a new energy. With regard to the reduction of global warming gas emission, it was revealed that a reduction effect of 16,540,000 t-CO2 can be obtained in twenty years, if comparison is made based on combustion of firewood. (NEDO)

8. Feasibility study on Ashuganj NGL Fractionation Plant

Energy Technology Data Exchange (ETDEWEB)

NONE

2001-03-01

A feasibility study has been performed on Ashuganj NGL Fractionation Plant being planned in the People's Republic of Bangladesh. The present study has discussed a plant to manufacture liquefied oil gas, automotive fuel, and diesel fuel from liquefied natural gas. The plan calls for the plant life of 20 years, liquefied natural gas as the raw material to be supplied continuously and stably from the gas reservoir areas via the existing pipelines, the storage tank to have a size of 10-day production, and the product to be transported by barges on Meghna River. As a result of the discussions, the liquefied oil gas produced annually will correspond to crude oil of 44,690 tons, and to 858,048 tons of crude oil cumulatively for 20 years of the plant life. This is an energy derived from unutilized natural gas, which is creation of a new energy. With regard to the reduction of global warming gas emission, it was revealed that a reduction effect of 16,540,000 t-CO2 can be obtained in twenty years, if comparison is made based on combustion of firewood. (NEDO)

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

DEFF Research Database (Denmark)

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

2016-01-01

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

10. Continuous Markovian Logics

DEFF Research Database (Denmark)

Mardare, Radu Iulian; Cardelli, Luca; Larsen, Kim Guldstrand

2012-01-01

Continuous Markovian Logic (CML) is a multimodal logic that expresses quantitative and qualitative properties of continuous-time labelled Markov processes with arbitrary (analytic) state-spaces, henceforth called continuous Markov processes (CMPs). The modalities of CML evaluate the rates...... of the exponentially distributed random variables that characterize the duration of the labeled transitions of a CMP. In this paper we present weak and strong complete axiomatizations for CML and prove a series of metaproperties, including the finite model property and the construction of canonical models. CML...... characterizes stochastic bisimilarity and it supports the definition of a quantified extension of the satisfiability relation that measures the "compatibility" between a model and a property. In this context, the metaproperties allows us to prove two robustness theorems for the logic stating that one can...

11. 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.

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

Directory of Open Access Journals (Sweden)

Wei Li

2014-01-01

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

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

Directory of Open Access Journals (Sweden)

Ping Zhou

2012-01-01

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

14. Continuing bonds and place.

Science.gov (United States)

Jonsson, Annika; Walter, Tony

2017-08-01

Where do people feel closest to those they have lost? This article explores how continuing bonds with a deceased person can be rooted in a particular place or places. Some conceptual resources are sketched, namely continuing bonds, place attachment, ancestral places, home, reminder theory, and loss of place. The authors use these concepts to analyze interview material with seven Swedes and five Britons who often thought warmly of the deceased as residing in a particular place and often performing characteristic actions. The destruction of such a place, by contrast, could create a troubling, haunting absence, complicating the deceased's absent-presence.

15. Introduction to Continuous Optimization

DEFF Research Database (Denmark)

Andreasson, Niclas; Evgrafov, Anton; Patriksson, Michael

optimal solutions for continuous optimization models. The main part of the mathematical material therefore concerns the analysis and linear algebra that underlie the workings of convexity and duality, and necessary/sufficient local/global optimality conditions for continuous optimization problems. Natural...... algorithms are then developed from these optimality conditions, and their most important convergence characteristics are analyzed. The book answers many more questions of the form “Why?” and “Why not?” than “How?”. We use only elementary mathematics in the development of the book, yet are rigorous throughout...

16. Continuous Platform Development

DEFF Research Database (Denmark)

Nielsen, Ole Fiil

low risks and investments but also with relatively fuzzy results. When looking for new platform projects, it is important to make sure that the company and market is ready for the introduction of platforms, and to make sure that people from marketing and sales, product development, and downstream......, but continuous product family evolution challenges this strategy. The concept of continuous platform development is based on the fact that platform development should not be a one-time experience but rather an ongoing process of developing new platforms and updating existing ones, so that product family...

17. Fractions Learning in Children With Mathematics Difficulties.

Science.gov (United States)

Tian, Jing; Siegler, Robert S

Learning fractions is difficult for children in general and especially difficult for children with mathematics difficulties (MD). Recent research on developmental and individual differences in fraction knowledge of children with MD and typically achieving (TA) children has demonstrated that U.S. children with MD start middle school behind their TA peers in fraction understanding and fall further behind during middle school. In contrast, Chinese children, who like the MD children in the United States score in the bottom one third of the distribution in their country, possess reasonably good fraction understanding. We interpret these findings within the framework of the integrated theory of numerical development. By emphasizing the importance of fraction magnitude knowledge for numerical understanding in general, the theory proved useful for understanding differences in fraction knowledge between MD and TA children and for understanding how knowledge can be improved. Several interventions demonstrated the possibility of improving fraction magnitude knowledge and producing benefits that generalize to fraction arithmetic learning among children with MD. The reasonably good fraction understanding of Chinese children with MD and several successful interventions with U.S. students provide hope for the improvement of fraction knowledge among American children with MD.

18. Modeling and analysis of fractional order DC-DC converter.

Science.gov (United States)

Radwan, Ahmed G; Emira, Ahmed A; AbdelAty, Amr M; Azar, Ahmad Taher

2017-07-11

19. Fractional ablative erbium YAG laser

DEFF Research Database (Denmark)

Taudorf, Elisabeth H; Haak, Christina S; Erlendsson, Andrés M

2014-01-01

laser parameters with tissue effects. MATERIALS AND METHODS: Ex vivo pig skin was exposed to a miniaturized 2,940 nm AFXL, spot size 225 µm, density 5%, power levels 1.15-2.22 W, pulse durations 50-225 microseconds, pulse repetition rates 100-500 Hz, and 2, 20, or 50 stacked pulses, resulting in pulse......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...... 190 to 347 µm. CONCLUSIONS: Pulse stacking with a small, low power 2,940 nm AFXL created reproducible shallow to deep micropores, and influenced micropore configuration. Mathematical modeling established relations between laser settings and micropore dimensions, which assists in choosing laser...

20. Studies on continuous fermentation

Energy Technology Data Exchange (ETDEWEB)

Ueda, K

1958-01-01

Continuous fermentation of molasses with a combined system of agitated vessel and flow pipe is studied. A new apparatus was designed. The rate of the fermentation was faster with this apparatus than with the former apparatus which was composed of two vessels.

1. Continuous Reinforced Concrete Beams

DEFF Research Database (Denmark)

Hoang, Cao Linh; Nielsen, Mogens Peter

1996-01-01

This report deals with stress and stiffness estimates of continuous reinforced concrete beams with different stiffnesses for negative and positive moments e.g. corresponding to different reinforcement areas in top and bottom. Such conditions are often met in practice.The moment distribution...

DEFF Research Database (Denmark)

Monahan, Amanda M; Sztain, Jacklynn F; Khatibi, Bahareh

2016-01-01

on cutaneous knee sensation in volunteers. METHODS: Bilateral adductor canal catheters were inserted in 24 volunteers followed by ropivacaine 0.2% administration for 8 hours. One limb of each subject was assigned randomly to a continuous infusion (8 mL/h) or automated hourly boluses (8 m...

3. Continuous Personal Improvement.

Science.gov (United States)

Emiliani, M. L.

1998-01-01

Suggests that continuous improvement tools used in the workplace can be applied to self-improvement. Explains the use of such techniques as one-piece flow, kanban, visual controls, and total productive maintenance. Points out misapplications of these tools and describes the use of fishbone diagrams to diagnose problems. (SK)

4. Continuity and Change.

Science.gov (United States)

Istance, David

1985-01-01

Examines issues related to continuity in education and educational change. Indicates that although schools must be responsive to changing social and economic conditions (and contribute to them), they must also be protected against fluctuating swings of educational fashion and safeguard their long-term mission, even when buffeted by short-term…

5. Promoting Continuing Education Programs.

Science.gov (United States)

Hendrickson, Gayle A.

This handbook is intended for use by institutions in marketing their continuing education programs. A section on "Devising Your Strategy" looks at identifying a target audience, determining the marketing approach, and developing a marketing plan and promotional techniques. A discussion of media options looks at the advantages and…

6. Continuous quality improvement

NARCIS (Netherlands)

Rohlin, Madeleine; Schaub, Rob M.H.; Holbrook, Peter; Leibur, Edvitar; Lévy, Gérard; Roubalikova, Lenka; Nilner, Maria; Roger-Leroi, Valerie; Danner, Gunter; Iseri, Haluk; Feldman, Cecile

2002-01-01

Versch. in: Eur J Dent Educ; 6 (Suppl. 3): 67–77 Continuous quality improvement (CQI) can be envisaged as a circular process of goal-setting, followed by external and internal evaluations resulting in improvements that can serve as goals for a next cycle. The need for CQI is apparent, because of

7. Continuous digital health

NARCIS (Netherlands)

Van Halteren, Aart; Gay, Vaĺerie

2015-01-01

A transformation is underway regarding how we deal with our health, not only because mobile Internet technology has made it possible to have continuous access to personal health information, but also because breaking the trend of ever-growing healthcare costs is increasingly necessary. Connectivity,

8. Continuous quality improvement

International Nuclear Information System (INIS)

Bourne, P.B.

