Local and global solutions of the Chern-Simons-Higgs system

We study low regularity solutions of the Chern-Simons-Higgs equations. The Lorentz gauge condition makes them hyperbolic equations with the null form. Under the Coulomb gauge condition they are formulated in the hyperbolic equation coupled with elliptic equation. The div-curl decomposition is used in the temporal gauge.     

ESTIMATES OF LOWER CRITICAL MAGNETICFIELD AND VORTEX PINNING BY INHOMO-GENEITIES IN TYPE II SUPERCONDUCTORS

The effect of an applied magnetic field on an inhomogeneous superconductor is studied and the value of the lower critical magnetic field HC1 at which superconducting vortices appear is estimated. In addition, the authors locate the vortices of local minimizers, which depends on the inhomogeneous term a(x).     

ESTIMATES OF LOWER CRITICAL MAGNETIC FIELD AND VORTEX PINNING BY INHOMOGENEITIES IN TYPE Ⅱ SUPERCONDUCTORS

The effect of an applied magnetic field on an inhomogeneous superconductor is studied and the value of the lower critical magnetic field Hc1 at which superconducting vortices appear is estimated. In addition, the authors locate the vortices of local minimizers, which depends on the inhomogeneous term a(x).     

Accurate Estimates of the Gamma Function Involving the PSI Function

The main result of this article is to establish new and accurate approximations of the gamma function in terms of the digamma function, that improve a result of Alzer and Batir [Appl. Math. Lett. 20(2007):778–781].     

Sharp-interface limit of the Allen-Cahn action functional in one space dimension

We analyze the sharp-interface limit of the action minimization problem for the stochastically perturbed Allen-Cahn equation in one space dimension. The action is a deterministic functional which is linked to the behavior of the stochastic process in the small noise limit. Previously, heuristic arguments and numerical results have suggested that the limiting action should “count” two competing costs: the cost to nucleate interfaces and the cost to propagate them. In addition, constructions have been used to derive an upper bound for the minimal action which was proved optimal on the level of scaling. In this paper, we prove that for d = 1, the upper bound achieved by the constructions is in fact sharp. Furthermore, we derive a lower bound for the functional itself, which is in agreement with the heuristic picture. To do so, we characterize the sharp-interface limit of the space-time energy measures. The proof relies on an extension of earlier results for the related elliptic problem. Mathematics Subject Classification (2000) 49J45, 35R60, 60F10     

Near boundary vortices in a magnetic Ginzburg-Landau model: Their locations via tight energy bounds

Given a bounded doubly connected domain G⊂R², we consider a minimization problem for the Ginzburg-Landau energy functional when the order parameter is constrained to take S¹-values on ∂G and have degrees zero and one on the inner and outer connected components of ∂G, correspondingly. We show that minimizers always exist for 0<λ<1 and never exist for λ?1, where λ is the coupling constant ( is the Ginzburg-Landau parameter). When λ→1−0 minimizers develop vortices located near the boundary, this results in the limiting currents with δ-like singularities on the boundary. We identify the limiting positions of vortices (that correspond to the singularities of the limiting currents) by deriving tight upper and lower energy bounds. The key ingredient of our approach is the study of various terms in the Bogomol'nyi's representation of the energy functional.     

Global relaxation and nonrelativistic limit of nonisentropic Euler-Maxwell systems

The aim of this paper is to investigate smooth solutions to Cauchy (or periodic) problem for a nonisentropic Euler-Maxwell system with small parameters. For initial data close to constant equilibrium states, we prove the global-in-time convergence of the Euler-Maxwell system as parameters go to zero. The limit systems are the drift-diffusion system and the nonisentropic Euler-Poisson system, respectively.     

Rates of convergence in certain limit theorem for extreme values

Let be independent random variables with the common negative binomial distribution with parameters r>0 and 1/n, where r is not necessarily an integer. We determine the limiting distribution of the random variable as n→∞, corresponding normalizing constants and the rate of convergence. For an integer r the connection with certain waiting time problems is indicated.     

关于伽玛函数的单调性质

伽玛函数的单调性质和对数完全单调性质被获得了.     

