STURM COMPARISON THEOREMS FOR SECOND ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS

In this paper, we first establish some differential inequalities and then some Sturm comparison theorems are derived for the second order neutral nonlinear differential equations. Our results generalize some classical Sturm comparison theorems.     

一类阶为偶数的高斯和显式计算的注记

给出指数2情形下阶数为2l_1~(r1)l_1~(r2)的高斯和的显式计算公式.证明方法直接利用Stickelberger理想分解定理,进而结果独立于其他指数2情形高斯和的结果而成立.     

我国IPO市场的周期性行为研究:1994-2010

对IPO冷热周期内的时变波动特征首次建立区制转换GARCH模型加以有效描述,以及用计数数据分位数回归模型研究发行数量和发行到上市持续期的关系。通对1994年1月至2010年8月间我国A股IPO市场新股的实证研究得到若干新结论:上市首日收益率和发行到上市的持续期是发行数量的诱因,导致这三个描述IPO行为主要变量的周期行为之间存在相位差;发行到上市的持续期的降低对发行数量的增加有积极地促进作用;除了发行数量在淡季状态波动持续性较强外,其他变量在淡旺季的波动持续性均较弱;旺季时(调整后的)上市首日收益率、发行数量的波动方差比淡季时大,而发行到上市的持续期则相反;我国A股IPO发行市场的淡旺季周期的形成主要受到IPO发行政策、宏观经济环境、投资者情绪的影响控制。     

Stochastic exponential synchronization of jumping chaotic neural networks with mixed delays

This paper deals with the exponential synchronization problem for a class of stochastic jumping chaotic neural networks with mixed delays and sector bounded nonlinearities. The mixed time delays under consideration comprise both discrete time-varying delays and distributed time delays. By applying the Finsler’s Lemma and constructing appropriate Lyapunov-Krasovskii functional based on delay partitioning, several improved delay-dependent feedback controllers with sector nonlinearities are developed to achieve the synchronization in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve no free weighting matrices, the computational burden is largely reduced. One numerical example is provided to demonstrate the effectiveness of the theoretical results.     

Sign or root of unity ambiguities of certain Gauss sums

Gauss sums play an important role in number theory and arithmetic geometry. The main objects of study in this paper are Gauss sums over the finite field with q elements. Recently, the problem of explicit evaluation of Gauss sums in the small index case has been studied in several papers. In the process of the evaluation, it is realized that a sign (or a root of unity) ambiguity unavoidably occurs. These papers determined the ambiguities by the congruences modulo L, where L is certain divisor of the order of Gauss sum. However, such method is unavailable in some situations. This paper presents a new method to determine the sign (root of unity) ambiguities of Gauss sums in the index 2 case and index 4 case, which is not only suitable for all the situations with q being odd, but also comparatively more efficient and uniform than the previous method.     

Existence of positive solutions to third order differential equations with advanced arguments and nonlocal boundary conditions

We use a fixed point theorem due to Avery and Peterson to establish the existence of at least three non-negative solutions of some nonlocal boundary value problems to third order differential equations with advanced arguments. An example is given to illustrate the main results.     

A new algorithm for decomposition of graphical models

In this paper, we combine Leimer’s algorithm with MCS-M algorithm to decompose graphical models into marginal models on prime blocks. It is shown by experiments that our method has an easier and faster implementation than Leimer’s algorithm.     

带小随机扰动的中偏差原理(英文)

本文研究了带小随机扰动的中偏差原理.运用收缩原理和指数逼近方法,Freidlin-Wentzell定理给出了Xε的大偏差原理,从而得到了Xε的中偏差原理.     

一类椭圆型半变分不等式解的存在性(英文)

本文研究了一类Dirichlet边界的椭圆型半变分不等式问题.利用非光滑形式的环绕定理和非光滑形式的对称山路定理,得到了在相应假设条件下此不等式问题至少有一个非平凡解和无穷多解.本文中非光滑势能在原点处关于算子+V(x)的第一正特征值λ是不完全共振的.