John Mackintosh Howie: An Appreciation

This year Professor John Howie celebrates his 70th birthday.     

Special Issue Dedicated to Professor Paul H.Rabinowitz's 80th Birthday

The conference Calculus of Variations—A celebration of Paul Rabinowitz's 80th birthday was held during Oct.31-Nov.2,2019 at UniHotel Jeju,Korea.The conference was dedi-cated to Professor Paul Rabinowitz on the occasion of his 80th birthday.The current special issues in the journal Analysis in Theory and Applications are formed by papers contributed by speakers in this conference.     

Shape-preserving properties and asymptotic behaviour of the semigroup generated by the Black-Scholes operator

The paper is devoted to a careful analysis of the shape-preserving properties of the strongly continuous semigroup generated by a particular second-order differential operator, with particular emphasis on the preservation of higher order convexity and Lipschitz classes. In addition, the asymptotic behaviour of the semigroup is investigated as well. The operator considered is of interest, since it is a unidimensional Black-Scholes operator so that our results provide qualitative information on the solutions of classical problems in option pricing theory in Mathematical Finance. The paper is dedicated to Professor Luigi Albano on the occasion of his 70th birthday.     

It was 30 years ago today when Laurens de Haan went the multivariate way

Since the publication of his masterpiece on regular variation and its application to the weak convergence of (univariate) sample extremes in 1970, Laurens de Haan (Thesis, Mathematical Centre Tract vol. 32, University of Amsterdam, 1970) is among the leading mathematicians in the world, with a particular focus on extreme value theory (EVT). On the occasion of his 70th birthday it is a great pleasure and a privilege to follow his route through multivariate EVT, which started only seven years later in 1977, when Laurens de Haan published his first paper on multivariate EVT, jointly with Sid Resnick.      

Projective planes with non-abelian simple collineation group fixing an oval

Dedicated to Professor Luigi A. Rosati on his 70th birthday     

The mean ergodic theorem for cosine operator functions with optimal and non-optimal rates

Dedicated to Professor Károly Tandori on the occasion of his 70 th birthday, in great respect     

Convex billiards

This article deals with (partly rather peculiar) properties of typical convex billiards. In particular, convex caustics, trajectories which terminate on the boundary and dense trajectories are investigated.Dedicated to Professor Curt Christian on the occasion of his 70th birthday     

On the newly generalized absolute Cesàro summability of orthogonal series

Dedicated to Professor Károly Tandori on the occasion of his 70th birthday with admiration and friendship     

The <Emphasis Type="Italic">p</Emphasis>-version of the boundary element method for weakly singular operators on piecewise plane open surfaces

We study piecewise polynomial approximations in negative order Sobolev norms of singularities which are inherent to Neumann data of elliptic problems of second order in polyhedral domains. The worst case of exterior crack problems in three dimensions is included. As an application, we prove an optimal a priori error estimate for the p-version of the BEM with weakly singular operators on polyhedral Lipschitz surfaces and piecewise plane open screens. The work of A. Bespalov was supported by the London Mathematical Society. The work of N. Heuer was supported by the FONDAP Programme in Applied Mathematics and Fondecyt project no. 1040615, both Chile. Dedicated to Professor Wolfgang L. Wendland on the occasion of his 70th birthday.     

A non-miquelian Laguerre plane satisfying a theorem of miquelian type

This note shows that a theorem of miquelian type known as (M2) holds in a certain non miquelian Laguerre plane of shear type as defined by Löwen and Pfüller[1].Dedicated to Professor H. Karzel on the occasion of his 70th birthday     

The optimal convergence of the h–p version of the boundary element method with quasiuniform meshes for elliptic problems on polygonal domains

In the framework of the Jacobi-weighted Besov spaces, we analyze the lower and upper bounds of errors in the h–p version of boundary element solutions on quasiuniform meshes for elliptic problems on polygons. Both lower bound and upper bound are optimal in h and p, and they are of the same order. The optimal convergence of the h–p version of boundary element method with quasiuniform meshes is proved, which includes the optimal rates for h version with quasiuniform meshes and the p version with quasiuniform degrees as two special cases. Dedicated to Professor Charles Micchelli on the occasion of his sixtieth birthday Mathematics subject classification (2000) 65N38. Benqi Guo: The work of this author was supported by NSERC of Canada under Grant OGP0046726 and was complete during visiting Newton Institute for Mathematical Sciences, Cambridge University for participating in special program “Computational Challenges in PDEs” in 2003. Norbert Heuer: This author is supported by Fondecyt project No. 1010220 and by the FONDAP Program (Chile) on Numerical Analysis. Current address: Mathematical Sciences, Brunel University, Uxbridge, U.K.     

