特殊符号模式的谱任意性研究

发布时间：2018-04-30 14:12

本文选题：幂零-雅可比 + 符号模式　；参考：《中北大学》2017年硕士论文

【摘要】：组合数学是基础数学中的一个分支,近年来,国内外对其研究的文献资料也越来越多.随着计算机数学的发展,组合数学成为了各个领域的研究对象.而符号模式是组合数学主要的组成部分,符号模式普遍的应用于各学科中,其主要的研究方面有:符号可解性、稳定性,符号模式矩阵的惯量、幂序列性质及其复推广等.本文主要研究组合数学中几类特殊的符号模式及其母模式是谱任意的.第一部分介绍了符号模式的研究基础和国内、外的发展形势,符号模式的一些定义、相关的一些结论以及本文主要的结论;第二部分讨论了一类含有3n个非零元的谱任意ray模式,且验证了它任意的母模式也为谱任意的;第三部分利用N-J方法证明了一类复符号模式是谱任意的,且验证了它的任意母模式的谱任意性;第四部分证明了一类复符号模式及它的任意的母模式为极小谱任意的.
[Abstract]:Combinatorial mathematics is a branch of basic mathematics. In recent years, there are more and more literature on it at home and abroad. With the development of computer mathematics, combinatorial mathematics has become the research object in various fields. Symbolic pattern is the main component of combinatorial mathematics. Symbolic pattern is widely used in various disciplines. Its main research aspects are: symbol solvability, stability, inertia of symbol pattern matrix, power sequence property and its complex generalization, and so on. In this paper, we mainly study some special symbolic patterns and their parent patterns in combinatorial mathematics, which are spectral arbitrary. The first part introduces the research foundation of the symbol pattern and the development situation in China and abroad, some definitions of the symbol pattern, some relevant conclusions and the main conclusions of this paper. In the second part, we discuss a class of spectral arbitrary ray patterns with 3n nonzero elements, and verify that any of its parent modes are spectral arbitrary, and in the third part, we prove that a class of complex symbolic patterns are spectral arbitrary by using N-J method. In the fourth part, we prove that a class of complex symbol patterns and any of its parent patterns are minimally spectral arbitrary.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157

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