{"title":"多面体上的 SL(n) 避变函数值估值","authors":"Zhongwen Tang , Jin Li , Gangsong Leng","doi":"10.1016/j.aam.2024.102693","DOIUrl":null,"url":null,"abstract":"<div><p>We present a complete classification of <span><math><mi>SL</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> contravariant, <span><math><mi>C</mi><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>∖</mo><mo>{</mo><mi>o</mi><mo>}</mo><mo>)</mo></math></span>-valued valuations on polytopes, without any additional assumptions. It extends the previous results of the second author Li (2020) <span>[10]</span> which have a good connection with the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> and Orlicz Brunn-Minkowski theory. Additionally, our results deduce a complete classification of <span><math><mi>SL</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> contravariant symmetric-tensor-valued valuations on polytopes.</p></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"SL(n) contravariant function-valued valuations on polytopes\",\"authors\":\"Zhongwen Tang , Jin Li , Gangsong Leng\",\"doi\":\"10.1016/j.aam.2024.102693\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We present a complete classification of <span><math><mi>SL</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> contravariant, <span><math><mi>C</mi><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>∖</mo><mo>{</mo><mi>o</mi><mo>}</mo><mo>)</mo></math></span>-valued valuations on polytopes, without any additional assumptions. It extends the previous results of the second author Li (2020) <span>[10]</span> which have a good connection with the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> and Orlicz Brunn-Minkowski theory. Additionally, our results deduce a complete classification of <span><math><mi>SL</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> contravariant symmetric-tensor-valued valuations on polytopes.</p></div>\",\"PeriodicalId\":50877,\"journal\":{\"name\":\"Advances in Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-04-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0196885824000241\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0196885824000241","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
SL(n) contravariant function-valued valuations on polytopes
We present a complete classification of contravariant, -valued valuations on polytopes, without any additional assumptions. It extends the previous results of the second author Li (2020) [10] which have a good connection with the and Orlicz Brunn-Minkowski theory. Additionally, our results deduce a complete classification of contravariant symmetric-tensor-valued valuations on polytopes.
期刊介绍：
Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas.
Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.
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