非齐次障碍问题的正则性结果

本文研究了非齐次椭圆方程的障碍问题,给出了二阶非齐次障碍问题解的定义,利用Poincar啨不等式,获得非齐次障碍问题的解及其导数的一些性质,填补了对非齐次障碍问题研究的空白.     

An attempt to differential Galois theory of second order polynomial system and solvable subgroup of M(o)bius transformations

By introducing the conception "relativistic differential Galois group" for the second order polynomial systems, we establish the relation between the conformal relativistic differential Galois group and the subgroup of M(o)bius transformations, and prove that the system is integrable in the sense of Liouville if its conformal relativistic differential Galois group is solvable with a derived length at most 2. Some omissions on the structures of solvable subgroups of M(o)bius transformations at the first author's article published in this journal in 1996 are refreshed in this paper.     

Persistence and global stability in a delayed Leslie-Gower type three species food chain

Our investigation concerns the three-dimensional delayed continuous time dynamical system which models a predator-prey food chain. This model is based on the Holling-type II and a Leslie-Gower modified functional response. This model can be considered as a first step towards a tritrophic model (of Leslie-Gower and Holling-Tanner type) with inverse trophic relation and time delay. That is when a certain species that is usually eaten can consume immature predators. It is proved that the system is uniformly persistent under some appropriate conditions. By constructing a proper Lyapunov function, we obtain a sufficient condition for global stability of the positive equilibrium.     

Transfer matrix for the open chain from giant gravitons

We construct the transfer matrix for the open chain with the centrally extended SU(2|2) symmetry attached to the so called Z=0 giant graviton brane. Using the reflection equations, unitarity property and crossing property, we show that this model is integrable.     

The parameter uniform numerical method for singularly perturbed parabolic reaction–diffusion problems on equidistributed grids

This article presents the study of singularly perturbed parabolic reaction–diffusion problems with boundary layers. To solve these problems, we use a modified backward Euler finite difference scheme on layer adapted nonuniform meshes at each time level. The nonuniform meshes are obtained by equidistribution of a positive monitor function, which involves the second-order spatial derivative of the singular component of the solution. The equidistributing monitor function at each time level allows us to use this technique to non-linear parabolic problems. The truncation error and the stability analysis are obtained. Parameter–uniform error estimates are derived for the numerical solution. To support the theoretical results, numerical experiments are carried out.     

Centered -discrepancy of random sampling and Latin hypercube design, and construction of uniform designs

In this paper properties and construction of designs under a centered version of the -discrepancy are analyzed. The theoretic expectation and variance of this discrepancy are derived for random designs and Latin hypercube designs. The expectation and variance of Latin hypercube designs are significantly lower than that of random designs. While in dimension one the unique uniform design is also a set of equidistant points, low-discrepancy designs in higher dimension have to be generated by explicit optimization. Optimization is performed using the threshold accepting heuristic which produces low discrepancy designs compared to theoretic expectation and variance.

     

一类三阶自治系统的积分法

研究一类三阶自治系统的积分方法,证明了在一定条件下,这类系统的积分问题归结为求解由该方程的系数所确定的Riccati方程     

异方差回归模型近邻型估计的相合性

本文研究异方差回归模型Ｙｉ＾（ｎ）＝ｇ（ｘｉ＾（ｎ））＋εｉ＾（ｎ）,ｉ＝１,…,ｎ,其中ｇ是右实函数,ｘｉ＾（ｎ）是非随机设计点列,εｉ＾（ｎ）是随机误差,文中定义了一类ｇ（ｘ）的近邻型估计ｇｎ（ｘ）＝（ｎ）∑（ｉ＝１）Ｗｍ（ｘ）Ｙｉ＾（ｎ）,得到了ｒ阶平均相全和渐近正态性,特别,在（∞）∑（ｎ＝１）（ｎ）∑（ｉ＝１）Ｅ／εｉ＾（ｎ）／＾ｓ／（ｎｉ）＾ｓ／ｒ〈∞,ｍａｘＥ（１≤ｉ≤ｎ）／εｉ（＾     

The Inverse Problem of the Calculus of Variations: Separable Systems

This paper deals with the inverse problem of the calculus of variations for systems of second-order ordinary differential equations. The case of the problem which Douglas, in his classification of pairs of such equations, called the separated case is generalized to arbitrary dimension. After identifying the conditions which should specify such a case for n equations in a coordinate-free way, two proofs of its variationality are presented. The first one follows the line of approach introduced by some of the authors in previous work, and is close in spirit, though being coordinate independent, to the Riquier analysis applied by Douglas for n = 2. The second proof is more direct and leads to the discovery that belonging to the separated case has an intrinsic meaning for the given second-order differential equations: the system is separable in the sense that it can be decoupled into n pairs of first-order equations.