Function Fs Research Articles

Identification of the scalar Preisach model with a single branch of descending hysteresis loop and numerical interpolation for the electrical steel sheet lamination with soft magnetic properties

The developed scalar Preisach model predicts the hysteresis behavior of the soft magnetic, electrical steel sheet. The experimental hysteresis loops of the electrical steel lamination prepare the Everett function required to predict the hysteresis behavior of the electrical steel lamination. We obtain the Everett function in two ways, from the series of minor loops and a single descending branch of a hysteresis loop. The Everett function has a closed algebraic form in the method using the minor loops. A genetic algorithm carries out the subsequent fitting based on the closed algebraic equation and optimization; however, the calculated flux values have highly deviated from the measured values. In another way, the Everett function consists of numerically driven Fs and B factorable functions. The values extracted from a limiting hysteresis loop determine the function Fs and B. The predicted values are correct, and the proposed method for determining the Everett function is only valid for soft magnetic materials representing symmetric and non-exchange-bias hysteresis behavior. While the method has application limitations to general magnetic hysteresis, it demonstrates the validity of using a function derived from experimentally measured hysteresis loops rather than a closed-algebraic equation to determine the Everett function. With the Everett surface the Preisach distribution function (PDF) is numerically derived and represents the difference in domain structure between two specimens.

Homogeneous generalized master equation for an arbitrary initial state of a many-particle classical system

A special projection operator is introduced, which exactly transforms the Nakajima–Zwanzig inhomogeneous Generalized Master Equation (GME) with an irrelevant initial condition term (a source) into a completely closed homogeneous GME (with no initial correlations term) for the relevant part of an N-particle distribution function FN(t) for an arbitrary initial distribution function FN(0) of a system of classical particles. It resolves the problem of the derivation of a closed linear evolution equation from the Liouville equation with no “molecular chaos” type approximation. The obtained equation is equivalent to the completely closed equation for s-particle (s≤N) distribution function Fs(t). The initial correlations are accounted for in this equation in the modified by the introduced projection operator kernel governing the evolution of Fs(t). This equation is further simplified by presenting its kernel in the linear in the particles’ density n approximation. In this approximation the equations for one-particle F1(t) and two-particle F2(t) distribution functions are derived. Special attention is given to analyzing the equation for F1(t) and showed that this equation in the Markov approximation can be written as the linear Boltzmann or Landau (for a small interparticle interaction) equations but with additional terms caused by initial correlations.

The correlation of pericoronary adipose tissue with coronary artery disease and left ventricular function

ObjectiveWe sought to investigate the correlation of pericoronary adipose tissue with coronary artery disease and left ventricular (LV) function.MethodsParticipants with clinically suspected coronary artery disease were enrolled. All participants underwent coronary computed tomography angiography (CCTA) and echocardiography followed by invasive coronary angiography (ICA) within 6 months. Pericoronary adipose tissue (PCAT) was extracted to analyze the correlation with the Gensini score and LV function parameters, including IVS, LVPW, LVEDD, LVESD, LVEDV, LVESV, FS, LVEF, LVM, and LVMI. The correlation between PCAT and the Gensini score was assessed using Spearman’s correlation analysis, and that between the PCAT volume or FAI and LV function parameters was determined using partial correlation analysis.ResultsOne hundred and fifty-nine participants (mean age, 64.55 ± 10.64 years; men, 65.4% [104/159]) were included in the final analysis. Risk factors for coronary artery disease, such as hypertension, diabetes, dyslipidemia, and a history of smoking or drinking, had no significant association with PCAT (P > 0.05), and there was also no correlation between PCAT and the Gensini score. However, the LAD-FAI was positively correlated with the IVS (r = 0.203, P = 0.013), LVPW (r = 0.218, P = 0.008), LVEDD (r = 0.317, P < 0.001), LVESD (r = 0.298, P < 0.001), LVEDV (r = 0.317, P < 0.001), LVESV (r = 0.301, P < 0.001), LVM (r = 0.371, P < 0.001), and LVMI (r = 0.304, P < 0.001). Also, the LCX-FAI was positively correlated with the LVEDD (r = 0.199, P = 0.015), LVESD (r = 0.190, P = 0.021), LVEDV (r = 0.203, P = 0.013), LVESV (r = 0.197, P = 0.016), LVM (r = 0.220, P = 0.007), and LVMI (r = 0.172, P = 0.036), and the RCA-FAI was positively correlated with the LVEDD (r = 0.258, P = 0.002), LVESD (r = 0.238, P = 0.004), LVEDV (r = 0.266, P = 0.001), LVESV (r = 0.249, P = 0.002), LVM (r = 0.237, P = 0.004), and LVMI (r = 0.218, P = 0.008), respectively. Finally, the total volume was positively correlated with FS (r = 0.167, P = 0.042).ConclusionThe FAI was positively correlated with the LV function but was not associated with the severity of coronary artery disease.

