OSCILLATION FOR SOLUTIONS OF SYSTEMS OF N-TH ORDER PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, some sufficient conditions for the oscillation for solutions to systems of n-th order partial functional differential equations are obtained.     

随机需求条件下的延迟发运策略模型及性质

本针对随机需求条件下物流配送中心的库存和运输联合决策问题，在基本库存和自身运输能力不足的情况下，提出对剩余客户订货需求采取部分延迟到下一期与部分利用第三方物流立即发运两相结合的策略，并在具有一般惩罚(损失)费延迟发运量限制的条件下，建立运输和库存相关总成本数学期望最小的优化模型，论证了该模型的主要性质，在此基础上很容易构造求解该类问题的优化方法。     

On the Statistics of Partial Quotients of Finite Continued Fractions

We refine the remainder estimate in the asymptotic formula, earlier obtained in a joint paper with V. A. Bykovskii, for Arnold's problem about Gauss-Kuzmin statistics.     

UNIFORM CONVERGENCE OF CESARO MEANS OF NEGATIVE ORDER OF DOUBLE TRIGONOMETRIC FOURIER SERIES

In this paper we prove that iff ∈ C([-π,π]2) and the function f is bounded partial p-variation for some p ∈ [1, ∞), then the double trigonometric Fourier series of a function f is uniformly (C;-α,-β) summable (α β＜ 1/p,α,β＞ 0) in the sense of Pringsheim. If α β≥ 1/p, then there exists a continuous function f0 of bounded partial double trigonometric Fourier series of fo diverge over cubes.     

Modification of Spatial Coherence by Means of Low-Order Zernike-Mode Adaptive Optics

Spatial coherence of the field modified by low-order adaptive optics is analyzed to establish a theoretical basis for the recent idea of using adaptive optics as a spatial coherence modifier. In this context low-order adaptive optics has the ability to correct some of the low-order aberrations specified by Zernike polynomials. The initial field to be modified is assumed to be a spatially partially coherent one resulting from phase disturbance. It is demonstrated, as in the previous study, that low-order adaptive optics serves to enhance the spatial coherence of the resultant field and that the effect of the enhancement becomes stronger as the spatial coherence of the initially partially coherent field increases. Potential applications of low-order adaptive optics as a spatial coherence modifier are briefly discussed.     

The Calogero–Bogoyavlenskii–Schiff Equation in 2+1 Dimensions

We use the classical and nonclassical methods to obtain symmetry reductions and exact solutions of the (2+1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation. Although this (2+1)-dimensional equation arises in a nonlocal form, it can be written as a system of differential equations and, in potential form, as a fourth-order partial differential equation. The classical and nonclassical methods yield some exact solutions of the (2+1)-dimensional equation that involve several arbitrary functions and hence exhibit a rich variety of qualitative behavior.     

基于部分变量反馈的混沌系统控制

提出了混沌系统部分变量逆序反馈控制器的定义，并以陈氏系统为例对该类控制器进行了研究，得出了部分变量正序和逆序控制器存在的条件，应用该条件扩展了有关文献的研究成果，得到了混沌系统的多种形式的反馈控制器.仿真结果显示，基于部分变量的混沌系统的控制是简单而有效的. 关键词： 部分变量反馈控制 逆序控制器 混沌系统     

Solid-phase oxidative halodecarboxylation of β-arylacrylic acids with the ceric ammonium nitrate—alkali halide system

The solid-phase oxidation of cinnamic, 4-methoxy- and 3,4-dimethoxycinnamic acids with Ce(NH₄)₂(NO₃)₆—MHal system leads to β-halostyrenes. Similar procedure in the absence of a metal halide results in a cleavage of the C=C bond giving the corresponding benzaldehydes. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 114–118, January, 2008.     

Numerical analysis of reversible A B C reaction-diffusion systems

We develop an effective numerical method of studying large-time properties of reversible reaction-diffusion systems of type A + B ↔ C with initially separated reactants. Using it we find that there are three types of asymptotic reaction zones. In particular we show that the reaction rate can be locally negative and concentrations of species A and B can be nonmonotonic functions of the space coordinate x, locally significantly exceeding their initial values. Received 6 June 2002 / Received in final form 20 January 2003 Published online 7 May 2003     

The completely positive and doubly nonnegative completion problems

We prove the following. Let G be an undirected graph. Every partially specified symmetric matrix, the graph of whose specified entries is G and each of whose fully specified submatrices is completely positive (equal to BB^T for some entrywise nonnegative matrix B), may be completed to a completely positive matrix if and only if G is a block-clique graph (a chordal graph in which distinct maximal cliques overlap in at most one vertex). The same result holds for matrices that are doubly nonnegative (entrywise nonnegative and positive semidefinite).