In this work, we examine the Lyubeznik numbers of squarefree monomial ideals that are linked. Also we study these numbers for almost complete intersection ideals.
{"title":"Lyubeznik numbers of almost complete intersection and linked ideals","authors":"Parvaneh Nadi, F. Rahmati","doi":"10.32917/h2021027","DOIUrl":"https://doi.org/10.32917/h2021027","url":null,"abstract":"In this work, we examine the Lyubeznik numbers of squarefree monomial ideals that are linked. Also we study these numbers for almost complete intersection ideals.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42292549","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}
A bstract . Suppose that a smooth map ð f ; g ; h Þ : R n ! R 3 , where n b 3, has a stable singularity at the origin. We characterize the stability of the function f : R n ! R and the map ð f ; g Þ : R n ! R 2 at the origin in terms of the discriminant set of ð f ; g ; h Þ .
{"title":"Local theory of singularities of three functions and the product maps","authors":"Kazuto Takao","doi":"10.32917/h2021020","DOIUrl":"https://doi.org/10.32917/h2021020","url":null,"abstract":"A bstract . Suppose that a smooth map ð f ; g ; h Þ : R n ! R 3 , where n b 3, has a stable singularity at the origin. We characterize the stability of the function f : R n ! R and the map ð f ; g Þ : R n ! R 2 at the origin in terms of the discriminant set of ð f ; g ; h Þ .","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43976942","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}
{"title":"${mathbf G}_a$-actions on the affine line over a non-reduced ring","authors":"Motoki Kuroda, S. Kuroda","doi":"10.32917/h2021011","DOIUrl":"https://doi.org/10.32917/h2021011","url":null,"abstract":"","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46630844","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}
A bridge position of a knot is said to be perturbed if there exists a cancelling pair of bridge disks. Motivated by the examples of knots admitting unperturbed strongly irreducible non-minimal bridge positions due to Jang-Kobayashi-Ozawa-Takao, we derive examples of unperturbed weakly reducible non-minimal bridge positions. Also, a bridge version of Gordon's Conjecture is proposed: the connected sum of unperturbed bridge positions is unperturbed.
{"title":"Unperturbed weakly reducible non-minimal bridge positions","authors":"Jung Hoon Lee","doi":"10.32917/h2022006","DOIUrl":"https://doi.org/10.32917/h2022006","url":null,"abstract":"A bridge position of a knot is said to be perturbed if there exists a cancelling pair of bridge disks. Motivated by the examples of knots admitting unperturbed strongly irreducible non-minimal bridge positions due to Jang-Kobayashi-Ozawa-Takao, we derive examples of unperturbed weakly reducible non-minimal bridge positions. Also, a bridge version of Gordon's Conjecture is proposed: the connected sum of unperturbed bridge positions is unperturbed.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2022-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43079401","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}
It is known that a connected and simply-connected Lie group admits only one left-invariant Riemannian metric up to scaling and isometry if and only if it is isomorphic to the Euclidean space, the Lie group of the real hyperbolic space, or the direct product of the three dimensional Heisenberg group and the Euclidean space of dimension n − 3. In this paper, we give a classification of left-invariant pseudo-Riemannian metrics of an arbitrary signature for the third Lie groups with n ≥ 4 up to scaling and automorphisms. This completes the classifications of left-invariant pseudo-Riemannian metrics for the above three Lie groups up to scaling and automorphisms.
{"title":"A classification of left-invariant pseudo-Riemannian metrics on some nilpotent Lie groups*","authors":"Yuji Kondo","doi":"10.32917/h2021054","DOIUrl":"https://doi.org/10.32917/h2021054","url":null,"abstract":"It is known that a connected and simply-connected Lie group admits only one left-invariant Riemannian metric up to scaling and isometry if and only if it is isomorphic to the Euclidean space, the Lie group of the real hyperbolic space, or the direct product of the three dimensional Heisenberg group and the Euclidean space of dimension n − 3. In this paper, we give a classification of left-invariant pseudo-Riemannian metrics of an arbitrary signature for the third Lie groups with n ≥ 4 up to scaling and automorphisms. This completes the classifications of left-invariant pseudo-Riemannian metrics for the above three Lie groups up to scaling and automorphisms.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44385849","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}
In this paper, we first consider relations between signatures of pseudoKähler metrics on a flag manifold and complex structures on a nilpotent Lie algebra corresponding to the flag manifold. On the nilpotent Lie algebra, we also consider complex structures which do not correspond to invariant complex structures on the flag manifold.
{"title":"Some relations between complex structures on compact nilmanifolds and flag manifolds","authors":"Takumi Yamada","doi":"10.32917/h2020027","DOIUrl":"https://doi.org/10.32917/h2020027","url":null,"abstract":"In this paper, we first consider relations between signatures of pseudoKähler metrics on a flag manifold and complex structures on a nilpotent Lie algebra corresponding to the flag manifold. On the nilpotent Lie algebra, we also consider complex structures which do not correspond to invariant complex structures on the flag manifold.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41992206","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}
Y. Hishikawa, Masaharu Nishio, Katsunori Shimomura, M. Yamada
We consider function spaces which consist of two parabolic Bloch spaces, and present reproducing formulas. As an application, we introduce Bloch type spaces which consist of solutions of a partial di¤erential equation ðLðaÞÞu 1⁄4 0, and investigate several properties.
{"title":"Function spaces induced by two parabolic Bloch spaces","authors":"Y. Hishikawa, Masaharu Nishio, Katsunori Shimomura, M. Yamada","doi":"10.32917/h2020031","DOIUrl":"https://doi.org/10.32917/h2020031","url":null,"abstract":"We consider function spaces which consist of two parabolic Bloch spaces, and present reproducing formulas. As an application, we introduce Bloch type spaces which consist of solutions of a partial di¤erential equation ðLðaÞÞu 1⁄4 0, and investigate several properties.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43375515","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}
A bstract . In this paper, we study two eigenvalue problems of the weighted Laplacian and get the Reilly-type bounds and isoperimetric type bounds for the first nonzero n eigenvalues on hypersurfaces of the Euclidean space. Besides, we give lower bounds for the first eigenvalue of weighted p -Laplacian on submanifolds with locally bounded weighted mean curvature. Meanwhile, several applications of these estimates have also been given.
{"title":"Estimates for eigenvalues of weighted Laplacian and weighted $p$-Laplacian","authors":"Feng Du, Jing Mao, Qiaoling Wang, C. Xia","doi":"10.32917/h2020086","DOIUrl":"https://doi.org/10.32917/h2020086","url":null,"abstract":"A bstract . In this paper, we study two eigenvalue problems of the weighted Laplacian and get the Reilly-type bounds and isoperimetric type bounds for the first nonzero n eigenvalues on hypersurfaces of the Euclidean space. Besides, we give lower bounds for the first eigenvalue of weighted p -Laplacian on submanifolds with locally bounded weighted mean curvature. Meanwhile, several applications of these estimates have also been given.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46068206","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}
Let $D$ be a division ring with center $F$, and $G$ a subnormal or quasinormal subgroup of $D^*$. We show that if $G$ is locally solvable, then $G$ is contained in $F$.
{"title":"Locally solvable subnormal and quasinormal subgroups in division rings","authors":"Le QUİ DANH, Huynh Viet Khanh","doi":"10.32917/h2020034","DOIUrl":"https://doi.org/10.32917/h2020034","url":null,"abstract":"Let $D$ be a division ring with center $F$, and $G$ a subnormal or quasinormal subgroup of $D^*$. We show that if $G$ is locally solvable, then $G$ is contained in $F$.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":"30 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82339805","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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