Structure of 6m±1 Order Imaginary Cube

This paper gives the notions of point matrix and equideviate point matrix.6m±1 orderimaginary cube is obtained by using a kind of spocial point matrix.(m is a nature number)     

广义凸空间上的重合点和几乎相似重合点及其应用(英文)

We introduce the concept of a weakly G-quasiconvex map with respect to a map on generalized convex spaces and use the concept to prove coincidence point theorems and almost-like coincidence point theorems. As applications of the above results, we derive almost fixed point theorems and fixed point theorem. These main results generalize and improve some known results in the literature.     

Coincidence Point Theorems,Intersection Theorems and Saddle Point Theorems on FC-spaces

In this paper, we first give the definitions of finitely continuous topological space and FC-subspace generated by some set, and obtain coincidence point theorem, whole intersection theorems and Ky Fan type matching theorems, and finally discuss the existence of saddle point as an application of coincidence point theorem.     

THE LIMIT SET OF A CONTINUOUS SELF-MAP OF THE TREE

Let f denote a continuous map of a tree T to itself. A point x ∈ T is called a 7-limit point of f if it is both an ω-limit point and an α-limit point. In the present paper, we show that (1) Ω-Γ is countable, (2) A -Γ and P - Γ are either empty or countably infinite, where P denotes the closure of the set of periodic points P.     

本刊英文版2021年64卷第1期(1-220)摘要

Nonsmooth critical point theory and applications to the spectral graph theory Kung-Ching Chang,Sihong Shao,Dong Zhang^Weixi Zhang.Existing critical point theories including metric and topological critical point theories are difficult to be applied directly to some concrete problems in particular polyhedral settings,because the notions of critical sets could be either very vague or too large.T o overcome these difficulties,w e develop the critical point theory for nonsmooth but Lipschitzian functions defined on convex polyhedrons.This yields natural extensions of classical results in the critical point theory,such as the Liusternik-Schnirelmann multiplicity theorem.More importantly,eigenvectors for some eigenvalue problems involving graph 1-Laplacian coincide with critical points of the corresponding functions on polytopes,which indicates that the critical point theory proposed in the present paper can be applied to study the nonlinear spectral graph theory.     

The Fixed Point Theorem for Some Contraction Mappings

The fixed point theorem has many important application in the theory of differential equations. The book of Kolmogorov and Fomin [9] provides excellent illustration of the use of fixed point theorem in analysis. Various contraction mappings and their fixed point theorem are given in B.E. Rhoades [10].     

MULTIPLE POINTS OF IMMERSIONS OF M~6■R~7

In this article, we determine the multiple point set of immersions of 6-dimensional manifolds into 7-dimensional Euclidean space R7. The method is to evaluate the characteristic numbers of these manifolds. By a certain method, these numbers can be read of from the Hurewicz image ofh : π7QMO(1) → H7QMO(1).In particular, we show that for any immersion of P 6 in R7 the double, 4-fold and 6-fold point manifolds are cobordant to boundaries and triple point manifolds cobordant to P 4, 5-fold point manifolds cobordant to P 2 and 7-fold point manifold are odd number.     

SOME PROPERTIES OF CHAIN RECURRENT POINTS OF FLOWS

In this paper, two geometric criteria for a point to be a non-chain recurrent point of flows on a compact Hausdorff topological space are given.     

On the Existence of Time-periodic Solution to the Compressible Heat-conducting Navier-Stokes Equations

We study in this article the compressible heat-conducting Navier-Stokes equations in periodic domain driven by a time-periodic external force. The existence of the strong time-periodic solution is established by a new approach. First, we reformulate the system and consider some decay estimates of the linearized system.Under some smallness and symmetry assumptions on the external force, the existence of the time-periodic solution of the linearized system is then identi?ed as the ?xed point of a Poincare′ map which is obtained by the Tychonoff ?xed point theorem.Although the Tychonoff ?xed point theorem cannot directly ensure the uniqueness,but we could construct a set-valued function, the ?xed point of which is the timeperiodic solution of the original system. At last, the existence of the ?xed point is obtained by the Kakutani ?xed point theorem. In addition, the uniqueness of timeperiodic solution is also studied.     

锥距离空间中压缩条件下的公共不动点定理(英文)

In order to develop and improve the fixed point theorems in cone metric spaces, some new fixed point theorems are presented for two mappings in cone metric spaces which satisfy contractive conditions, where the cone is not necessarily normal. Our results generalize fixed point theorems of Abbas, Jungck and Stojan Radenovi in cone metric spaces.     

非游荡算子的性质*

本文研究一类具有混纯性质的线性算子:非游荡算子,该类算子仅在无穷维线性空间中.我们给出非游荡算子紧集上的超循环分解.     

Nilpotent operators similar to irreducible operators

We give a necessary and sufficient condition for the nilpotent operators to be similiar to irreducible operators, and give an answer to D. A. Herrero Conjectures for nilpotent operators.     

广义弱亚正规算子的正规性

主要研究了T是广义弱亚正规算子时,T~t是拟正规算子的充要条件是T是拟正规算子.并且举例说明了存在非次正规的广义弱亚正规算子T使得T~t是次正规的.     

冯·诺依曼代数的可测算子的性质

本文研究了冯·诺依曼代数的可测算子的基本性质,定义了阶梯算子,证明了任意一个正可测算子可以由阶梯算子在定义域内按照强算子拓扑逼近,从而证明了任意一个可测算子可以由投影在定义域内按照强算子拓扑逼近.此外,还讨论了可测算子与有界算子的复合算子的可测性.     

Disjointly homogeneous Banach lattices and compact products of operators

The notion of disjointly homogeneous Banach lattice is introduced. In these spaces every two disjoint sequences share equivalent subsequences. It is proved that on this class of Banach lattices the product of a regular AM-compact and a regular disjointly strictly singular operators is always a compact operator.     

解析函数的Banach空间上之复合算子

本文研究了一类解析函数的Ｂａｎａｃｈ空间Ｘ上之复合算子，这类空间包含了Ｂｌｏｃｈ空间，并且可看作Ｂｅｒｇｍａｎ空间Ｌ１ａ（Ｄ）中具有原子分解的解析函数的对偶空间．我们刻划了这类空间上紧复合算子及Ｆｒｅｄｈｏｌｍ复合算子的特征，此外，还研究了具有闭值域的复合算子．     

M/Mk,B/1算子的豫解集

首先运用Phillips定理和Fattorini定理证明M／M^k，^B／1排队模型概率瞬态解的存在唯一性，然后通过研究对应于M／M^k，^B／1排队模型的主算子的共轭算子的豫解集得到该主算子的豫解集：在虚轴上除了零点外其它所有点都属于该主算子的豫解集．     

Fredholm Operators and Riesz Theory for Polynomially Compact Operators

In this article, we give a characterization of a class of bounded Fredholm operators on a Banach space which is developed to present some general existence results of the operators equation of the second kind. The obtained results are used to describe the Riesz–Schauder theory of compact operators in the more general setting of polynomially compact operators.     

Stable and stabilizable means involving linear operator arguments

In this paper we extend the stability and stabilizability concepts from the case that the variables are positive real numbers to the case that the variables are positive linear operators. Since the algebra of bounded linear operators is not commutative, such extension does not appear to be obvious. As applications, iterative operator algorithms, converging to some operator means, are discussed.