Summary: We discuss orthogonal Chebyshev-Frolov lattices, their generating matrices and their use in Frolov cubature formula. We give a detailed account on coordinate-permuted systems that lead to fast computation and enumeration of such lattices. In particular, we explain the recurrences identified in (K. Suzuki and T. Yoshiki, Hiroshima Math. J., 49(1):139-159, 2019) via a plain constructive approach exhibiting a new hierarchical basis of polynomials. Dual Chebyshev-Frolov lattices and their generating matrices are also studied. Lattices enumeration in axis-parallel boxes is discussed.
{"title":"On generation and enumeration of orthogonal Chebyshev-Frolov lattices","authors":"Moulay Abdellah Chkifa","doi":"10.32917/h2021046","DOIUrl":"https://doi.org/10.32917/h2021046","url":null,"abstract":"Summary: We discuss orthogonal Chebyshev-Frolov lattices, their generating matrices and their use in Frolov cubature formula. We give a detailed account on coordinate-permuted systems that lead to fast computation and enumeration of such lattices. In particular, we explain the recurrences identified in (K. Suzuki and T. Yoshiki, Hiroshima Math. J., 49(1):139-159, 2019) via a plain constructive approach exhibiting a new hierarchical basis of polynomials. Dual Chebyshev-Frolov lattices and their generating matrices are also studied. Lattices enumeration in axis-parallel boxes is discussed.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43067029","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}
Hiroki Watanabe, Masashi Hyodo, Takatoshi Sugiyama, T. Seo
{"title":"Test for equality of standardized generalized variance with different dimensions under high-dimensional settings","authors":"Hiroki Watanabe, Masashi Hyodo, Takatoshi Sugiyama, T. Seo","doi":"10.32917/h2021025","DOIUrl":"https://doi.org/10.32917/h2021025","url":null,"abstract":"","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.2,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49565432","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 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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":null,"pages":null},"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}
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