一类耦合非线性Schroedinger方程组的集中现象

在二维空间中考虑了一类非线性Schroedinger方程组．在能量守恒及质量守恒的基础上，通过对解的极限行为的研究，建立了一系列解在原点的局部恒等式，得到了方程组的径向对称爆破解的集中性质．     

扰动非线性Schroedinger方程组的动力性态

研究具周期边界条件的扰动非线性Schroedinger方程组的动力性态，首先，在常值平面上用线性算子的谱对扰动和未扰动系统进行动力性态分析，然后利用奇异扰动理论和不动点原理证明局部不变流形的存在性．     

非线性Schroedinger方程的整体吸引子

本文讨论了一类带调和势｜x｜^2的非线性Schroedinger方程解的长时间行为，证明了整体吸引子的存在性．     

无界域上Schroedinger型方程的指数吸引子

本在[1]的基础上,证明了Schroedinger型方程δ1u=(k iβ）△u-|u|'u-λu-g(x),u(x,0)=u0,其中k,p,λ>0,x∈R^n在加权sobolev空间中指数吸引子的存在性。     

带调和势的超临界非线性Schrdinger方程的最佳门槛

考虑带调和势的超临界非线性Schroedinger方程，解决了该方程整体解和爆破解存在所依赖的初始条件的最佳分界门槛．通过构造两类强制变分问题和建立局部不变半流，运用势井方法和凹方法，获得了该方程在两个不同的空间中的整体解和爆破解的最佳门槛条件．     

（2＋1）维非线性Schroedinger型方程的同宿轨道

研究了几类（2＋1）维非线性Schroedinger型方程同宿轨道的问题．利用Hirota双线性算子方法，通过给出的相关变换，得到了包括（2＋1）维的长短波相互作用方程，广义Zakharov方程，Mel’nikov方程和g-Schroedinger方程的同宿轨道解的显式解析表达式，从而讨论了这些方程的同宿轨道．     

一类广义Boussinesq方程解的Blowup

该文利用Ｆｏｕｒｉｅｒ变换方法研究一类广义Ｂｏｕｓｓｉｎｅｓｑ方程ｕｔｔ－ｕｘｘ＝ｂｕｘｘｘ＋ａ（ｕｐ）ｘｘ＋ｃｕｑ的初边值问题的局部解的存在性与整体解的不存在性．其中ｂ＞０，ａ，ｃ为任意实数，ｐ≥１，ｑ≥１为整数．我们得到了上述问题的局部解存在和解在有限时刻ｂｌｏｗｕｐ的一些充分条件并且给出了几个具体实例．     

在分子晶体中的一类广义非线性Schroedinger方程组的初边值问题

研究了在分子晶体中的一类广义非线性Schroedinger方程组的初边值问题．应用先验估计的方法，得到了整体解的存在性．     

R^3中带势项的非线性Schroedinger方程的L^2集中现象

该文主要讨论带调和势项的非线性Schroedinger方程的L^2集中现象;同时也对破裂点的分布进行了估计,并且给出了整体适定性的条件.     

Boussinesq型方程的周期边界问题与初值问题的解的存在性

本文研究“坏的Ｂｏｕｓｓｉｎｅｓｑ型方程ｕｔｔ－ｂｕｘｘｘ＝σ（ｕ）ｘｘ的周期边界问题与初值问题的解的存在性问题，其中ｂ〉０为常数，证明了在相当宽松的条件下，上述问题存在局部广义解。     

参激白噪声作用下蔡电路的脉冲控制

考察了参激白噪声和脉冲信号联合作用下蔡电路的渐近P阶矩稳定性问题,得到该随机脉冲系统的比较系统,从而可由该确定性比较系统的稳定性得到原随机脉冲系统的渐近P阶矩稳定性.并从理论上得到能使该随机脉冲系统渐近P阶矩稳定的参数取值范围,即在稳定区域内取值的参数组合能够用脉冲方法对该随机蔡电路实现混沌控制.最后用数值仿真验证了理论结果的正确性.     

