光纤环形镜线形腔掺Er3+光纤激光器输出特性的数值分析

在分析光纤环形镜工作原理的基础上,给出了基于光纤环形镜的线形腔掺Er3+光纤激光器相位和幅度的振荡条件.通过求解速率方程,理论分析了其输出特性,获得了稳态条件下激光器输出功率、阈值泵浦功率和斜率效率的解析表达式.推导出激光器工作所需掺Er3+光纤最短长度,并在给定泵浦光功率时,在特定输出波长上获得最大输出功率所需最佳掺Er3+光纤长度的表达式,且通过实验进行了验证.     

一类强阻尼波方程解的存在性和爆破性

讨论一类强阻尼波方程解的局部存在性,并利用势井理论研究解的整体存在性和爆破性.     

五阶势MKdV方程的一个不变性

§1Introduction Asweknow,Backlundtransformation[1-3]isaverypowerfulwayforfindingnonline evolutionequations.Inrecentdecades,Painlevéanalysis[4]hasbecomeaverypopu methodtoobtainBacklundtransformation.Inreference[5],fordevelopingthetheory Painlevéanalysis,AndrewPickeringintroduceanewexpansionvariableZwhichsatisf thefollowingRicattiSystem:Zx=1-AZ-BZ2,Zt=-C+(AC+Cx)Z-(D-BC)Z2.(1.Astheapplicationofthenewexpansionvaraible,thepotentialfifth-orderMKd equation(PMKdV5)-vxt+(vxxxxx-10k2v2…     

四元数广义奇异值分解及其应用

This paper derives a theorem of generalized singular value decomposition of quaternion matrices(QGSVD),studies the solution of general quaternion matrix equation AXB-CYD=E,and obtains quaternionic Roth's theorem.This paper also suggestssufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation.     

带常利率的Erlang(2)风险模型的罚金折现期望函数

The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.     

广义Gr(o)tzsch环函数的近似凹凸性

In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa （r） by studying the monotonieity,convexity or concavity of certain composites of μa（r） are obtained.     

二阶差分方程的奇性边值问题

主要采用上下解方法,研究了一类带有奇性的二阶差分方程的两点边值问题,给出了一系列正解的存在条件.     

Existence and Approximate Controllability of Solutions for an Impulsive Evolution Equation with Nonlocal Conditions in Banach Space

In this article, we study the existence of mild solutions and approximate controllability for non-autonomous impulsive evolution equations with nonlocal conditions in Banach space. The existence of mild solutions and some conditions for approximate controllability of these non-autonomous impulsive evolution equations are given by using the Krasnoselskii''s fixed point theorem, the theory of evolution family and the resolvent operator. In particular,the impulsive functions are supposed to be continuous and the nonlocal item is divided into Lipschitz continuous and completely bounded. An example is given as an application of the results.     

Existence of Three Weak Solutions for a Class of Quasi-Linear Elliptic Operators with a Mixed Boundary Value Problem Containing $p(\cdot )$-Laplacian in a Variable Exponent Sobolev Space

In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing $p(\cdot )$-Laplacian. More precisely, we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.     

The Upper Semicontinuity of Random Attractors for Non-Autonomous Stochastic Plate Equations with Multiplicative Noise and Nonlinear Damping

Based on the existence of pullback attractors for the non-autonomous stochastic plate equations with multiplicative noise and nonlinear damping defined in the entire space $\mathbb{R}^n$ by Xiaobin Yao in \cite{Yao4}, in the paper, we further investigate the upper semicontinuity of pullback attractors for the problem.