零级函数的值分布

该文对单位圆内零级亚纯函数证明了一个值分布的定理，并构造了二个例子说明这个定理是精确的。     

连续映射的渐近行为

本文采用“追溯”法，获得连续映射ｆ的非渐近周期点集为零测集的一个充分条件。     

WEAK LIMITS OF EMPIRICAL MEASURES FOR A FAMILY OF DIFFUSION PROCESSES

This paper considers diffusion processes {X^∈(t)} on R^2, which are pertur-bations of dynamical system {X(t)} (dX(t) = b(X(t))dt) on R^2. By means of weakconvergence of probability measures, the authors characterize the limit behavior for em-pirical measures of {X^∈(t)} in a neighborhood domain of saddle point of the dynamicalsystem as the perturbations tend to zero.     

Solving discrete systems of nonlinear equations

We study the existence problem of a zero point of a function defined on a finite set of elements of the integer lattice Zⁿ of the n-dimensional Euclidean space Rⁿ. It is assumed that the set is integrally convex, which implies that the convex hull of the set can be subdivided in simplices such that every vertex is an element of Zⁿ and each simplex of the triangulation lies in an n-dimensional cube of size one. With respect to this triangulation we assume that the function satisfies some property that replaces continuity. Under this property and some boundary condition the function has a zero point. To prove this we use a simplicial algorithm that terminates with a zero point within a finite number of iterations. The standard technique of applying a fixed point theorem to a piecewise linear approximation cannot be applied, because the ‘continuity property’ is too weak to assure that a zero point of the piecewise linear approximation induces a zero point of the function itself. We apply the main existence result to prove the existence of a pure Cournot-Nash equilibrium in a Cournot oligopoly model. We further obtain a discrete analogue of the well-known Borsuk-Ulam theorem and a theorem for the existence of a solution for the discrete nonlinear complementarity problem.     

Banach空间中m-d增生映射零点的强弱收敛定理

本文研究了m-d增生映射的零点以及有限个m-d增生映射公共零点的迭代设计问题.利用Lyapunov泛函与广义f投影映射等技巧,在Banach空间中,证明了迭代序列强收敛或弱收敛到m-d增生映射的零点或有限个m-d增生映射的公共零点.与以往的相关研究工作相比,迭代设计中考虑了误差项、迭代格式被简化、限定条件被削弱.     

正则化HSS预处理鞍点矩阵的特征值估计

最近,Bai和Benzi针对鞍点问题提出了一类正则化HSS（Regularized Hermitian and skew-Hermitian splitting,RHSS）预处理子（BIT Numer.Math.,57（2017）287-311）.为了进一步分析RHSS预处理子的效果,本文重点研究了RHSS预处理鞍点矩阵特征值的估计,分析了复特征值实部和模的上下界、实特征值的上下界,还给出了特征值均为实数的充分条件.当正则化矩阵取为零矩阵时,RHSS预处理子退化为HSS预处理子,分析表明本文给出的复特征值实部的界比已有的结果更精确.数值算例验证了本文给出的理论结果.     

圆内零级亚纯函数的充满圆及应用

本文研究了圆内零级亚纯函数的充满圆序列,获得了在关于型函数的Borel点附近存在充满圆序列,从而得到了Hayman点的存在性.     

EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM

The existence and multiplicity of positive solutions to a periodic boundary value problem for nonlinear third-order ordinary differential equation are established, based on the zero point theorem concerning cone expansion and compression of order type. Our main approach is different from the previous papers on the existence of multiple positive solutions to the similar problem.     

Existence Theorems for Set-valued Operators in Banach Spaces

In this paper, we study the problem of existence of zero points for set-valued operators in Banach spaces. We present a simple condition which can be used to verify that under some conditions, set-valued operators have zero points. Furthermore, we derive the surjectivity result and the Kakutani fixed point theorem by using this condition.      

Sur une approche probabiliste d’un problème d’analyse semi-classique

For an even functional on a Banach space, the symmetric mountain pass lemma gives a sequence of critical values which converges to zero. Under the same assumptions on the functional, this paper establishes a new critical point theorem which provides a sequence of critical points converging to zero. The theorem is applied to sublinear elliptic equations. Then a sequence of solutions converging to zero is obtained.     

