We investigate the foliation defined by the kernel of an exact presymplectic form dα of rank 2 n on a (2 n + r )-dimensional closed manifold M . For r = 2, we prove that the foliation has at least two leaves which are homeomorphic to a 2-dimensional torus, if M admits a locally free T 2 -action which preserves dα and satisfies that the function α ( Z 2 ) is constant, where Z 1 , Z 2 are the infinitesimal generators of the T 2 -action. We also give its generalization for r ≥ 1.
{"title":"Compact leaves of the foliation defined by the kernel of a T2-invariant presymplectic form","authors":"A. Hagiwara","doi":"10.5036/mjiu.54.1","DOIUrl":"https://doi.org/10.5036/mjiu.54.1","url":null,"abstract":"We investigate the foliation defined by the kernel of an exact presymplectic form dα of rank 2 n on a (2 n + r )-dimensional closed manifold M . For r = 2, we prove that the foliation has at least two leaves which are homeomorphic to a 2-dimensional torus, if M admits a locally free T 2 -action which preserves dα and satisfies that the function α ( Z 2 ) is constant, where Z 1 , Z 2 are the infinitesimal generators of the T 2 -action. We also give its generalization for r ≥ 1.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81948842","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":"Biographical Sketch of Professor Humio Ichimura","authors":"","doi":"10.5036/mjiu.54.i","DOIUrl":"https://doi.org/10.5036/mjiu.54.i","url":null,"abstract":"","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"69 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74992917","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":"Biographical Sketch of Professor Toshio Horiuchi","authors":"","doi":"10.5036/mjiu.53.i","DOIUrl":"https://doi.org/10.5036/mjiu.53.i","url":null,"abstract":"","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89316987","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 this paper we prove the boundedness of the generalized fractional integral operator I ρ on generalized Campanato spaces with variable growth condition, which is a generalization and improvement of previous results, and then, we establish the boundedness of I ρ on their bi-preduals. We also prove the boundedness of I ρ on their preduals by the duality.
{"title":"Generalized fractional integral operators on Campanato spaces and their bi-preduals","authors":"S. Yamaguchi, E. Nakai","doi":"10.5036/mjiu.53.17","DOIUrl":"https://doi.org/10.5036/mjiu.53.17","url":null,"abstract":"In this paper we prove the boundedness of the generalized fractional integral operator I ρ on generalized Campanato spaces with variable growth condition, which is a generalization and improvement of previous results, and then, we establish the boundedness of I ρ on their bi-preduals. We also prove the boundedness of I ρ on their preduals by the duality.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84217849","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}
For a fixed integer n ≥ 1, let p = 2 nℓ + 1 be a prime number with an odd prime number ℓ and let F = F p,ℓ be the real abelian field of conductor p and degree ℓ . When n ≤ 21, we show that a prime number r does not divide the class number h F of F whenever r is a primitive root modulo ℓ with the help of computer. This generalizes a result of Jakubec and Mets¨ankyl¨a for the case n = 1.
对于固定整数n≥1，设p = 2n, n + 1为具有奇数素数的素数，设F = F p, r为导体p的实阿贝尔场，阶为r。当n≤21时，利用计算机证明了素数r不能除类数h F (F)，当r为本原根模r时。这推广了Jakubec和Mets在n = 1情况下的结果。
{"title":"Indivisibility of the class number of a real abelian field of prime conductor","authors":"S. Fujima, H. Ichimura","doi":"10.5036/MJIU.53.1","DOIUrl":"https://doi.org/10.5036/MJIU.53.1","url":null,"abstract":"For a fixed integer n ≥ 1, let p = 2 nℓ + 1 be a prime number with an odd prime number ℓ and let F = F p,ℓ be the real abelian field of conductor p and degree ℓ . When n ≤ 21, we show that a prime number r does not divide the class number h F of F whenever r is a primitive root modulo ℓ with the help of computer. This generalizes a result of Jakubec and Mets¨ankyl¨a for the case n = 1.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85340747","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 this paper, we prove that any non-constant real rational function appears as a time transformation of a caloric morphism, mapping which preserves caloric functions, between semi-eucledean spaces.
{"title":"Rational function and time transformation of caloric morphism on semi-euclidean spaces","authors":"Katsunori Shimomura","doi":"10.5036/mjiu.53.35","DOIUrl":"https://doi.org/10.5036/mjiu.53.35","url":null,"abstract":"In this paper, we prove that any non-constant real rational function appears as a time transformation of a caloric morphism, mapping which preserves caloric functions, between semi-eucledean spaces.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77478209","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 consider a p-Laplace equation ∆pV + h(V ) = 0, with an arbitrary C-nonlinearity h, in a bounded domain and supplemented with the Neumann boundary condition. We prove a necessary condition for zeros of h = h(V ) to be touched by non-constant solutions to this problem.
{"title":"Criterion toward understanding non-constant solutions to p-Laplace Neumann boundary value problem","authors":"Kanako Suzuki","doi":"10.5036/mjiu.52.1","DOIUrl":"https://doi.org/10.5036/mjiu.52.1","url":null,"abstract":"We consider a p-Laplace equation ∆pV + h(V ) = 0, with an arbitrary C-nonlinearity h, in a bounded domain and supplemented with the Neumann boundary condition. We prove a necessary condition for zeros of h = h(V ) to be touched by non-constant solutions to this problem.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"20 1","pages":"1-13"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89538295","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 bounded domain of R N ( N (cid:21) 1) whose boundary @ Ω is a C 2 compact manifolds. In the present paper we shall study a variational problem relating the weighted Hardy inequalities established in [4]. As weights we adopt powers of the distance function (cid:14) ( x ) to the boundary @ Ω. study a
{"title":"Weighted Hardy's inequalities and the variational problem with compact perturbations","authors":"Hiroshi Ando, T. Horiuchi","doi":"10.5036/mjiu.52.15","DOIUrl":"https://doi.org/10.5036/mjiu.52.15","url":null,"abstract":"Let Ω be a bounded domain of R N ( N (cid:21) 1) whose boundary @ Ω is a C 2 compact manifolds. In the present paper we shall study a variational problem relating the weighted Hardy inequalities established in [4]. As weights we adopt powers of the distance function (cid:14) ( x ) to the boundary @ Ω. study a","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74064502","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}
A subsemigroup of a torsion-free abelian group is called grading monoid. This is a note on star operations in ideal theory of grading monoids. Explicitly, we study stability, ascents-descents, and Kronecker function rings of semistar operations on grading monoids.
{"title":"Note on star operations on monoids","authors":"Ryuki Matsuda","doi":"10.5036/MJIU.51.13","DOIUrl":"https://doi.org/10.5036/MJIU.51.13","url":null,"abstract":"A subsemigroup of a torsion-free abelian group is called grading monoid. This is a note on star operations in ideal theory of grading monoids. Explicitly, we study stability, ascents-descents, and Kronecker function rings of semistar operations on grading monoids.","PeriodicalId":18362,"journal":{"name":"Mathematical Journal of Ibaraki University","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74476319","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：