Functional reduction of one-loop Feynman integrals with arbitrary masses

A method of functional reduction for the dimensionally regularized one-loop Feynman integrals with massive propagators is described in detail.The method is based on a repeated application of the functional relations proposed by the author. Explicit formulae are given for reducing one-loop scalar integrals to a simpler ones, the arguments of which are the ratios of polynomials in the masses and kinematic invariants. We show that a general scalar n-point integral, depending on n(n + 1)/2 generic masses and kinematic variables, can be expressed as a linear combination of integrals depending only on n variables. The latter integrals are given explicitly in terms of hypergeometric functions of (n − 1) dimensionless variables. Analytic expressions for the 2-, 3- and 4-point integrals, that depend on the minimal number of variables, were also obtained by solving the dimensional recurrence relations. The resulting expressions for these integrals are given in terms of Gauss’ hypergeometric function 2F1, the Appell function F1 and the hypergeometric Lauricella — Saran function FS. A modification of the functional reduction procedure for some special values of kinematic variables is considered.

Plantago asiatica L. seeds extract protects against cardiomyocyte injury in isoproterenol- induced cardiac hypertrophy by inhibiting excessive autophagy and apoptosis in mice

BackgroundCardiac hypertrophy is the early stage of many heart diseases, such as coronary heart disease, hypertension, valvular dysfunction and cardiomyopathy. Cardiomyocyte autophagy and apoptosis play an important role in the process of cardiac hypertrophic response. Plantago asiatica L. seeds extract (PASE) is prepared from a traditional herbal medicine in Asia with tremendous pharmacological activities. However, whether PASE could relieve cardiac hypertrophy has not been elucidated. The present study is aimed to investigate the effect of PASE on cardiac hypertrophy and explore its potential underlying mechanism. MethodsCardiac hypertrophy was induced in C57BL/6 mice by subcutaneous injection of isoproterenol (ISO) for two weeks. Meanwhile, the mice were intraperitoneally injected with PASE at dosages of 20, 40 and 80 mg/kg/day. Cardiac hypertrophy was evaluated by echocardiographic examination, haematoxylin and eosin staining and quantitative real-time polymerase chain reaction. Expressions of proteins involved in autophagy and apoptosis such as Beclin1, p62, LC3II, Bax, Bcl-2 and Cleaved-caspase-3 were detected by western blot analysis. Western blot, transient transfection, acridine orange staining, TUNEL staining and autophagy inducer were used to observe the effect and explore the mechanism of PASE on cardiomyocyte and H9c2 cells with excessive autophagy and apoptosis induced by ISO. ResultsISO induction for two weeks disturbed the myocardial contractility and cardiac function of left ventricles of mice. PASE treated mice showed significantly improved cardiac function indexes, including EF, FS, SV and CO, compared with the ISO group. Treatment with PASE also decreased the heart weight/body weight ratio and cardiomyocyte size, and downregulated the mRNA and protein expressions of hypertrophic markers ANP, BNP, and β-MHC. Furthermore, the changes of autophagy and apoptosis markers, such as LC3II, Beclin1, p62, Bcl-2, Bax and Cleaved-caspase-3 induced by ISO were resumed by PASE treatment. Consistently, PASE demonstrated similar effects on ISO-induced H9c2 cells as it did in vivo. In addition, PASE could counteract the increased autophagy induced by the autophagy inducer, rapamycin. ConclusionPASE attenuated ISO-induced cardiac hypertrophy in mice by inhibiting excessive autophagy and apoptosis in cardiomyocytes. The novel findings may pave the way for the clinical usage of PASE for the prevention of heart diseases related with cardiac hypertrophy.

Identification of time scales of the violation of the Stokes–Einstein relation in Yukawa liquids

We investigate the origin of the violation of the Stokes–Einstein (SE) relation in two-dimensional Yukawa liquids. Using comprehensive molecular dynamics simulations, we identify the time scales supporting the violation of the SE relation D∝(η/T)−1, where D is the self-diffusion coefficient and η is the shear viscosity. We first compute the self-intermediate scattering function Fs(k,t), the non-Gaussian parameter α2, and the autocorrelation function of the shear stress Cη(t). The time scales obtained from these functions include the structural relaxation time τα, the peak time of the non-Gaussian parameter τα2, and the shear stress relaxation time τη. We find that τη is coupled with D for all temperatures indicating the SE preservation; however, τα and τα2 are decoupled with D at low temperatures indicating the SE violation. Surprisingly, we find that the origins of this violation are related to the non-exponential behavior of the autocorrelation function of the shear stress and non-Gaussian behavior of the distribution function of particle displacements. These results confirm dynamic heterogeneity that occurs in two-dimensional Yukawa liquids that reflect the presence of regions in which dust particles move faster than the rest when the liquid cools to below the phase transition temperature.

