形状及其代数的对角分解

IF 1.7 3区工程技术 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Ai Edam-Artificial Intelligence for Engineering Design Analysis and Manufacturing Pub Date : 2022-02-09 DOI:10.1017/S0890060421000238

Djordje Kristic

{"title":"形状及其代数的对角分解","authors":"Djordje Kristic","doi":"10.1017/S0890060421000238","DOIUrl":null,"url":null,"abstract":"Abstract The formal approach to shapes and their algebras, as it appears in shape grammar theory, has been reviewed. It starts with geometric elements and their partial algebras, continues to shapes, their algebras, and boundaries, as well as algebras that calculate with shapes and their boundaries. There is a number of new concepts introduced along the way. These include diagonal decompositions and their algebras which simplify calculations with shapes, b-paired diagonal decompositions which extend calculations with shapes and their boundaries from diagonal shapes only to all shapes, and m-order boundaries which extend the concept of shape boundaries and allow for calculations with multiple representations of shapes. It also shows that algebras of shapes are infinite direct sums of diagonal algebras.","PeriodicalId":50951,"journal":{"name":"Ai Edam-Artificial Intelligence for Engineering Design Analysis and Manufacturing","volume":" ","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2022-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Diagonal decompositions of shapes and their algebras\",\"authors\":\"Djordje Kristic\",\"doi\":\"10.1017/S0890060421000238\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The formal approach to shapes and their algebras, as it appears in shape grammar theory, has been reviewed. It starts with geometric elements and their partial algebras, continues to shapes, their algebras, and boundaries, as well as algebras that calculate with shapes and their boundaries. There is a number of new concepts introduced along the way. These include diagonal decompositions and their algebras which simplify calculations with shapes, b-paired diagonal decompositions which extend calculations with shapes and their boundaries from diagonal shapes only to all shapes, and m-order boundaries which extend the concept of shape boundaries and allow for calculations with multiple representations of shapes. It also shows that algebras of shapes are infinite direct sums of diagonal algebras.\",\"PeriodicalId\":50951,\"journal\":{\"name\":\"Ai Edam-Artificial Intelligence for Engineering Design Analysis and Manufacturing\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2022-02-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ai Edam-Artificial Intelligence for Engineering Design Analysis and Manufacturing\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1017/S0890060421000238\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ai Edam-Artificial Intelligence for Engineering Design Analysis and Manufacturing","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1017/S0890060421000238","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}

引用次数: 1

摘要

形状及其代数的形式化方法，因为它出现在形状语法理论，已经审查。它从几何元素和它们的部分代数开始，继续到形状、它们的代数和边界，以及用形状和它们的边界计算的代数。在此过程中引入了许多新概念。这些包括对角分解及其代数，它简化了形状的计算，b对对角分解将形状及其边界的计算从对角形状扩展到所有形状，m阶边界扩展了形状边界的概念并允许使用多种形状表示进行计算。还证明了形状代数是对角代数的无穷直和。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Diagonal decompositions of shapes and their algebras

Abstract The formal approach to shapes and their algebras, as it appears in shape grammar theory, has been reviewed. It starts with geometric elements and their partial algebras, continues to shapes, their algebras, and boundaries, as well as algebras that calculate with shapes and their boundaries. There is a number of new concepts introduced along the way. These include diagonal decompositions and their algebras which simplify calculations with shapes, b-paired diagonal decompositions which extend calculations with shapes and their boundaries from diagonal shapes only to all shapes, and m-order boundaries which extend the concept of shape boundaries and allow for calculations with multiple representations of shapes. It also shows that algebras of shapes are infinite direct sums of diagonal algebras.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Ai Edam-Artificial Intelligence for Engineering Design Analysis and Manufacturing 工程技术-工程：制造

CiteScore

4.40

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original articles about significant AI theory and applications based on the most up-to-date research in all branches and phases of engineering. Suitable topics include: analysis and evaluation; selection; configuration and design; manufacturing and assembly; and concurrent engineering. Specifically, the journal is interested in the use of AI in planning, design, analysis, simulation, qualitative reasoning, spatial reasoning and graphics, manufacturing, assembly, process planning, scheduling, numerical analysis, optimization, distributed systems, multi-agent applications, cooperation, cognitive modeling, learning and creativity. AI EDAM is also interested in original, major applications of state-of-the-art knowledge-based techniques to important engineering problems.