Solitary waves and their bifurcations of KdV like equation with higher order nonlinearity

We investigate the KdV like equation with higher order nonlinearity ut + a(1 +bun)unux + uxxx = 0with n ≥ 1, a, b ∈ R and α≠ 0. The bifurcations and explicit expressions of solitary wave solutions for theequation are discussed by using the bifurcation method and qualitative theory of dynamical systems. Thebifurcation diagrams, existence and number of the solitary waves are given.     

非线性薛定谔模型边界场算子的形式因子

讨论了可积开边界条件下的非线性薛定谔模型，给出了其贝特本征态的内积和模长.在此基础上得到了边界场算子的形式因子. 这些结果均被表达成由谱参量的函数所构成的行列式. 关键词： 可积模型 形式因子 反散射     

具有某种断面的半群的研究进展

本文综述了几类具有特殊断面的半群的近期研究结果。在介绍逆半群和正则半群的一般结构之后，概述了具有逆断面的正则半群的结构和同余格的研究成果。总结了作为逆断面的推广的可裂断面，纯正断面，正则^*－断面和恰当断面。提出了可以进一步研究的重要的问题。     

关于一类具有相同非负群逆和M-P逆的非负矩阵的进一步研究

1引言设A是n阶非负方阵．设矩阵方程(1)AXA=A,(2)XAX=X,(3)(AX)~T= AX,(4)(XA)~T=XA,(5)AX=XA．A具有非负广义逆是指存在非负方阵X满足方程(1)～(4),并记为A~(?)．A具有非负群逆是指存在非负方阵X满足方程(1),(2),(5),并记为A~#．在A~(?)存在的前提下,两者相同的充分必要条件有(a)AA~(?)=A~(?)A；(b)A~(?)=p(A),其     

解奇异非光滑方程组的牛顿法和不精确牛顿法

本文主要解决奇异非光滑方程组的解法。应用一种新的次微分的外逆，我们提出了牛顿法和不精确牛顿法，它们的收敛性同时也得到了证明。这种方法能更容易在一引起实际应用中实现。这种方法可以看作是已存在的解非光滑方程组的方法的延伸。     

一类无穷下三角矩阵的代数性质

修正了 [4,5]中的 Jabotinsky矩阵,得到并证明了一类无穷下三角矩阵T（f）的一些性质,最后,导出了一些与导数相关的反演关系和组合恒等式.     

Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

Periodic Optical Pulses in Nonlinear Optical Fibers

We discuss the problem of transmitting polarized pulses along optical fibers with variable dispersion. The dissipation and mean dispersion are assumed to be zero, which allows using the model of the vector nonlinear Schrödinger equation. We consider an optical fiber consisting of arms of equal length, which is assumed to be large. We propose an asymptotic recursive procedure for calculating the amplitude and the phase of an optical pulse propagating along the optical cable with variable dispersion.     

辐射传递蒙特卡洛法精度分析及数值试验

本文建立了蒙特卡洛法模拟散射参与性介质内辐射传递计算模型。对蒙特卡洛法的计算精度及运行时间进行了较为详细的分析,提出了几种判断计算精度的方法。同时,借助蒙特卡洛法模拟辐射传递过程,进行数值“辐射实验”。利用该“实验结果”进行了物性反问题研究。在已知光学厚度的前提下,得到散射反照率与后半球辐射热流之间的单值函数关系。     

On the Behaviors of Hyperspace Topologies for Subspaces

For a topological space X we denote by CL(X) the collection of all nonempty closed subsets of X. Suppose we have a map T which assigns in some coherent way to every topological space X some topology T(X) on CL(X). In this paper we study continuity and inverse continuity of the map iA,X :(CL(A),T{A)) → (CL(X),T(X)) defined by iA,x(F) = F whenever F ∈CL(A), for various assignment T; in particular, for locally finite topology, upper Kuratowski topology, and Attouch-Wets topology, etc.