代写硕士论文-《Minkowski平面上的切线与割线》
【摘要】 Minkowski空间几何在Banach空间几何理论和Banach空间局部理论,扮演着不可忽视的角色。此外,它在优化理论、运筹学、组合几何、离散和计算几何中有着广泛的应用。因此,研究Minkowski几何具有非常重要的意义。全文共分三章,主要工作如下:本文首先阐述了国内外研究现状、课题的目的和意义、及本文的主要研究内容。然后介绍Minkowski空间的基本理论知识,回顾了Birkhoff正交和等腰正交的相关定义和基本性质,熟悉了Radon平面和对称的Minkowski平面的基本理论,再次深化理解了严格凸性和光滑性及三角不等式相关理论。为后文的证明奠定了理论基础。本文主要对了Minkowski平面上的切线和内积空间之间的特征进行了深入探讨,加强了前人的一个已知结果,并得到了欧氏空间中的割线定理在Minkowski空间中成立的条件;与此同时,对切线与严格凸性、光滑性之间的关系以及割线与三角不等式之间的关系也进行了研究。
【Abstract】 Minkowski Geometry plays an important role in Banach Space Theory and Local Theory of Banach Spaces, and it has many applications in Optimization, Operation Reasearch, Combinatorial Geometry, Discrete and Computational Geometry. Therefore there is a good reason to study it carefully.First we survey main results in this research field, show the objective of this research project and the main problems that we will study.Then preliminaries of Minkowski Geometry, including orthogonality types, Radon planes, symmetric Minkowski planes, strict convexity, smoothness, and triangle inequality, which are important for our study, are collected.Tangent segment and related characterization of inner product spaces are discussed, an existing result is strengthened and a condition to ensure the Secant segment Theorem holding in Minkowski spaces is obtained. Furthermore, the relation between tangent segment and strict convexity and smoothness, and the relation between secant segment and triangle inequality are studied.
硕士论文代写【关键词】 Birkhoff正交性； 等腰正交； 严格凸性； Minkowski平面； 内积空间；
【Key words】 Birkhoff orthogonality； isosceles orthogonality； strict convexity； Minko-wski plane； inner product spaces；