Scalar 1-loop Feynman integrals as meromorphic functions in space-time dimension d

The long-standing problem of representing the general massive one-loop Feynman integral as a meromorphic function of the space-time dimension d has been solved for the basis of scalar one- to four-point functions with indices one. In 2003 the solution of difference equations in the space-time dimension allowed to determine the necessary classes of special functions: self-energies need ordinary logarithms and Gauss hypergeometric functions F12, vertices need additionally Kampé de Fériet-Appell functions F1, and box integrals also Lauricella-Saran functions FS. In this study, alternative recursive Mellin-Barnes representations are used for the representation of n-point functions in terms of (n−1)-point functions. The approach enabled the first derivation of explicit solutions for the Feynman integrals at arbitrary kinematics. In this article, we scetch our new representations for the general massive vertex and box Feynman integrals and derive a numerical approach for the necessary Appell functions F1 and Saran functions FS at arbitrary kinematical arguments.

How closely do many-body potentials describe the structure and dynamics of Cu-Zr glass-forming alloy?

Molecular dynamics investigations of the structure and dynamics of Cu64.5Zr35.5 metallic glass-forming alloy have been carried out using five different semi-empirical, many-body interaction potentials based on the Finnis-Sinclair model [M. I. Mendelev et al., J. Appl. Phys. 102, 043501 (2007) (MSK); M. I. Mendelev et al., Philos. Mag. 89, 967 (2009) (MKOSYP); L. Ward et al., e-print arXiv:1209.0619 (2012) (WAFW)] and the embedded-atom model [Y. Q. Cheng et al., Phys. Rev. Lett. 102, 245501 (2009) (CMS) and N. Jakse et al., Phys. Rev. B 85, 174201 (2012) (JNP)]. Although the total static structure factor of the alloy for all the five interaction potentials is, in general, found to be in good agreement with the experimental results, the investigation of a local structure in terms of icosahedral short-range order reveals that the effect of the interaction potential (especially the cohesive part) on the structure of the alloy is not as trivial as it seems. For MSK and JNP potentials, the self-intermediate scattering function Fs(q, t), q-dependence of the structural relaxation time τα in the low-q region, and the self-diffusion coefficient, Ds, for Cu-atoms in the alloy are in excellent agreement with the experimental results. The results for MKOSYP, CMS, and WAFW potentials deviate significantly from the experiment and suggest the dynamics of the alloy to be faster. The difference in the description of the dynamics of the alloy by different potentials is found to be due to the difference in the relevant energy scales corresponding to the temperature scales. τα and Ds exhibit Arrhenius temperature dependence in the high temperature regime above the melting temperature. We also suggest that the attractive forces influence the dynamics of the liquid alloy significantly, which is against the mere perturbative role assigned to the attractive forces in the van der Waals picture of liquids that has been challenged in the recent years. As the five interaction potentials are frequently employed to study thermodynamic, mechanical, and transport properties of Cu-Zr alloys, our study also provides a suitability check for these potentials.

IFSs consisting of generalized convex contractions

AbstractIn this paper we introduce the concept of iterated function system consisting of generalized convex contractions. More precisely, given n ∈ ℕ*, an iterated function system consisting of generalized convex contractions on a complete metric space (X; d) is given by a finite family of continuous functions (fi)i ∈I, fi: X → X, having the property that for every ω ∈ λn(I) there exists a family of positive numbers (aω;υ)υ∈Vn(I)such that:x; y ∈ X. Here λn(I) represents the family of words with n letters from I, Vn(I) designates the family of words having at most n - 1 letters from I, while, if ω1= ω1ω2... ωp, by fωwe mean fω1⃘fω2⃘... ⃘ fωp. Denoting such a system by S = ((X; d); n; (fi)i∈I), one can consider the function FS: K(X) → K(X) described by, for all B ∈ K(X), where K(X) means the set of non-empty compact subsets of X. Our main result states that FSis a Picard operator for every iterated function system consisting of generalized convex contractions S.

