THE RADICALS OF HOPF MODULE ALGEBRAS

ＴＨＥＲＡＤＩＣＡＬＳＯＦＨＯＰＦＭＯＤＵＬＥＡＬＧＥＢＲＡＳＺＨＡＮＧＳＨＯＵＣＨＵＡＮ＊ＡｂｓｔｒａｃｔＴｈｅｃｈａｒａｃｔｅｒｉｚａｔｉｏｎｏｆＨ－ｐｒｉｍｅｒａｄｉｃａｌｉｓｇｉｖｅｎｉｎｍａｎｙｗａｙｓ．Ｍｅａｎｔｉｍｅ，ｔｈｅｒｅｌａｔｉ...     

A BLACK－SCHOLES FORMULA FOR OPTIONPRICINGWITHDIVIDENDS

ＡＢＬＡＣＫ－ＳＣＨＯＬＥＳＦＯＲＭＵＬＡＦＯＲＯＰＴＩＯＮＰＲＩＣＩＮＧＷＩＴＨＤＩＶＩＤＥＮＤＳ＊ＸＵＷＥＮＳＨＥＮＧＡＮＤＷＵＺＨＥＮＡｂｓｔｒａｃｔ．ＷｅｏｂｔａｉｎａＢｌａｃｋ－Ｓｃｈｏｌｅｓｆｏｒｍｕｌａｆｏｒｔｈｅａｒｂｉｔｒａｇｅ－ｆ...     

IRRATIONAL ROTATION c^＊—ALGEBRA FOR GROUPOID c^＊—ALGEBRA

ＩＲＲＡＴＩＯＮＡＬＲＯＴＡＴＩＯＮｃ－ＡＬＧＥＢＲＡＦＯＲＧＲＯＵＰＯＩＤｃ－ＡＬＧＥＢＲＡ￥ＣＨＥＮＸＩＡＯＭＡＮ；ＸＵＱＩＮＧＸＩＡＮＧ；ＸＵＳＨＥＮＧＺＨＩ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，Ｆ＇ｕｄａｎＵｎｉｖｅｒｓｉｔｙ，Ｓｈ...     

GLOBAL CONVERCENCE OF THE FLETCHER-REEVES ALGORITHM WITH INEXACT LINESEARCH

ＧＬＯＢＡＬＣＯＮＶＥＲＣＥＮＣＥＯＦＴＨＥＦＬＥＴＣＨＥＲ－ＲＥＥＶＥＳＡＬＧＯＲＩＴＨＭＷＩＴＨＩＮＥＸＡＣＴＬＩＮＥＳＥＡＲＣＨ￥ＬＩＵＧＵＡＮＧＨＵＩ；ＨＡＮＪＩＹＥ；ＡＮＤＹＩＮＨＯＮＧＸＩＡＡｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｉ...     

6-CANONICAL MAPS OFNONSINGULAR MINIMAL 3-FOLDS

６－ＣＡＮＯＮＩＣＡＬＭＡＰＳＯＦＮＯＮＳＩＮＧＵＬＡＲＭＩＮＩＭＡＬ３－ＦＯＬＤＳ￥ＣＨＥＮＭＥＮＧＡｂｓｔｒａｃｔ：Ｔｈｅａｉｍｏｆｔｈｉｓｐａｐｅｒｉｓｔｏｓｔｕｄｙ６－ｃａｎｏｎｉｃａｌｓｙｓｔｅｍｏｆａｎｏｎｓｉｎｇｕｌａｒｍｉｎｉｍａｌ３...     

A modified Frank-Wolfe algorithm and its convergence properties

ＡＭＯＤＩＦＩＥＤＦＲＡＮＫ－ＷＯＬＦＥＡＬＧＯＲＩＴＨＭＡＮＤＩＴＳＣＯＮＶＥＲＧＥＮＣＥＰＲＯＰＥＲＴＩＥＳＷＵＦＡＮＧ（吴方）ＷＵＳＨＩＱＵＡＮ（吴士泉）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ,ｔｈｅＣｈｉｎｅｓｅＡｃａｄ...     

