Weighted product of point clouds and simplicial complexes

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-02-09 DOI:10.1007/s00200-024-00644-8

Archana Babu, Sunil Jacob John, Baiju Thankachan

引用次数: 0

Abstract

This paper extends the concept of weighted point clouds and weighted simplicial complexes by introducing product point clouds and product simplicial complexes within a commutative ring with unity. Within an integral domain, the introduction of a weighted product chain group, along with the induced product weighted homomorphism and weighted product boundary maps, leads to significant outcomes and findings. To explore the algebraic characteristics of a weighted product structure, we introduce the concept of weighted product homology. This homology considers the relationship of weights assigned to elements within the structure and their impact on the structure’s underlying algebraic properties.

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点云和简单复数的加权乘积

本文通过在具有统一性的交换环中引入积点云和积简复数，扩展了加权点云和加权简复数的概念。在积分域内，引入加权积链群以及诱导积加权同态和加权积边界映射，会带来重要的结果和发现。为了探索加权积结构的代数特征，我们引入了加权积同调的概念。这种同源性考虑了分配给结构中元素的权重关系及其对结构基本代数特性的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applicable Algebra in Engineering Communication and Computing 工程技术-计算机：跨学科应用

CiteScore

2.90

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Algebra is a common language for many scientific domains. In developing this language mathematicians prove theorems and design methods which demonstrate the applicability of algebra. Using this language scientists in many fields find algebra indispensable to create methods, techniques and tools to solve their specific problems. Applicable Algebra in Engineering, Communication and Computing will publish mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Its scope includes, but is not limited to, vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology. Purely theoretical papers will not primarily be sought, but papers dealing with problems in such domains as commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, which are of interest for applications in the above mentioned fields are relevant for this journal. On the practical side, technology and know-how transfer papers from engineering which either stimulate or illustrate research in applicable algebra are within the scope of the journal.