New geometric properties of Banach spaces

In this paper, we introduce new geometric properties as generalizations of p‐uniform smoothness and q‐uniform convexity of Banach spaces. Furthermore, using generalized Beckner's inequality, we characterize the properties in terms of norm inequalities. As an application, we consider the duality relation.     

A note on meromorphic convexity

We give examples of Stein domains D in C ² such that C ² ? D is either completely pluripolar or union of germs of (principal) hypersurfaces not intersecting D such that D fails to be meromorphically convex in C ². © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Design and G connection of developable surfaces through Bézier geodesics

For potential application in shoemaking and garment manufacture industries, the G¹ connection of (1, k) developable surfaces with abutting geodesic is important. In this paper, we discuss the developable surface which contains a given 3D Bézier curve as geodesic and prove the corresponding conclusions in detail. Primarily we study G¹ connection of developable surfaces through abutting cubic Bézier geodesics and give some examples.     

Normal structure and some geometric parameters related to the modulus of U-convexity in banach spaces

We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters U~ax(ε) and βx (ε), both related to Gao’s modulus of U-convexity of a Banach space X, are introduced. Their properties and the relationships with normal structure are studied. Some existing results involving normal structure and fixed points for non-expansive mappings in Banach spaces are improved.     

Geodesic Ptolemy spaces and fixed points

In this paper we study the regularity of geodesic Ptolemy spaces and apply our findings to metric fixed point theory. It is an open question whether such spaces with a continuous midpoint map are CAT(0) spaces. We prove that if a certain uniform continuity is imposed on such a midpoint map then these spaces, if complete, are reflexive (that is, the intersection of decreasing families of bounded closed and convex subsets is nonempty) and that bounded sequences have unique asymptotic centers. These properties will then be applied to yield a series of fixed point results specific to CAT(0) spaces.     

On constant elasticity of substitution – Constant elasticity of transformation Directional Distance Functions

This paper aims to present non-linear CES (Constant Elasticity of Substitution)–CET (Constant Elasticity of Transformation) Directional Distance Functions. These measures inherit the structure of the standard Directional Distance Functions and that of the CES–CET technology. These functions allow non-parametric estimation of efficiency scores through linear programming method. Besides, the CES –CET technology gives the opportunity to explore α-returns to scale assumption for the new distance functions. The duality theory is investigated through pseudo profit, cost and revenue functions. The dual standpoint provides non-linear adjusted prices that can occur into non-linear pricing practices. An application is proposed to give an illustrative example of the primal CES–CET Directional Distance Functions.     

Topological laminations on surfaces

We present and prove a topological characterization of geodesic laminations on hyperbolic surfaces of finite type.     

函数两种凸性定义等价性的今惑前世之初探

通过研究中点凸函数和一般凸函数这两种凸性定义的早期发展历史和凸性性质来探索两种凸性定义的等价性.结果表明,两种凸性定义不等价;但是,当函数满足连续、可微、半连续和有界这四个条件中的任何一个条件时,两种凸性定义等价.     

成批到达排队系统的随机比较

本文研究成批到达排队系统中队长过程的随机比较问题．利用随机比较方法我们对成批到达指数服务的多服务台排队系统进行分析,得到了该排队系统中队长过程的随机比较以及队长函数关于时间的凹性和凸性．同时我们也给出了成批到达一般服务的单服务台排队系统队长过程、稳态队长的随机比较以及队长函数关于时间的凹性和凸性．     

Cocompact CAT(0) spaces are almost geodesically complete

We prove that, under mild conditions, a cocompact CAT(0) space is almost geodesically complete.