广义Lebesgue-Ramanujan-Nagell方程研究的新进展

广义Lebesgue-Ramanujan-Nagell方程是数论中一类重要的Diophantine方程.本文介绍了此类方程的近期结果和尚未解决的问题.     

一类非线性差分方程正解的不存在性

本文研究一类非线性差分方程及其对偶方程,给出了方程不存在正解的充分条件,所得结论改进了[1]的结果。     

关于函数方程的若干进展

本文介绍了单实变量的函数方程的若干新进展，包括迭代根、Ｓｃｈｒｏｄｅｒ方程和多项式型迭代方程的结果。基本内容有：Ｉ．引言：迭代与相关问题；Ⅱ．迭代根：存在性；Ⅲ．迭代根：唯一性、可微性和分枝；Ⅳ．多项式型迭代方程。     

关于发展方程的守恒率的一个标记

本文使用微分代数的技巧，研究了发展方程的守恒率与对应的行波所满足方程的首次积分之间的关系．通过文本给出的结果，我们研究了Burgers方程和Burgers—KdV方程的可积性，证明了这两类方程都只有一个守恒率．利用本文给出的方法，可以通过常微分方程的研究方法来研究某些非线性发展方程．     

MKdV和FPU方程的李点对称

本文研究了离散微分方程的李对称问题.利用差分方程的延拓方法和交换流方法,我们求得了若干重要的差分方程、微分差分方程的李对称,推广了对称性分析法在连续微分方程讨论时的结果.     

非线性Volterra积分方程非平凡解的逼近方法及其应用

本文对一类具有卷积核的非线性Ｖｏｌｔｅｒｒａ型积分方程进行了讨论，给出了关于这类方程的非平凡解的存在性和解的逼近方法的一些结果。通过有关微分方程问题的实例，说明了所给结果的重要应用。     

带密度的不可压Euler方程在临界Besov空间中的适定性

本文证明了带密度的不可压Euler方程在临界Besov空间中的局部适定性,并且只用涡度场给出了强解的一个爆破准则.另外,本文关于带密度的不可压磁流体方程得到了类似结果.     

ODE方程精确解及其应用

本文得到了一类ＯＤＥ方程精确解,并给出了它在Ｃｈａｆｆａ－Ｉｎｆａｎｔｅ方程和波方程上的应用。     

R∧N上的临界非齐次多重调和方程的多解存在性

讨论了R∧N上带负扰动的临界非齐次多重调和方程的多解存在性,首先由泛函弱连续性方法获得方程的第一个解,再由山路引理获得方程的第二个解,本文的这种求解方法和这些结果不仅适用于R∧N上的二阶椭圆方程,而且也适用于尚未解决的R∧N上的双调和方程。     

具偏差变元的Lienard型方程的周期解

在本文中，Ｌｉｅｎａｒｄ型方程具有周期解存在性的结果推广到具偏差变元的Ｌｉｅｎａｒｄ型方程。     

高阶变系数泛函方程解的振动性

讨论了高阶变系数泛函微分方程解的振动性,并给出了这类高阶变系数函数方程解的若干新振动准则.结果推广了目前已有的某些结果.并且给出了在差分方程中的应用.     

Meromorphic solutions of some types of complex differential-difference equations

Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some properties of meromorphic solutions, and we obtain some results, which are the improvements and extensions of some results in references. Examples show that our results are precise.     

关于更新风险模型中破产概率的若干结果

进一步研究了更新风险模型中破产概率的问题，在假定索赔额分布是重尾时，证明了若干重要结果，得到了与经典的Crammer—Lunderberg模型相一致的结论．并义推广和改进了部分已有文献中的结果。     

On commutativity of near-rings with generalized derivations

In this paper we prove some theorems of commutativity for near-rings with generalized derivations. As a consequence of the results obtained, we generalize some published results. Also, we give some examples to show that some conditions in some results obtained are not redundant.     

On the solutions of a second order nonlinear system with almost periodic forcing

A second order almost periodic perturbed nonlinear system with small parameter is discussed in this paper. Based on some analytical techniques and the method of averaging, some sufficient conditions are obtained for existence of one almost periodic solution. Also some suitable conditions are given for existence of two almost periodic solutions. The obtained new results generalized the known results in Seifert [1], [3] and He [2], [4]. Finally, some applications are presented to illustrate that our results are a good generalization of the known results.     

Existence and global attractivity of solutions of a nonlinear functional integral equation

This paper presents some results concerning the existence, uniform local attractivity and global attractivity of solutions for a functional integral equation, via measure of noncompactness. Our results improve and extend some previous results obtained in other studies. We will also include some examples which show that our results are applicable where the previous ones are not.     

APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES

In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.     

图的因子和因子分解的若干进展

本文综述了图的的因子和因子分解近年来的一些新结果。主要有图的因子与各种参数之间的关系,图有某种因子的一些充分必要条件,特别是图有ｋ－因子的一些充分条件以及关于图的因子分解和正交因子分解的一些新结果。文中提出了一些新的问题和猜想。     

Approximate duality of g-frames in Hilbert spaces

In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.     

脉冲三点边值问题的变号解

本文首先使用拓扑度和不动点指数方法,得到了关于抽象空间中算子方程变号解及多个变号解存在的几个结果,然后将所得结果应用于一类含脉冲三点边值问题,得到了变号解及多个变号解的存在性结果.