Let α be an anti-integral element of degree t over an integral domain R and φα(X) the minimal polynomial of α over the quotient field of R. Let β be a linear fractional transform of α, that is, β=cα-d/aα-b(a, b, c, d∈R, ad-bc∈R*)where R* is the group of units of R. First we describe I[β], the denominator ideal of β, in terms of I[α] and φα(a, b) where φα(X, Y)=Xtφα(Y/X). Next we introduce the ideal ˜{I}[α] concerning integral property of α and α-1. Then we describe ˜{I}[β] by using I[α], φα(a, b) and φα(c, d).
{"title":"A note on denominator ideals of linear fractional transforms of an anti-integral element over an integral domain","authors":"Junro Sato, Kiyoshi Baba, KEN-ICHI Yoshida","doi":"10.5036/MJIU.34.29","DOIUrl":"https://doi.org/10.5036/MJIU.34.29","url":null,"abstract":"Let α be an anti-integral element of degree t over an integral domain R and φα(X) the minimal polynomial of α over the quotient field of R. Let β be a linear fractional transform of α, that is, β=cα-d/aα-b(a, b, c, d∈R, ad-bc∈R*)where R* is the group of units of R. First we describe I[β], the denominator ideal of β, in terms of I[α] and φα(a, b) where φα(X, Y)=Xtφα(Y/X). Next we introduce the ideal ˜{I}[α] concerning integral property of α and α-1. Then we describe ˜{I}[β] by using I[α], φα(a, b) and φα(c, d).","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"7 1","pages":"29-31"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75913457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Using some inequalities for real numbers and integrals we point out here some new inequalities for the moments of guessing mapping which generalize and improve the recent results of Arikan [2], Dragomir and van der Hoek [3]-[4] and Dragomir [10].
本文利用实数和积分的一些不等式，提出了猜测映射矩的一些新的不等式，推广和改进了Arikan[2]、Dragomir and van der Hoek[3]-[4]和Dragomir[10]的最新结果。
{"title":"On Some Inequalities for the Moments of Guessing Mapping","authors":"S. Dragomir, J. Pecaric, J. Hoek","doi":"10.5036/MJIU.34.1","DOIUrl":"https://doi.org/10.5036/MJIU.34.1","url":null,"abstract":"Using some inequalities for real numbers and integrals we point out here some new inequalities for the moments of guessing mapping which generalize and improve the recent results of Arikan [2], Dragomir and van der Hoek [3]-[4] and Dragomir [10].","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"7 1","pages":"1-16"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84089215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We give a partial answer to the problem: Given a connected finite CW Hopf space X, determine sets P of prime numbers such that every multiplication on the P-localization XP of X is a P-localization of a multiplication on X. A complete answer is given when X is of rank at most 2 or a simple Lie group.
{"title":"Multiplications on a localized Hopf space","authors":"H. Ōshima","doi":"10.5036/MJIU.33.17","DOIUrl":"https://doi.org/10.5036/MJIU.33.17","url":null,"abstract":"We give a partial answer to the problem: Given a connected finite CW Hopf space X, determine sets P of prime numbers such that every multiplication on the P-localization XP of X is a P-localization of a multiplication on X. A complete answer is given when X is of rank at most 2 or a simple Lie group.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"87 1","pages":"17-21"},"PeriodicalIF":0.0,"publicationDate":"2001-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84203864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On transformations which preserve poly-temperatures of degree m","authors":"Katsunori Shimomura","doi":"10.5036/MJIU.33.23","DOIUrl":"https://doi.org/10.5036/MJIU.33.23","url":null,"abstract":"","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"31 1","pages":"23-34"},"PeriodicalIF":0.0,"publicationDate":"2001-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82876392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Prime and semiprime acts over monoids with zero","authors":"J. Ahsan, Zhongkui Liu","doi":"10.5036/MJIU.33.9","DOIUrl":"https://doi.org/10.5036/MJIU.33.9","url":null,"abstract":"","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"19 1","pages":"9-15"},"PeriodicalIF":0.0,"publicationDate":"2001-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76551767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Some inequalities of Jensen's type and their applications for the Csiszar f-divergence are given.
给出了一些Jensen型不等式及其在Csiszar f-散度中的应用。
{"title":"Some Inequalities for (m, M)-Convex Mappings and Applications for the Csiszár Φ-Divergence in Information Theory","authors":"S. Dragomir","doi":"10.5036/MJIU.33.35","DOIUrl":"https://doi.org/10.5036/MJIU.33.35","url":null,"abstract":"Some inequalities of Jensen's type and their applications for the Csiszar f-divergence are given.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"27 1","pages":"35-50"},"PeriodicalIF":0.0,"publicationDate":"2001-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74061839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Note on Larsen-McCarthy's Multiplicative Theory of Ideals","authors":"Ryuki Matsuda","doi":"10.5036/MJIU.32.1","DOIUrl":"https://doi.org/10.5036/MJIU.32.1","url":null,"abstract":"","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"5 1","pages":"1-9"},"PeriodicalIF":0.0,"publicationDate":"2000-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81655904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Some Results Deduced From the Equality R[1/α]=R[1/(α-a)]","authors":"M. Kanemitsu, KEN-ICHI Yoshida","doi":"10.5036/MJIU.32.11","DOIUrl":"https://doi.org/10.5036/MJIU.32.11","url":null,"abstract":"","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"16 1","pages":"11-17"},"PeriodicalIF":0.0,"publicationDate":"2000-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82582901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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