1985-01-01

This paper describes the various statistical tools used at the Hanford Engineering Development Laboratory to achieve continuous quality improvement in the development of Breeder Reactor Technology and in reactor operations. The role of the quality assurance professionals in this process, including quantifiable measurements using actual examples, is provided. The commitment to quality improvement through top management involvement is dramatically illustrated

9. Continuous feedback fluid queues

NARCIS (Netherlands)

Scheinhardt, Willem R.W.; van Foreest, N.D.; Mandjes, M.R.H.

2003-01-01

We investigate a fluid buffer which is modulated by a stochastic background process, while the momentary behavior of the background process depends on the current buffer level in a continuous way. Loosely speaking the feedback is such that the background process behaves as a Markov process' with

10. Continuing Medical Education

African Journals Online (AJOL)

A review article willintroduce readers to the educational subject matter, along with one-page summarises (in print) of additional articles that may be accessed in full online. We will continue to offer topical and up-to-date CME material. Readers are encouraged to register with samj.org.za to receive future notifications of new ...

11. Equivalence of hyperfractionated and continuous brachytherapy in a rat tumor model and remarkable effectiveness when preceded by external irradiation.

NARCIS (Netherlands)

Veninga, T.; Visser, A.G.; Berg, A.P. van den; Hooije, C.M. van; Geel, C.A. van; Levendag, P.C.

2001-01-01

PURPOSE: In clinical brachytherapy, there is a tendency to replace continuous low-dose-rate (LDR) irradiation by either single-dose or fractionated high-dose-rate (HDR) irradiation. In this study, the equivalence of LDR treatments and fractionated HDR (2 fractions/day) or pulsed-dose-rate (PDR, 4

12. Generalized hydrodynamic correlations and fractional memory functions

Science.gov (United States)

Rodríguez, Rosalio F.; Fujioka, Jorge

2015-12-01

A fractional generalized hydrodynamic (GH) model of the longitudinal velocity fluctuations correlation, and its associated memory function, for a complex fluid is analyzed. The adiabatic elimination of fast variables introduces memory effects in the transport equations, and the dynamic of the fluctuations is described by a generalized Langevin equation with long-range noise correlations. These features motivate the introduction of Caputo time fractional derivatives and allows us to calculate analytic expressions for the fractional longitudinal velocity correlation function and its associated memory function. Our analysis eliminates a spurious constant term in the non-fractional memory function found in the non-fractional description. It also produces a significantly slower power-law decay of the memory function in the GH regime that reduces to the well-known exponential decay in the non-fractional Navier-Stokes limit.

13. The fractional oscillator process with two indices

International Nuclear Information System (INIS)

Lim, S C; Teo, L P

2009-01-01

We introduce a new fractional oscillator process which can be obtained as a solution of a stochastic differential equation with two fractional orders. Basic properties such as fractal dimension and short-range dependence of the process are studied by considering the asymptotic properties of its covariance function. By considering the fractional oscillator process as the velocity of a diffusion process, we derive the corresponding diffusion constant, fluctuation-dissipation relation and mean-square displacement. The fractional oscillator process can also be regarded as a one-dimensional fractional Euclidean Klein-Gordon field, which can be obtained by applying the Parisi-Wu stochastic quantization method to a nonlocal Euclidean action. The Casimir energy associated with the fractional field at positive temperature is calculated by using the zeta function regularization technique

14. Fractional RC and LC Electrical Circuits

Directory of Open Access Journals (Sweden)

Gómez-Aguilar José Francisco

2014-04-01

Full Text Available In this paper we propose a fractional differential equation for the electrical RC and LC circuit in terms of the fractional time derivatives of the Caputo type. The order of the derivative being considered is 0 < ɣ ≤1. To keep the dimensionality of the physical parameters R, L, C the new parameter σ is introduced. This parameter characterizes the existence of fractional structures in the system. A relation between the fractional order time derivative ɣ and the new parameter σ is found. The numeric Laplace transform method was used for the simulation of the equations results. The results show that the fractional differential equations generalize the behavior of the charge, voltage and current depending of the values of ɣ. The classical cases are recovered by taking the limit when ɣ = 1. An analysis in the frequency domain of an RC circuit shows the application and use of fractional order differential equations.

15. COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments

International Nuclear Information System (INIS)

Thompson, I.J.; Barnett, A.R.

1985-01-01

The routine COULCC calculates both the oscillating and the exponentially varying Coulomb wave functions, and their radial derivations, for complex eta(Sommerfeld parameter), complex energies and complex angular momenta. The functions for uncharged scattering (spherical Bessels) and cylindrical Bessel functions are special cases which are more easily solved. Two linearly independent solutions are found, in general, to the differential equation f''(x)+g(x)f(x)=0, where g(x) has x 0 , x -1 and x -2 terms, with coefficients 1, -2eta and -lambda(lambda+1), respectively. (orig.)

16. On a connection between Stieltjes continued fraction, KAM theory and E-infinity theory

International Nuclear Information System (INIS)

Marek-Crnjac, L.

2004-01-01

In the present work we establish a connection between El Naschie's E-infinity theory and Stieltjes solution of the problem on the distribution of mass along a line and KAM theory following Gantmacher and Krein mechanical interpretation of Stieltjes' classical research on the subject

17. Fractional Bateman—Feshbach Tikochinsky Oscillator

Science.gov (United States)

2014-02-01

In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these things in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman—Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grünwald—Letnikov approach, which is power series expansion of the generating function.

18. Early Predictors of Middle School Fraction Knowledge

OpenAIRE

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...

19. Operator Fractional Brownian Motion and Martingale Differences

Directory of Open Access Journals (Sweden)

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.

20. Utilization of Different Corn Fractions by Broilers

OpenAIRE

Costa, SIFR; Stringhini, JH; Ribeiro, AML; Pontalti, G; MacManus, C

2015-01-01

ABSTRACTThis study was conducted to evaluate the nutritional values of fractions of damaged corn. One hundred and eighty 22-d-old Cobb 500 male broilers were distributed in batteries according to a completely randomized design with six treatments of six replicates each. The treatments consisted of diets containing five corn fractions, classified as sound, fermented, insect-damaged, mold-damaged, or reference corn. The test diets consisted of 60% of reference diet + 40% of each corn fraction. ...

1. Fractional Order Models of Industrial Pneumatic Controllers

Directory of Open Access Journals (Sweden)

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.

2. Fractional Bateman—Feshbach Tikochinsky Oscillator

International Nuclear Information System (INIS)

2014-01-01

In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these things in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman—Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grünwald—Letnikov approach, which is power series expansion of the generating function. (physics of elementary particles and fields)

3. On some fractional order hardy inequalities

Directory of Open Access Journals (Sweden)

Kufner Alois

1997-01-01

Full Text Available Weighted inequalities for fractional derivatives ( fractional order Hardy-type inequalities have recently been proved in [4] and [1]. In this paper, new inequalities of this type are proved and applied. In particular, the general mixed norm case and a general twodimensional weight are considered. Moreover, an Orlicz norm version and a multidimensional fractional order Hardy inequality are proved. The connections to related results are pointed out.

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

Institute of Scientific and Technical Information of China (English)

Kecai Cao; Yang Quan Chen; Daniel Stuart

2016-01-01

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

5. Improving Children's Knowledge of Fraction Magnitudes.

Directory of Open Access Journals (Sweden)

Lisa K Fazio

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

6. The realization problem for positive and fractional systems

CERN Document Server

2014-01-01

This book addresses the realization problem of positive and fractional continuous-time and discrete-time linear systems. Roughly speaking the essence of the realization problem can be stated as follows: Find the matrices of the state space equations of linear systems for given their transfer matrices. This first book on this topic shows how many well-known classical approaches have been extended to the new classes of positive and fractional linear systems. The modified Gilbert method for multi-input multi-output linear systems, the method for determination of realizations in the controller canonical forms and in observer canonical forms are presented. The realization problem for linear systems described by differential operators, the realization problem in the Weierstrass canonical forms and of the descriptor linear systems for given Markov parameters are addressed. The book also presents a method for the determination of minimal realizations of descriptor linear systems and an extension for cone linear syste...

7. A Recurrent Neural Network for Nonlinear Fractional Programming

Directory of Open Access Journals (Sweden)

Quan-Ju Zhang

2012-01-01

Full Text Available This paper presents a novel recurrent time continuous neural network model which performs nonlinear fractional optimization subject to interval constraints on each of the optimization variables. The network is proved to be complete in the sense that the set of optima of the objective function to be minimized with interval constraints coincides with the set of equilibria of the neural network. It is also shown that the network is primal and globally convergent in the sense that its trajectory cannot escape from the feasible region and will converge to an exact optimal solution for any initial point being chosen in the feasible interval region. Simulation results are given to demonstrate further the global convergence and good performance of the proposing neural network for nonlinear fractional programming problems with interval constraints.

