Pub Date : 2018-10-01DOI: 10.14492/HOKMJ/1537948833
Hisayasu Kurata, M. Yamasaki
For a hyperbolic infinite network, it is well-known that Green potentials with finite energy are Dirichlet potentials. Conversely, if a Dirichlet potential has non-positive Laplacian, then it is a Green potential with finite energy. In this paper, we study whether a Dirichlet potential can be expressed as a difference of two Green potentials with finite energy. Comparisons of the Dirichlet sum of a function and that of its Laplacian play important roles in our study. As a by-product, we obtain a Riesz decomposition of a function whose Laplacian is a Dirichlet function.
{"title":"Discrete Green Potentials with Finite Energy","authors":"Hisayasu Kurata, M. Yamasaki","doi":"10.14492/HOKMJ/1537948833","DOIUrl":"https://doi.org/10.14492/HOKMJ/1537948833","url":null,"abstract":"For a hyperbolic infinite network, it is well-known that Green potentials with finite energy are Dirichlet potentials. Conversely, if a Dirichlet potential has non-positive Laplacian, then it is a Green potential with finite energy. In this paper, we study whether a Dirichlet potential can be expressed as a difference of two Green potentials with finite energy. Comparisons of the Dirichlet sum of a function and that of its Laplacian play important roles in our study. As a by-product, we obtain a Riesz decomposition of a function whose Laplacian is a Dirichlet function.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46604075","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 : 2018-10-01DOI: 10.14492/HOKMJ/1537948835
S. Ohno, T. Sakai, H. Urakawa
On a smooth foliated map from a complete, possibly non-compact, foliated Riemannian manifold into another foliated Riemannian manifold of which transversal sectional curvature is non-positive, we will show that, if it is transversally biharmonic and has the finite energy and finite bienergy, then it is transversally harmonic.
{"title":"Rigidity of transversally biharmonic maps between foliated Riemannian manifolds","authors":"S. Ohno, T. Sakai, H. Urakawa","doi":"10.14492/HOKMJ/1537948835","DOIUrl":"https://doi.org/10.14492/HOKMJ/1537948835","url":null,"abstract":"On a smooth foliated map from a complete, possibly non-compact, foliated Riemannian manifold into another foliated Riemannian manifold of which transversal sectional curvature is non-positive, we will show that, if it is transversally biharmonic and has the finite energy and finite bienergy, then it is transversally harmonic.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.14492/HOKMJ/1537948835","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43242116","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 : 2018-10-01DOI: 10.14492/HOKMJ/1537948830
L. Birbrair, J. Costa, E. S. Filho
{"title":"Topological bi-$mathcal{K}$-equivalence of pairs of map germs","authors":"L. Birbrair, J. Costa, E. S. Filho","doi":"10.14492/HOKMJ/1537948830","DOIUrl":"https://doi.org/10.14492/HOKMJ/1537948830","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.14492/HOKMJ/1537948830","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46778524","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 : 2018-10-01DOI: 10.14492/hokmj/1537948829
Takaaki Ito
A tropical polynomial is called R-polynomial if it can be realized as the minimum finishing time of a project network. R-polynomials satisfy the term extendability condition, and correspond to simple graphs. We give a characterization of R-polynomials in terms of simple graphs.
{"title":"A characterization for tropical polynomials being the minimum finishing time of project networks","authors":"Takaaki Ito","doi":"10.14492/hokmj/1537948829","DOIUrl":"https://doi.org/10.14492/hokmj/1537948829","url":null,"abstract":"A tropical polynomial is called R-polynomial if it can be realized as the minimum finishing time of a project network. R-polynomials satisfy the term extendability condition, and correspond to simple graphs. We give a characterization of R-polynomials in terms of simple graphs.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46610906","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 : 2018-10-01DOI: 10.14492/hokmj/1537948825
M. Duman, Ümmügülsüm Ögüt, R. Keskin
{"title":"Generalized Lucas Numbers of the form $wx^{2}$ and $wV_{m}x^{2}$","authors":"M. Duman, Ümmügülsüm Ögüt, R. Keskin","doi":"10.14492/hokmj/1537948825","DOIUrl":"https://doi.org/10.14492/hokmj/1537948825","url":null,"abstract":"","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.14492/hokmj/1537948825","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45558646","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 : 2018-10-01DOI: 10.14492/hokmj/1537948824
T. Noda
In this paper, we provide a new invariant for partial differential equations (PDEs) under contact transformations by using nilpotent graded Lie algebras. By virtue of this invariant, various geometric behavior of PDEs can be understood. As a typical class, we clarify geometric behavior of second-order PDEs in terms of our
{"title":"On a certain invariant of differential equations associated with nilpotent graded Lie algebras","authors":"T. Noda","doi":"10.14492/hokmj/1537948824","DOIUrl":"https://doi.org/10.14492/hokmj/1537948824","url":null,"abstract":"In this paper, we provide a new invariant for partial differential equations (PDEs) under contact transformations by using nilpotent graded Lie algebras. By virtue of this invariant, various geometric behavior of PDEs can be understood. As a typical class, we clarify geometric behavior of second-order PDEs in terms of our","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.14492/hokmj/1537948824","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45863683","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 : 2018-10-01DOI: 10.14492/HOKMJ/1537948834
Jing Mao, N. Xiang
Abstract. For an (n − 1)-dimensional compact orientable smooth metric measure space ` M, g, e−f dvg ́ embedded in an n-dimensional compact orientable Riemannian manifold N , we successfully give a lower bound for the first nonzero eigenvalue of the drifting Laplacian on M , provided the Ricci curvature of N is bounded from below by a positive constant and the weighted function f on M satisfies two constraints.
