In this paper, we study power similarity of operators. In particular, we show that if $T in mathit{PS}(H)$ (defined below) for some hyponormal operator $H$, then $T$ is subscalar. From this result, we obtain that such an operator with rich spectrum has a nontrivial invariant subspace. Moreover, we consider invariant and hyperinvariant subspaces for $T in mathit{PS}(H)$.
本文研究了算子的幂相似度。特别地，我们证明了如果$T In mathit{PS}(H)$(定义见下)对于一些次正规算子$H$，则$T$是子标量。由此得到了这样一个富谱算子具有非平凡不变子空间。此外，我们考虑$T in mathit{PS}(H)$的不变子空间和超不变子空间。
{"title":"ON OPERATORS WHICH ARE POWER SIMILAR TO HYPONORMAL OPERATORS","authors":"Sungeun Jung, E. Ko, Mee-Jung Lee","doi":"10.18910/57659","DOIUrl":"https://doi.org/10.18910/57659","url":null,"abstract":"In this paper, we study power similarity of operators. In particular, we show that if $T in mathit{PS}(H)$ (defined below) for some hyponormal operator $H$, then $T$ is subscalar. From this result, we obtain that such an operator with rich spectrum has a nontrivial invariant subspace. Moreover, we consider invariant and hyperinvariant subspaces for $T in mathit{PS}(H)$.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":"1 1","pages":"833-847"},"PeriodicalIF":0.4,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67869624","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 extend the notion of intrinsic linking to directed graphs. We give methods of constructing intrinsically linked directed graphs, as well as complicated directed graphs that are not intrinsically linked. We prove that the double directed version of a graph G is intrinsically linked if and only if G is intrinsically linked. One Corollary is that J6, the complete symmetric directed graph on 6 vertices (with 30 directed edges), is intrinsically linked. We further extend this to show that it is possible to find a subgraph of J6 by deleting 6 edges that is still intrinsically linked, but that no subgraph of J6 obtained by deleting 7 edges is intrinsically linked. We also show that J6 with an arbitrary edge deleted is intrinsically linked, but if the wrong two edges are chosen, J6 with two edges deleted can be embedded linklessly.
{"title":"INTRINSIC LINKING IN DIRECTED GRAPHS","authors":"Joel Foisy, H. Howards, N. Rich","doi":"10.18910/57670","DOIUrl":"https://doi.org/10.18910/57670","url":null,"abstract":"We extend the notion of intrinsic linking to directed graphs. We give methods of constructing intrinsically linked directed graphs, as well as complicated directed graphs that are not intrinsically linked. We prove that the double directed version of a graph G is intrinsically linked if and only if G is intrinsically linked. One Corollary is that J6, the complete symmetric directed graph on 6 vertices (with 30 directed edges), is intrinsically linked. We further extend this to show that it is possible to find a subgraph of J6 by deleting 6 edges that is still intrinsically linked, but that no subgraph of J6 obtained by deleting 7 edges is intrinsically linked. We also show that J6 with an arbitrary edge deleted is intrinsically linked, but if the wrong two edges are chosen, J6 with two edges deleted can be embedded linklessly.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":"52 1","pages":"817-831"},"PeriodicalIF":0.4,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67871169","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}
Antonio G. García, M. A. Hernández-Medina, A. Portal
The study of the hypercyclicity of an operator is an old problem in mathematics; it goes back to a paper of Birkhoff in 1929 proving the hypercyclicity of the translation operators in the space of all entire functions with the topology of uniform convergence on compact subsets. This article studies the hypercyclicity of translation operators in some general reproducing kernel Hilbert spaces of entire functions. These spaces are obtained by duality in a complex separable Hilbert space H by means of an analytic H-valued kernel. A link with the theory of de Branges spaces is also established. An illustrative example taken from the Hamburger moment problem theory is included.
