Pub Date : 2019-06-01DOI: 10.14492/HOKMJ/1562810510
Jiangtao Shi
In this paper we prove that a finite group in which all non-nilpotent maximal subgroups are normal must have a Sylow tower, which improves Theorem 1.3 of [Finite groups with non-nilpotent maximal subgroups, Monatsh Math. 171 (2013) 425–431.].
{"title":"A finite group in which all non-nilpotent maximal subgroups are normal has a Sylow tower","authors":"Jiangtao Shi","doi":"10.14492/HOKMJ/1562810510","DOIUrl":"https://doi.org/10.14492/HOKMJ/1562810510","url":null,"abstract":"In this paper we prove that a finite group in which all non-nilpotent maximal subgroups are normal must have a Sylow tower, which improves Theorem 1.3 of [Finite groups with non-nilpotent maximal subgroups, Monatsh Math. 171 (2013) 425–431.].","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46482247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-01DOI: 10.14492/HOKMJ/1562810507
R. Abu-Dawwas, M. Bataineh, Adeela Da'keek
Let G be a group with identity e, R be a G-graded ring and M be a G-graded R-module. In this article, we introduce the concept of graded weak comultiplication modules. A graded R-module M is said to be graded weak comultiplication if for every graded prime R-submodule N of M , N = (0 :M I) for some graded ideal I of R. We study graded weak comultiplication modules and give several results.
设G为恒等式为e的群，R为G阶环，M为G阶R模。在本文中，我们引入了梯度弱乘法模的概念。如果对于M的每一个分级素数r子模N，对于r的某些分级理想I, N = (0: m1)，则一个分级r模M是分级弱乘法。
{"title":"Graded weak comultiplication modules","authors":"R. Abu-Dawwas, M. Bataineh, Adeela Da'keek","doi":"10.14492/HOKMJ/1562810507","DOIUrl":"https://doi.org/10.14492/HOKMJ/1562810507","url":null,"abstract":"Let G be a group with identity e, R be a G-graded ring and M be a G-graded R-module. In this article, we introduce the concept of graded weak comultiplication modules. A graded R-module M is said to be graded weak comultiplication if for every graded prime R-submodule N of M , N = (0 :M I) for some graded ideal I of R. We study graded weak comultiplication modules and give several results.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42738004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-01DOI: 10.14492/HOKMJ/1562810517
H. Srivastava, B. Khan, N. Khan, Q. Z. Ahmad
{"title":"Coefficient inequalities for $q$-starlike functions associated with the Janowski functions","authors":"H. Srivastava, B. Khan, N. Khan, Q. Z. Ahmad","doi":"10.14492/HOKMJ/1562810517","DOIUrl":"https://doi.org/10.14492/HOKMJ/1562810517","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.14492/HOKMJ/1562810517","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48072582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We explore the relationship in metric spaces between different properties related to the Besicovitch covering theorem, and also consider weak versions of doubling, in connection to the non-uniqueness of centers and radii in arbitrary metric spaces.
{"title":"Besicovitch and doubling type properties in metric spaces","authors":"J. M. Aldaz","doi":"10.14492/hokmj/2021-528","DOIUrl":"https://doi.org/10.14492/hokmj/2021-528","url":null,"abstract":"We explore the relationship in metric spaces between different properties related to the Besicovitch covering theorem, and also consider weak versions of doubling, in connection to the non-uniqueness of centers and radii in arbitrary metric spaces.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42855998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-02-01DOI: 10.14492/HOKMJ/1550480647
Takashi Hirotsu
A Châtelet surface over a field is a typical geometrically rational surface. Its Chow group of zero-cycles has been studied as an important birational invariant by many researchers since the 1970s. Recently, S. Saito and K. Sato obtained a duality between the Chow and Brauer groups from the Brauer–Manin pairing. For a Châtelet surface over a local field, we combine their result with the known calculation of the Chow group to determine the structure and generators of the Brauer group of a regular proper flat model of the surface over the integer ring of the base field.
{"title":"Brauer groups of Châtelet surfaces over local fields","authors":"Takashi Hirotsu","doi":"10.14492/HOKMJ/1550480647","DOIUrl":"https://doi.org/10.14492/HOKMJ/1550480647","url":null,"abstract":"A Châtelet surface over a field is a typical geometrically rational surface. Its Chow group of zero-cycles has been studied as an important birational invariant by many researchers since the 1970s. Recently, S. Saito and K. Sato obtained a duality between the Chow and Brauer groups from the Brauer–Manin pairing. For a Châtelet surface over a local field, we combine their result with the known calculation of the Chow group to determine the structure and generators of the Brauer group of a regular proper flat model of the surface over the integer ring of the base field.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.14492/HOKMJ/1550480647","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48780245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-02-01DOI: 10.14492/hokmj/1550480649
S. Rezaei
Let a denote an ideal in a commutative Noetherian local ring (R,m) and M a non-zero finitely generated R-module of dimension d. Let d := dim(M/aM). In this paper we calculate the annihilator of the top formal local cohomology module Fda(M). In fact, we prove that AnnR(F d a(M)) = AnnR(M/UR(a,M)), where UR(a,M) := ∪{N : N ⩽ M and dim(N/aN) < dim(M/aM)}. We give a description of UR(a,M) and we will show that AnnR(F d a(M)) = AnnR(M/ ∩pj∈AsshRM∩V(a) Nj), where 0 = ∩n j=1 Nj denotes a reduced primary decomposition of the zero submodule 0 in M and Nj is a pj-primary submodule of M , for all j = 1, . . . , n. Also, we determine the radical of the annihilator of Fda(M). We will prove that √ AnnR(Fa(M)) = AnnR(M/GR(a,M)), where GR(a,M) denotes the largest submodule of M such that AsshR(M) ∩ V(a) ⊆ AssR(M/GR(a,M)) and AsshR(M) denotes the set {p ∈ AssM : dimR/p = dimM}.