CLASSIFICATION OF AF-ALGEBRAS AND THEIR DIMENSION GROUPS

ＣＬＡＳＳＩＦＩＣＡＴＩＯＮＯＦＡＦ－ＡＬＧＥＢＲＡＳＡＮＤＴＨＥＩＲＤＩＭＥＮＳＩＯＮＧＲＯＵＰＳ￥ＨＵＡＮＧＺＨＡＯＢＯＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｇｉｖｅｓｔｈｅｉｎｔｒｉｎｓｉｃｃｈａｒａｃｔｅｒｏｆｔｈｅｃｌａｓｓｉｆｉｃａｔｉｏｎ...     

A PDE PROBLEM ARSING FROM CALCULATION OF THE MODEL FOR CONTINUOUS CASTING OF STEEL

ＡＰＤＥＰＲＯＢＬＥＭＡＲＳＩＮＧＦＲＯＭＣＡＬＣＵＬＡＴＩＯＮＯＦＴＨＥＭＯＤＥＬＦＯＲＣＯＮＴＩＮＵＯＵＳＣＡＳＴＩＮＧＯＦＳＴＥＥＬ￥ＪＩＡＮＧＬＩＳＨＡＮＧ；ＬＩＵＺＵＨＡＮ；ＹＩＦＡＨＵＡＩ；ＡＮＤＹＵＥＸＩＮＧＹＥＡｂｓｔｒａｃｔ：Ｔｈｉ...     

ON THE HARISH－CHANDRA HOMOMORPHISM FOR THE CHEVALLEY GROUPS OVER P－ADIC FIELD

ＯＮＴＨＥＨＡＲＩＳＨ－ＣＨＡＮＤＲＡＨＯＭＯＭＯＲＰＨＩＳＭＦＯＲＴＨＥＣＨＥＶＡＬＬＥＹＧＲＯＵＰＳＯＶＥＲＰ－ＡＤＩＣＦＩＥＬＤ￥ＣＨＥＮＺＨＯＮＧＨＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉａｎｇｔａｎＵｎｉｖｅｒｓｉｔｙｔＸｉ...     

THE CONVERGENCE OF GLOWINSKI'S ALGORITHM FOR ELLIPTIC PROBLEMS

ＴＨＥＣＯＮＶＥＲＧＥＮＣＥＯＦＧＬＯＷＩＮＳＫＩ＇ＳＡＬＧＯＲＩＴＨＭＦＯＲＥＬＬＩＰＴＩＣＰＲＯＢＬＥＭＳＣＨＵＤＥＬＩＮ（储德林）；ＨＵＸＩＡＮＣＨＥＮＧ（胡显承）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｔｓｉｎｇ－Ｈｕ...     

LOCAL C-SEMIGROUPS AND LOCAL C-COSINE FUNCTIONS

0IntroductionLetB(X)betheBanachspaceofallboundedlinearoperatorsonaBanachspaceX.CEB(X)isinjective.Alloperatorsarelinear.D(A),Im(A),andP(A)denotethedomain,theimage,andtheresolventsetofoperatorA,respectivelyNandRdenotethesetofallnaturalnumbersandthesetofallrealnumbers.TheconceptoflocalC-sernigroupsalldlocalC-cosinefunctionwereintroducedbyTanakaandOkazawain[1]tF.HuangandT.Huangin[21,respectively.Aspointedoutin[3]and[2]thatnotalllocalC-sendgroups(C--cosinefunctions)canbeextendedtobeC-se…     

指数有界的C余弦算子函数

本文引入了指数有界的Ｃ余弦算子函数的生成元，讨论了生成元的基本性质，建立了相应的生成定理、逼近定理及扰动定理．最后给出了指数有界的Ｃ余弦算子函数与指数有界的Ｃ半群的基本联系．     

双连续n次积分C余弦函数的逼近定理

基于双连续半群概念,引入一致双连续半群序列概念,借助Laplace变换和Trotter-Kato定理,考察双连续n次积分C余弦函数与C-预解式之间的关系,得到逼近定理的稳定性条件,进而得出双连续n次积分C余弦函数逼近定理.从而对Banach空间强连续半群逼近定理和双连续半群逼近定理进行了推广,为相应抽象的Cauchy问题提供了解决方案.     

