A Comparative Analysis of the New -3(-n) - 1 Remer Conjecture and a Proof of the 3n + 1 Collatz Conjecture

This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.

泛函分析课程中有界算子理论的教学探讨

泛函分析课程是一门极其重要的数学专业课程,兼有理论性强和高度的抽象性等特点,采用传统的教师为主体的教学模式往往教学效果不佳.以有界算子理论这部分内容为例探索了研讨型教学模式,主要对比了l^1空间上有界线性算子全体与列和有界的无限维矩阵空间的等距同构关系,以及c0空间上有界线性算子全体与行和有界且每列元素趋于0的无限维矩阵空间的等距同构关系.讨论了序列空间l^∞到l^∞中的有界线性算子全体与无限维矩阵空间的关系.证明了行和有界的无限维矩阵可诱导出一个l^∞到l^∞的有界线性算子,通过反例说明了此对应不构成l^∞上的有界线性算子与行和有界的无限维矩阵空间的同构映射,丰富了泛函分析的教学内容和方法.

差分有界干扰的最优抑制

提出了离散ＳＩＳＯ系统中差分有界干扰的最优抗扰设计问题，讨论了控制对象含（１－ｚ）－１和不含（１－ｚ）－１两种情况下问题的解法，并证明了上述两种情况都可以转化为现有ι１优化理论能够解决的问题．

Smarandache函数在两数列上的下界估计

设S(n)是Smarandache函数,其中n是一正整数.讨论Smarandache函数S(n)在数列F((2k),1)=F(n,1)=n2n+1(n=2k)与数列G(2n,1)=(2n)2n+1上的下界估计.基于初等方法证明了:当偶数n≥6时,有S(F((2k),1))=S(F(n,1))≥6×2n+1;当n≥4时,有S(G(2n,1))≥6×2n+1.