8. Continuous venovenous haemodialysis

DEFF Research Database (Denmark)

Jensen, Dorte Møller; Bistrup, C; Pedersen, R S

1996-01-01

A simple three-pump-based system for the performance of continuous venovenous haemodialysis is described. The method employs access to the circulation via a double-lumen catheter, and by means of a standard extracorporeal peristaltic pump the blood is circulated through a haemofiltration filter....... Standard solutions for peritoneal dialysis are administered in a single-pass manner countercurrent to the blood flow. To control the dialysate flow through the filter, two separate pumps designed for intravenous infusion are used. Anticoagulation is achieved by means of continuous heparin infusion....... This three-pump system is effective in controlling the fluid balance and the level of azotemia. Furthermore, this system makes haemodialysis possible in spite of severe haemodynamic instability. The system is easy to use and inexpensive. 3 patients participated in the study....

9. Continuous Fiber Ceramic Composites

Energy Technology Data Exchange (ETDEWEB)

Fareed, Ali [Honeywell Advanced Composites Inc. (HACI), Newark, DE (United States); Craig, Phillip A. [Honeywell Advanced Composites Inc. (HACI), Newark, DE (United States)

2002-09-01

Fiber-reinforced ceramic composites demonstrate the high-temperature stability of ceramics--with an increased fracture toughness resulting from the fiber reinforcement of the composite. The material optimization performed under the continuous fiber ceramic composites (CFCC) included a series of systematic optimizations. The overall goals were to define the processing window, to increase the robustinous of the process, to increase process yield while reducing costs, and to define the complexity of parts that could be fabricated.

10. Deconstructing continuous flash suppression

OpenAIRE

Yang, Eunice; Blake, Randolph

2012-01-01

In this paper, we asked to what extent the depth of interocular suppression engendered by continuous flash suppression (CFS) varies depending on spatiotemporal properties of the suppressed stimulus and CFS suppressor. An answer to this question could have implications for interpreting the results in which CFS influences the processing of different categories of stimuli to different extents. In a series of experiments, we measured the selectivity and depth of suppression (i.e., elevation in co...

11. Safety Campaign Continues

CERN Multimedia

2002-01-01

If you see this poster, stop and read it! This is the third poster produced by TIS Division as part of its information campaign on health and safety in the workplace. It provides statistics on occupational accidents at CERN. You will see that, as in the rest of Europe, falls, slips and trips continue to be the main cause of accident. So, eyes open and take care! For more information : http://safety.cern.ch/

12. Robust continuous clustering.

Science.gov (United States)

2017-09-12

Clustering is a fundamental procedure in the analysis of scientific data. It is used ubiquitously across the sciences. Despite decades of research, existing clustering algorithms have limited effectiveness in high dimensions and often require tuning parameters for different domains and datasets. We present a clustering algorithm that achieves high accuracy across multiple domains and scales efficiently to high dimensions and large datasets. The presented algorithm optimizes a smooth continuous objective, which is based on robust statistics and allows heavily mixed clusters to be untangled. The continuous nature of the objective also allows clustering to be integrated as a module in end-to-end feature learning pipelines. We demonstrate this by extending the algorithm to perform joint clustering and dimensionality reduction by efficiently optimizing a continuous global objective. The presented approach is evaluated on large datasets of faces, hand-written digits, objects, newswire articles, sensor readings from the Space Shuttle, and protein expression levels. Our method achieves high accuracy across all datasets, outperforming the best prior algorithm by a factor of 3 in average rank.

13. Control and switching synchronization of fractional order chaotic systems using active control technique

KAUST Repository

2013-01-01

This paper discusses the continuous effect of the fractional order parameter of the Lü system where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. Four different synchronization cases are introduced based on the switching parameters. Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time. The nonstandard finite difference method is used for the numerical solution of the fractional order master and slave systems. Many numeric simulations are presented to validate the concept for different fractional order parameters.

14. Control and switching synchronization of fractional order chaotic systems using active control technique

KAUST Repository

2013-03-13

This paper discusses the continuous effect of the fractional order parameter of the Lü system where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. Four different synchronization cases are introduced based on the switching parameters. Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time. The nonstandard finite difference method is used for the numerical solution of the fractional order master and slave systems. Many numeric simulations are presented to validate the concept for different fractional order parameters.

15. The come-back of hypo fractionation?

International Nuclear Information System (INIS)

Cosset, J.M.

2005-01-01

Hypo-fractionation (i.e. the use of fewer higher fractional doses than usual) is not a new concept. It had actually been proposed in the early year of Radiotherapy by the German and Austrian specialists. In the seventy's, supported by the - wrong - hypotheses which gave birth to the NSD (Nominal Standard Dose), hypo-fractionation reappears. The consequential increase of late complications which was observed led the radiation oncologists to give up again using large doses per fraction, except for a few specific situations, such as palliative treatments. We are recently facing a new 'come-back' of hypo-fractionation, in particular for breast and prostate cancers. In the case of breast cancer, the aim is clearly to look for more 'convenience' for both the patients and the physicians, proposing shorter irradiation schedules including a lesser number of fractions. Some 'modestly' hypo-fractionated schemes have been proposed and used, without apparently altering the efficacy/toxicity ratio, but these results have been seriously questioned. As for prostate cancer, the situation is different, since in that case new radiobiological data are at the origin of the newly proposed hypo-fractionation schedules. A number of papers actually strongly suggested that the fractionation sensitivity of prostate cancer could be higher than the one of the tissues responsible for late toxicity (i.e the exact opposite of the classical dogma). Based on those data, several hypo-fractionated schemes have been proposed, with a few preliminary results looking similar to the ones obtained by the classical schedules. However, no randomized study is available so far, and a few recent radiobiological data are now questioning the new dogma of the high fractionation sensitivity of prostate cancer. For those two - frequent - cancers, it seems therefore that prudence should prevail before altering classical irradiation schedules which have proven their efficacy, while staying open to new concepts and

16. Hydrogen solubility measurements of analyzed tall oil fractions and a solubility model

International Nuclear Information System (INIS)

Uusi-Kyyny, Petri; Pakkanen, Minna; Linnekoski, Juha; Alopaeus, Ville

2017-01-01

Highlights: • Hydrogen solubility was measured in four tall oil fractions between 373 and 597 K. • Continuous flow synthetic isothermal and isobaric method was used. • A Henry’s law model was developed for the distilled tall oil fractions. • The complex composition of the samples was analyzed and is presented. - Abstract: Knowledge of hydrogen solubility in tall oil fractions is important for designing hydrotreatment processes of these complex nonedible biobased materials. Unfortunately measurements of hydrogen solubility into these fractions are missing in the literature. This work reports hydrogen solubility measured in four tall oil fractions between 373 and 597 K and at pressures from 5 to 10 MPa. Three of the fractions were distilled tall oil fractions their resin acids contents are respectively 2, 20 and 23 in mass-%. Additionally one fraction was a crude tall oil (CTO) sample containing sterols as the main neutral fraction. Measurements were performed using a continuous flow synthetic isothermal and isobaric method based on the visual observation of the bubble point. Composition of the flow was changed step-wise for the bubble point composition determination. We assume that the tall oil fractions did not react during measurements, based on the composition analysis performed before and after the measurements. Additionally the densities of the fractions were measured at atmospheric pressure from 293.15 to 323.15 K. A Henry’s law model was developed for the distilled tall oil fractions describing the solubility with an absolute average deviation of 2.1%. Inputs of the solubility model are temperature, total pressure and the density of the oil at 323.15 K. The solubility of hydrogen in the CTO sample can be described with the developed model with an absolute average deviation of 3.4%. The solubility of hydrogen increases both with increasing pressure and/or increasing temperature. The more dense fractions of the tall oil exhibit lower hydrogen

17. Isotope Fractionation Studies in Prestellar Cores: The Case of Nitrogen

Science.gov (United States)

Milam, Stefanie N.; Charnley, Steven B.

2011-01-01

Isotopically fractionated material is found in many solar system objects, including meteorites and comets. It is considered, in some cases, to trace interstellar material that was incorporated into the solar system without undergoing significant processing, thus preserving the fractionation. In interstellar molecular clouds, ion-molecule chemistry continually cycles nitrogen between the two main reservoirs - N and N2 - leading to only minor N-15 enrichments. Charnley and Rodgers showed that depletion of CO removes oxygen from the gas and weakens this cycle such that significant N-15 fractionation can occur for N2 and other N-bearing species in such cores. Observations are being conducted at millimeter and submillimeter wavelengths employing various facilities in order to both spatially and spectrally, resolve emission from these cores. A preliminary study to obtain the N-14/N-15 ratio in nitriles (HCN and HNC) was conducted at the Arizona Radio Observatory's 12m telescope on Kitt Peak, AZ. Spectra were obtained at high resolution (0.08 km/s) in order to resolve dynamic properties of each source as well as to resolve hyperfine structure present in certain isotopologues. This study included four dark cloud cores, observed to have varying levels of molecular depletion: L1521E, L1498, L1544, and L1521F. Previous studies of the N-14/N-15 ratio towards LI544 were obtained with N2H+ and NIH3, yielding ratios of 446 and >700, respectively. The discrepancy observed in these two measurements suggests a strong chemical dependence on the fractionation of nitrogen. Ratios (C,N, and D) obtained from isotopologues for a particular molecule are likely tracing the same chemical heritage and are directly comparable within a given source. Results and comparisons between the protostellar evolutionary state and isomer isotope fractionation as well as between other N-bearing species will be presented.

