Tohoku Mathematical Journal最新文献

{"title":"An inverse problem for a class of lacunary canonical systems with diagonal Hamiltonian","authors":"Masatoshi Suzuki","doi":"10.2748/tmj.20210816","DOIUrl":"https://doi.org/10.2748/tmj.20210816","url":null,"abstract":"Hamiltonians are 2-by-2 positive semidefinite real symmetric matrix-valued functions satisfying certain conditions. In this paper, we solve the inverse problem for which recovers a Hamiltonian from the solution of a first-order system attached to a given Hamiltonian, consisting of ordinary differential equations parametrized by a set of complex numbers, under certain conditions for the solutions. This inverse problem is a generalization of the inverse problem for two-dimensional canonical systems.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41605876","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":"Simple foliated flows","authors":"J. '. L'opez, Y. Kordyukov, E. Leichtnam","doi":"10.2748/tmj.20201015b","DOIUrl":"https://doi.org/10.2748/tmj.20201015b","url":null,"abstract":"We describe transversely oriented foliations of codimension one on closed manifolds that admit simple foliated flows.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41735227","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":"Growth estimates for meromorphic solutions of higher order algebraic differential equations","authors":"S. Makhmutov, Jouni Rattya, Toni Vesikko","doi":"10.2748/tmj.20191118","DOIUrl":"https://doi.org/10.2748/tmj.20191118","url":null,"abstract":"We establish pointwise growth estimates for the spherical derivative of solutions of the first order algebraic differential equations. A generalization of this result to higher order equations is also given. We discuss the related question of when for a given class $X$ of meromorphic functions in the unit disc, defined by means of the spherical derivative, and $m in mathbb{N} setminus {1}$, $f^min X$ implies $fin X$. An affirmative answer to this is given for example in the case of $mathord{rm UBC}$, the $alpha$-normal functions with $alphage1$ and certain (sufficiently large) Dirichlet type classes.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42703127","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":"Algebraic cycles and Verra fourfolds","authors":"R. Laterveer","doi":"10.2748/tmj/1601085625","DOIUrl":"https://doi.org/10.2748/tmj/1601085625","url":null,"abstract":"This note is about the Chow ring of Verra fourfolds. For a general Verra fourfold, we show that the Chow group of homologically trivial $1$-cycles is generated by conics. We also show that Verra fourfolds admit a multiplicative Chow-K\"unneth decomposition, and draw some consequences for the intersection product in the Chow ring of Verra fourfolds.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47302010","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":"Quinary lattices and binary quaternion hermitian lattices","authors":"T. Ibukiyama","doi":"10.2748/TMJ/1561082596","DOIUrl":"https://doi.org/10.2748/TMJ/1561082596","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","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":"46701859","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":"Steady states of FitzHugh-Nagumo system with non-diffusive activator and diffusive inhibitor","authors":"Yingguo Li, A. Marciniak-Czochra, I. Takagi, Boying Wu","doi":"10.2748/TMJ/1561082598","DOIUrl":"https://doi.org/10.2748/TMJ/1561082598","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","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":"44687144","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":"Characteristic cycles of highest weight Harish-Chandra modules and the Weyl group action on the conormal variety","authors":"L. Barchini","doi":"10.2748/TMJ/1561082595","DOIUrl":"https://doi.org/10.2748/TMJ/1561082595","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2748/TMJ/1561082595","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48758655","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":"The conservativeness of Girsanov transformed symmetric Markov processes","authors":"Yusuke Miura","doi":"10.2748/TMJ/1561082597","DOIUrl":"https://doi.org/10.2748/TMJ/1561082597","url":null,"abstract":"","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2748/TMJ/1561082597","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49285504","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 flat projective variety with $D_8$-holonomy","authors":"F. Johnson","doi":"10.2748/TMJ/1561082601","DOIUrl":"https://doi.org/10.2748/TMJ/1561082601","url":null,"abstract":"We show explicitly that the compact flat Kähler manifold of complex dimension three with D8 holonomy studied by Dekimpe, Halenda and Szczepanski ([5] p. 367) possesses the structure of a nonsingular projective variety. This corrects a previous statement by H. Lange in [9] that the holonomy group of a hyperelliptic threefold is necessarily abelian. The study of flat Riemannian manifolds, begun by Bieberbach [2], has subsequently acquired a very extensive literature. See, for example, [3],[4],[13],[14]. In a paper published in the Tohoku Mathematical Journal [9], H. Lange investigated closed flat manifolds of real dimension six which, in addition, possess the structure of nonsingular complex projective varieties which have finite étale coverings by abelian varieties. In Lange’s terminology such varieties are called hyperelliptic three-folds. The significant claim of Lange’s paper is that the (finite) holonomy group of such a hyperelliptic three-fold is necessarily abelian. In particular, Lange claims that the dihedral group of order eight† does not occur as a holonomy group in this context. Lange’s claim is mistaken, however. In the present paper we show explicitly that the compact flat Kähler manifold of complex dimension three with D8 holonomy studied by Dekimpe, Halenda and Szczepanski ([5] p. 367) does indeed possess the structure of a nonsingular projective variety. In fact, the existence of this complex algebraic structure was previously shown, in a very general context, by the present author in the paper [7]. However, as Lange also makes a statement which explicitly claims to contradict the main result of [7] it seems appropriate, in setting the matter straight, to give a direct, and elementary, construction of the algebraic structure whose existence Lange denies. The present paper is organised as follows; in §1 we give a brief review of the theory of flat Riemannian manifolds as it pertains both to Kähler manifolds and projective varieties; in §2 we give a completely elementary criterion which guarantees that some flat Riemannian manifolds admit the structure of a nonsingular complex algebraic variety. Whilst this criterion does not immediately apply to the most general cases, it is quite sufficient to deal with all cases in which the holonomy group is D8. In §3 we construct an explicit complex algebraic structure for the Kähler manifold of Dekimpe, Halenda and Szczepanski. This can be checked by direct calculation and requires very little theory beyond an appeal to the criterion of §2. 2010 MSC Primary 53C29; Secondary 14F35, 14K02, 32J27.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","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":"46252553","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":"The Leibniz rule for the Dirichlet and the Neumann Laplacian","authors":"T. Iwabuchi","doi":"10.2748/tmj.20211112","DOIUrl":"https://doi.org/10.2748/tmj.20211112","url":null,"abstract":"We study the bilinear estimates in the Sobolev spaces with the Dirichlet and the Neumann boundary condition. The optimal regularity is revealed to get such estimates in the half space case, which is related to not only smoothness of functions and but also boundary behavior. The crucial point for the proof is how to handle boundary values of functions and their derivatives.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46922181","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}