{"title":"Lipschitz characterization for exponentially weighted Bergman spaces of the unit ball","authors":"Hong-Rae Cho, Soohyun Park","doi":"10.3792/PJAA.95.70","DOIUrl":"https://doi.org/10.3792/PJAA.95.70","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88308857","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}
Consider a surface $S$ immersed in the Lorentz-Minkowski 3-space $boldsymbol R^3_1$. A complete light-like line in $boldsymbol R^3_1$ is called an entire null line on the surface $S$ in $boldsymbol R^3_1$ if it lies on $S$ and consists of only null points with respect to the induced metric. In this paper, we show the existence of embedded space-like maximal graphs containing entire null lines. If such a graph is defined on a convex domain in $boldsymbol R^2$, then it must be a light-like plane. Our example is critical in the sense that it is defined on a certain non-convex domain.
{"title":"Space-like maximal surfaces containing entire null lines in Lorentz-Minkowski 3-space","authors":"S. Akamine, M. Umehara, Kotaro Yamada","doi":"10.3792/pjaa.95.97","DOIUrl":"https://doi.org/10.3792/pjaa.95.97","url":null,"abstract":"Consider a surface $S$ immersed in the Lorentz-Minkowski 3-space $boldsymbol R^3_1$. A complete light-like line in $boldsymbol R^3_1$ is called an entire null line on the surface $S$ in $boldsymbol R^3_1$ if it lies on $S$ and consists of only null points with respect to the induced metric. In this paper, we show the existence of embedded space-like maximal graphs containing entire null lines. If such a graph is defined on a convex domain in $boldsymbol R^2$, then it must be a light-like plane. Our example is critical in the sense that it is defined on a certain non-convex domain.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72604558","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 discuss the flatness property of some fiber type contractions of complex smooth projective varieties of arbitrary dimensions. We relate the flatness of some morphisms having one-dimensional fibers with their conic bundles structures, also in the general case in which some mild singularities of the varieties are admitted.
{"title":"A note on flatness of some fiber type contractions","authors":"E. Romano","doi":"10.3792/pjaa.95.103","DOIUrl":"https://doi.org/10.3792/pjaa.95.103","url":null,"abstract":"We discuss the flatness property of some fiber type contractions of complex smooth projective varieties of arbitrary dimensions. We relate the flatness of some morphisms having one-dimensional fibers with their conic bundles structures, also in the general case in which some mild singularities of the varieties are admitted.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78288017","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 famous identity of Gauss gives a closed form expression for the values of the digamma function $psi(x)$ at rational arguments $x$ in terms of elementary functions. Linear combinations of such values are intimately connected with a conjecture of Erdős which asserts non vanishing of an infinite series associated to a certain class of periodic arithmetic functions. In this note we give a different proof for the identity of Gauss using an orthogonality like relation satisfied by these functions. As a by product we are able to give a new interpretation for $n$th Catalan number in terms of these functions.