18. Can a sponge fractionate isotopes?

Science.gov (United States)

Patel, B; Patel, S; Balani, M C

1985-03-22

activities can be modified is by fractionation on the basis of mass of isotope. In view of the remarkable concentration factors observed for stable and radioactive isotopes of the same element and the specific activities reached, it is desirable that species of sponges, especially from the coastal and estuarine environments, be monitored to detect levels of pollution due to anthropogenic substances.

19. Representations of the Magnitudes of Fractions

Science.gov (United States)

Schneider, Michael; Siegler, Robert S.

2010-01-01

We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and denominators as separate whole numbers. However,…

20. A Computational Model of Fraction Arithmetic

Science.gov (United States)

Braithwaite, David W.; Pyke, Aryn A.; Siegler, Robert S.

2017-01-01

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

1. Void Fraction Instrument operation and maintenance manual

International Nuclear Information System (INIS)

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

1994-09-01

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

2. Safety of protein hydrolysates, fractions thereof and

NARCIS (Netherlands)

Gertjan Schaafsma

2009-01-01

This paper evaluates the safety for humans with regard to consumption of protein hydrolysates and fractions thereof, including bioactive peptides. The available literature on the safety of protein, protein hydrolysates, fractions thereof and free amino acids on relevant food legislation is reviewed

3. Fractional ablative laser skin resurfacing: a review.

Science.gov (United States)

Tajirian, Ani L; Tarijian, Ani L; Goldberg, David J

2011-12-01

Ablative laser technology has been in use for many years now. The large side effect profile however has limited its use. Fractional ablative technology is a newer development which combines a lesser side effect profile along with similar efficacy. In this paper we review fractional ablative laser skin resurfacing.

4. Forced splitting of fractions in CE

NARCIS (Netherlands)

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

5. Fractions Learning in Children with Mathematics Difficulties

Science.gov (United States)

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…

6. Paper Plate Fractions: The Counting Connection

Science.gov (United States)

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…

7. Fractional supersymmetry through generalized anyonic algebra

International Nuclear Information System (INIS)

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

2001-01-01

The construction of anyonic operators and algebra is generalized by using quons operators. Therefore, the particular version of fractional supersymmetry is constructed on the two-dimensional lattice by associating two generalized anyons of different kinds. The fractional supersymmetry Hamiltonian operator is obtained on the two-dimensional lattice and the quantum algebra U q (sl 2 ) is realized. (author)

8. The Whole Story: Understanding Fraction Computation

Science.gov (United States)

Dixon, Juli K.; Tobias, Jennifer M.

2013-01-01

What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…

9. Estimation's Role in Calculations with Fractions

Science.gov (United States)

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…

10. Unpacking Referent Units in Fraction Operations

Science.gov (United States)

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…

11. Mass fractionation processes of transition metal isotopes

Science.gov (United States)

Zhu, X. K.; Guo, Y.; Williams, R. J. P.; O'Nions, R. K.; Matthews, A.; Belshaw, N. S.; Canters, G. W.; de Waal, E. C.; Weser, U.; Burgess, B. K.; Salvato, B.

2002-06-01

Recent advances in mass spectrometry make it possible to utilise isotope variations of transition metals to address some important issues in solar system and biological sciences. Realisation of the potential offered by these new isotope systems however requires an adequate understanding of the factors controlling their isotope fractionation. Here we show the results of a broadly based study on copper and iron isotope fractionation during various inorganic and biological processes. These results demonstrate that: (1) naturally occurring inorganic processes can fractionate Fe isotope to a detectable level even at temperature ˜1000°C, which challenges the previous view that Fe isotope variations in natural system are unique biosignatures; (2) multiple-step equilibrium processes at low temperatures may cause large mass fractionation of transition metal isotopes even when the fractionation per single step is small; (3) oxidation-reduction is an importation controlling factor of isotope fractionation of transition metal elements with multiple valences, which opens a wide range of applications of these new isotope systems, ranging from metal-silicate fractionation in the solar system to uptake pathways of these elements in biological systems; (4) organisms incorporate lighter isotopes of transition metals preferentially, and transition metal isotope fractionation occurs stepwise along their pathways within biological systems during their uptake.

12. Gauge invariance and fractional quantized Hall effect

International Nuclear Information System (INIS)

Tao, R.; Wu, Y.S.

1984-01-01

It is shown that gauge invariance arguments imply the possibility of fractional quantized Hall effect; the Hall conductance is accurately quantized to a rational value. The ground state of a system showing the fractional quantized Hall effect must be degenerate; the non-degenerate ground state can only produce the integral quantized Hall effect. 12 references

13. Fractional Josephson vortices: oscillating macroscopic spins

Energy Technology Data Exchange (ETDEWEB)

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

2007-11-15

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

14. Making Sense of Fractions and Percentages

Science.gov (United States)

Whitin, David J.; Whitin, Phyllis

2012-01-01

Because fractions and percentages can be difficult for children to grasp, connecting them whenever possible is beneficial. Linking them can foster representational fluency as children simultaneously see the part-whole relationship expressed numerically (as a fraction and as a percentage) and visually (as a pie chart). NCTM advocates these…

15. On Fractional Order Hybrid Differential Equations

Directory of Open Access Journals (Sweden)

Mohamed A. E. Herzallah

2014-01-01

Full Text Available We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.

16. 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.

17. Wigner distribution and fractional Fourier transform

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.; Boashash, B.

2003-01-01

We have described the relationship between the fractional Fourier transform and the Wigner distribution by using the Radon-Wigner transform, which is a set of projections of the Wigner distribution as well as a set of squared moduli of the fractional Fourier transform. We have introduced the concept

18. Fractional-Fourier-domain weighted Wigner distribution

NARCIS (Netherlands)

Stankovic, L.; Alieva, T.; Bastiaans, M.J.

2001-01-01

A fractional-Fourier-domain realization of the weighted Wigner distribution (or S-method), producing auto-terms close to the ones in the Wigner distribution itself, but with reduced cross-terms, is presented. The computational cost of this fractional-domain realization is the same as the

19. Airborne release fractions/rates and respirable fractions for nonreactor nuclear facilities. Volume 2, Appendices

International Nuclear Information System (INIS)

1994-12-01

This document contains compiled data from the DOE Handbook on Airborne Release Fractions/Rates and Respirable Fractions for Nonreactor Nuclear facilities. Source data and example facilities utilized, such as the Plutonium Recovery Facility, are included

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

Science.gov (United States)

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.

1. 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.

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

Energy Technology Data Exchange (ETDEWEB)

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

1982-01-01

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

3. Spectroscopy of fractional Josephson vortex molecules

Energy Technology Data Exchange (ETDEWEB)

Goldobin, Edward; Gaber, Tobias; Buckenmaier, Kai; Kienzle, Uta; Sickinger, Hanna; Koelle, Dieter; Kleiner, Reinhold [Physikalisches Institut - Experimentalphysik II, Center for Collective Quantum Phenomena, Universitaet Tuebingen, Auf der Morgenstelle 14, D-72076 Tuebingen (Germany)

2010-07-01

Using tiny current injectors we create {kappa} discontinuities of the Josephson phase in a long Josephson junction. The junction reacts at the discontinuities by creating fractional Josephson vortices of size {lambda}{sub J} pinned at them. Such vortices carry the flux {phi}, which is a fraction of the magnetic flux quantum {phi}{sub 0}{approx}2.07 x 10{sup -15} Wb. Being pinned, a fractional vortex has an eigenfrequency (localized mode), which depends on {kappa} and applied bias current, and which lays within the plasma gap. If one considers a molecule consisting of several coupled fractional vortices, the eigenfrequency will split into several modes. We report on spectroscopy of a fractional vortex molecule performed in the thermal regime.

4. 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.

5. Continuous multivariate exponential extension

International Nuclear Information System (INIS)

Block, H.W.