冷贮备冗余系统可靠度预计的递归算法

基于贮备科系统的特点,运用折方法得出一种用计算机求冷贮备冗余系统可靠度的方法,并将该计算方法用于两个计算实例。     

The Automorphism Group and the Convex Subgraphs of the Quadratic Forms Graph in Characteristic 2

We determine the automorphism group and the convex subgraphs of the quadratic forms graph Quad(n,q),q even.A. Munemasa: A part of this research was completed during this author's visit at the Institute for System Analysis, Moscow, as a Heizaemon Honda fellow of the Japan Association for Mathematical SciencesD.V. Pasechnik: A part of this research was completed when this author held a position at the Institute for System Analysis, MoscowS.V. Shpectorov: A part of this research was completed during this author's visit at the University of Technology, Eindhoven     

CUTTING CORNERS PRESERVES LIPSCHITZ CONTINUITY

ＣＵＴＴＩＮＧＣＯＲＮＥＲＳＰＲＥＳＥＲＶＥＳＬＩＰＳＣＨＩＴＺＣＯＮＴＩＮＵＩＴＹ￥ＦＥＮＧＹＵＹＵ（Ｄｅｐｔ．ｏｆＭａｔｈ．ＵＳＴＣ，Ｈｅｆｅｉ，２３００２６，Ｐ．Ｒ．Ｃｈｉｎａ）ＪＥＲＮＥＪＫＯＺＡＫ（Ｄｅｐｔ．ｏｆＭａｔｈ．Ｕｎｉｖｅｒｓｉｔ...     

Global attractability and permanence for a new stage-structured delay impulsive ecosystem

In this paper, a new stage-structured delay ecosystem with impulsive effect is formulated and some dynamical properties of this system is investigated.By using comparison theorem and the stroboscopic technique, we prove the existence of the predator-extinction periodic solution of this system and obtain some sufficient conditions to guarantee the global attractivity of the prey-extinction periodic solution. In the final, we also obtain the permanence of this system. It should be pointed out that the new mathematical method used in this paper can also be applied to investigate such other ecosystems corresponding to both impulsive and delay differential equations.     

Global BV solution for a non-local coupled system modeling the dynamics of dislocation densities

In this paper, we study a non-local coupled system arising in the modeling of the dynamics of dislocation densities in crystals. For this system, the global existence and uniqueness are available only for continuous viscosity solutions. In the present paper, we investigate the global time existence of this system by considering BV initial data. Based on a fundamental uniform BV estimate and the finite speed of propagation property of this system, we show, in a particular setting, the global existence of discontinuous viscosity solutions of this problem.     

一类一维的辐射流体力学方程组激波的存在性

该文主要讨论一维空间中一类辐射流体力学方程组的激波. 由Rankine-Hugoniot条件及熵条件得此问题可表述为关于辐射流体力学方程组带自由边界的初边值问题. 首先通过变量代换, 将其自由边界转换为固定边界, 然后研究关于此非线性方程组的一个初边值问题解的存在唯一性. 为此先构造了此问题的一个近似解, 然后分别通过Picard迭代与Newton迭代对此非线性问题构造近似解序列. 通过一系列估计与紧性理论得到此近似解序列的收敛性, 其极限即为原辐射热力学方程组的一个激波.     

Measuring the strength of trade unions and identifying the privileged groups: A two-dimensional approach and its implementation

Trade unions were important actors in the advanced capitalist countries until the late 1970s, but since the 1980s, union membership is declining. Whether this decline has been homogenous is crucial. Because unions may still have power and non-homogenous decline implies that some groups benefit from this power disproportionately. However, we don’t have instruments to scrutinize this dynamic properly. To fill the gap, this study develops a model that identifies privileged groups within trade unions by informing us about the relative strength of a group within trade unions, the ability of this group to use the union power, and the extent to which union members belonging to the group would advance the interests of the entire group by using this power.     

我国高等教育发展统计特征的PLS通径模型分析

借鉴UNESCO教育指标体系框架,建构我国高等教育发展统计指标体系;采用PLS通径模型这一结构方程建模新技术对建构的指标体系进行验证,并对2006年我国高等教育发展状况进行分析,获得客观统计指标数据特征。     

离散型指数差分布

本文提出了一个离散型概率分布:指数差分布,推导了该分布的最可能成功次数、数学期望和方差,探讨了该分布与几何分布的关系,给出了该分布在马尔可夫链模型中的应用。