{"title":"Bounds for Multiple Recurrence Rate and Dimension","authors":"Michihiro Hirayama","doi":"10.3836/TJM/1502179281","DOIUrl":"https://doi.org/10.3836/TJM/1502179281","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47181199","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":"Homology of the Complex of All Non-trivial Nilpotent Subgroups of a Finite Non-solvable Group","authors":"N. Iiyori, M. Sawabe","doi":"10.3836/TJM/1502179264","DOIUrl":"https://doi.org/10.3836/TJM/1502179264","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42680035","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":"Classification of Very Cuspidal Representations of $mathrm{GL}_m(D)$","authors":"Kazutoshi Kariyama","doi":"10.3836/TJM/1502179296","DOIUrl":"https://doi.org/10.3836/TJM/1502179296","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42875735","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":"A Calculation of the Hyperbolic Torsion Polynomial of a Pretzel Knot","authors":"Takayuki Morifuji","doi":"10.3836/TJM/1502179265","DOIUrl":"https://doi.org/10.3836/TJM/1502179265","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42002762","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":"Conformal Slant Riemannian Maps to Kähler Manifolds","authors":"M. Akyol, B. Şahin","doi":"10.3836/TJM/1502179277","DOIUrl":"https://doi.org/10.3836/TJM/1502179277","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42537659","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":"Crystallographic Groups Arising from Teichmüller Spaces","authors":"Yukio Matsumoto","doi":"10.3836/TJM/1502179302","DOIUrl":"https://doi.org/10.3836/TJM/1502179302","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47839232","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}
This is a continuation of the paper [K1] on the foundation of log geometry in the sense of Fontaine-Illusie. Here we discuss mainly log flat topologies, especially log flat descent theory. This paper was started around 1991, and was circulated as an incomplete preprint for a long time. Since then, some contents of this paper have been reproduced by several authors with proofs ([Ha], [KS], [Ni], [Na2], [Ol], ...). A. Moriwaki [M] also studied flat descents in the category of log schemes. In the parts which were incomplete in the circulated preprint, we sometimes referred to these papers instead of completing the original proofs. In particular, the author does not claim the results with ∗ (i.e., two theorems 7.1, 7.2 and one proposition 6.5) are his results. Since the paper is already referred to in many published works, in the other parts, we preferred to preserve the original, circulated form. In both parts, we tried to preserve the original numberings of definitions and propositions. The author wishes to express his special thanks to Chikara Nakayama who helped him a lot in the completion of this paper. He is also thankful to Luc Illusie, Takeshi Saito, Takeshi Kajiwara, and Takeshi Tsuji for helpful discussions. The author is partially supported by NSF Award 1601861.
{"title":"Logarithmic Structures of Fontaine-Illusie. II ---Logarithmic Flat Topology","authors":"Kazuya Kato","doi":"10.3836/tjm/1502179316","DOIUrl":"https://doi.org/10.3836/tjm/1502179316","url":null,"abstract":"This is a continuation of the paper [K1] on the foundation of log geometry in the sense of Fontaine-Illusie. Here we discuss mainly log flat topologies, especially log flat descent theory. This paper was started around 1991, and was circulated as an incomplete preprint for a long time. Since then, some contents of this paper have been reproduced by several authors with proofs ([Ha], [KS], [Ni], [Na2], [Ol], ...). A. Moriwaki [M] also studied flat descents in the category of log schemes. In the parts which were incomplete in the circulated preprint, we sometimes referred to these papers instead of completing the original proofs. In particular, the author does not claim the results with ∗ (i.e., two theorems 7.1, 7.2 and one proposition 6.5) are his results. Since the paper is already referred to in many published works, in the other parts, we preferred to preserve the original, circulated form. In both parts, we tried to preserve the original numberings of definitions and propositions. The author wishes to express his special thanks to Chikara Nakayama who helped him a lot in the completion of this paper. He is also thankful to Luc Illusie, Takeshi Saito, Takeshi Kajiwara, and Takeshi Tsuji for helpful discussions. The author is partially supported by NSF Award 1601861.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47849095","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}
L. Buhovsky, A. Logunov and S. Tanny proved the (strong) Poisson bracket conjecture by Leonid Polterovich in dimension 2. In this note, instead of open cover consisting of displaceable sets in their work, we consider open cover constituted of topological discs and give a necessary and sufficient condition that Poisson bracket invariants of these covers are positive.
{"title":"The Poisson Bracket Invariant for Open Covers Consisting of Topological Disks on Surfaces","authors":"Kun Shi, Guangcun Lu","doi":"10.3836/tjm/1502179384","DOIUrl":"https://doi.org/10.3836/tjm/1502179384","url":null,"abstract":"L. Buhovsky, A. Logunov and S. Tanny proved the (strong) Poisson bracket conjecture by Leonid Polterovich in dimension 2. In this note, instead of open cover consisting of displaceable sets in their work, we consider open cover constituted of topological discs and give a necessary and sufficient condition that Poisson bracket invariants of these covers are positive.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47728860","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}
Chunhua Li, Y. Nishii, Yuji Sagawa, Hideaki Sunagawa
This is a sequel to the paper "Large time asymptotics for a cubic nonlinear Schrodinger system in one space dimension" by the same authors. We continue to study the Cauchy problem for the two-component system of cubic nonlinear Schrodinger equations in one space dimension. We provide criteria for large time decay or non-decay in $L^2$ of the small amplitude solutions in terms of the Fourier transforms of the initial data.
{"title":"Large Time Asymptotics for a Cubic Nonlinear Schrödinger\u0000 System in One Space Dimension, II","authors":"Chunhua Li, Y. Nishii, Yuji Sagawa, Hideaki Sunagawa","doi":"10.1619/fesi.64.361","DOIUrl":"https://doi.org/10.1619/fesi.64.361","url":null,"abstract":"This is a sequel to the paper \"Large time asymptotics for a cubic nonlinear Schrodinger system in one space dimension\" by the same authors. We continue to study the Cauchy problem for the two-component system of cubic nonlinear Schrodinger equations in one space dimension. We provide criteria for large time decay or non-decay in $L^2$ of the small amplitude solutions in terms of the Fourier transforms of the initial data.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48828258","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 give a characterization of all complete smooth toric varieties whose rational homotopy is of elliptic type. All such toric varieties of complex dimension not more than three are explicitly described.
{"title":"Rationally Elliptic Toric Varieties","authors":"I. Biswas, V. Muñoz, A. Murillo","doi":"10.3836/tjm/1502179327","DOIUrl":"https://doi.org/10.3836/tjm/1502179327","url":null,"abstract":"We give a characterization of all complete smooth toric varieties whose rational homotopy is of elliptic type. All such toric varieties of complex dimension not more than three are explicitly described.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42415694","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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