{"title":"Hypercyclicity of translation operators in a reproducing kernel Hilbert space of entire functions induced by an analytic Hilbert-space-valued kernel","authors":"Antonio G. García, M. A. Hernández-Medina, A. Portal","doi":"10.18910/57669","DOIUrl":"https://doi.org/10.18910/57669","url":null,"abstract":"The study of the hypercyclicity of an operator is an old problem in mathematics; it goes back to a paper of Birkhoff in 1929 proving the hypercyclicity of the translation operators in the space of all entire functions with the topology of uniform convergence on compact subsets. This article studies the hypercyclicity of translation operators in some general reproducing kernel Hilbert spaces of entire functions. These spaces are obtained by duality in a complex separable Hilbert space H by means of an analytic H-valued kernel. A link with the theory of de Branges spaces is also established. An illustrative example taken from the Hamburger moment problem theory is included.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":"52 1","pages":"581-599"},"PeriodicalIF":0.4,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67871086","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 the percolation on the k-out graph Gout(n, k). The critical probability of it is 1 k+ √ k2−k . Similarly to the random graph G(n, p), in a scaling window 1 k+ √ k2−k ( 1 + O(n−1/3) ) , the sequence of sizes of large components rescaled by n−2/3 converges to the excursion lengths of a Brownian motion with some drift. Also, the size of the largest component is O(log n) in the subcritical phase, and O(n) in the supercritical phase. The proof is based on the analysis of the exploration process.
{"title":"THE CONVERGENCE OF THE EXPLORATION PROCESS FOR CRITICAL PERCOLATION ON THE k-OUT GRAPH","authors":"Y. Ota","doi":"10.18910/57663","DOIUrl":"https://doi.org/10.18910/57663","url":null,"abstract":"We consider the percolation on the k-out graph Gout(n, k). The critical probability of it is 1 k+ √ k2−k . Similarly to the random graph G(n, p), in a scaling window 1 k+ √ k2−k ( 1 + O(n−1/3) ) , the sequence of sizes of large components rescaled by n−2/3 converges to the excursion lengths of a Brownian motion with some drift. Also, the size of the largest component is O(log n) in the subcritical phase, and O(n) in the supercritical phase. The proof is based on the analysis of the exploration process.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":"52 1","pages":"677-719"},"PeriodicalIF":0.4,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67869933","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 the present paper, we discuss the relationship between the Galois extension corresponding to the kernel of the pro-l outer Galois representation associated to a hyperbolic curve over a number eld and l-moderate points of the hyperbolic curve. In particular, we prove that, for a certain hyperbolic curve, the Galois extension under consideration is generated by the coordinates of the l-moderate points of the hyperbolic curve. This may be regarded as an analogue of the fact that the Galois extension corresponding to the kernel of the l-adic Galois representation associated to an abelian variety is generated by the coordinates of the torsion points of the abelian variety of l-power order. Moreover, we discuss an application of the argument of the present paper to the study of the Fermat equation.
{"title":"On the kernels of the pro-l outer Galois representations associated to hyperbolic curves over number fields","authors":"Yuichiro Hoshi","doi":"10.18910/57635","DOIUrl":"https://doi.org/10.18910/57635","url":null,"abstract":"In the present paper, we discuss the relationship between the Galois extension corresponding to the kernel of the pro-l outer Galois representation associated to a hyperbolic curve over a number eld and l-moderate points of the hyperbolic curve. In particular, we prove that, for a certain hyperbolic curve, the Galois extension under consideration is generated by the coordinates of the l-moderate points of the hyperbolic curve. This may be regarded as an analogue of the fact that the Galois extension corresponding to the kernel of the l-adic Galois representation associated to an abelian variety is generated by the coordinates of the torsion points of the abelian variety of l-power order. Moreover, we discuss an application of the argument of the present paper to the study of the Fermat equation.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":"52 1","pages":"647-675"},"PeriodicalIF":0.4,"publicationDate":"2015-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67864946","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}
R.E. Caflish and J.H. Maddocks analyzed the dynamics of a plana r slender elastic rod. We consider a thin elastic rod in an N-dimensional riemannian manifold. The former model represents an elastic rod with positive thi ckness, and the equation becomes a semilinear wave equation. Our model represents an infinitely thin elastic rod, and the equation becomes a 1-dimensional semilinear pl ate equation. We prove the short time existence of solutions. We also discuss the be aviour of the solution when the resistance goes to infinity, and find that the solutio n converges to a solution of a gradient flow equation.
