Divisibility properties of a class of binomial sums

We study congruence and divisibility properties of a class of combinatorial sums that involve products of powers of two binomial coefficients, and show that there is a close relationship between these sums and the theorem of Wolstenholme. We also establish congruences involving Bernoulli numbers, and finally we prove that under certain conditions the sums are divisible by all primes in specific intervals.     

On Morrey’s estimate of the Sobolev norms of solutions of elliptic equations

We give a complete proof of Morrey’s estimate for the W ^1,p -norm of a solution of a second-order elliptic equation on a domain in terms of the L ₁-norm of this solution. The dependence of the constant in this estimate on the coefficients of the equation is investigated.     

Unified Solution of the Expected Maximum of a Discrete Time Random Walk and the Discrete Flux to a Spherical Trap

Two random-walk related problems which have been studied independently in the past, the expected maximum of a random walker in one dimension and the flux to a spherical trap of particles undergoing discrete jumps in three dimensions, are shown to be closely related to each other and are studied using a unified approach as a solution to a Wiener-Hopf problem. For the flux problem, this work shows that a constant c = 0.29795219 which appeared in the context of the boundary extrapolation length, and was previously found only numerically, can be derived analytically. The same constant enters in higher-order corrections to the expected-maximum asymptotics. As a byproduct, we also prove a new universal result in the context of the flux problem which is an analogue of the Sparre Andersen theorem proved in the context of the random walker's maximum.     

The improved LaSalle-type theorems for stochastic functional differential equations

The main aim of this paper is to improve some results obtained by Mao [X. Mao, The LaSalle-type theorems for stochastic functional differential equations, Nonlinear Stud. 7 (2000) 307-328]. Our new theorems give better results while conditions imposed are much weaker than in the paper mentioned above. For example, we need only the local Lipschitz condition but neither the linear growth condition nor the bounded moment condition on the solutions. To guarantee the existence and uniqueness of the global solution to the underlying stochastic functional differential equation (SFDE) under the weaker conditions imposed in this paper, we establish a generalised existence-and-uniqueness theorem which covers a wider class of nonlinear SFDEs as demonstrated by the examples discussed in this paper. Moreover, from our improved results follow some new criteria on the stochastic asymptotic stability for SFDEs.     

江苏-西部能源需求-供给模型及其动力学分析

根据江苏省能源需求与西部能源供给及江苏省能源进口量之间相互支持、相互制约的复杂关系建立了江苏-西部能源需求-供给系统．分析了系统的稳态、周期、分叉、混沌等若干动力学行为．通过调节参数可以使系统处于稳定发展或周期震荡区域中．基于Silnikov定理,应用待定系数法,求出了能源系统的同宿轨的表达式．证明了在两个平衡点处均有Silnikov型的同宿轨．根据Silnikov定理确保了能源系统有Smale马蹄和马蹄形混沌．     

一类螺旋映射的增长与掩盖定理

In this paper,we deduce growth and covering theorem for f(x)by the other means,where f(x)is strongly spiral-like mapping of typeβwith orderαdefined on Unit Ball B of complex Banach space,and still give growth upper bound and distortion upper bound for subordinate mapping.     

Positive Solutions to Singular Boundary Value Problems with Sign Changing Nonlinearities on the Half-Line via Upper and Lower Solutions

This paper presents a lower and upper solution technique for singular second order boundary value problems on the half line.     

Computer-Generated Holograms Based on the Three-Dimensional Fourier Spectrum

A method to synthesize a computer-generated hologram (CGH) of real-existing objects from projection images is proposed. Different from other similar methods, our method enables the synthesis of a CGH with only one-dimensional (1-D) mechanical scanning of the objects. Our method is connected with the three-dimensional (3-D) Fourier spectrum of the objects by the 3-D central slice theorem (CST). Two efficient recording techniques for projection images and numerical experiments to verify our principle is discussed. A comparison between the two techniques is also presented from the viewpoint of diffraction efficiency. © 2005 The Optical Society of Japan     

Complex Polynomial Vector Fields Having a Finitely Curved Orbit

The author proves that a non-singular polynomial vector field without invariant lines and having an entire finitely curved transcendent orbit on C^2 must be equivalent to a trivial vector field by a holomorphic change of coordinates. Other classification results are obtained for polynomial vector fields having a finitely curved orbit on C^2.     

g-期望关于凸(凹)函数的Jensen不等式

在文[8]的基础上和彭实戈提出的关于g-期望的最基本的条件下,证明了g-期望关于凸(凹)函数的Jensen不等式在一般意义下成立当且仅当g是关于(y,z)的超齐次(次齐次)生成元且不依赖于y．