一类多偏差变元的二阶微分方程周期解

本文利用重合度理论研究了一类二阶多偏差变元的微分方程 x＂（t）＋f（t,x（t）,x（t-τ0（t））,x＇（t））＋∑nj=1g（x（t-τj（t）））=p（t） 的周期解问题，得到了存在周期解的新的结果．     

Moment Problem and Spectral Theorem

Hausdorff momentum problem and its relations to spectral theorem for bounded Hilbert space operators are treated. A generalization for some ordered algebras is shown, where projections are replaced by idempotents.     

Hopenwasser理想的距离公式

在［１］中Ａ．Ｈｏｐｅｎｗａｓｓｅｒ讨论了Ｎｅｓｔ代数的一类超凝聚理想，称为Ｈｏｐｅｎｗａｓｓｅｒ理想，本文将给出这类理想的距离公式，这个结果一般化为［２］中的距离公式．特别地，我们得到了Ｎｅｓｔ代数的Ｊａｃｏｂｓｏｎ根和Ｌａｒｓｏｎ强根的距离公式．     

Probabilistic models of multidimensional piecewise expanding mappings

Strongly chaotic systems (e.g., piecewise expanding mappings) exhibit diffusion-like behavior in the sense of central limit theorems. To find more precise statements about the similarity to probabilistic diffusion, we study how the evolution of probability densities underd-dimensional piecewise expanding mappings can be modeled by Markov processes with smooth transition probabilities (such as diffusion processes). Our results can be viewed as a special type of local limit theorem.     

ON THE EXISTENCE OF ZERO POINTS OF A CONTINUOUS FUNCTION

IPreliminarlesTheee。etOOk totot比OO。stsllCCdCSdO‘lOll‘。山OOqll时1OO/(。)＝。,SS山 SFSSdPoint Theorems[‘’,”],Degree Theory【9,15]．In general these are used when f aPPlies a set ora space on itself．Cm眈inn眈ion Methods can be used to test the existence ofa solution whenf pplies a set or a sp。e on it咖‘－’,”－“l,or aPPlies a set or sP。m another sP。,s。M see here．wrthermore,contlnuulon methods pve us the exlstence ofcurves wb讪 can beused to CalCttlue the Sdutionsl6…     

The system of generalized vector equilibrium problems with applications

In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a solution of these systems. As an application, we derive existence results for a solution of a more general Nash equilibrium problem for vector-valued functions.     

Generalization of the Rödseth–Gupta Theorem on Binary Partitions

In this article, we give a new proof of the Rödseth–Gupta theorem on binary partitions and give one possible generalization of this theorem.     

Weak and Strong Convergence Theorems for a Nonexpansive Mapping and an Equilibrium Problem

In this paper, we introduce two iterative sequences for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem in a Hilbert space. Then, we show that one of the sequences converges strongly and the other converges weakly.     

Occupation measures for Markov chains

We give simple proofs of large deviation theorems for the occupation measure of a Markov chain using a regeneration argument to establish existence and convexity theory to identify the rate function.     

Multiple positive solutions for discrete nonlocal boundary value problems

In this paper, we investigate a second-order nonlinear difference equation with sign-changing nonlinearity subject to two different sets of nonlocal boundary conditions. The explicit expressions of the associated Green's functions are presented. By using a recently developed fixed point theorem, we establish sufficient conditions for the existence of multiple positive solutions of the boundary value problem.