{"title":"ON MOTION OF AN ELASTIC WIRE IN A RIEMANNIAN MANIFOLD AND SINGULAR PERTURBATION","authors":"N. Koiso","doi":"10.18910/57640","DOIUrl":"https://doi.org/10.18910/57640","url":null,"abstract":"R.E. Caflish and J.H. Maddocks analyzed the dynamics of a plana r slender elastic rod. We consider a thin elastic rod in an N-dimensional riemannian manifold. The former model represents an elastic rod with positive thi ckness, and the equation becomes a semilinear wave equation. Our model represents an infinitely thin elastic rod, and the equation becomes a 1-dimensional semilinear pl ate equation. We prove the short time existence of solutions. We also discuss the be aviour of the solution when the resistance goes to infinity, and find that the solutio n converges to a solution of a gradient flow equation.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":"52 1","pages":"453-473"},"PeriodicalIF":0.4,"publicationDate":"2015-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67867722","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}
without requiring that f g a.e. in. Here denotes the outer unit normal vector on . It should be noted that the assumptions f g and f ¥ g in are needed in previous literature (see e.g. [9] and the references therei n). We also provide an application to the existence of positive solutions for a class of sin gular p-Laplacian boundary value problems with asymptoticallyp-linear nonlinearity. Let d(x) D d(x, ) be the distance fromx to , we prove the following result:
{"title":"A COMPARISON PRINCIPLE AND APPLICATIONS TO ASYMPTOTICALLY p-LINEAR BOUNDARY VALUE PROBLEMS","authors":"D. D. Hai","doi":"10.18910/57658","DOIUrl":"https://doi.org/10.18910/57658","url":null,"abstract":"without requiring that f g a.e. in. Here denotes the outer unit normal vector on . It should be noted that the assumptions f g and f ¥ g in are needed in previous literature (see e.g. [9] and the references therei n). We also provide an application to the existence of positive solutions for a class of sin gular p-Laplacian boundary value problems with asymptoticallyp-linear nonlinearity. Let d(x) D d(x, ) be the distance fromx to , we prove the following result:","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":"52 1","pages":"393-408"},"PeriodicalIF":0.4,"publicationDate":"2015-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67870118","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 give a new approach to find a dually flat Finsle r m tric. As its application, we produce many new spherically symmetric dua lly flat Finsler metrics by using known projective spherically symmetric Finsler me trics.
{"title":"On the construction of dually flat Finsler metrics","authors":"Libing Huang, Huaifu Liu, X. Mo","doi":"10.18910/57649","DOIUrl":"https://doi.org/10.18910/57649","url":null,"abstract":"In this paper, we give a new approach to find a dually flat Finsle r m tric. As its application, we produce many new spherically symmetric dua lly flat Finsler metrics by using known projective spherically symmetric Finsler me trics.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":"52 1","pages":"377-391"},"PeriodicalIF":0.4,"publicationDate":"2015-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67868691","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}
The gonality sequence ( dr )r 1 of a curve of genusg encodes, for < g, important information about the divisor theory of the curve. Mostly i is very difficult to compute this sequence. In general it grows rather modestly ( made precise below) but for curves with special moduli some “unexpected jumps” m ay occur in it. We first determine all integersg > 0 such that there is no such jump, for all curves of genusg. Secondly, we compute the leading numbers (up to r D 19) in the gonality sequence of an extremal space curve, i.e. of a space curve of maximal geometric genus w.r.t. its degree.
{"title":"Algebraic curves violating the slope inequalities","authors":"Takaomi Kato, G. Martens","doi":"10.18910/57641","DOIUrl":"https://doi.org/10.18910/57641","url":null,"abstract":"The gonality sequence ( dr )r 1 of a curve of genusg encodes, for < g, important information about the divisor theory of the curve. Mostly i is very difficult to compute this sequence. In general it grows rather modestly ( made precise below) but for curves with special moduli some “unexpected jumps” m ay occur in it. We first determine all integersg > 0 such that there is no such jump, for all curves of genusg. Secondly, we compute the leading numbers (up to r D 19) in the gonality sequence of an extremal space curve, i.e. of a space curve of maximal geometric genus w.r.t. its degree.","PeriodicalId":54660,"journal":{"name":"Osaka Journal of Mathematics","volume":"52 1","pages":"423-437"},"PeriodicalIF":0.4,"publicationDate":"2015-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67867311","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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