C-cosine Operator Functions and the Second Order Abstract Cauchy Problem

Ｃ－ｃｏｓｉｎｅＯｐｅｒａｔｏｒＦｕｎｃｔｉｏｎｓａｎｄｔｈｅＳｅｃｏｎｄＯｒｄｅｒ　ＡｂｓｔｒａｃｔＣａｕｃｈｙＰｒｏｂｌｅｍＷａｎｇＨａｉｙａｎ（王海燕）（ＤｅｐａｒｔｍｅｔｎｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＭｅｃｈａｎｉｃｓ，Ｓｏｕｔｈｅａｓｔ...     

On α-times integrated C-cosine functions and abstract Cauchy problem I

In this paper we first investigate some basic properties concerning nondegenerate α-times integrated C-cosine functions on a Banach space X, and then characterize their generator A in terms of the unique existence of strong solutions of the following abstract Cauchy problem: for t>0, u(0)=x, u^′(0)=y.     

On the Stability of the Feasible Set in Linear Optimization

This paper deals with the stability of two families of linear optimization problems, each one formed by the dual problems to the members of the other family. We characterize the problems of these families that are stable in the sense that they remain consistent (inconsistent) under sufficiently small arbitrary perturbations of all the data. This characterization is established in terms of the lower semicontinuity property of the feasible set mapping and the boundedness of the optimal set of the corresponding coupled problem. Other continuity properties of the feasible set mapping are also derived. This stability theory extends some well-known theorems of Williams and Robinson on the stability of ordinary linear programming problems to linear optimization problems with infinitely many variables or constraints.     

A local minimax characterization for computing multiple nonsmooth saddle critical points

This paper is concerned with characterizations of nonsmooth saddle critical points for numerical algorithm design. Most characterizations for nonsmooth saddle critical points in the literature focus on existence issue and are converted to solve global minimax problems. Thus they are not helpful for numerical algorithm design. Inspired by the results on computational theory and methods for finding multiple smooth saddle critical points in [14, 15, 19, 21, 23], a local minimax characterization for multiple nonsmooth saddle critical points in either a Hilbert space or a reflexive Banach space is established in this paper to provide a mathematical justification for numerical algorithm design. A local minimax algorithm for computing multiple nonsmooth saddle critical points is presented by its flow chart. Dedicated to Terry Rockafellar on his 70th birthday     

On the Solution of Min-sum-min Problems

One class of min-sum-min problems is discussed in the paper. Min-sum-min problems appear in a natural way in many applications (e.g., in cluster analysis, pattern recognition, classification theory etc.). Like min-max-min problems, min-sum-min problems represent a very important family of nonsmooth problems. Problems of this type can be treated by means of the existing tools of Nonsmooth Analysis. However, most of algorithms available provide a local minimizer only, since they are based on necessary conditions which are of local nature. In the paper it is proved that the original problem can be reduced to the problem of minimizing a finite number of sum-functions. A necessary condition for a global minimum and a sufficient condition for a local minimum are stated. The necessary condition is of nonlocal nature. An algorithm (so-called Exchange algorithm) for finding points, satisfying necessary conditions, is described. An ɛ-Exchange algorithm is formulated, allowing, in principle, to escape from a ‘shallow’ local minimizer. An example is presented to illustrate the results and algorithms. An application of the proposed algorithms to solving one clustering problem is also given. Numerical results are provided.AMS Subject Classification:90C30, 49J40.     

A note on solvability of a class of linear complementarity problems

We give a characterization of unique solvability of an infinite family of linear complementarity problems of a special form by means of a finite subset of this family.     

A characterization of Kruskal sharing rules for minimum cost spanning tree problems

In Tijs et al. (Eur J Oper Res 175:121–134, 2006) a new family of cost allocation rules is introduced in the context of cost spanning tree problems. In this paper we provide the first characterization of this family by means of population monotonicity and a property of additivity.