1975-01-01

The Freund-Weinman multivariate exponential extension is generalized to the case of nonidentically distributed marginal distributions. A fatal shock model is given for the resulting distribution. Results in the bivariate case and the concept of constant multivariate hazard rate lead to a continuous distribution related to the multivariate exponential distribution (MVE) of Marshall and Olkin. This distribution is shown to be a special case of the extended Freund-Weinman distribution. A generalization of the bivariate model of Proschan and Sullo leads to a distribution which contains both the extended Freund-Weinman distribution and the MVE

6. Continuity and consensus

DEFF Research Database (Denmark)

Abrahamson, Peter

2010-01-01

maternal leave. These changes can be explained as adjustments to post-industrial conditions within a political culture relying on class compromises and a broad consensus informed by expert advice coming from civil servants and ad hoc policy commissions. The paper concludes that changes in Danish family...... policy reflect changing conditions for employment and the minding of children and that there has been a high degree of continuity and consensus about the change, as indicated by the strong increase in female labour market involvement....

7. Continuous Integration in CFMGR

CERN Document Server

Frohlingsdorf, David

2017-01-01

Cfmgr is a managing tool for network devices. At the moment there is no way to automatically check the working behaviour of the tool, meaning that a lot of effort is spend into manually testing the tool after an update. During my stay at CERN I developed a black-box testing framework for Cfmgr according to Continuous Integration practices and successfully deployed the framework using Jenkins and Docker. This report discusses in detail how the framework works and how it can be conﬁgured, and equally gives a broad problem description and outlines future work directions.

International Nuclear Information System (INIS)

Benjamin, R.S.; Chawla, S.P.; Ewer, M.S.; Hortobagyi, G.N.

1986-01-01

This chapter discusses the diminished cardiotoxicity as well as diminished nausea and vomiting with continuous infusions of adriamycin to patients undergoing radiation therapy, particularly with infusions of 48 hours or longer, and best with 96-hour infusions, the longest duration that has been studied systematically. In breast cancer, data show that more adriamycin is better, but only for a selected subgroup of patients: those with complete remission. The diminished cardiotoxicity makes the use of adriamycin more attractive in the adjuvant situation, where increased safety will decrease the chances of long-term complications and make retreatment easy for cured patients who develop second malignancies

9. Continuous Shearlet Tight Frames

KAUST Repository

Grohs, Philipp

2010-10-22

Based on the shearlet transform we present a general construction of continuous tight frames for L2(ℝ2) from any sufficiently smooth function with anisotropic moments. This includes for example compactly supported systems, piecewise polynomial systems, or both. From our earlier results in Grohs (Technical report, KAUST, 2009) it follows that these systems enjoy the same desirable approximation properties for directional data as the previous bandlimited and very specific constructions due to Kutyniok and Labate (Trans. Am. Math. Soc. 361:2719-2754, 2009). We also show that the representation formulas we derive are in a sense optimal for the shearlet transform. © 2010 Springer Science+Business Media, LLC.

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

OpenAIRE

Kumar, Sanjay

2018-01-01

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

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

Directory of Open Access Journals (Sweden)

Arman Aghili

2014-01-01

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

12. Removal of transuranics from Johnston Island soil by fractional classification

International Nuclear Information System (INIS)

Sunderland, N.R.

1987-01-01

The following conclusions were reached as a result of the research conducted with the TRUclean process on Johnston Island: Processed materials will have a total TRU activity of less than 500 Bq/Kg. Approximately 90% of the TRU activity in coral/soil is removed by a single pass through the fractional classification process. A volume reduction of greater than 90% of the original contaminated volume can be achieved with the returned ''clean'' volume less than or equal to the cleanup criteria. Reprocessing or multiple staging of the process units will yield overall efficiencies of greater than 90%. Continued testing at Nevada Test Site confirmed these conclusions

13. Selection of LWR cycle length and fuel reload fraction

International Nuclear Information System (INIS)

Driscoll, M.J.; Handwerk, C.S.; McMahon, M.V.

1997-01-01

The continuing evolution of fuel having ever higher burnup capability and the increased emphasis on high plant capacity factor to keep nuclear power cost-competitive, motivates re-examination of some basic fuel management strategies. Specifically, what are the economic optimum goals for the fraction of core to be refueled, 1/n, and the length of the intra-refueling cycle, T c . The authors present a simple model to study these questions. They conclude that unless substantial improvements in technology are forthcoming, or economic circumstances change significantly, departure from 2- to 4-batch management, or longer than 2- to 3-year cycles in LWRs is not supported by their analysis

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

Directory of Open Access Journals (Sweden)

Sheng-Ping Yan

2014-01-01

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

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

Directory of Open Access Journals (Sweden)

Hossein Jafari

2016-04-01

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

16. Single fraction versus multiple fraction radiotherapy for palliation of painful vertebral bone metastases: A prospective study

Directory of Open Access Journals (Sweden)

Dipanjan Majumder

2012-01-01

Conclusions: Different fractionation of radiation has same response and toxicity in treatment of vertebral bone metastasis. Single fraction RT may be safely used to treat these cases as this is more cost effective and less time consuming. Studies may be conducted to find out particular subgroup of patients to be benefitted more by either fractionation schedule; however, our study cannot comment on that issue.

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

NARCIS (Netherlands)

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

2016-01-01

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

18. Landsat Data Continuity Mission

Science.gov (United States)

,

2012-01-01

The Landsat Data Continuity Mission (LDCM) is a partnership formed between the National Aeronautics and Space Administration (NASA) and the U.S. Geological Survey (USGS) to place the next Landsat satellite in orbit in January 2013. The Landsat era that began in 1972 will become a nearly 41-year global land record with the successful launch and operation of the LDCM. The LDCM will continue the acquisition, archiving, and distribution of multispectral imagery affording global, synoptic, and repetitive coverage of the Earth's land surfaces at a scale where natural and human-induced changes can be detected, differentiated, characterized, and monitored over time. The mission objectives of the LDCM are to (1) collect and archive medium resolution (30-meter spatial resolution) multispectral image data affording seasonal coverage of the global landmasses for a period of no less than 5 years; (2) ensure that LDCM data are sufficiently consistent with data from the earlier Landsat missions in terms of acquisition geometry, calibration, coverage characteristics, spectral characteristics, output product quality, and data availability to permit studies of landcover and land-use change over time; and (3) distribute LDCM data products to the general public on a nondiscriminatory basis at no cost to the user.

19. Integrated, Continuous Emulsion Creamer.

Science.gov (United States)

Cochrane, Wesley G; Hackler, Amber L; Cavett, Valerie J; Price, Alexander K; Paegel, Brian M

2017-12-19

Automated and reproducible sample handling is a key requirement for high-throughput compound screening and currently demands heavy reliance on expensive robotics in screening centers. Integrated droplet microfluidic screening processors are poised to replace robotic automation by miniaturizing biochemical reactions to the droplet scale. These processors must generate, incubate, and sort droplets for continuous droplet screening, passively handling millions of droplets with complete uniformity, especially during the key step of sample incubation. Here, we disclose an integrated microfluidic emulsion creamer that packs ("creams") assay droplets by draining away excess oil through microfabricated drain channels. The drained oil coflows with creamed emulsion and then reintroduces the oil to disperse the droplets at the circuit terminus for analysis. Creamed emulsion assay incubation time dispersion was 1.7%, 3-fold less than other reported incubators. The integrated, continuous emulsion creamer (ICEcreamer) was used to miniaturize and optimize measurements of various enzymatic activities (phosphodiesterase, kinase, bacterial translation) under multiple- and single-turnover conditions. Combining the ICEcreamer with current integrated microfluidic DNA-encoded library bead processors eliminates potentially cumbersome instrumentation engineering challenges and is compatible with assays of diverse target class activities commonly investigated in drug discovery.

Science.gov (United States)

Jacobs, Ken; Karpf, Ron

2011-03-01

A number of Pulfrich 3-D movies and TV shows have been produced, but the standard implementation has inherent drawbacks. The movie and TV industries have correctly concluded that the standard Pulfrich 3-D implementation is not a useful 3-D technique. Continuously Adjustable Pulfrich Spectacles (CAPS) is a new implementation of the Pulfrich effect that allows any scene containing movement in a standard 2-D movie, which are most scenes, to be optionally viewed in 3-D using inexpensive viewing specs. Recent scientific results in the fields of human perception, optoelectronics, video compression and video format conversion are translated into a new implementation of Pulfrich 3- D. CAPS uses these results to continuously adjust to the movie so that the viewing spectacles always conform to the optical density that optimizes the Pulfrich stereoscopic illusion. CAPS instantly provides 3-D immersion to any moving scene in any 2-D movie. Without the glasses, the movie will appear as a normal 2-D image. CAPS work on any viewing device, and with any distribution medium. CAPS is appropriate for viewing Internet streamed movies in 3-D.

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

KAUST Repository

Liu, Dayan

2015-03-31

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

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

Science.gov (United States)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

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

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

International Nuclear Information System (INIS)

Feng Qing-Hua

2014-01-01

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

4. Continuous alcoholic fermentation

Energy Technology Data Exchange (ETDEWEB)

Smidrkal, M; Nejedly, A

1956-01-01

Results are given of investigations on the continuous production of ethanol on a laboratory and on a semi-commercial scale. The suggested devices are particularly described. Under constant conditions the production cycle required 12 to 17 days, the acidity being 4.0 to 415 ml. 0.1 N NaOH/100 ml and the concentration of fermented wort 10.5 to 11%. The maximum production from 1 h of fermentation space during 24 h was 8.67 l of absolute alcohol when the efflux was divided into several basins; when the efflux of sweet wort was collected into one basin only, the maximum production was 7.20 l of absolute alcohol. The amount of alcohol produced was 62.20 l/100 kg sugar.

