集中力拉伸作用下的不可压缩橡胶类锥体

分析了受集中力拉伸作用下不可压缩橡胶类锥体尖端附近的应力分布及形变行为。给出了锥体尖端应力场的渐近解，当锥角为１８０°时，即为非线性的Ｂｏｕｓｓｉｎｅｓｑ问题的解。     

Solutions with moving singularities for a semilinear parabolic equation

We consider the Cauchy problem for a semilinear heat equation with power nonlinearity. It is known that the equation has a singular steady state in some parameter range. Our concern is a solution with a moving singularity that is obtained by perturbing the singular steady state. By formal expansion, it turns out that the remainder term must satisfy a certain parabolic equation with inverse-square potential. From the well-posedness of this equation, we see that there appears a critical exponent. Paying attention to this exponent, for a prescribed motion of the singular point and suitable initial data, we establish the time-local existence, uniqueness and comparison principle for such singular solutions. We also consider solutions with multiple singularities.     

Positive solutions for fourth‐order singular nonlinear differential equation with variable‐coefficient

By application of Green's function and some fixed‐point theorems, that is, Leray–Schauder alternative principle and Schauder's fixed point theorem, we establish two new existence results of positive periodic solutions for nonlinear fourth‐order singular differential equation with variable‐coefficient, which extend and improve significantly existing results in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

On the singularities of composition of entire functions

Let f be an entire function. A point zo is called a critical point of f if f'(zo) = 0, and f(zo) is called a critical value (or an algebraic singularity) of f. Next a ∈ (C^) is said to be an asymptotic value (or a transcendental singularity) of f if there exists a curve Γ:[0,1]→(C^) such that limt→1Γ(t)=∞ and limt→1(foΓ)(t)=a. In this paper we find relations between the asymptotic values of f, g and f o g, relations between critical points of f, g and f o g and also in the case when the two functions f and g are semi-conjugated with another entire function.     

偶特征有限正交空间中的几个计数公式及应用

设Fq(n)是Fq上的n维正交空间,设P是任一个给定的m维全奇异子空间.计算了F(qn)中满足dim(P∩Q)=i的r维全奇异子空间Q的个数,给出了用子空间构作认证码的例子.     

Periodic solutions of singular second order equations at resonance

In this paper, we study the existence of positive periodic solutions for singular second order equations x" + n²/4x+h(x) = p(t), where h has a singularity at the origin and n is a positive integer. We give an explicit condition to ensure the existence of positive periodic solutions when h is an unbounded perturbation at infinity by using qualitative analysis and topological degree theory.     

双调和方程解的存在性和不存在性

主要采用山路几何与Pohozaev恒等式的方法,通过对临界位势和非线性项是否临界的讨论,分别论证了双调和椭圆型方程解的存在性和不存在性.     

关于《数值分析》教材中一道习题的商榷

指出研究生教材<数值分析>中习题的一处疏忽性错误,并给出几种可供参考的解法和必要的讨论.     

A gradient flow for the prescribed Gaussian curvature problem on a closed Riemann surface with conical singularity

In this note, we prove that the abstract gradient flow introduced by Baird-Fardoun-Regbaoui [2] is well-posed on a closed Riemann surface with conical singularity. Long time existence and convergence of the flow are proved under certain assumptions. As an application, the prescribed Gaussian curvature problem is solved when the singular Euler characteristic of the conical surface is non-positive.