Super-polynomial convergence and tractability of multivariate integration for infinitely times differentiable functions

We investigate multivariate integration for a space of infinitely times differentiable functions Fs,u:={f∈C∞[0,1]s∣‖f‖Fs,u<∞}, where ‖f‖Fs,u:=supα=(α1,…,αs)∈N0s‖f(α)‖L1/∏j=1sujαj, f(α):=∂∣α∣∂x1α1⋯∂xsαsf and u={uj}j≥1 is a sequence of positive decreasing weights. Let e(n,s) be the minimal worst-case error of all algorithms that use n function values in the s-variate case. We prove that for any u and s considered e(n,s)≤C(s)exp(−c(s)(logn)2) holds for all n, where C(s) and c(s) are constants which may depend on s. Further we show that if the weights u decay sufficiently fast then there exist some 1<p<2 and absolute constants C and c such that e(n,s)≤Cexp(−c(logn)p) holds for all s and n. These bounds are attained by quasi-Monte Carlo integration using digital nets. These convergence and tractability results come from those for the Walsh space into which Fs,u is embedded.

Heterogeneous dynamics in linear polymer melts near glass transition temperature

Equilibrium molecular dynamics simulations of a model linear polymer melt is carried out near its glass transition temperature Tc. We have elucidated the role played by intra and inter chain monomers in formation of secondary structures using radial distribution functions on reduction of temperature towards Tc. Our studies on dynamics using intermediate scattering function Fs(k,t) shows step like relaxation, which is a signature of heterogeneous dynamics of the glassy domains that is widely known in earlier studies of glass transition. Further studies of heterogeneity in the dynamics using four-point correlation function x4 s(t) shows the growth of correlated region in this system as temperature is reduced towards Tc.

HYPERgeometric functions DIfferential REduction (HYPERDIRE): MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: [formula omitted] and [formula omitted] Horn-type hypergeometric functions of three variables

HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: the first one, FdFunction, for manipulations with Appell hypergeometric functions FD of r variables; and the second one, FsFunction, for manipulations with Lauricella–Saran hypergeometric functions FS of three variables. Both functions are related with one-loop Feynman diagrams. Program summaryProgram title: HYPERDIRECatalogue identifier: AEPP_v3_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPP_v3_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public LicenseNo. of lines in distributed program, including test data, etc.: 310No. of bytes in distributed program, including test data, etc.: 7666Distribution format: tar.gzProgramming language: MathematicaComputer: All computers running MathematicaOperating system: All operating systems running MathematicaClassification: 4.4.Catalogue identifier of previous version: AEPP_v1_0Journal reference of previous version: Comput. Phys. Comm. 184 (2013) 2332Does the new version supersede the previous version?: No. It is an extension to the previous program, which performs reductions of hypergeometric functions pFp, F1, F2, F3 and F4Nature of problem: Reduction of hypergeometric functions FD and FS to the set of basis functionsSolution method: Differential reductionReasons for new version: New algorithms for the reduction of multivariable Lauricella functions, Horn functions, (hypergeometric functions FD and FS)Summary of revisions: HYPERDIRE is a project devoted to the creation of a set of Mathematica based programs for the differential reduction of hypergeometric functions. The current version includes two parts: the first one, FdFunction, for manipulations with Appell hypergeometric functions FD of r variables; and the second one, FsFunction, for manipulations with Lauricella–Saran hypergeometric functions FS of three variables. Both functions are related with one-loop Feynman diagrams.Running time: Depends on the complexity of problem

Sparse permutations with low differential uniformity

We study the functions Fs,t,γ(x)=xs+γTr(xt) on F2n. We describe the set of such permutations and the explicit expressions of their compositional inverses. Further we consider special classes of such functions, for which we determine the size of their image set, the algebraic degree and the differential uniformity.

Energy loss in the ECPSSR theory and its calculation with exact integration limits

ECPSSR cross sections for inner-shell ionization are compared with numerical calculations that use correct and wrong expressions for exact limits of momentum transfer. For very adiabatic collisions, the employment of the wrong expression, as done in several popularly utilized computer codes, overestimates the cross sections up to two orders of magnitude. By contrast, even in such collisions the original ECPSSR approach of Brandt and Lapicki that approximates the effect of projectile energy loss by a multiplicative correction function fS and the relativistic effects by a relativistically corrected electron mass yields cross sections that are in agreement within a factor of two with respect to the calculation with hydrogenic Dirac wavefunctions and exact limits of integration with no relativistic correction. For plane-wave Born approximation calculations, the relativistic corrected expressions of the exact limits of integration are presented. The cross section calculated with such limits differs from the ECPSSR calculation using the fS-function by less than 2% in the region of lowest collision velocities covered by experiments. A straightforward modification of the existing computer codes with the correct expression for exact momentum transfer is suggested.