5. Spaces of continuous functions

CERN Document Server

Groenewegen, G L M

2016-01-01

The space C(X) of all continuous functions on a compact space X carries the structure of a normed vector space, an algebra and a lattice. On the one hand we study the relations between these structures and the topology of X, on the other hand we discuss a number of classical results according to which an algebra or a vector lattice can be represented as a C(X). Various applications of these theorems are given. Some attention is devoted to related theorems, e.g. the Stone Theorem for Boolean algebras and the Riesz Representation Theorem. The book is functional analytic in character. It does not presuppose much knowledge of functional analysis; it contains introductions into subjects such as the weak topology, vector lattices and (some) integration theory.

6. Geochemical importance of isotopic fractionation during respiration

International Nuclear Information System (INIS)

Schleser, G.; Foerstel, H.

1975-01-01

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

7. Fractional Bhatnagar-Gross-Krook kinetic equation

Science.gov (United States)

Goychuk, Igor

2017-11-01

The linear Boltzmann equation (LBE) approach is generalized to describe fractional superdiffusive transport of the Lévy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and infinite variance. It is completely characterized by the two scattering rates, one fractional and a normal one, which defines also the mean scattering rate. We formulate a general fractional LBE approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral leading to a fractional generalization of the Bhatnagar, Gross and Krook (BGK) kinetic equation. Here, at each scattering event the particle velocity is completely randomized and takes a value from equilibrium Maxwell distribution at a given fixed temperature. We show that the retardation effects are indispensable even in the limit of infinite mean scattering rate and argue that this novel fractional kinetic equation provides a viable alternative to the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and its generalization by Friedrich et al. based on the picture of divergent mean time between scattering events. The case of divergent mean time is also discussed at length and compared with the earlier results obtained within the fractional KFP. Also a phenomenological fractional BGK equation without retardation effects is proposed in the limit of infinite scattering rates. It cannot be, however, rigorously derived from a scattering model, being rather clever postulated. It this respect, this retardationless equation is similar to the fractional KFP by Barkai and Silbey. However, it corresponds to the opposite, much more physical limit and, therefore, also presents a viable alternative.

8. Diffusive Fractionation of Lithium Isotopes in Olivine Grain Boundaries

Science.gov (United States)

Homolova, V.; Watson, E. B.

2012-12-01

produced in the grain boundaries versus the lattices of the individual grains of the 'dunite rock'. The model assumes a linear grain boundary juxtaposed to the long side of a rectangular crystal lattice. During a simulation, the diffusant may directly enter the lattice or the grain boundary. Once in the grain boundary, the diffusant may then continue to diffuse away from the source until the end of the simulation or, alternatively, it may be incorporated into the lattice at some point during its travels down the grain boundary. The model system is similar to that considered by Whipple-LeClaire (1963) and our model results agree well with their analytical solution. Preliminary modeling results show that the distinctive minimum in the isotopic ratio is only produced when diffusive fractionation occurs in the grain boundary and not when the fractionation occurs only in the lattice. This suggests that the isotopic profile observed in the experiments may be a product of diffusive fractionation in grain boundaries. Implications of these results extend to the longevity of Li isotopic heterogeneities in the mantle, and suggest that the isotopes of other elements, which have a large relative mass difference, may also be diffusively fractionated by grain boundary diffusion.

9. Applications of fractional calculus in physics

CERN Document Server

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

10. Hypo fractionated prostate treatment by volumearcotherapy modulated

International Nuclear Information System (INIS)

Clemente Gutierrez, F.; Perez Vara, C.; Prieto Villacorta, M.

2013-01-01

Several studies have been proposed over the years schemes of hypo-fractionated treatment for prostate cancer. Such schemes have been designed in order to increase local control of the disease and reduce complications. They are in addition a clear improvement from the point of view logistical and organizational for treatment centres and the patient. the hypo-fractionated treatments are possible because the ratio a/b for prostate carcinoma is comparable, and even below, the surrounding healthy tissues. This work presents the scheme adopted in our Center for the hypo-fractionated treatment of the cancer of prostate by arco therapy volumetric modulated. (Author)

11. Fractional calculus in bioengineering, part 3.

Science.gov (United States)

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

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

Science.gov (United States)

Toomarian, Elizabeth Y; Hubbard, Edward M

2017-07-12

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

13. Catalytic quality improvement of waste polyolefin originated fractions

Directory of Open Access Journals (Sweden)

Tóth O.

2018-03-01

Full Text Available The demand for alternative fuels having low greenhouse gases emission is continuously growing worldwide. Therefore it is preferred to produce new, waste originated components. One option is the recycling of plastic waste with cracking. The produced hydrocarbon fraction is not suitable for fuels thus it is important to improve its quality. The aim of our experimental work was to study the quality improvement of this cracked fraction (PPCGO and crude oil based middle distillates (different composition with co-processing. Our goal was to produce high quality diesel fuel blending components. We studied the effect of process parameters on the quality of products. Ni (2.3% Mo (11.0% P (2.3%/Al2O3 catalyst was used. During the experiments we studied the hydrogenation of olefins, saturation of aromatics and desulphurization. The hydrogenation of olefins was practically complete at 300°C. It took place at significantly higher speed than the desulphurization reactions. In case of light gas oil feedstock the products had significantly lower sulphur contents; below 10 mg/kg already at 340°C. We determined that the cracked fraction had beneficial effect on the performance properties of the products. In case of all feedstock combinations, we found process parameters which can be used to produce high-quality diesel fuel blending components on the tested catalyst.

14. Effects of genistein following fractionated lung irradiation in mice

International Nuclear Information System (INIS)

Para, Andrea E.; Bezjak, Andrea; Yeung, Ivan W.T.; Van Dyk, Jake; Hill, Richard P.

2009-01-01

Background and purpose: This study investigated protection of lung injury by genistein following fractionated doses of radiation and its effect on tumor response. Material and methods: C3H/HeJ mice were irradiated (100 kVp X-rays) with 9 fractions of 3.1 Gy over 30 days (approximately equivalent to 10 Gy single dose) and were maintained on a genistein diet (∼10 mg/kg). Damage was assessed over 28 weeks in lung cells by a cytokinesis block micronucleus (MN) assay and by changes in breathing rate and histology. Tumor protection was assessed using a colony assay to determine cell survival following in situ irradiation of small lung nodules (KHT fibrosarcoma). Results: Genistein caused about a 50% reduction in the MN damage observed during the fractionated radiation treatment and this damage continued to decrease at later times to background levels by 16 weeks. In mice not receiving Genistein MN levels remained well above background out to 28 weeks after irradiation. Genistein reduced macrophage accumulation by 22% and reduced collagen deposition by 28%. There was minimal protection against increases in breathing rate or severe morbidity during pneumonitis. No tumor protection by genistein treatment was observed. Conclusions: Genistein at the dose levels used in this study partially reduced the extent of fibrosis developing in mouse lung caused by irradiation but gave minimal protection against pneumonitis. There was no evidence that genistein caused protection of small tumors growing in the lung.

15. In vitro antioxidant and anticancer effects of solvent fractions from Prunella vulgaris var. lilacina.

Science.gov (United States)

Hwang, Yu-Jin; Lee, Eun-Ju; Kim, Haeng-Ran; Hwang, Kyung-A

2013-11-09

Recently, considerable attention has been focused on exploring the potential antioxidant properties of plant extracts or isolated products of plant origin. Prunella vulgaris var. lilacina is widely distributed in Korea, Japan, China, and Europe, and it continues to be used to treat inflammation, eye pain, headache, and dizziness. However, reports on the antioxidant activities of P. vulgaris var. lilacina are limited, particularly concerning the relationship between its phenolic content and antioxidant capacity. In this study, we investigated the antioxidant and anticancer activities of an ethanol extract from P. vulgaris var. lilacina and its fractions. Dried powder of P. vulgaris var. lilacina was extracted with ethanol, and the extract was fractionated to produce the hexane fraction, butanol fraction, chloroform fraction and residual water fraction. The phenolic content was assayed using the Folin-Ciocalteu colorimetric method. Subsequently, the antioxidant activities of the ethanol extract and its fractions were analyzed employing various antioxidant assay methods including DPPH, FRAP, ABTS, SOD activity and production of reactive oxygen species. Additionally, the extract and fractions were assayed for their ability to exert cytotoxic activities on various cancer cells using the MTT assay. We also investigated the expression of genes associated with apoptotic cell death by RT-PCR. The total phenolic contents of the ethanol extract and water fraction of P. vulgaris var. lilacina were 303.66 and 322.80 mg GAE/g dry weight (or fractions), respectively. The results showed that the ethanol extract and the water fraction of P. vulgaris var. lilacina had higher antioxidant content than other solvent fractions, similar to their total phenolic content. Anticancer activity was also tested using the HepG2, HT29, A549, MKN45 and HeLa cancer cell lines. The results clearly demonstrated that the P. vulgaris var. lilacina ethanol extract induced significant cytotoxic effects

16. The fractional Fourier transform and applications

Science.gov (United States)

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.

