关于S—系统的纯性

设Ｓ是幺半群，在右Ｓ－系范畴Ａｃｔ－Ｓ中，有两种纯性的概念，分别被Ｎｏｒｍａｋ，Ｇｏｕｌｄ和Ｒｅｎｓｈａｗ所研究。我们分别称之为ＮＧ－纯性和Ｒ－纯性，本文考虑ＮＧ－纯性和Ｒ－纯性的关系。我们证明了ＮＧ－纯性蕴含Ｒ－纯性，并且给出例子说明反过来是不对的，最后我们引入了关系正合序列的概念，并用来研究循环系的Ｒ－纯循环子系的性质。     

STEKLOV－POINCARE算子与自然积分算子及GREEN函数间的关系

ＳＴＥＫＬＯＶ－ＰＯＩＮＣＡＲＥ算子与自然积分算子及ＧＲＥＥＮ函数间的关系余德浩（中国科学院计算数学与科学工程计算研究所）ＯＮＲＥＬＡＴＩＯＮＳＨＩＰＢＥＴＷＥＥＮＳＴＥＫＬＯＶ－ＰＯＩＮＣＡＲＥＯＰＥＲＡＴＯＲＳＡＮＤＮＡＴＵＲＡＬＩＮＴＥＧＲＡＬ...     

某些广义迭代法的Stein－Rosenberg型定理与比较定理

某些广义迭代法的Ｓｔｅｉｎ－Ｒｏｓｅｎｂｅｒｇ型定理与比较定理王新民（中国金融学院）ＳＴＥＩＷ－ＲＯＳＥＮＢＥＲＧＴＹＰＥＴＨＥＯＲＳＭＳＡＮＤＣＯＭＭＭＳＯＮＴＨＥＯＲＥＭＳＦＯＲＳＯＭＥＧＥＮＥＲＡＬＩＺＥＤＩＴＥＲＡＩＶＥＭＥＴＨＯＤＳ￥Ｗａｎ...     

SINGULAR BOUNDARY PROPERTIES OF HARMONIC FUNCTIONS AND FRACTAL ANALYSIS

ＳＩＮＧＵＬＡＲＢＯＵＮＤＡＲＹＰＲＯＰＥＲＴＩＥＳＯＦＨＡＲＭＯＮＩＣＦＵＮＣＴＩＯＮＳＡＮＤＦＲＡＣＴＡＬＡＮＡＬＹＳＩＳＷＥＮＺＨＩＹＩＮＧＺＨＡＮＧＹＩＰＩＮＧＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪａｎｕａｒｙ１１，１９９５．Ｒｅｖｉ...     

MAXIMUM CYCLE－MEANS OF WEIGHTED DIGRAPHS

ＭＡＸＩＭＵＭＣＹＣＬＥ－ＭＥＡＮＳＯＦＷＥＩＧＨＴＥＤＤＩＧＲＡＰＨＳ＊Ｒ．Ａ．ＣＵＮＩＮＧＨＡＭＥ－ＧＲＥＥＮＡＮＤＬＩＮＹＩＸＵＮＡｂｓｔｒａｃｔ．Ｃｏｍｐｕｔｉｎｇｔｈｅｍａｘｉｍｕｍｃｙｃｌｅ－ｍｅａｎｏｆａｗｅｉｇｈｔｅｄｄｉｇｒａｐｈｉ...     

