On the decomposition map of Grothendieck groups

This article is a part of the doctoral dissertation of the author at the University of Minnesota under the guidance of Professor Morton E. Harris. The author wishes to express his gratitude to Professor Harris for his advice and suggestions     

Preface

These two special issues of Acta Mathematica Scientia are dedicated to Professor James Glimm on the occasion of his seventy-fifth birthday.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

Investigation of a macroeconomic model by the method of region analysis

A macroeconomic model on the relation between economic growth and the environment is investigated with the aim of illustrating how the method of region analysis can be used in solving practical problems formulated as regular optimal control problems with state constraints.This paper was written when the author was invited by Professor R. Bulirsch to work at the Munich University of Technology with the assistance of the Alexander Von Humboldt Foundation. The author would like to express his sincere gratitude to the Alexander Von Humboldt Foundation and to Professor Bulirsch.     

樊■——为数学而生,数学乃是他的生命

本文概括与综述樊■先生在拓扑群、非线性与凸分析、不动点理论、算子理论、线性代数与矩阵论、数学规划、逼近论等分支领域的重大学术成就与奠基性贡献,展现樊■在数学上那炉火纯青、出神入化的境界与独特的风格:条件自然,论断凝练,证明优美,应用广泛.     

Contributions of Lo Yang to Value Distribution Theory

Professor Lo Yang is a world famous mathematician of our country. He made a lot of outstanding achievements in the value distribution theory of function theory, which are highly rated and widely quoted by domestic and foreign scholars. He also did a lot of work to develop Chinese mathematics. It can be said that Professor Yang is one of the mathematicians who made main influences on the mathematical development in modern China. This paper briefly introduces Professor Yang’s life, mainly discusses his academic achievement and influence, and briefly describes his contributions to the Chinese mathematics community.     

Dedication

This is the first of two issues of Linear and Multilinear Algebra commemorating the years of service Henryk Minc has given to linear algebra. Professor Mine, now Emeritus Professor at the University of California at Santa Barbara, continues his work as an active linear algebraist. We wish him success with his forthcoming books and papers.     

对话李克正教授：为什么学习代数几何

以与首都师范大学的李克正教授对话的方式,通过其口简要介绍代数几何这门重要学科在我国的早期发展情况,详细回忆李克正教授在国外学习代数几何的过程,以及他回国后的教学与研究成果,并通俗地阐述代数几何方法对于解决重大数论问题所起的关键作用．     

On finite dimensional subspaces of Banach spaces

The common Banach spaces are investigated with respect to some properties of their finite dimensional subspaces. The contribution to the paper of the second author is part of his Ph.D. thesis prepared at the Hebrew University of Jerusalem under the supervision of Professor A. Dvoretzky. The authors wish to thank Professor A. Dvoretzky for the interest he showed in the paper and for his helpful advice.     

Sets of degrees of computable fields

Given a Σ₂ (resp. Σ₁) degree of recursive unsolvability a, a computable field (resp. a computable field with a splitting algorithm)F is constructed in any given characteristic, such that the set of dimensions of all finite extensions ofF has degree a. This is part of an M.Sc. Thesis presented at The Hebrew University. The author wishes to express his indebtedness to his Supervisor Professor H. Gaifman for his constant guidance and encouragement. Thanks are also due to Professor G. Sabbagh (University of Paris VII) for several useful suggestions.     

Gauss-Newton methods for the complementarity problem

Mangasarian has shown that the solution of the complementarity problem is equivalent to the solution of a system of nonlinear equations. In this paper, we propose a damped Gauss-Newton algorithm to solve this system, prove that under appropriate hypotheses one gets rapid local convergence, and present computational experience.The author would like to thank Professor Michael Ferris for pointing out a flaw in one of the proofs in an earlier preprint of this paper (Ref. 1). He is grateful to Professor Olvi Mangasarian for bringing to his attention additional references relevant to the material in this paper, and for his suggestions which resulted in a greatly improved presentation.     

A Review of the Report of the Committee on Policy Optimisation

When the Government Committee on Policy Optimisation published its report, the Committee of Professors in Operational Research was concerned to discover that there had been no formal input from the Operational Research community into the evidence which was taken. As a first stage in deciding what should be done, the Committee of Professors invited Professor S. L. Cook to write an appreciation and a criticism of the report. The Associate Editor, as a member of the Committee of Professors, was impressed by the outstanding quality of Professor Cook's note and suggested to him that, subject to minor editing changes such as rewriting his appreciation in the third person, Professor Cook might wish to have his note published in this journal.On the day that the Associate Editor received Professor Cook's acceptance of this invitation, he also heard of his untimely death. This paper, therefore, is published posthumously and is as Steve Cook wrote it, apart from the minor changes referred to above. The compassion and breadth of vision of Steve Cook shines through in every sentence.     

Preface: Special issue in honor of Claude-Michel Brauner

This special issue of the Journal of Applied Analysis and Computation is dedicated to Claude-Michel Brauner on the occasion of his 70th birthday. Claude-Michel Brauner is Emeritus Professor at the university of Bordeaux (IMB) and was Professor at the School of Mathematical Sciences of Xiamen University for eight years. Furthermore, he is corresponding member of the SMAI (french SIAM) for China and has played a significant role in Sino-French cooperation in applied mathematics. In June 9-12, 2017 the Sino-French Conference on Modeling, Mathematical Analysis and Computation was held in Xiamen University to celebrate his 70th birthday. This volume gathers carefully selected contributions from invited speakers and participants of the conference; it reflects the large variety of the themes addressed during this event.     

On pelczynski’s paper “universal bases”

A short proof is given to a theorem of Pelczynski concerning universal bases. This is part of the author’s Ph.D. thesis written at the Hebrew University of Jerusalem under the supervision of Professor J. Lindenstrauss. The author wishes to thank Professor Lindenstrauss for his guidance.     

A remark on bases and reflexivity in Banach spaces

LetX be a Banach space with a basis. It is proved that if (a) all bases ofX are shrinking, or (b) all bases ofX are boundedly complete, thenX is reflexive. Research supported by Grant AF EOAR 66-18. This is part of the author’s Ph.D. thesis prepared at The Hebrew University of Jerusalem, under the supervision of Professor A. Dvoretzky and Professor J. Lindenstrauss. The author wishes to thank Professor Lindenstrauss for his valuable remarks.     

Minimal annulus of a convex body

It is my pleasant duty to thank Professor P. Gruber for his suggestions.     

The Academic Career and Accomplishment of Professor Gu Chaohao

In his unremitting efforts to train mathematics talents, Professor Gu has greatly helped to bring up a large number of students, leading them onto their own way of mathematical research. Now many of them have become leaders or the backbone force in their respective departments and special areas. Because of his significant contributions to the educational cause of China, Professor Gu has been awarded many honors and titles such as the national advanced worker in 1956, a national labor model of the education in 1993, etc. Moreover, some university textbooks written by him with his group have received prizes for excellence from the state.     

A Nyström method for boundary integral equations in domains with corners

Summary We give a convergence and error analysis for a Nyström method on a graded mesh for the numerical solution of boundary integral equations for the harmonic Dirichlet problem in plane domains with corners.

Dedicated to Professor L. Collatz on the occassion of his 80th birthday