17. On the Scaled Fractional Fourier Transformation Operator

International Nuclear Information System (INIS)

Hong-Yi, Fan; Li-Yun, Hu

2008-01-01

Based on our previous study [Chin. Phys. Lett. 24 (2007) 2238] in which the Fresnel operator corresponding to classical Fresnel transform was introduced, we derive the fractional Fourier transformation operator, and the optical operator method is then enriched

18. Analysis of Nonlinear Fractional Nabla Difference Equations

Directory of Open Access Journals (Sweden)

2015-01-01

Full Text Available In this paper, we establish sufficient conditions on global existence and uniqueness of solutions of nonlinear fractional nabla difference systems and investigate the dependence of solutions on initial conditions and parameters.

19. Steffensen's integral inequality for conformable fractional integrals

Directory of Open Access Journals (Sweden)

Mehmet Zeki Sarikaya

2017-09-01

Full Text Available The aim of this paper is to establish some Steffensen’s type inequalities for conformable fractional integral. The results presented here would provide generalizations of those given in earlier works.

20. Some Improvements of Conformable Fractional Integral Inequalities

Directory of Open Access Journals (Sweden)

Fuat Usta

2017-07-01

Full Text Available In this study, we wish to set up and present some new conformable fractional integral inequalities of the Gronwall type which have a great variety of implementation area in differential and integral equations.

1. Fractional Diffusion in Gaussian Noisy Environment

Directory of Open Access Journals (Sweden)

Guannan Hu

2015-03-01

Full Text Available We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic heat equations of the following form: \\(D_t^{(\\alpha} u(t, x=\\textit{B}u+u\\cdot \\dot W^H\\, where \\(D_t^{(\\alpha}\\ is the Caputo fractional derivative of order \\(\\alpha\\in (0,1\\ with respect to the time variable \\(t\\, \\(\\textit{B}\\ is a second order elliptic operator with respect to the space variable \\(x\\in\\mathbb{R}^d\\ and \\(\\dot W^H\\ a time homogeneous fractional Gaussian noise of Hurst parameter \\(H=(H_1, \\cdots, H_d\\. We obtain conditions satisfied by \\(\\alpha\\ and \\(H\\, so that the square integrable solution \\(u\\ exists uniquely.

2. Tunneling time in space fractional quantum mechanics

Science.gov (United States)

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.

3. Fractional flux quanta in Josephson junctions

Energy Technology Data Exchange (ETDEWEB)

Goldobin, E.; Buckenmaier, K.; Gaber, T.; Kemmler, M.; Pfeiffer, J.; Koelle, D.; Kleiner, R. [Physikalisches Inst. - Experimentalphysik II, Univ. Tuebingen (Germany); Weides, M.; Kohlstedt, H. [Center of Nanoelectronic Systems for Information Technology (CNI), Research Centre Juelich (Germany); Siegel, M. [Inst. fuer Mikro- und Nanoelektronische Systeme, Univ. Karlsruhe (Germany)

2007-07-01

Fractional Josephson vortices may appear in the so-called 0-{kappa} Josephson junctions ({kappa} is an arbitrary number) and carry magnetic flux {phi}, which is a fraction of the magnetic flux quantum {phi}{sub 0}{approx}2.07 x 10{sup -15} Wb. Their properties are very different from the usual integer fluxons: they are pinned, and often represent the ground state of the system with spontaneous circulating supercurrent. They behave as well controlled macroscopic spins and can be used to construct bits, qubits, tunable photonic crystals and to study the (quantum) physics of spin systems. In this talk we discuss recent advances in 0-{pi} junction technology and present recent experimental results: evidence of the spontaneous flux in the ground state, spectroscopy of the fractional vortex eigenfrequencies and observation of dynamics effects related to the flipping of the fractional vortices. (orig.)

4. Intervals between multiple fractions per day

International Nuclear Information System (INIS)

Fowler, J.F.

1988-01-01

Assuming the linear quadratic model for dose-response curves enables the proportion of repairable damage to be calculated for any size of dose per fraction. It is given by the beta (dose squared) term, and represents a larger proportion of the total damage for larger doses per fraction, but also for late-reacting than for early-reacting tissues. For example at 2 Gy per fraction, repairable damage could represent nearly half the total damage in late-reacting tissues but only one fifth in early-reacting tissues. Even if repair occurs at the same rate in both tissues, it will obviously take longer for 50% of the damage to fade to an undetectable level (3 or 5%) than for 20% to do so. This means that late reactions require longer intervals than early reactions when multiple fraction per day radiotherapy is planned, even if the half-lives of repair are not different. (orig.)

5. Fractionated irradiation and haematopoiesis. Pt. 3

International Nuclear Information System (INIS)

Ninkov, V.; Karanovic, D.; Savovski, K.

1982-01-01

The effect of total single fractionated irradiation with short time interval on heamatopoietic regeneration of the bone marrow and spleen was investigated. Also, the importance of first dose, when dose of 600 R was divided in two unequal fractions with time interval of 300 s was studied. The investigation was performed on 25 day old rats. The dose of 600 R (X-rays) was divided on: 500 + 100, 400 + 200, 300 + 300, 200 + 400 or 100 + 500 R with time interval of 150, 300 or 600 s. Ten days after irradiation the changes in blood, bone marrow and spleen were observed. After unequal fractionated dose with interval of 600 s slight effect was found. The results after intervals of 600 s and 300 s were significant, when the total dose was divided in two equal doses. The first dose has no promoting role in haematopoietic regeneration when total dose was unequally fractionated. (orig.) [de

6. Phytotoxic characterization of various fractions of Launaea ...

African Journals Online (AJOL)

2011-06-15

Jun 15, 2011 ... evaluate the allelopathic properties of the various fractions of L. .... (2008) that, essential oil isolated from Turkish Origanum acutidens and their phenolic ... extracts of some Indian medicinal plants for antibacterial activity.

7. Bio-oil fractionation and condensation

Science.gov (United States)

Brown, Robert C; Jones, Samuel T; Pollard, Anthony

2013-07-02

A method of fractionating bio-oil vapors which involves providing bio-oil vapors comprising bio-oil constituents is described. The bio-oil vapors are cooled in a first stage which comprises a condenser having passages for the bio-oil separated by a heat conducting wall from passages for a coolant. The coolant in the condenser of the first stage is maintained at a substantially constant temperature, set at a temperature in the range of 75 to 100.degree. C., to condense a first liquid fraction of liquefied bio-oil constituents in the condenser of the first stage. The first liquid fraction of liquified bio-oil constituents from the condenser in the first stage is collected. Also described are steps for subsequently recovering further liquid fractions of liquefied bio-oil constituents. Particular compositions of bio-oil condensation products are also described.

8. Numerical study of fractional nonlinear Schrodinger equations

KAUST Repository

Klein, Christian; Sparber, Christof; Markowich, Peter A.

2014-01-01

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

9. Fractional diffusion equations and anomalous diffusion

CERN Document Server

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.

10. Analysis of low-temperature tar fractions

Energy Technology Data Exchange (ETDEWEB)

1952-01-01

A preliminary comparative study was made on the applicability of the methods commonly used for the type analysis of petroleum products to the low-temperature tar fractions. The usability of chromatography was also studied.

11. Void fraction prediction in saturated flow boiling

International Nuclear Information System (INIS)

2005-01-01

Full text of publication follows: An essential element in thermal-hydraulics is the accurate prediction of the vapor void fraction, or fraction of the flow cross-sectional area occupied by steam. Recently, the author has suggested to calculate void fraction working exclusively with thermodynamic properties. It is well known that the usual 'flow' quality, merely a mass flow rate ratio, is not at all a thermodynamic property because its expression in function of thermodynamic properties includes the slip ratio, which is a parameter of the process not a function of state. By the other hand, in the classic and well known expression of the void fraction - in function of the true mass fraction of vapor (also called 'static' quality), and the vapor and liquid densities - does not appear the slip ratio. Of course, this would suggest a direct procedure for calculating the void fraction, provided we had an accurate value of the true mass fraction of vapor, clearly from the heat balance. However the classic heat balance is usually stated in function of the 'flow' quality, what sounds really contradictory because this parameter, as we have noted above, is not at all a thermodynamic property. Then we should check against real data the actual relationship between the thermodynamic properties and the applied heat. For saturated flow boiling just from the inlet of the heated tube, and not having into account the kinetic and potential terms, the uniform applied heat per unit mass of inlet water and per unit length (in short, specific linear heat) should be closely related to a (constant) slope of the mixture enthalpy. In this work, we have checked the relation between the specific linear heat and the thermodynamic enthalpy of the liquid-vapor mixture using the actual mass fraction. This true mass fraction is calculated using the accurate measurements of the outlet void fraction taken during the Cambridge project by Knights and Thom in the sixties for vertical and horizontal

12. Stochastic Evolution Equations Driven by Fractional Noises

Science.gov (United States)

2016-11-28

paper is to establish the weak convergence, in the topology of the Skorohod space, of the ν-symmetric Riemann sums for functionals of the fractional...stochastic heat equation with fractional-colored noise: existence of the solution. ALEA Lat. Am. J. Probab. Math . Stat. 4 (2008), 57–87. [8] P. Carmona, Y...Hu: Strong disorder implies strong localization for directed polymers in a random environment. ALEA Lat. Am. J. Probab. Math . Stat. 2 (2006), 217

13. Unanswered Quibbles with Fractional Reserve Free Banking

OpenAIRE

Bagus, Philipp; Howden, David

2011-01-01

In this article we reply to George Selgin’s counterarguments to our article “Fractional Reserve Free Banking: Some Quibbles”. Selgin regards holding cash as saving while we focus on the real savings necessary to maintain investment projects. Real savings are unconsumed real income. Variations in real savings are not necessarily equal to variations in cash holdings. We show that a coordinated credit expansion in a fractional reserve free banking (FRFB) system is possible and that precautionary...

