Sufficient optimality conditions and duality in vector optimization with invex-convexlike functions

We prove the Kuhn-Tucker sufficient optimality condition, the Wolfe duality, and a modified Mond-Weir duality for vector optimization problems involving various types of invex-convexlike functions. The class of such functins contains many known generalized convex functions. As applications, we demonstrate that, under invex-convexlikeness assumptions, the Pontryagin maximum principle is a sufficient optimality condition for cooperative differential games. The Wolfe duality is established for these games.The author is indebted to the referees and Professor W. Stadler for valuable remarks and comments, which have been used to revise considerably the paper.     

Generalized Christoffel functions and error of positive quadrature

The author gives some upper and lower bounds for the generalized Christoffel functions related to a Ditzian-Totik generalized weight. As an application, an error estimate of Gauss quadrature formula inL ₁-weighted norm is derived.Dedicated to Prof. Luigi Gatteschi on the occasion of his 70th birthdayWork sponsored by MURST 40%.     

A numerically stable algorithm for two server queue models

In this paper, we consider a queueing system in which there are two exponential servers, each having his own queue, and arriving customers will join the shorter queue. Based on the results given in Flatto and McKean, we rewrite the formula for the probability that there are exactlyk customers in each queue, wherek = 0, 1,…. This enables us to present an algorithm for computing these probabilities and then to find the joint distribution of the queue lengths in the system. A program and numerical examples are given.     

Banach空间上算子张量积的联合谱

本文主要研究了 Banach 空间上交换算子组的张量积以及 Banach 代数的张量积中交换元组的 Taylor 联合谱,推广了 Vasilescu,F.H.及 Wrobel,V.等人结果。     

A PICARD TYPE THEOREM AND BLOCH LAW

Ａ ＰＩＣＡＲＤ ＴＹＰＥ ＴＨＥＯＲＥＭ ＡＮＤ ＢＬＯＣＨ ＬＡＷ ￥ＹＥＹＡＳＨＥＮＧＡｂｓｔｒａｃｔ：Ａｐｉｃａｒｄｔｙｐｅｔｈｅｏｒｅｍｉｓｐｒｏｖｅｄ，ａｎｄａｃｏｕｎｔｅｒｅｘａｍｐｌｅｉｓｇｉｖｅｎｔｏｓｈｏｗｔｈａｔｔｈｅＢｏｌｃｈ...     

Tangent cones and Dini derivatives

We prove a property of the Bouligand tangent cone to the epigraph (or to the graph) of a locally Lipschitz function. It is also shown how this result can be used in determining Dini sequences. Finally, some relationships between such a cone and Dini derivatives are provided.     

Hypersurface with Constant Main Curvature Symmetric Functions

ＨｙｐｅｒｓｕｒｆａｃｅｗｉｔｈＣｏｎｓｔａｎｔＭａｉｎＣｕｒｖａｔｕｒｅＳｙｍｍｅｔｒｉｃＦｕｎｃｔｉｏｎｓ￥ＷｕＢａｏｑｉａｎｇ；ＳｏｎｇＨｏｎｇｚａｏ（ＸｕｚｈｏｕＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ，２２１００９）（ＨｅｎａｎＵｎｉｖｅｒｓｉｔｙ，...     

角域上的调和函数与条件Brown运动

设中的角域．该文绘出了A上正调和函数的Martin表示，讨论了极小调和函数与条件Brown运动的一个0—1律之间的关系，并给出了A上极小调和函数的表现形式，     

Some remarks on the Jensen-Hadamard inequalities and applications

We provide some inequalities and integral inequalities connected to the Jensen-Hadamard inequalities for convex functions. In particular, we give some refinements to these inequalities. Some natural applications and further extensions are given.

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Sunto Forniamo alcune diseguaglianze e diseguaglianze integrali connesse alle dise-gueglianze di Jensen-Hadamard per funzioni convesse. In particolare, diamo qualche miglioramento di queste diseguaglianze. Alcune applicazioni naturali ed ulteriori estensioni sono date.

     

Finite dimensional semisimple Q-algebras

A Q-algebra can be represented as an operator algebra on an infinite dimensional Hilbert space. However we don’t know whether a finite n-dimensional Q-algebra can be represented on a Hilbert space of dimension n except n = 1, 2. It is known that a two dimensional Q-algebra is just a two dimensional commutative operator algebra on a two dimensional Hilbert space. In this paper we study a finite n-dimensional semisimple Q-algebra on a finite n-dimensional Hilbert space. In particular we describe a three dimensional Q-algebra of the disc algebra on a three dimensional Hilbert space. Our studies are related to the Pick interpolation problem for a uniform algebra.