Sylow－正规化子属于群系F的有限群

设Ｆ是可解的，子群闭的，由｛ｆ（Ｐ）｝所局部定义的群系，Ｆｐ是由｛ｆ（ｑ）｝定义的ｐ－局部定义群系．Ｎ为幂零群系．本文证明了：１）设Ｆ满足：任一群属于Ｆ，当且仅当，对每ｐ．其ｐ－Ｓｙｌｏｗ－正规化子属于Ｆｐ．于是“群Ｇ∈Ｎ．Ｆ（幂零由Ｆ的扩张）的充要条件是，对每Ｐ，其ｐ－Ｓｙｌｏｗ－正规化子的Ｆｐ剩余次正规于Ｇ内．２）群Ｇ为超可解的充要条件是，对每ｐ，其ｐ－Ｓｙｌｏｗ－正规化子为ｐ－超可解，且其幂零剩余次正规于Ｇ内．若对每ｐ，群Ｇ的ｐ－Ｓｙｌｏｗ子群无商群与ｐ２－次对称群的ｐ－Ｓｙｌｏｗ子群同构，则称Ｇ为Ｂ－群．３）设Ｇ为Ｂ－群，又群系Ｆ含于σ－Ｓｙｌｏｗ塔群系内．于是①Ｇ∈Ｆ，当且仅当，对每ｐ，Ｇ的ｐ－Ｓｙｌｏｗ－正规化属于Ｆｐ；②Ｇ∈Ｎ·Ｆ，当且仅当，对每ｐ，Ｇ的ｐ－Ｓｙｌｏｗ－正规化子的Ｆｐ剩余在Ｇ内次正规．     

NON-ISOMORPHIC GROUPS WITH ISOMORPHICSPECTRAL TABLES AND BURNSIDE MATRICES

ＮＯＮ－ＩＳＯＭＯＲＰＨＩＣＧＲＯＵＰＳＷＩＴＨＩＳＯＭＯＲＰＨＩＣＳＰＥＣＴＲＡＬＴＡＢＬＥＳＡＮＤＢＵＲＮＳＩＤＥＭＡＴＲＩＣＥＳ￥Ｗ．ＫＩＭＭＥＲＬＥ；Ｋ．Ｗ．ＲＯＧＧＥＮＫＡＭＰ（ＭａｔｈｅｍａｔｉｓｃｈｅｓｉｎｓｔｉｔｕｔＢ，Ｕｎｉｖｅｒｓ...     

关于SF－环的几点注记

本文中，我们证明了如下主要结果：Ⅰ　对于环Ｒ，下面条件是等价的：（１）Ｒ是Ａｒｔｉｎ半单环；（２）Ｒ是左ＳＦ－环，且Ｒ满足特殊右零化于降链条件；（３）Ｒ是左ＳＦ－环和Ｉ－环，且Ｒ￣Ｒ具有有限Ｇｏｌｄｉｅ维数。Ⅱ对于环Ｒ，下面条件是等价的：（１）Ｒ是ＶｏｎＮｅｕｍａｎｎ正则环；（２）Ｒ是左ＳＦ－环，且每个苛异循环左Ｒ－模的极大子模是平坦的。     

A REMARK ON THE HAUSDORFF DIMENSION OF CERTAIN NON-SELF-SIMILAR ATTRACTORS

ＡＲＥＭＡＲＫＯＮＴＨＥＨＡＵＳＤＯＲＦＦＤＩＭＥＮＳＩＯＮＯＦＣＥＲＴＡＩＮＮＯＮＳＥＬＦＳＩＭＩＬＡＲＡＴＴＲＡＣＴＯＲＳＬＩＵＨＯＮＧＧＥＮＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＪｕｎｅ４，１９９４．ＲｅｖｉｓｅｄＡｕｇｕｓｔ８，１９９６．...     

TENSOR PRODUCT OF SEMIGROUPSAND THE EQUATION AC-CB=Q

ＴＥＮＳＯＲＰＲＯＤＵＣＴＯＦＳＥＭＩＧＲＯＵＰＳＡＮＤＴＨＥＥＱＵＡＴＩＯＮＡＣ－ＣＢ＝Ｑ￥ＷＡＮＧＳＨＥＮＧｗａＮＧ；Ｉ．ＥＲＤＥＬＹＩＡｂｓｔｒａｃｔ：Ｐｒｏｐｅｒｔｉｅｓｆｏｒｔｅｎｓｏｒｐｒｏｄｕｃｔｓｏｆｓｅｍｉｇｒｏｕｐｓａｒｅｃｏｎｓ...     

