On a Problem Proposed by Kartsatos

§１．ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＬｅｔＸｂｅａｒｅａｌｒｅｆｌｅｘｉｖｅＢａｎａｃｈｓｐａｃｅｗｉｔｈｎｏｒｍａｎｄｎｏｒｍａｌｉｚｅｄｄｕａｌｉｔｙｍａｐｐｉｎｇＪ．Ａｓｕｓｕａｌ，ｗｅｓｕｐｐｏｓｅｔｈａｔｔｈｅｓｐ...     

STRONG LAWS FOR α-MIXING SEQUENCE PROCESSES INDEXED BY SETS

ＳＴＲＯＮＧＬＡＷＳＦＯＲα－ＭＩＸＩＮＧＳＥＱＵＥＮＣＥＰＲＯＣＥＳＳＥＳＩＮＤＥＸＥＤＢＹＳＥＴＳ￥ＸＵＢＩＮＧＡｂｓｔｒａｃｔ：ＬｅｔＪ＝｛１，２，．．．｝ｄａｎｄｌｅｔ｛Ｘｊ，ｊ∈Ｊ｝ｂｅａｎａ－ｍｉｘｉｎｇｓｅｑｕｅｎｃｅｗｈｉｃｈｉｓｎｏ...     

FractalpaternsofFractureinSandwichCompositeMaterialsunderBiaxialTension

ＦｒａｃｔａｌｐａｔｅｒｎｓｏｆＦｒａｃｔｕｒｅｉｎＳａｎｄｗｉｃｈＣｏｍｐｏｓｉｔｅＭａｔｅｒｉａｌｓｕｎｄｅｒＢｉａｘｉａｌＴｅｎｓｉｏｎ１ＪｉｎｇＦＡＮＧ，ＸｕｅｆｅｎｇＹＡＯ＆ＪｉａＱＩ（Ｄｅｐｔ．ｏｆＭｅｃｈａｎｉｃｓ＆Ｅｎｇｎｇ．Ｓｃｉｅ...     

EXISTENCE FOR A FREE BOUNDARY PROBLEM IN GROUND FREEZING

ＥＸＩＳＴＥＮＣＥＦＯＲＡＦＲＥＥＢＯＵＮＤＡＲＹＰＲＯＢＬＥＭＩＮＧＲＯＵＮＤＦＲＥＥＺＩＮＧＧＵＡＮＺＨＩＣＨＥＮＧＷＡＮＧＸＵＪＩＡＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪａｎｕａｒｙ１７，１９９５．ＲｅｖｉｓｅｄＪａｎｕａｒｙ２７，１９...     

MATHEMATICAL ANALYSIS OF SOME NEURAL NETWORKS FOR SOLVING LINEAR AND QUADRATIC PROGRAMMING

ＺＨＡＮＧＸＩＡＮＧＳＵＮ（章祥荪）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）ＲｅｃｅｉｖｅｄＪｕｎｅ１８，１９９４．Ｔｈｉｓｗｏｒｋｉ...     

关于Banach空间中Lipschitz强伪压缩映象的带误差的Ishikawa型迭代序列

设Ｘ是任意实Ｂａｎａｃｈ空间Ｅ的闭子空间;Ｔ：Ｘ → Ｘ是 Ｌｉｐｓｃｈｉｔｚ强伪压缩映象,使得Ｔｘ＊＝ｘ＊,对某ｘ＊∈Ｘ．在没有条件 　之下,本文证明了带误差的Ｉｓｈｉｋａｗａ型迭代序列强收敛到ｘ＊．另外,相关结果又证明了,当Ｔ：Ｅ→Ｅ是Ｌｉｐｓｃｈｉｔｚ强增生算子时,带误差的Ｉｓｈｉｋａｗａ型迭代序列强收敛到方程Ｔｘ＝ｆ的唯一解．     

EXISTENCE OF HOPF BIFURCATION PROBLEMS WITH JUMPING NONLINEARITIES

ＥＸＩＳＴＥＮＣＥＯＦＨＯＰＦＢＩＦＵＲＣＡＴＩＯＮＰＲＯＢＬＥＭＳＷＩＴＨＪＵＭＰＩＮＧＮＯＮＬＩＮＥＡＲＩＴＩＥＳＨｅＸｉａｎｇｊｉａｎ＆ＪｉａｎｇＺｈｕｈａｎ（ＳｔａｔｉｓｔｉｃｓａｎｄＣｏｍｐｕｔｉｎｇＳｃｉｅｎｃｅ，Ｕｎｉｖｅｒｓｉｔｙｏｆ...     

