Skew Models II

If g and G are the pdf and the cdf of a distribution symmetric around 0 then the pdf 2g(u)G(λ u) is said to define a skew distribution. In this paper, we provide a mathematical treatment of the skew distributions when g and G are taken to come from one of Pearson type II, Pearson type VII or the generalized t distribution.      

Dual frames in connected with generalized sampling in shift-invariant spaces

The aim of this article is to derive stable generalized sampling in a shift-invariant space by using some special dual frames in L²(0,1). These sampling formulas involve samples of filtered versions of the functions in the shift-invariant space. The involved samples are expressed as the frame coefficients of an appropriate function in L²(0,1) with respect to some particular frame in L²(0,1). Since any shift-invariant space with stable generator is the image of L²(0,1) by means of a bounded invertible operator, our generalized sampling is derived from some dual frame expansions in L²(0,1).     

Analogues of the Kolosov–Muskhelishvili General Representation Formulas and Cauchy–Riemann Conditions in the Theory of Elastic Mixtures

Analogues of the well-known Kolosov–Muskhelishvili formulas of general representations are obtained for nonhomogeneous equations of statics in the case of the theory of elastic mixtures. It is shown that in this theory the displacement and stress vector components, as well as the stress tensor components, are represented through four arbitrary analytic functions.The usual Cauchy–Riemann conditions are generalized for homogeneous equations of statics in the theory of elastic mixtures.     

A compactness result for Kähler Ricci solitons

In this paper we prove a compactness result for compact Kähler Ricci gradient shrinking solitons. If (Mi,gi) is a sequence of Kähler Ricci solitons of real dimension n?4, whose curvatures have uniformly bounded Ln/2 norms, whose Ricci curvatures are uniformly bounded from below and μ(gi,1/2)?A (where μ is Perelman's functional), there is a subsequence (Mi,gi) converging to a compact orbifold (M_∞,g_∞) with finitely many isolated singularities, where g_∞ is a Kähler Ricci soliton metric in an orbifold sense (satisfies a soliton equation away from singular points and smoothly extends in some gauge to a metric satisfying Kähler Ricci soliton equation in a lifting around singular points).     

拟线性抛物型方程广义解的局部有界性

本文给出了一类较广泛的拟线性抛物型方程广义解的局部有界性,进而也得到了解的Holder连续性.     

On generalized gradients

In this paper we present a concept of the construction of generalized gradients by considering a development of directional derivatives into spherical harmonics. This leads to a derivation system as a system of generalized partial derivatives. Necessary conditions for local extrema for a broad class of not necessarily differentiable function can be given and a characterization of points of differentiability can be proved by using generalized gradients.     

Asymptotic expansions of integrals of two Bessel functions via the generalized hypergeometric and Meijer functions

Asymptotic expansions of certain finite and infinite integrals involving products of two Bessel functions of the first kind are obtained by using the generalized hypergeometric and Meijer functions. The Bessel functions involved are of arbitrary (generally different) orders, but of the same argument containing a parameter which tends to infinity. These types of integrals arise in various contexts, including wave scattering and crystallography, and are of general mathematical interest being related to the Riemann—Liouville and Hankel integrals. The results complete the asymptotic expansions derived previously by two different methods — a straightforward approach and the Mellin-transform technique. These asymptotic expansions supply practical algorithms for computing the integrals. The leading terms explicitly provide valuable analytical insight into the high-frequency behavior of the solutions to the wave-scattering problems.     

一些非线性发展方程的显式行波解

该文给出了一种构造非线性发展方程显式行波解的方法并用该方法得到了Hirota-Satsuma方程组,一类非线性常微分方程以及广义耦合标量场方程组的显式行波解.     

二阶椭圆型微分方程解的振动定理

考虑二阶非线性椭圆型微分方程∑^n_{i,j}∂/∂x_i{A_{i,j}(x,y)∂/∂x_j}+q(x)f(y)=0 (E)，其中q(x)在外区域 Ω∈R\+n上变号. 利用偏Riccati变换和积分平均技巧, 建立了方程(E)所有解振动的充分准则.