临界情况下Heteroclinic环的稳定性

关于Heteroclinic环(包括Homoclinic环)的稳定性,目前仅有和在粗情况下的结果。对n=1时的临界情况有作者和钱敏的结果,而对其它情况,至今尚无法判定Heteroclimc环的稳定性。 本文对一般的临界情况给出了Heteroclinic环的稳定性判据,所得的结果包括并推广了作者和钱敏的原有结果并对这些结果给予统一的证明。 利用本文的主要结果,最后讨论了极限环的存在性及从Heteroclinic环分支出极限环的问题。     

具无限时滞的非自治捕食者-食饵系统的持久性

本文采用新的方法研究了具无限时滞的非自治、非卷积的捕食者－食饵系统的持久性问题，得到了新的、有趣的结果。本文的结果包含已知的结果作为特例．     

具有控制系数的高阶线性微分方程复振荡的一个结果

该文考虑具有控制系数 A\-0 和系数仅有有限个极点的高阶线性齐次微分方程（1.1）。得到了一个复振荡结果，该结果是J. K. Langley［11］等作者在整系数下相应结果的推广。     

无穷远分界线的稳定性和产生极限环的条件

本文给出了无穷远分界线稳定性的判据以及从无穷远分界线产生极限环的条件，其结果包括了［７］，［８］的主要结果。     

概率求解的类型

<正>开动脑筋求概率,最为关键的有两点,第一是要清楚我们所关注的事件包含了哪些结果;第二是要清楚所有机会均等的结果.这两种结果的个数之比就是我们所要求的概率.因此,在计算概率的时候,我们所关注的结果和所有机会均等的结果这两个方面的找寻变得尤为重要.一、寻找我们所关注的结果在大多数情况下,所有机会均等的结果比较好找,对于我们所关注的结果,我们可以通过列举的方法寻找.图1例1(2012年内江)如图1所示,A、B是边长为1的正方形组成的网格的两个格点,在格点中任意放置点C,恰好能使△ABC的面积为1的概率是.     

具有单边约束的基本分岔问题的新分岔模式

含约束分岔是非线性动力系统周期解分岔研究中遇到的普遍问题,然而现有的奇异性理论关于此类问题的结果还很少。作为探讨和补充,给出余维数不大于3的10种基本分岔在约束情况下的转迁集和摄动保持分岔图的计算结果。可为约束分岔问题的研究提供直接利用的结果。     

模糊群决策结果的可信性评估

模糊数是群决策中常用的决策结果表达形式.研究了模糊群决策结果的可信性评估问题.认为群决策结果的可信性与模糊群决策结果的模糊度和一致度存在强相关,因此,模糊群决策结果可信性评估主要就是对群决策结果的模糊度和一致度的计算,创新提出了基于群隶属函数的模糊度和一致度的计算方法,并给出了基于模糊度和一致度的专家模糊数决策结果综合评价值的计算方法,最后,在此基础上求得专家模糊评估结果的可信度和群决策结果的可信度.     

Banach空间中线性算子的Drazin广义逆的表示

1981年,1985年,2000年,乔三正、蔡东汉、魏益民分别给出Drazin广义逆不同形式的表示．本文将对上述结果进行推广,给出Drazin广义逆的统一表示,使上述三个结果均成为本文主要结果的特例．在本文主要结果的基础上,利用算子谱理论,给出Drazin广义逆的一种逼近形式的表示,同时给出逼近解的估计．此结果推广了蔡东汉、魏益民的相应结果．     

某些差分多项式的亏量

Halburd和Korhonen指出研究复域差分的值分布问题对进一步研究复域差分与差分方程具有十分重要的意义.本文得到了关于有限级亚纯函数的差分多项式的亏量为一些结果,其中部分结果可视为微分多项式相应结果的差分模拟.同时,我们在一定条件下给出了经典的Valiron-Mohon'ko定理的一个差分模拟结果,并且作为本文中的一个重要工具出现.这些结果推广了前人已有结果.     

钥匙编码的若干计数问题

本文考察钥匙编码的若干计数问题,给出它们的显表达式,这些结果均优于文[1],[2]的相应的结果。     

An entire function and its derivatives sharing a polynomial

In this paper, we study the growth of solutions of a first-order linear differential equation and that of a second-order linear differential equation. From this we obtain some uniqueness theorems of a nonconstant entire function and its first derivative having the same fixed points with the same multiplicities. The results in this paper also improve some known results. Some examples show that the results in this paper are best possible.     

The uniqueness of an entire function sharing a small entire function with its derivatives

In this paper, we prove a theorem on the growth of a solution of a linear differential equation. From this we obtain some uniqueness theorems concerning that a nonconstant entire function and its derivatives sharing a small entire function. The results in this paper improve many known results. Some examples are provided to show that the results in this paper are the best possible.     

Monochromatic and Heterochromatic Subgraphs in Edge-Colored Graphs - A Survey

Nowadays the term monochromatic and heterochromatic (or rainbow, multicolored) subgraphs of an edge-colored graph appeared frequently in literature, and many results on this topic have been obtained. In this paper, we survey results on this subject. We classify the results into the following categories: vertex-partitions by monochromatic subgraphs, such as cycles, paths, trees; vertex partition by some kinds of heterochromatic subgraphs; the computational complexity of these partition problems; some kinds of large monochromatic and heterochromatic subgraphs. We have to point out that there are a lot of results on Ramsey type problem of monochromatic and heterochromatic subgraphs. However, it is not our purpose to include them in this survey because this is slightly different from our topics and also contains too large amount of results to deal with together. There are also some interesting results on vertex-colored graphs, but we do not include them, either. Supported by NSFC, PCSIRT and the “973” program.     

Qualitative analysis of a new Lorenz‐type chaotic system and its simulation

In this paper, the ultimate bound for a new chaotic system is derived based on stability theory of dynamical systems. The meaningful contribution of this article is that the results presented in this paper contain the existing results as special cases. Finally, numerical simulations are given to verify the effectiveness and correctness of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.     

On scalar equilibrium problem in generalized convex spaces

In this paper we prove the existence of a solution to the scalar equilibrium problem in generalized convex space. As applications, we derive results on the best approximations and simultaneous approximations. The results of this paper generalize some known results in the literature.     

Merit functions for general variational inequalities

In this paper, we consider some classes of merit functions for general variational inequalities. Using these functions, we obtain error bounds for the solution of general variational inequalities under some mild conditions. Since the general variational inequalities include variational inequalities, quasivariational inequalities and complementarity problems as special cases, results proved in this paper hold for these problems. In this respect, results obtained in this paper represent a refinement of previously known results for classical variational inequalities.     

Convergence criteria of modified Noor iterations with errors for asymptotically nonexpansive mappings

In this paper, weak and strong convergence theorems of the modified Noor iterations with errors are established for asymptotically nonexpansive mappings in Banach spaces. The results obtained in this paper extend and improve the several recent results in this area.     

Well-posed variational inequalities

In this paper, we introduce the concept of well-posedness for general variational inequalities and obtain some results under pseudomonotonicity. It is well known that monotonicity implies pseudomonotonicity, but the converse is not true. In this respect, our results represent an improvement and refinement of the previous known results. Since the general variational inequalities include (quasi) variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems.     

UNIQUENESS OF DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS

In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible.     

一类型变分不等式解的存在性唯一性问题及其对力学中的Signorini问题的应用

在本文中,我们研究了一类变分不等式解的存在性和唯一性问题,作为应用,讨论了力学中的著名的Signorini问题,改进了这一问题有解的条件.