矩的数学理论方法

IF 0.3 Q3 SOCIAL SCIENCES, INTERDISCIPLINARY
Bulatnikova Irina Vyacheslavovna
{"title":"矩的数学理论方法","authors":"Bulatnikova Irina Vyacheslavovna","doi":"10.46925//rdluz.40.05","DOIUrl":null,"url":null,"abstract":"Infinite matrices play an important role in many aspects of analysis, algebra, differential equations, andthetheory of mechanical vibrations.Jacobi matrices are interestingbecause they are the simplest representatives of symmetric operators in infinite-dimensional space. they are used in interpolation theory, quantum physics, moment problem.In this paper, basedon the elements of Jacobi matrix, itwill be determinedthe type of the operator that occurs when processing the results of measurements of random variables. The first type of operators arematrices,for which the moment problem has a unique solution, and Jacobi matrix generates a specific moment problem. The second type of operators arematrices, for which the moment problem has many solutions, and Jacobi matrix is said to generate an indeterminate moment problem.","PeriodicalId":42302,"journal":{"name":"Revista de la Universidad del Zulia","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Method of Mathematical Theory of Moments\",\"authors\":\"Bulatnikova Irina Vyacheslavovna\",\"doi\":\"10.46925//rdluz.40.05\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Infinite matrices play an important role in many aspects of analysis, algebra, differential equations, andthetheory of mechanical vibrations.Jacobi matrices are interestingbecause they are the simplest representatives of symmetric operators in infinite-dimensional space. they are used in interpolation theory, quantum physics, moment problem.In this paper, basedon the elements of Jacobi matrix, itwill be determinedthe type of the operator that occurs when processing the results of measurements of random variables. The first type of operators arematrices,for which the moment problem has a unique solution, and Jacobi matrix generates a specific moment problem. The second type of operators arematrices, for which the moment problem has many solutions, and Jacobi matrix is said to generate an indeterminate moment problem.\",\"PeriodicalId\":42302,\"journal\":{\"name\":\"Revista de la Universidad del Zulia\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-05-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista de la Universidad del Zulia\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46925//rdluz.40.05\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"SOCIAL SCIENCES, INTERDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista de la Universidad del Zulia","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46925//rdluz.40.05","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"SOCIAL SCIENCES, INTERDISCIPLINARY","Score":null,"Total":0}
引用次数: 0

摘要

无限矩阵在分析、代数、微分方程和机械振动理论的许多方面起着重要的作用。雅可比矩阵很有趣,因为它们是无限维空间中对称算子的最简单表示。它们被用于插值理论,量子物理,力矩问题。本文从雅可比矩阵的元素出发,确定了处理随机变量测量结果时发生的算子的类型。第一类算子是矩阵,其矩问题有唯一解,雅可比矩阵生成一个特定的矩问题。第二类算子是矩阵,其矩问题有很多解,雅可比矩阵产生的是一个不定矩问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Method of Mathematical Theory of Moments
Infinite matrices play an important role in many aspects of analysis, algebra, differential equations, andthetheory of mechanical vibrations.Jacobi matrices are interestingbecause they are the simplest representatives of symmetric operators in infinite-dimensional space. they are used in interpolation theory, quantum physics, moment problem.In this paper, basedon the elements of Jacobi matrix, itwill be determinedthe type of the operator that occurs when processing the results of measurements of random variables. The first type of operators arematrices,for which the moment problem has a unique solution, and Jacobi matrix generates a specific moment problem. The second type of operators arematrices, for which the moment problem has many solutions, and Jacobi matrix is said to generate an indeterminate moment problem.
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
Revista de la Universidad del Zulia
Revista de la Universidad del Zulia SOCIAL SCIENCES, INTERDISCIPLINARY-
自引率
33.30%
发文量
74
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信