幺半群的内射类及投射类刻画

类比于一般环上模的内射类,定义了幺半群上的S-系的内射类和投射类,并利用它们刻画了几类特殊的幺半群．证明了完全内射幺半群和完全拟内射幺半群是等价的．并且证明了对于标致幺半群S,它是完全投射的当且仅当它是完全拟投射的当且仅当它上面的投射S-系构成了一个投射类．     

On Retractable S-Acts

In this paper we introduce a class of right S-acts called retractable S-acts which are right S-acts with homomorphisms into their all subacts. We also give some classifications of monoids by comparing such acts with flatness properties.     

幺半群上的广义内射S-系(英文)

本文考虑拟内射、伪内射、核内射以及支内射S-系的性质,重点讨论这些广义内射S-系的上的线性方程组的性质.例如,A是核内射S-系当且仅当A的任意收缩核B上的任意A-相容线性方程组在B上是可解的;A是支内射S-系当且仅当同构于A的任一分支的S-系B上的任意A-相容线性方程组在B上是可解的.进而讨论了伪内射、核内射以及支内射S-系的融合余积的性质.最后给出了一个充分条件,基于此条件核内射和支内射S-系是等价的.     

Radical and Torsion Theory for Acts

After recapitulating the rudiments of the Kurosh-Amitsur radical theory of S-acts, hereditary radicals are discussed. The hereditary Hoehnke radical assignments r which designate a Rees congruence r(A) to each S-act A, are the hereditary Kurosh-Amitsur radical assignments. Then the corresponding radical as well as semisimple classes are characterized. Equivalence classes of injective S-acts determine hereditary torsion assignments t, these are just the hereditary Hoehnke radicals, but the congruence t(A) of A need not be a Rees congruence. Torsion and torsionfree classes are characterized; several hereditary torsion assignments may determine the same torsion class which is always a radical class closed under taking subacts. Examples show that a hereditary torsion assignment need not be a hereditary radical.     

关于所有强平坦右S-系是正则系的幺半群(英)

本论文考虑了所有强平坦右S-系是正则系的幺半群的刻画,证明了所有强平坦右S-系是正则S-系当且仅当S是右PSF幺半群并且S的每一个左coilpasible子幺半群包含左零元．该结果对Kilp和Knauer在文献[7]中的问题给出了一个新的回答．     

C(P)系对幺半群的刻画

设S是幺半群.本文介绍并研究了正则右系的一个推广.一个右S-系A称为C(P)系,如果A的所有循环子系满足条件(P).本文证明了右C(P)系形成了右S-系的一个新的类,同时,C(P)性质为幺半群同调分类研究提供了新思路.     

本质子系满足链条件

Let S be a semigroup with zero and an S-act be a centered left S-act. This paper is devoted to the study of chain conditions on PS-acts. We prove that a PS-act having finite decomposition has ACC (DCC) on all subacts if it has ACC (DCC) on essential subacts. Moreover, a PS-act with ACC (DCC) on essential subacts has ACC (DCC) on all subacts if and only if it has finite decomposition. We characterize the structure of a PS-act and generalize some results of the Goldie dimension and semisimple S-acts.     

关于左完全幺半群

设Ｓ是左完全幺半群．本文讨论了左，右Ｓ－系的链条件，特别地证明了右Ｓ－系的Ｂｊｏｒｋ定理．     

Singularity Results for Functional Equations Driven by Linear Fractional Transformations

We consider functional equations driven by linear fractional transformations, which are special cases of de Rham’s functional equations. We consider Hausdorff dimension of the measure whose distribution function is the solution. We give a necessary and sufficient condition for singularity. We also show that they have a relationship with stationary measures.     

An Interior Point Heuristic for the Hamiltonian Cycle Problem via Markov Decision Processes

We consider the Hamiltonian cycle problem embedded in a singularly perturbed Markov decision process (MDP). More specifically, we consider the HCP as an optimization problem over the space of long-run state-action frequencies induced by the MDP's stationary policies. We show that Hamiltonian cycles (if any) correspond to the global minima of a suitably constructed indefinite quadratic programming problem over the frequency space. We show that the above indefinite quadratic can be approximated by quadratic functions that are `nearly convex' and as such suitable for the application of logarithmic barrier methods. We develop an interior-point type algorithm that involves an arc elimination heuristic that appears to perform rather well in moderate size graphs. The approach has the potential for further improvements.