14. The Value Proposition for Fractionated Space Architectures

Science.gov (United States)

2006-09-01

fractionation “mass penalty” assumptions , the expected launch costs are nearly a factor of two lower for the fractionated system than for the monolith...humidity variations which may affect fire propagation speed. 23 The Capital Asset Pricing Model ( CAPM ...spacecraft, can be very significant. In any event, however, the assumption that spacecraft cost scales roughly linearly with its mass is an artifact of

International Nuclear Information System (INIS)

Wang Wei; Gu Zhongdao

1992-01-01

A quad Constant Fraction (Amplitude and Rise Time Compensation) Discriminator Circuit is described, which is based on the ECL high-speed dual comparator AD 9687. The CFD (ARCD) is of the constant fraction timing type (the amplitude and rise time compensation timing type) employing a leading edge discriminator to eliminate error triggers caused by noises. A timing walk measurement indicates a timing walk of less than +- 150 ps from -50 mV to -5 V

16. Water dynamics in different biochar fractions.

Science.gov (United States)

Conte, Pellegrino; Nestle, Nikolaus

2015-09-01

Biochar is a carbonaceous porous material deliberately applied to soil to improve its fertility. The mechanisms through which biochar acts on fertility are still poorly understood. The effect of biochar texture size on water dynamics was investigated here in order to provide information to address future research on nutrient mobility towards plant roots as biochar is applied as soil amendment. A poplar biochar has been stainless steel fractionated in three different textured fractions (1.0-2.0 mm, 0.3-1.0 mm and <0.3 mm, respectively). Water-saturated fractions were analyzed by fast field cycling (FFC) NMR relaxometry. Results proved that 3D exchange between bound and bulk water predominantly occurred in the coarsest fraction. However, as porosity decreased, water motion was mainly associated to a restricted 2D diffusion among the surface-site pores and the bulk-site ones. The X-ray μ-CT imaging analyses on the dry fractions revealed the lowest surface/volume ratio for the coarsest fraction, thereby corroborating the 3D water exchange mechanism hypothesized by FFC NMR relaxometry. However, multi-micrometer porosity was evidenced in all the samples. The latter finding suggested that the 3D exchange mechanism cannot even be neglected in the finest fraction as previously excluded only on the basis of NMR relaxometry results. X-ray μ-CT imaging showed heterogeneous distribution of inorganic materials inside all the fractions. The mineral components may contribute to the water relaxation mechanisms by FFC NMR relaxometry. Further studies are needed to understand the role of the inorganic particles on water dynamics. Copyright © 2015 John Wiley & Sons, Ltd.

17. Continuous composite riser

Energy Technology Data Exchange (ETDEWEB)

Slagsvold, L. [ABB Offshore Systems (Norway)

2002-12-01

The industry is now looking at developing reserves in waters depths of up to 3000 m (10000 ft). When moving into deeper waters the un-bonded flexible riser becomes very heavy and introduces large hang-off forces on the vessel. We are therefore investigating riser concepts incorporating new materials and with a simpler cross section that can be used for floating production. Advanced composite materials have properties such as, low weight, high strength, good durability and very good fatigue performance. Composite materials are slowly being exploited in the oil industry; they are being prototype tested for drilling risers and small diameter lines. Part of the process for the industry to accept larger diameter production risers made out of composite materials is to understand both the advantages and limitations. A new continuous composite riser system is being developed which capitalizes on the technical benefits of this material while addressing the known constraints. The fully bonded riser is being developed for ultra deep waters and its' characteristics include high temperature (160 deg C), high pressure (500 barg min), light weight, chemical resistant, good insulation, excellent fatigue characteristics and installation by reeling. The concept is based on the use of a thermoplastic liner together with a thermoplastic carbon fibre composite. This paper summarises the ongoing development, which has a goal to manufacture and qualify an 8'' riser, and includes all the steps in a production process from material qualification to the winding process and analytical modelling. (author)

18. Continuous cell recycle fermentation

Energy Technology Data Exchange (ETDEWEB)

Warren, R K; Hill, G A; MacDonald, D G

1991-10-01

A cell recycle fermentor using a cross-flow membrane filter has been operated for extended periods. Productivities as high as 70 g/l/h were obtained at a cell concentration of 120 g/l and a product concentration of 70 g/l. The experimental results were then fitted to previously derived biokinetic models (Warren et al., 1990) for a continuous stirred tank fermentor. A good fit for growth rate was found and the cell yield was shown to decrease with product concentration. The product yield, however, was found to remain nearly constant at all cell, substrate and product concentrations. These biokinetics, along with a previous model for the membrane filter (Warren et al., 1991) were then used in a simulalation to estimate the costs of producing ethanol in a large scale system. This simulation was optimized using a variant of the steepest descent method from which a fermentor inlet substrate concentration of 150 g/l and a net cost of \$CAN 253.5/1000 L ethanol were projected. From a sensitivity analysis, the yield parameters were found to have the greatest effect on ethanol net cost of the fermentor parameters, while the operating costs and the profit was found to be most sensitive to the wheat raw material cost and to the dried grains by-product value. 55 refs., 11 tabs., 7figs.

19. Deconstructing continuous flash suppression.

Science.gov (United States)

Yang, Eunice; Blake, Randolph

2012-03-08

In this paper, we asked to what extent the depth of interocular suppression engendered by continuous flash suppression (CFS) varies depending on spatiotemporal properties of the suppressed stimulus and CFS suppressor. An answer to this question could have implications for interpreting the results in which CFS influences the processing of different categories of stimuli to different extents. In a series of experiments, we measured the selectivity and depth of suppression (i.e., elevation in contrast detection thresholds) as a function of the visual features of the stimulus being suppressed and the stimulus evoking suppression, namely, the popular "Mondrian" CFS stimulus (N. Tsuchiya & C. Koch, 2005). First, we found that CFS differentially suppresses the spatial components of the suppressed stimulus: Observers' sensitivity for stimuli of relatively low spatial frequency or cardinally oriented features was more strongly impaired in comparison to high spatial frequency or obliquely oriented stimuli. Second, we discovered that this feature-selective bias primarily arises from the spatiotemporal structure of the CFS stimulus, particularly within information residing in the low spatial frequency range and within the smooth rather than abrupt luminance changes over time. These results imply that this CFS stimulus operates by selectively attenuating certain classes of low-level signals while leaving others to be potentially encoded during suppression. These findings underscore the importance of considering the contribution of low-level features in stimulus-driven effects that are reported under CFS.

20. Fractionation for Biodiesel Purification Using Supercritical Carbon Dioxide

Directory of Open Access Journals (Sweden)

Chao-Yi Wei

2014-02-01

Full Text Available In recent years, biodegradable and alternative biodiesel has attracted increased attention worldwide. Producing biodiesel from biomass involves critical separation and purification technology. Conventional technologies such as gravitational settling, decantation, filtration, water washing, acid washing, organic solvent washing and absorbent applications are inefficient, less cost effective and environmentally less friendly. In this study supercritical carbon dioxide (SC-CO2 with few steps and a low environmental impact, was used for biodiesel fractionation from impure fatty acid methyl ester (FAME solution mixes. The method is suitable for application in a variety of biodiesel production processes requiring subsequent stages of purification. The fractionation and purification was carried out using continuous SC-CO2 fractionation equipment, consisting of three columns filled with stainless steel fragments. A 41.85% FAME content solution mix was used as the raw material in this study. Variables were a temperature range of 40–70 °C, pressure range of 10–30 MPa, SC-CO2 flow rate range of 7–21 mL/min and a retention time range of 30–90 min. The Taguchi method was used to identify optimal operating conditions. The results show that a separated FAME content of 99.94% was verified by GC-FID under optimal fractionation conditions, which are a temperature of 40 °C of, a pressure level of 30MPa and a flow rate of 7 mL/min of SC-CO2 for a retention time of 90 min.