Extremal functions for the Caffarelli-Kohn-Nirenberg inequalities: A simple proof of the symmetry

In this article, we give a simple proof of the result due to Lin and Wang ensuring the foliated Schwarz symmetry of the extremal functions for the Caffarelli-Kohn-Nirenberg inequalities. This new proof uses a direct and powerful method due to Bartsch, Weth and Willem using polarizations.     

反射倒向随机微分方程的逆比较问题(Ⅰ)

在Briand,Coquet,Hu,Memin,Peng[1],Coquet,Hu,Memin,Peng[2],Chen[3],Jiang [8]等中,研究了倒向随机微分方程的逆比较定理,就是通过比较倒向随机微分方程的解来比较倒向随机微分方程的生成元问题．在文[9]中Li和Tang首次研究了反射倒向随机微分方程的逆比较问题．本文考虑在更一般的条件下,反射倒向随机微分方程的生成元的逆比较问题．     

一类并行数值Schwarz格式的收敛性及比较定理

本文对［１］给出的一类求解椭圆型偏微分方程的并行数值Ｓｃｈｗａｒｚ格式作了进一步的分析，给出了一个新的收敛定理，根据该收敛定理，可以把文［１］中的主要收敛快慢进行了比较，得出了一些比较结果。     

广义线性回归极大似然估计的强相合性

设有该文第1节所描述的广义线性回归模型,以$underline{lambda}_n$和$overline{lambda}_n$分别记$sumlimits_{i=1}^{n}Z_iZ_i^{prime}$的最小和最大特征根,$hat{beta}_n$记$beta_0$的极大似然估计.在文献[1]中,当{$Z_i,ige1$}有界时得到$hat{beta}_n$强相合的充分条件,在自然联系和非自然联系下分别为$underline{lambda}_nrightarrowinfty$, $(overline{lambda}_n)^{1/2+delta}=O(underline{lambda}_n)$（对某$delta>0$)以及$underline{lambda}_nrightarrowinfty$, $overline{lambda}_n=O(underline{lambda}_n)$.作者将后一结果改进为只要求$(overline{lambda}_n)^{1/2+delta}=O(underline{lambda}_n)$,从而与自然联系情况下的条件达到一致.     

Nonlinear models of suspension bridges

Nonlinear variational equations describing one type of suspension bridges are proposed and studied. The variational equations describe the behaviour of road bed, main cables and cable stays. The road bed is described by two functions connected with vertical and horizontal deformation of any cross section. The main cable is considered to be perfectly flexible and inextensible. The cable stays only resist tensile forces. The variational equations are derived from the principle of minimum potential energy. The existence of solution is based on the Brouwer Fixed Point Theorem. The local uniqueness and continuous dependence on the data represented by gravitational forces acting on the road bed are studied. The local results are based on the Implicit Function Theorem for Banach spaces. A certain stability criterion for suspension bridges is formulated and this criterion indicates how to influence the stability of suspension bridges.     

Maximum principles for discrete-time nonlinear stochastic control systems

In this paper we treat discrete-time stochastic control systems. Using corresponding results for systems, which are linear with respect to the state variables, we derive under convexity assumptions optimality conditions in form of maximum principles     

Positive Reachability for Diffusion Equations

Counterexamples are constructed for some plausible conjectures. Typical of these: as the Maximum Principle ensures that positive boundary data give a positive state at time T from 0 initial data, one might (plausibly, but falsely) conjecture that all positive terminal states should be approximately reachable in this way, i.e., subject to the requirement that the boundary data stays nonnegative.     

Some Oscillation Theorems for Second Order Differential Equations

In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation

扩张原理的一种新的表现形式

提出一种基于“模糊点”的模糊集合的分解定理，在此分解定理的基础上给出模糊扩张原理的一种新的表现形式。新的扩张原理与以往人们所提出的扩张原理是等价的，而表现形式更为直观、简便。同时，利用该扩张原理得到模糊复合函数以及多元模糊关系合成运算的合理解释。     

The Comparison Theorems of Kolmogorov Type on a Convolution Class of Functions

ＴｈｅＣｏｍｐａｒｉｓｏｎ　ＴｈｅｏｒｅｍｓｏｆＫｏｌｍｏｇｏｒｏｖＴｙｐｅｏｎａＣｏｎｖｏｌｕｔｉｏｎＣｌａｓｓｏｆＦｕｎｃｔｉｏｎｓＣｈｅｎＤｉｒｏｎｇ（陈迪荣_（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＢｅｉｊｉｎｇＮｏｒｍａｌＵｎｉｖ?..     

ON A STRONG ROOTED THEOREM OF ONE CLASS OF COMPLEX ANALYTIC SYSTEMS

ＯＮ　Ａ　ＳＴＲＯＮＧ　ＲＯＯＴＥＤ　ＴＨＥＯＲＥＭ　ＯＦ　ＯＮＥ　ＣＬＡＳＳ　ＯＦ　ＣＯＭＰＬＥＸ　ＡＮＡＬＹＴＩＣ　ＳＹＳＴＥＭＳＯＮＡＳＴＲＯＮＧＲＯＯＴＥＤＴＨＥＯＲＥＭＯＦＯＮＥＣＬＡＳＳＯＦＣＯＭＰＬＥＸＡＮＡＬＹＴＩＣＳＹＳＴＥＭＳ￥Ｌ...     

On the nonexistence of solutions for random differential equations in banach spaces ∗

Random differential equations in Banach spaces without solutions are considered. Some density results are established.     

A Cauchy's Integral Formula for Functions with Values in a Universal Clifford Algebra and its Applications

In this paper, we obtain Cauchy's integral formula on certain distinguished boundary for functions with values in a universal Clifford algebra, which is similar to the classical Cauchy's integral formula on the distinguished boundary of polycylinder for several complex variables. By using it, both the mean value theorem and the maximum modulus theorem are given.     

广义线性模型中极大拟似然估计的强收敛速度

在sup_{i ≥1}E||y_i||^2+α < ∞(对某个α > 0)和其它正则条件下, 证明了一般联系函数的多维广义线性模型拟似然估计的强相合性, 并得到了强收敛速度, 其中 y_i 是响应变量. 此结果是对文献中相应结果的改进.     

Existence and Comparison Results for First Order Periodic Implicit Difference Equations with Maxima

In this paper, we establish comparison results (maximum principles) which allow us to use the monotone method and the method of upper and lower solutions in order to build convergent sequences to the solutions of difference equations of the type j u k = f k , u k +1 , max l ] { k m h +1,…, k +1} u l , k ] I , u 0 = u T , with j u k = u k +1 m u k , I ={0,1,…, T m 1} and f ] C ( I 2 R 2 R , R ).