关于伽玛函数和不完全伽玛函数单调性的注记

利用含有两参数拓广加权平均值的单调性和不等式,我们证明了三类比的伽玛函数在条件r＞0,s＞0和x＞0下是递增的,Γ(s),Γ(s,x)和γ(s,x)分别表示伽玛函数和不完全伽玛函数.据此关于伽玛函数和不完全伽玛函数的单调性结果和不等式被推广了,同时给出了伽玛函数一些结果的证明.     

On some properties of the Gamma function

Anderson and Qiu (1997) conjectured that the function is concave for 1$">. In this paper we prove this conjecture. We also study the monotonicity of some functions connected with the psi-function and derive inequalities for and .

     

Numerical Representations of the Incomplete Gamma Function of Complex-Valued Argument

Various approaches to the numerical representation of the incomplete Gamma function (m+1/2,z) for complex arguments z and non-negative small integer indices m are compared with respect to numerical fitness (accuracy and speed). We consider power series, Laurent series, classical numerical methods of sampling the basic integral representation, and others not yet covered by the literature. The most suitable scheme is the construction of Taylor expansions around nodes of a regular, fixed grid in the z-plane, which stores a static matrix of higher derivatives. This is the obvious extension to a procedure that is in common use for real-valued z.     

有关Gamma函数的一个双不等式

本文将文献[1]中的双边不等式从自然数推广至实数,证明了下面不等式成立:(x/e)~x(2πx)~(1/2)(1 1/(12x))<Γ(x 1)<(x/e)~x(2πx)~(1/2)(1 1/(12x-0.5)),其中x≥1.     

On the technique for passing to the limit in nonlinear elliptic equations

We consider the problem of passing to the limit in a sequence of nonlinear elliptic problems. The “limit” equation is known in advance, but it has a nonclassical structure; namely, it contains the p-Laplacian with variable exponent p = p(x). Such equations typically exhibit a special kind of nonuniqueness, known as the Lavrent’ev effect, and this is what makes passing to the limit nontrivial. Equations involving the p(x)-Laplacian occur in many problems of mathematical physics. Some applications are included in the present paper. In particular, we suggest an approach to the solvability analysis of a well-known coupled system in non-Newtonian hydrodynamics (“stationary thermo-rheological viscous flows”) without resorting to any smallness conditions.     

Existence of global bounded weak solutions to nonsymmetric systems of Keyfitz-Kranzer type

In this paper, we study the global L^∞ solutions for the Cauchy problem of nonsymmetric system (1.1) of Keyfitz-Kranzer type. When n=1, (1.1) is the Aw-Rascle traffic flow model. First, we introduce a new flux approximation to obtain a lower bound ρε,δ?δ>0 for the parabolic system generated by adding “artificial viscosity” to the Aw-Rascle system. Then using the compensated compactness method with the help of L¹ estimate of wε,δx(⋅,t) we prove the pointwise convergence of the viscosity solutions under the general conditions on the function P(ρ), which includes prototype function , where γ∈(−1,0)∪(0,∞), A is a constant. Second, by means of BV estimates on the Riemann invariants and the compensated compactness method, we prove the global existence of bounded entropy weak solutions for the Cauchy problem of general nonsymmetric systems (1.1).     

On the Self-Decomposability of Euler's Gamma Function

Let be Euler's Gamma function. We prove that, for all 0, > 0, > 0, > 0, the function (( + iz)/() ^{i z)} , z R ¹, is a self-decomposable characteristic function from the Thorin class and derive its explicit canonical form. Similarly to [1], we also describe several classes of Lévy-type stochastic processes related to .     

第Ⅱ类非自共轭锥上的Gamma函数

本文将Ｇａｍｍａ函数及Ｓｉｅｇｅｌ积分推广到一般的第Ⅱ类非自共轭锥上,作为其应用,显示给出了以这些锥为底的管状域的Ｃａｕｃｈｙ－Ｓｚｅｇｏｅ核和形式Ｐｏｉｓｓｏｎ核。     

Pointwise Estimates for Linear Combinations of Gamma Operators

For linear combinations of Gamma operators G_n,r(f,x), we give an equivalent theorem with (f,t), where (f,t) are the Ditzian-Totik moduli of smoothness ( ).AMS Subject Classification (1991): 41A25, 41A36.Supported by NSF of Hebei ProvinceSupported by NSF of Hebei Province