{"title":"Estimates for the first eigenvalue of the drifting Laplacian on embedded hypersurfaces","authors":"Jing Mao, N. Xiang","doi":"10.14492/HOKMJ/1537948834","DOIUrl":"https://doi.org/10.14492/HOKMJ/1537948834","url":null,"abstract":"Abstract. For an (n − 1)-dimensional compact orientable smooth metric measure space ` M, g, e−f dvg ́ embedded in an n-dimensional compact orientable Riemannian manifold N , we successfully give a lower bound for the first nonzero eigenvalue of the drifting Laplacian on M , provided the Ricci curvature of N is bounded from below by a positive constant and the weighted function f on M satisfies two constraints.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.14492/HOKMJ/1537948834","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47975515","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 : 2018-10-01DOI: 10.14492/hokmj/1537948826
Jiangtao Shi, R. Hou, Cui Zhang
We obtain a complete classification of finite groups in which all noncyclic proper subgroups are nonnormal, and we apply this classification to investigate some structures of finite groups.
{"title":"The influence of nonnormal noncyclic subgroups on the structure of finite groups","authors":"Jiangtao Shi, R. Hou, Cui Zhang","doi":"10.14492/hokmj/1537948826","DOIUrl":"https://doi.org/10.14492/hokmj/1537948826","url":null,"abstract":"We obtain a complete classification of finite groups in which all noncyclic proper subgroups are nonnormal, and we apply this classification to investigate some structures of finite groups.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.14492/hokmj/1537948826","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41944496","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 : 2018-08-25DOI: 10.14492/hokmj/1602036025
R. Laterveer
Kapustka and Rampazzo have exhibited pairs of Calabi-Yau threefolds $X$ and $Y$ that are L-equivalent and derived equivalent, without being birational. We complete the picture by showing that $X$ and $Y$ have isomorphic Chow motives.
{"title":"On the motive of Kapustka–Rampazzo's Calabi-Yau threefolds","authors":"R. Laterveer","doi":"10.14492/hokmj/1602036025","DOIUrl":"https://doi.org/10.14492/hokmj/1602036025","url":null,"abstract":"Kapustka and Rampazzo have exhibited pairs of Calabi-Yau threefolds $X$ and $Y$ that are L-equivalent and derived equivalent, without being birational. We complete the picture by showing that $X$ and $Y$ have isomorphic Chow motives.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43336554","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 consider an abstract pair-interaction model in quantum field theory with a coupling constant $lambdain {mathbb R}$ and analyze the Hamiltonian $H(lambda)$ of the model. In the massive case, there exist constants $lambda_{rm c} lambda_{rm c}$ is different from that for $lambdain (lambda_{{rm c},0}, lambda_{rm c})$. As for the case $lambda
{"title":"Spectral analysis of an abstract pair interaction model","authors":"Keisuke Asahara, Daiju Funakawa","doi":"10.14492/hokmj/2018-876","DOIUrl":"https://doi.org/10.14492/hokmj/2018-876","url":null,"abstract":"We consider an abstract pair-interaction model in quantum field theory with a coupling constant $lambdain {mathbb R}$ and analyze the Hamiltonian $H(lambda)$ of the model. In the massive case, there exist constants $lambda_{rm c} lambda_{rm c}$ is different from that for $lambdain (lambda_{{rm c},0}, lambda_{rm c})$. As for the case $lambda<lambda_{{rm c},0}$, we show that $H(lambda)$ is unbounded from above and below. In the massless case, $lambda_{rm c}$ coincides with $lambda_{{rm c},0}$.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2018-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46388646","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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