Definition of Alloy Substitute Thermal Capacity Using the Simple Macrosegregation Models

Abstract Mathematical description of alloys solidification in a macro scale can be formulated using the one domain method (fixed domain approach). The energy equation corresponding to this model contains the parameter called a substitute thermal capacity (STC). The analytical form of STC results from the assumption concerning the course of the function fS = fS (T) describing the changes of solid state volumetric fraction and the temperature at the point considered. Between border temperatures TS , TL the function fS changes from 1 to 0. In this paper the volumetric fraction fS (more precisely fL = 1- fS ) is found using the simple models of macrosegregation (the lever arm rule, the Scheil model). In this way one obtains the formulas determining the course of STC resulting from the certain physical considerations and this approach seems to be closer to the real course of thermal processes proceeding in domain of solidifying alloy.

Thomae type formula for K3 surfaces given by double covers of the projective plane branching along six lines

In this paper, we give a Thomae type formula for K3 surfaces X given by double covers of the projective plane branching along six lines. This formula gives relations between theta constants on the bounded symmetric domain of type I22 and period integrals of X. Moreover, we express the period integrals by using the hypergeometric function FS of four variables. As applications of our main theorem, we define ℝ4-valued sequences by mean iterations of four terms, and express their common limits by the hypergeometric function FS.

On the growth of cocompact hyperbolic Coxeter groups

For an arbitrary cocompact hyperbolic Coxeter group G with a finite generator set S and a complete growth function fS(x)=P(x)/Q(x), we provide a recursion formula for the coefficients of the denominator polynomial Q(x). It allows us to determine recursively the Taylor coefficients and to study the arithmetic nature of the poles of the growth function fS(x) in terms of its subgroups and exponent variety. We illustrate this in the case of compact right-angled hyperbolic n-polytopes. Finally, we provide detailed insight into the case of Coxeter groups with at most 6 generators, acting cocompactly on hyperbolic 4-space, by considering the three combinatorially different families discovered and classified by Lannér, Kaplinskaya and Esselmann, respectively.

One-dimensional distributions of subordinators with upper truncated Lévy measure, and applications

Given a pure-jump subordinator (i.e. nondecreasing Lévy process with no drift) with continuous Lévy measure ν, we derive a formula for the distribution function Fs (x; t) at time t of the associated subordinator whose Lévy measure is the restriction of ν to (0,s]. It will be expressed in terms of ν and the marginal distribution function F (⋅; t) of the original process. A generalization concerning an arbitrary truncation of ν will follow. Under certain conditions, an analogous formula will be obtained for the nth derivative, ∂nFs (x; t) ∂ xn. The requirement that ν is continuous is shown to have no intrinsic meaning. A number of interesting results involving the size ordered jumps of subordinators will be derived. An appropriate approximation for the small jumps of a gamma process will be considered, leading to a revisiting of the generalized Dickman distribution.

A theory for drag partition over rough surfaces

We present a theory for drag partition over rough surfaces of arbitrary roughness density. The total drag is partitioned into a pressure drag, a ground‐surface drag, and a roughness‐element‐surface skin drag. The theory is simple but allows for the estimations of drag partition functions, friction velocity, zero‐displacement height, and roughness length. The model estimates of these quantities are compared with observations and the model is found to perform well. The theory explains several known facts from observations such as the dependency of aerodynamic roughness length on roughness density. It is shown that drag partition is governed entirely by two functions fr and fs which represent the dependencies of surface drag coefficient and the roughness drag coefficient on roughness density. Under the condition of fr = fs, the Raupach (1992) model is derived without assumptions in addition to the drag laws.

Nonparametric estimation for censored lifetimes suffering from unknown selection bias

In a population of individuals, where the random variable (r.v.) σ denotes the birth time and X the lifetime, we consider the case, where an individual can be observed only if its life-line $$\mathcal{L}$$ (σ, X) = {(σ + y, y), 0 ≤ y ≤ X} intersects a given Borel set S in ℝ × ℝ+. Denoting by σ S and X S the birth time and lifetime for the observed individuals, we point out that the distribution function (d.f.) F S of the r.v. X S suffers from a selection bias in the sense that F S = ∝ w d F/μ S, where w and μ S depend only on the distribution of σ and on F, the d.f. of X. Assuming in addition that the r.v. X S is randomly right-censored as soon as the individual is selected, we construct a productlimit estimator $$\hat F_\mathcal{S} $$ for the d.f. F S and a nonparametric estimator ŵ for the weight function w. We prove a consistency result for ŵ and a weak convergence result for $$\hat F_\mathcal{S} $$ . We establish in addition an exponential bound for $$\hat F_\mathcal{S} $$ .