ON THE TOTAL COLORING OF GRAPH G ∨H

ＯＮＴＨＥＴＯＴＡＬＣＯＬＯＲＩＮＧＯＦＧＲＡＰＨＧ∨Ｈ￥ＸｕＢａｏｇａｎｇ（许宝刚）（Ｍａｔｈ．ｏｆＤｅｐｔ．，ＳｈａｎｄｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｊｉｎａｎ２５０１００，Ｃｈｉｎａ．）Ａｂｓｔｒａｃｔ：Ｔｈｅｔｏｔａｌｃｈｒｏｍａｔｉｃｎｕｍｂ...     

A J-CONVEX SUBSET WHICH IS NOT PSH-CONVEX

ＡＪ－ＣＯＮＶＥＸＳＵＢＳＥＴＷＨＩＣＨＩＳＮＯＴＰＳＨ－ＣＯＮＶＥＸＢｕＳｈａｎｇｑｕａｎ（步尚全）（Ｄｅｐａｒｔｍｅｎｔｏｆａｐｐｌｉｅｄｍａｔｈｅｍａｔｉｃｓ，ＴｓｉｎｇｈｕａＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ１０００８４，Ｃｈｉｎａ）Ａｂｓ...     

MAXIMUM TREES OF SUBSETS

ＭＡＸＩＭＵＭＴＲＥＥＳＯＦＳＵＢＳＥＴＳＷｕＳｈｉｑｕａｎ（巫世权）（Ｉｎｓｔ．ｏｆＡｐｐｌ．Ｍａｔｈ．，ＣｈｉｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，ＰＯＢｏｘ２７３４，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：ＬｅｔＸｂｅａｆ...     

B_p上α凸映照

该文对当α≥0时给出Bp上α凸映照与星形映照之间的关系，给出一些Bp上α凸映照的例子.     

单位圆到凸区域上的调和拟共形映照

设F（x）=p（x）e^ir（x）为单位圆周到约当凸曲线Γ上的保向同胚映照.本文证明:若ess inf|F’（x）|>0且对于一切的φ∈R有|F（φ+x）+F（φ-x）-2F（φ）|≤M|x|^α,这里α>1,M为正常数,则ω=P[F]（z）为单位圆到凸区域Ω=int（Γ）上为调和拟共形映照.     

极大单调算子和m增生映射值域的扰动定理及在非线性微分方程上的应用

利用不动点定理,分别证明了在自反Banach空间中极大单调算子值域扰动的抽象结论和在H ilbert空间中m增生映射值域的扰动结果,这些结论是对以往一些工作的推广;然后,利用文中的新结论讨论了一类微分方程解的存在性.     

集值映射与不动点

应用D关于β对应关系是正常的构架,引用子集法,通过取凸包与闭包,由单值映射构造集值映射,利用Kakutani不动点定理,讨论几种类型的集值映射的不动点.     

Criteria for biholomorphic convex mappings on the unit ball in Hilbert spaces

In this paper, we give a necessary and sufficient condition that a locally biholomorphic mapping f on the unit ball B in a complex Hilbert space X is a biholomorphic convex mapping, which improves some results of Hamada and Kohr and solves the problem which is posed by Graham and Kohr. From this, we derive some sufficient conditions for biholomorphic convex mapping. We also introduce a linear operator in purpose to construct some concrete examples of biholomorphic convex mappings on B in Hilbert spaces. Moreover, we give some examples of biholomorphic convex mappings on B in Hilbert spaces.     

关于相关系间的同构映射

建立了相关系间的同构映射,给出了相关系间同构映射的一些等价条件,并通过具体的同构映射揭示出相关系的一些内在本质.     

Starlike and convex rational mappings on infinite dimensional domains

We give starlike criteria for a class of rational mappings on the open unit ball of a complex Banach space. We also give a sufficient condition for these mappings to be convex when they are defined in Hilbert spaces. These criteria facilitate the construction of concrete examples of starlike and convex mappings on infinite dimensional domains (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

向量均衡问题

本首先引进了集值映射的伪单调性，利用Ky Fan引理以及KKM映射对一般向量均衡问题建立了相应的存在性定理．     

Strong convergence theorems by Halpern-Mann iterations for relatively nonexpansive mappings in Banach spaces

In this paper, we modify Halpern and Mann’s iterations for finding a fixed point of a relatively nonexpansive mapping in a Banach space. Consequently, a strong convergence theorem for a nonspreading mapping is deduced. Using a concept of duality theorems, we also obtain analogue results for certain generalized nonexpansive and generalized nonexpansive type mappings. Finally, we discuss two strong convergence theorems concerning two types of resolvents of a maximal monotone operator in a Banach space.     

拓扑向量空间中的几个锥广义凸映射

本文引进拓扑向量空间中的几个锥伪凸映射的概念,并且讨论了它们之间及其它的锥广义凸映射之间的关系,最后,给出一个显示各种关系的图表。