A defense of the honour of an unjustly neglected little geometry or a combinatorial approach to the projective plane of order five

In this paper, we consider the projective plane of order five from a combinatorial point of view. We shall see many of its properties (such as its uniqueness and existence, the order of the full collineation group and Segre's theorem) by looking at a structure as simple as the complete graph on six vertices.To Professor Dr. G. Pickert on the occasion of his 70th birthday.     

Fractional powers of self-adjoint operators and Trotter-Kato product formula

We study error bounds in the operator norm topology for the Trotter-Kato product formula. We prove that they depend on fractional power conditions (domains and relative boundedness) for operators involved in this formula.Dedicated to Professor M.Sh.BIRMAN on the occassion of his 70th birthday.     

1.5-Q-superlinear convergence of an exterior-point method for constrained optimization

We introduce and analyze an exterior-point method (EPM) for constrained optimization problems with both inequality constraints and equations. We show that under the standard second-order optimality conditions the EPM converges to the primal–dual solution with 1.5-Q-superlinear rate. Dedicated to Professor Gil Strang on the occasion on his 70th birthday.     

A synthetic construction of the Figueroa planes

The constructions of the Figueroa planes by Figueroa, Hering-Schaeffer and Dempwolff make essential use of the collineation groups. Here we give a synthetic construction of these planes, which avoids coordinates and groups.Dedicated to Professor Hanfried Lenz on the occasion of his 70th birthday     

许宝騄先生的学术成就——谨以此文纪念许宝騄先生诞辰100周年

许宝騄先生是我国概率统计学科的主要奠基人、中国科学院院士、北京大学一级教授.本文回顾许宝騄先生的毕生科研工作,着重阐述了许先生在数理统计学和概率论的10个方面的研究成果及其对学科发展的影响,以此纪念许宝騄先生诞辰100周年暨逝世40周年.     

Scalar curvature of a certain CR-submanifold of complex projective space

We study an n-dimensional, compact, minimal CR-submanifold of CR-dimension n − 1 and give a sufficient condition for the submanifold to be a tube over a totally geodesic complex subspace. Dedicated to Professor U-Hang Ki on his 60th birthday This work is supported by the research grant of the Catholic University of Taegu-Hyosung in 1996.     

Generalized quasiconvexities,cone saddle points,and minimax theorem for vector-valued functions

We establish the following theorems: (i) an existence theorem for weak type generalized saddle points; (ii) an existence theorem for strong type generalized saddle points; (iii) a generalized minimax theorem for a vector-valued function. These theorems are generalizations and extensions of the author's recent results. For such extensions, we propose new concepts of convexity and continuity of vector-valued functions, which are weaker than ordinary ones. Some of the proofs are based on a few key observations and also on the Browder coincidence theorem or the Tychonoff fixed-point theorem. Also, the minimax theorem follows from the existence theorem for weak type generalized saddle points. The main spaces with mathematical structures considered are real locally convex spaces and real ordered topological vector spaces.This paper is dedicated to Professor Kensuke Tanaka on his sixtieth birthday.This paper was written when the author was a visitor at the Department of Mathematical Science, Graduate School of Science and Technology, Niigata University, Niigata, Japan. The author is indebted to Prof. K. Tanaka for suggesting this work.The author is very grateful to Prof. P. L. Yu for his useful encouragement and suggestions and to the referees for their valuable suggestions and comments.     

Review of testing issues in extremes: in honor of Professor Laurens de Haan

As a leading statistician in extreme value theory, Professor Laurens de Haan has made significant contribution in both probability and statistics of extremes. In honor of his 70th birthday, we review testing issues in extremes, which include research done by Professor Laurens de Haan and many others. In comparison with statistical estimation in extremes, research on testing has received less attention. So we also point out some practical questions in this direction.