Rational points and Galois points for a plane curve over a finite field

We study the relationship between rational points and Galois points for a plane curve over a finite field. It is known that the set of Galois points coincides with that of rational points of the projective plane if the curve is the Hermitian, Klein quartic or Ballico–Hefez curve. The author proposes a problem: Does the converse hold true? If the curve of genus zero or one has a rational point, we have an affirmative answer.     

Mode Interaction at a Triple Zero Point of O(2) symmetric Nonlinear Systems with Two Parameters

§ 1.Introduction　Consider the nonlinear ODE with two parametersut+ g(u,λ,α) =0 (1 .1 )and its steady-state equationg(u,λ,α) =0 , (1 .2 )where g:U× R2 → U is a sufficiently smooth nonlinear mapping,and U a finitedimensional Hilbertspace.We remark thatitis easy to generalize ourresults to the casewhere g:U×R2→ V and U and V are infinite dimensional Hilbert spaces.So(1 .1 ) canbe e.g. a PDE. We assume that g is O(2 ) symmetric (equivalent,commutable) ,thatisγg(u,λ,α) =g(γu,…     

一类函数第一积分中值定理中值点的渐近性

给出了当积分区间的两个端点都为被积函数的若干次零点时,第一积分中值定理中值点的渐近性质.     

Nest代数上的在零点广义可导映射

设A为B（H）的子代数,　是A到B（H）的线性映射,我们说　在0点广义可导（广义双边可导）,如果对任意的S,T∈A且ST=0（ST=0或TS=0）,有　（ST）=　（S）T+S　（T）-S　（I）T.本文主要得到如下结果:（1）有限Nest代数上的每个范数拓扑连续的在0点广义可导的线性映射是广义内导子;（2）若N是完备Nest且H_　 H,则algN上的每个范数拓扑连续的在0点广义双边可导的线性映射是广义内导子.     

Split common fixed point and common null point problem

In this paper, we present a new algorithm for solving the split common null point and common fixed point problem, to find a point that belongs to the common element of common zero points of an infinite family of maximal monotone operators and common fixed points of an infinite family of demicontractive mappings such that its image under a linear transformation belongs to the common zero points of another infinite family of maximal monotone operators and its image under another linear transformation belongs to the common fixed point of another infinite family of demicontractive mappings in the image space. We establish strong convergence for the algorithm to find a unique solution of the variational inequality, which is the optimality condition for the minimization problem. As special cases, we shall use our results to study the split equilibrium problems and the split optimization problems.     

A local convergence property of primal-dual methods for nonlinear programming

We prove a new local convergence property of some primal-dual methods for solving nonlinear optimization problems. We consider a standard interior point approach, for which the complementarity conditions of the original primal-dual system are perturbed by a parameter driven to zero during the iterations. The sequence of iterates is generated by a linearization of the perturbed system and by applying the fraction to the boundary rule to maintain strict feasibility of the iterates with respect to the nonnegativity constraints. The analysis of the rate of convergence is carried out by considering an arbitrary sequence of perturbation parameters converging to zero. We first show that, once an iterate belongs to a neighbourhood of convergence of the Newton method applied to the original system, then the whole sequence of iterates converges to the solution. In addition, if the perturbation parameters converge to zero with a rate of convergence at most superlinear, then the sequence of iterates becomes asymptotically tangent to the central trajectory in a natural way. We give an example showing that this property can be false when the perturbation parameter goes to zero quadratically.      

Banach关于增生算子零点的修正Mann迭代的注

A more general form of modified Mann iterations which converges strongly to a zero point of an m-accretive operator is given. The work in this paper is an extension and complement of the corresponding result of Kim T.H. and Xu H.K in 2005     

On the proximal point method in Hadamard spaces

Proximal point method is one of the most influential procedure in solving nonlinear variational problems. It has recently been introduced in Hadamard spaces for solving convex optimization, and later for variational inequalities. In this paper, we study the general proximal point method for finding a zero point of a maximal monotone set-valued vector field defined on a Hadamard space and valued in its dual. We also give the relation between the maximality and Minty’s surjectivity condition, which is essential for the proximal point method to be well-defined. By exploring the properties of monotonicity and the surjectivity condition, we were able to show under mild assumptions that the proximal point method converges weakly to a zero point. Additionally, by taking into account the metric subregularity, we obtained the local strong convergence in linear and super-linear rates.     

ON THE INSTABILITY OF SOLUTIONS TO A NONLINEAR VECTOR DIFFERENTIAL EQUATION OF FOURTH ORDER

This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.     

Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings

In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.