关于剩余类环的扩展的研究

作者对非结合环给出扩展的概念,即给定2个非结合环A和B,对任一非结合环R,称R是A被B的扩展,当且仅当A是R的理想且R/A≌B.对非结合环的扩展,文中证明了一个类似于Schreier群扩张定理的结果.作为应用,对给定的自然数m≥2,n≥2,文章刻画了模n的剩余类环Z_n被模m的剩余类环Z_m扩展所得到的有限环R的构造,证明了R可以用满足一定条件的自然数对(u,r)来描述,同时写出了R的理想和单侧理想的具体形状.作者还进一步证明,R是结合的当且仅当R=Z_nZ_m,且当R=Z_nZ_m时,R的每个理想都是Z_n的一个理想与Z_m的一个理想的直和,即此时R的理想是相对平凡的.     

Mapping properties of the zero-balanced hypergeometric functions

In this paper, the order of convexity of $z_2{F}_1(a,b;c;z)$ is given under certain conditions on the positive real parameters a, b and c. We show also that the image domains of the unit disc $\mathbb{D}$ under some shifted zero-balanced hypergeometric functions $z_2{F}_1(a,b;a+b;z)$ are convex and bounded by two horizontal lines. This solves a problem raised by Ponnusamy and Vuorinen in [10].     

Generalized Integral Representations for Functions with Values in C（V_（3,3））

By using the solution to the Helmholtz equation u-λu = 0(λ ≥ 0),the explicit forms of the so-called kernel functions and the higher order kernel functions are given.Then by the generalized Stokes formula,the integral representation formulas related with the Helmholtz operator for functions with values in C(V3,3) are obtained.As application of the integral representations,the maximum modulus theorem for function u which satisfies Hu = 0 is given.     

两个平均值问题的注记

利用函数得幂级数展开式,证明了两个平均值定理相反问题的解均为多项式函数.     

积分微分方程线性多步方法的散逸性

研究一类积分微分方程线性多步方法（p,σ）的散逸性．当积分项用复合求积公式逼近时,证明了线性多步方法是有限维散逸的．这说明该方法很好地继承了系统本身所具有的重要性质．这一结论为数值求解这一类微分方程提供了更多的选择．     

Schwarz-type problem of nonhomogeneous Cauchy-Riemann equation on a triangle

We consider the Schwarz-type boundary-value problem (BVP) of the nonhomogeneous Cauchy-Riemann equation on an isosceles orthogonal triangle. By the technique of plane parqueting and the Cauchy-Pompeiu formula on the triangle, the Schwarz-Poisson formula is obtained. We also investigate boundary behaviors of the Schwarz-type operator and the Pompeiu-type operator. Especially, boundary-values at the corners are proved to exist. Finally, the solution of the Schwarz-type BVP is explicitly obtained.     

Extremal and Barabanov semi-norms of a semigroup generated by a bounded family of matrices

Let S={Si}_i∈I be an arbitrary family of complex n-by-n matrices, where 1?n<∞. Let denote the joint spectral radius of S, defined as

     

Conditional Fredholm determinant for the S-periodic orbits in Hamiltonian systems

For S being a symplectic orthogonal matrix on R2n, the S-periodic orbits in Hamiltonian systems are a solution which satisfies x(0)=Sx(T) for some period T. This paper is devoted to establishing the theory of conditional Fredholm determinant in studying the S-periodic orbits in Hamiltonian systems. First, we study the property of the conditional Fredholm determinant, such as the Fréchet differentiability, the splittingness for the cyclic type symmetric solutions. Also, we generalize the Hill formula originally gotten by Hill and Poincaré. More precisely, let M be the monodromy matrix of the S-periodic orbits, then we get the formula relating the characteristic polynomial of the matrix SM and the conditional Fredhom determinant. Moreover, we study the relation of the conditional Fredholm determinant and the relative Morse index. Applications to the problem of linear stability for the S-periodic orbits are given.