设a表示交换诺瑟局部环(R,m)中的理想，m表示维数为d的非零有限生成R模。设d:= dim(m /aM)。本文计算了上形式局部上同模Fda(M)的湮灭子。事实上，我们证明了AnnR(F d a(M)) = AnnR(M/UR(a,M))，其中UR(a,M):=∪{N: N≤M and dim(N/aN) < dim(M/aM)}。我们给出了UR(a,M)的一个描述，并且我们将证明AnnR(F d a(M)) = AnnR(M/∩pj∈AsshRM∩V(a) Nj)，其中0 =∩n j=1 Nj表示M中的零子模块0的一个约简初分解，并且Nj是M的一个pj-主子模块，对于所有j=1，…， n。同时，我们确定了Fda(M)湮灭子的原子量。我们将证明√AnnR(Fa(M)) = AnnR(M/GR(a,M))，其中GR(a,M)表示M的最大子模块，使得AssR(M)∩V(a)≤AssR(M/GR(a,M))，且AssR(M)表示集合{p∈AssM: dimR/p = dimM}。
{"title":"On the annihilators of formal local cohomology modules","authors":"S. Rezaei","doi":"10.14492/hokmj/1550480649","DOIUrl":"https://doi.org/10.14492/hokmj/1550480649","url":null,"abstract":"Let a denote an ideal in a commutative Noetherian local ring (R,m) and M a non-zero finitely generated R-module of dimension d. Let d := dim(M/aM). In this paper we calculate the annihilator of the top formal local cohomology module Fda(M). In fact, we prove that AnnR(F d a(M)) = AnnR(M/UR(a,M)), where UR(a,M) := ∪{N : N ⩽ M and dim(N/aN) < dim(M/aM)}. We give a description of UR(a,M) and we will show that AnnR(F d a(M)) = AnnR(M/ ∩pj∈AsshRM∩V(a) Nj), where 0 = ∩n j=1 Nj denotes a reduced primary decomposition of the zero submodule 0 in M and Nj is a pj-primary submodule of M , for all j = 1, . . . , n. Also, we determine the radical of the annihilator of Fda(M). We will prove that √ AnnR(Fa(M)) = AnnR(M/GR(a,M)), where GR(a,M) denotes the largest submodule of M such that AsshR(M) ∩ V(a) ⊆ AssR(M/GR(a,M)) and AsshR(M) denotes the set {p ∈ AssM : dimR/p = dimM}.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.14492/hokmj/1550480649","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42853403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-02-01DOI: 10.14492/hokmj/1550480646
E. Nakai, Tsuyoshi Yoneda
We give new viewpoints of Campanato spaces with variable growth condition for applications to the Navier-Stokes equation. Namely, we formulate a blowup criteria along maximum points of the 3D-Navier-Stokes flow in terms of stationary Euler flows and show that the properties of Campanato spaces with variable growth condition are very useful for this formulation, since variable growth condition can control the continuity and integrability of functions on the neighborhood at each point. Our criterion is different from the Beale-Kato-Majda type and Constantin-Fefferman type criterion. If geometric behavior of the velocity vector field near the maximum point has a kind of stationary Euler flow configuration up to a possible blowup time, then the solution can be extended to be the strong solution beyond the possible blowup time. As another application we also mention the Cauchy problem for the NavierStokes equation.
{"title":"Applications of Campanato spaces with variable growth condition to the Navier-Stokes equation","authors":"E. Nakai, Tsuyoshi Yoneda","doi":"10.14492/hokmj/1550480646","DOIUrl":"https://doi.org/10.14492/hokmj/1550480646","url":null,"abstract":"We give new viewpoints of Campanato spaces with variable growth condition for applications to the Navier-Stokes equation. Namely, we formulate a blowup criteria along maximum points of the 3D-Navier-Stokes flow in terms of stationary Euler flows and show that the properties of Campanato spaces with variable growth condition are very useful for this formulation, since variable growth condition can control the continuity and integrability of functions on the neighborhood at each point. Our criterion is different from the Beale-Kato-Majda type and Constantin-Fefferman type criterion. If geometric behavior of the velocity vector field near the maximum point has a kind of stationary Euler flow configuration up to a possible blowup time, then the solution can be extended to be the strong solution beyond the possible blowup time. As another application we also mention the Cauchy problem for the NavierStokes equation.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.14492/hokmj/1550480646","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44221430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We analyze the asymptotic behavior of solutions to wave equations with strong damping terms. If the initial data belong to suitable weighted $L^1$ spaces, lower bounds for the difference between the solutions and the leading terms in the Fourier space are obtained, which implies the optimality of expanding methods and some estimates proposed in this paper.
{"title":"Optimal leading term of solutions to wave equations with strong damping terms","authors":"Hironori Michihisa","doi":"10.14492/hokmj/2018-920","DOIUrl":"https://doi.org/10.14492/hokmj/2018-920","url":null,"abstract":"We analyze the asymptotic behavior of solutions to wave equations with strong damping terms. If the initial data belong to suitable weighted $L^1$ spaces, lower bounds for the difference between the solutions and the leading terms in the Fourier space are obtained, which implies the optimality of expanding methods and some estimates proposed in this paper.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46347856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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