(m,n)-半环与系统的广义容错代数

IF 1.2 Q2 MATHEMATICS, APPLIED

Journal of Applied Mathematics Pub Date : 2013-01-01 DOI:10.1155/2013/482391

Syed Eqbal Alam, Shrisha Rao, B. Davvaz

{"title":"(m,n)-半环与系统的广义容错代数","authors":"Syed Eqbal Alam, Shrisha Rao, B. Davvaz","doi":"10.1155/2013/482391","DOIUrl":null,"url":null,"abstract":"We propose a new class of mathematical structures called(m,n)-semirings(which generalize the usual semirings) and describe their basic properties. We define partial ordering and generalize the concepts of congruence, homomorphism, and so forth, for(m,n)-semirings. Following earlier work by Rao (2008), we consider systems made up of several components whose failures may cause them to fail and represent the set of such systems algebraically as an(m,n)-semiring. Based on the characteristics of these components, we present a formalism to compare the fault-tolerance behavior of two systems using our framework of a partially ordered(m,n)-semiring.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2013/482391","citationCount":"7","resultStr":"{\"title\":\"(m,n)-Semirings and a Generalized Fault-Tolerance Algebra of Systems\",\"authors\":\"Syed Eqbal Alam, Shrisha Rao, B. Davvaz\",\"doi\":\"10.1155/2013/482391\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose a new class of mathematical structures called(m,n)-semirings(which generalize the usual semirings) and describe their basic properties. We define partial ordering and generalize the concepts of congruence, homomorphism, and so forth, for(m,n)-semirings. Following earlier work by Rao (2008), we consider systems made up of several components whose failures may cause them to fail and represent the set of such systems algebraically as an(m,n)-semiring. Based on the characteristics of these components, we present a formalism to compare the fault-tolerance behavior of two systems using our framework of a partially ordered(m,n)-semiring.\",\"PeriodicalId\":49251,\"journal\":{\"name\":\"Journal of Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2013-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1155/2013/482391\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2013/482391\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2013/482391","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 7

摘要

我们提出了一类新的数学结构，称为(m,n)-半环(它推广了通常的半环)，并描述了它们的基本性质。对于(m,n)-半环，我们定义了偏序，并推广了同余、同态等概念。根据Rao(2008)的早期工作，我们考虑由几个组件组成的系统，这些组件的故障可能导致它们失效，并将这些系统的集合代数地表示为(m,n)-半环。基于这些组件的特征，我们提出了一种比较两个系统容错行为的形式化方法，使用我们的部分有序(m,n)-半环框架。

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

(m,n)-Semirings and a Generalized Fault-Tolerance Algebra of Systems

We propose a new class of mathematical structures called(m,n)-semirings(which generalize the usual semirings) and describe their basic properties. We define partial ordering and generalize the concepts of congruence, homomorphism, and so forth, for(m,n)-semirings. Following earlier work by Rao (2008), we consider systems made up of several components whose failures may cause them to fail and represent the set of such systems algebraically as an(m,n)-semiring. Based on the characteristics of these components, we present a formalism to compare the fault-tolerance behavior of two systems using our framework of a partially ordered(m,n)-semiring.

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

Journal of Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

3.2 months

期刊介绍： Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics.