We raise a problem on coextensions and (cid:12)nd partial answers.
我们提出了一个关于上延和(cid:12)的问题和部分答案。
{"title":"A problem on coextensions","authors":"H. Ōshima","doi":"10.5036/MJIU.51.27","DOIUrl":"https://doi.org/10.5036/MJIU.51.27","url":null,"abstract":"We raise a problem on coextensions and (cid:12)nd partial answers.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"190 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83558218","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}
In semi-euclidean spaces, conformal mappings are consists of similarities, inversions, and Bateman mapping [14]. In this note, we shall discuss problems whether there exist caloric morphisms with Bateman space mapping for radial semi-euclidean metrics. It is based on the similar arguments as were used in [8], [9], and [10].
{"title":"Existence and non-existence of caloric morphisms with Bateman space-mapping for radial metrics","authors":"Katsunori Shimomura","doi":"10.5036/MJIU.51.1","DOIUrl":"https://doi.org/10.5036/MJIU.51.1","url":null,"abstract":"In semi-euclidean spaces, conformal mappings are consists of similarities, inversions, and Bateman mapping [14]. In this note, we shall discuss problems whether there exist caloric morphisms with Bateman space mapping for radial semi-euclidean metrics. It is based on the similar arguments as were used in [8], [9], and [10].","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87485473","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}
Let p be a prime number of the form p = 2 ℓ +1 with some odd prime number ℓ . For such a prime number p , it is shown that the relative class number h (cid:0) p of the p th cyclotomic (cid:12)eld Q ( (cid:16) p ) is odd when 2 remains prime in Q ( (cid:16) ℓ ) + by Estes [3], Stevenhagen [11] and Mets(cid:127)ankyl(cid:127)a [8] using a Bernoulli number associated to Q ( (cid:16) p ). In this note, we give an alternative proof of the assertion using a cyclotomic unit of Q ( (cid:16) p ) + .
{"title":"Note on class number parity of an abelian field of prime conductor, III","authors":"H. Ichimura","doi":"10.5036/mjiu.51.39","DOIUrl":"https://doi.org/10.5036/mjiu.51.39","url":null,"abstract":"Let p be a prime number of the form p = 2 ℓ +1 with some odd prime number ℓ . For such a prime number p , it is shown that the relative class number h (cid:0) p of the p th cyclotomic (cid:12)eld Q ( (cid:16) p ) is odd when 2 remains prime in Q ( (cid:16) ℓ ) + by Estes [3], Stevenhagen [11] and Mets(cid:127)ankyl(cid:127)a [8] using a Bernoulli number associated to Q ( (cid:16) p ). In this note, we give an alternative proof of the assertion using a cyclotomic unit of Q ( (cid:16) p ) + .","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"88 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74465555","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}
Let 1 < p < 1 and let Ω be a bounded domain of R N ( N (cid:21) 1). In this paper, we consider a class of second order quasilinear elliptic operators A in Ω including the p -Laplace operator ∆ p . First we establish various type of Kato’s inequalities for A when A u is a Radon measure. Then we prove the inverse maximum principle and describe the strong maximum principle. For this purpose it is crucial to introduce a notion of admissible class for the operator A and use it effectively. y
{"title":"Kato's inequalities for admissible functions to quasilinear elliptic operators A","authors":"Xiaojing Liu, T. Horiuchi","doi":"10.5036/MJIU.51.49","DOIUrl":"https://doi.org/10.5036/MJIU.51.49","url":null,"abstract":"Let 1 < p < 1 and let Ω be a bounded domain of R N ( N (cid:21) 1). In this paper, we consider a class of second order quasilinear elliptic operators A in Ω including the p -Laplace operator ∆ p . First we establish various type of Kato’s inequalities for A when A u is a Radon measure. Then we prove the inverse maximum principle and describe the strong maximum principle. For this purpose it is crucial to introduce a notion of admissible class for the operator A and use it effectively. y","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"79 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89838602","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}
Let R be an integral domain with quotient field K , let h (resp., g, f) be the non-zero R -submodules of K (resp., the non-zero fractional ideals of R , the finitely generated non-zero fractional ideals of R ), and let { x, y } be a subset of the set { f, g, h } of symbols. For a semistar operation (cid:63) on R , if ( EE 1 ) (cid:63) = ( EE 2 ) (cid:63) implies E 1 (cid:63) = E 2 (cid:63) for every E ∈ x and every E 1 , E 2 ∈ y, then (cid:63) is called xy-cancellative. Let (cid:63) be a gg-cancellative semistar operation on R which is an extension of a star operation on R . In this paper, we show that (cid:63) need not be gh-cancellative.
{"title":"A gg not gh-cancellative semistar operation which is an extension of a star operation","authors":"Ryuki Matsuda","doi":"10.5036/MJIU.50.1","DOIUrl":"https://doi.org/10.5036/MJIU.50.1","url":null,"abstract":"Let R be an integral domain with quotient field K , let h (resp., g, f) be the non-zero R -submodules of K (resp., the non-zero fractional ideals of R , the finitely generated non-zero fractional ideals of R ), and let { x, y } be a subset of the set { f, g, h } of symbols. For a semistar operation (cid:63) on R , if ( EE 1 ) (cid:63) = ( EE 2 ) (cid:63) implies E 1 (cid:63) = E 2 (cid:63) for every E ∈ x and every E 1 , E 2 ∈ y, then (cid:63) is called xy-cancellative. Let (cid:63) be a gg-cancellative semistar operation on R which is an extension of a star operation on R . In this paper, we show that (cid:63) need not be gh-cancellative.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":" 103","pages":"1-4"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91415462","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}
In our paper [2], we have classified simple regular polyhedral BP-complexes, which are polyhedral complexes satisfying certain natural conditions on their vertex structures. As an addendum of this classification, we prove that 2-skeletons of higher dimensional regular polytopes are simple regular polyhedral complexes, but not polyhedral BP-complexes. The proof is done by a detailed investigation of their vertex structures.
{"title":"Structure of 2-skeletons of higher dimensional regular polytopes","authors":"Fumiko Ohtsuka","doi":"10.5036/MJIU.50.27","DOIUrl":"https://doi.org/10.5036/MJIU.50.27","url":null,"abstract":"In our paper [2], we have classified simple regular polyhedral BP-complexes, which are polyhedral complexes satisfying certain natural conditions on their vertex structures. As an addendum of this classification, we prove that 2-skeletons of higher dimensional regular polytopes are simple regular polyhedral complexes, but not polyhedral BP-complexes. The proof is done by a detailed investigation of their vertex structures.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"76 1","pages":"27-33"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86060571","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}
Let Ω be a smooth bounded domain of R . In this paper, we study the equivalences among three capacities and Hausdorff measure. First we present the equivalence between p-capacity Cp(K) and p-Laplace-capacitiy C∆p(K) relative to Ω for any compact set K ⊂ Ω. Secondly we establish the equivalence between p-Laplace capacity Cp(K, ∂Ω) relative to ∂Ω and Hausdorff measure HN−1(K) for any compact set K ⊂ ∂Ω.
{"title":"The equivalences among p-capacity, p-Laplace-capacities and Hausdorff measure","authors":"Xiaojing Liu, T. Horiuchi","doi":"10.5036/MJIU.50.5","DOIUrl":"https://doi.org/10.5036/MJIU.50.5","url":null,"abstract":"Let Ω be a smooth bounded domain of R . In this paper, we study the equivalences among three capacities and Hausdorff measure. First we present the equivalence between p-capacity Cp(K) and p-Laplace-capacitiy C∆p(K) relative to Ω for any compact set K ⊂ Ω. Secondly we establish the equivalence between p-Laplace capacity Cp(K, ∂Ω) relative to ∂Ω and Hausdorff measure HN−1(K) for any compact set K ⊂ ∂Ω.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"15 1","pages":"5-13"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82377623","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}
In [8] Matsuda has investigated stability of a semistar operation. In this paper we extend the notion of stability of a semistar operation to the presemistar operation case and we shall study stability properties of presemistar operations.
{"title":"Note on the stability of a presemistar operation","authors":"A. Okabe","doi":"10.5036/mjiu.50.35","DOIUrl":"https://doi.org/10.5036/mjiu.50.35","url":null,"abstract":"In [8] Matsuda has investigated stability of a semistar operation. In this paper we extend the notion of stability of a semistar operation to the presemistar operation case and we shall study stability properties of presemistar operations.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"35 1","pages":"35-52"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73050402","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}
Pub Date : 2017-01-01DOI: 10.1007/978-3-319-65874-2_15
Ryuki Matsuda
{"title":"A gg-Cancellative Semistar Operation on an Integral Domain Need Not Be gh-Cancellative","authors":"Ryuki Matsuda","doi":"10.1007/978-3-319-65874-2_15","DOIUrl":"https://doi.org/10.1007/978-3-319-65874-2_15","url":null,"abstract":"","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"2 1","pages":"299-305"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82056581","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}
In [O3], we introduced the notion of presemistar operation as a general-ization of the notion of semistar operation and gave some characterizations of presemistar operations. In this paper we shall give some new characterizations of presemistar operations. We also introduced the notion of an s.e.a.b. presemistar operation in [O3]. One of the main results of this paper is to show that there exists an example of a proper presemistar operation which is e.a.b. but is not s.e.a.b. . We also give two methods of construction which will provide many new examples of presemistar operations.
在[03]中，我们引入了预星运算的概念作为半星运算概念的一般化，并给出了预星运算的一些表征。本文给出了星前运算的一些新的性质。我们还在[03]中引入了s.a.b.前置星操作的概念。本文的主要结果之一是证明了存在一种合适的前导星运算，它是e - a - b，但不是e - a - b。我们还给出了两种构造方法，这将为预星运算提供许多新的例子。
{"title":"Some results on presemistar operations","authors":"A. Okabe","doi":"10.5036/MJIU.49.11","DOIUrl":"https://doi.org/10.5036/MJIU.49.11","url":null,"abstract":"In [O3], we introduced the notion of presemistar operation as a general-ization of the notion of semistar operation and gave some characterizations of presemistar operations. In this paper we shall give some new characterizations of presemistar operations. We also introduced the notion of an s.e.a.b. presemistar operation in [O3]. One of the main results of this paper is to show that there exists an example of a proper presemistar operation which is e.a.b. but is not s.e.a.b. . We also give two methods of construction which will provide many new examples of presemistar operations.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"119 1","pages":"11-22"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77089591","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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