{"title":"Erdősian functions and an identity of Gauss","authors":"T. Chatterjee, Suraj Singh Khurana","doi":"10.3792/PJAA.95.58","DOIUrl":"https://doi.org/10.3792/PJAA.95.58","url":null,"abstract":"A famous identity of Gauss gives a closed form expression for the values of the digamma function $psi(x)$ at rational arguments $x$ in terms of elementary functions. Linear combinations of such values are intimately connected with a conjecture of Erdős which asserts non vanishing of an infinite series associated to a certain class of periodic arithmetic functions. In this note we give a different proof for the identity of Gauss using an orthogonality like relation satisfied by these functions. As a by product we are able to give a new interpretation for $n$th Catalan number in terms of these functions.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","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":"77855582","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":"Absolute multiple sine functions","authors":"N. Kurokawa, Hidekazu Tanaka","doi":"10.3792/PJAA.95.41","DOIUrl":"https://doi.org/10.3792/PJAA.95.41","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81761642","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":"Termination of extremal rays of divisorial type for the power of étale endomorphisms","authors":"Yoshio Fujimoto","doi":"10.3792/PJAA.95.47","DOIUrl":"https://doi.org/10.3792/PJAA.95.47","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89234992","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 introduce an interpolation between Euler integral and Laplace integral: Euler-Laplace integral. We show, when parameters $d$ of the integrand is non-resonant, the $mathcal{D}$-module corresponding to Euler-Laplace integral is naturally isomorphic to GKZ hypergeometric system $M_A(d)$ where $A$ is a generalization of Cayley configuration. As a topological counterpart of this isomorphism, we establish an isomorphism between certain rapid decay homology group and holomorphic solutions of $M_A(d)$. Based on these foundations, we give a combinatorial method of constructing a basis of rapid decay cycles by means of regular triangulations. The remarkable feature of this construction is that this basis of cycles is explicitly related to $Gamma$-series solutions. In the last part, we concentrate on Euler integral representations. We determine the homology intersection matrix with respect to our basis of cycles when the regular triangulation is unimodular. As an application, we obtain closed formulae of the quadratic relations of Aomoto-Gelfand hypergeometric functions in terms of bipartite graphs.
{"title":"Euler and Laplace integral representations of GKZ hypergeometric functions II","authors":"Saiei-Jaeyeong Matsubara-Heo","doi":"10.3792/pjaa.96.015","DOIUrl":"https://doi.org/10.3792/pjaa.96.015","url":null,"abstract":"We introduce an interpolation between Euler integral and Laplace integral: Euler-Laplace integral. We show, when parameters $d$ of the integrand is non-resonant, the $mathcal{D}$-module corresponding to Euler-Laplace integral is naturally isomorphic to GKZ hypergeometric system $M_A(d)$ where $A$ is a generalization of Cayley configuration. As a topological counterpart of this isomorphism, we establish an isomorphism between certain rapid decay homology group and holomorphic solutions of $M_A(d)$. Based on these foundations, we give a combinatorial method of constructing a basis of rapid decay cycles by means of regular triangulations. The remarkable feature of this construction is that this basis of cycles is explicitly related to $Gamma$-series solutions. In the last part, we concentrate on Euler integral representations. We determine the homology intersection matrix with respect to our basis of cycles when the regular triangulation is unimodular. As an application, we obtain closed formulae of the quadratic relations of Aomoto-Gelfand hypergeometric functions in terms of bipartite graphs.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75898076","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":"Hitting times to spheres of Brownian motions with drifts starting from the origin","authors":"Yuji Hamana","doi":"10.3792/PJAA.95.37","DOIUrl":"https://doi.org/10.3792/PJAA.95.37","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87037853","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 study the geometry of two-torsion points of elliptic curves in order to distinguish the embedded topology of reducible plane curves consisting of a smooth cubic and its tangent lines. As a result, we obtain a new family of Zariski N-ples consisting of such curves.
为了区分由光滑三次面及其切线组成的可约平面曲线的内嵌拓扑，本文研究了椭圆曲线的双扭转点几何。结果，我们得到了一个由这样的曲线组成的新的Zariski n -ple族。
{"title":"Zariski tuples for a smooth cubic and its tangent lines","authors":"S. Bannai, H. Tokunaga","doi":"10.3792/pjaa.96.004","DOIUrl":"https://doi.org/10.3792/pjaa.96.004","url":null,"abstract":"In this paper, we study the geometry of two-torsion points of elliptic curves in order to distinguish the embedded topology of reducible plane curves consisting of a smooth cubic and its tangent lines. As a result, we obtain a new family of Zariski N-ples consisting of such curves.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81309672","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":"Examples of isometric immersions of $mathbf{R}^{2}$ into $mathbf{R}^{4}$ with vanishing normal curvature","authors":"H. Mori","doi":"10.3792/PJAA.95.21","DOIUrl":"https://doi.org/10.3792/PJAA.95.21","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83480904","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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