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Tokyo Journal of Mathematics最新文献

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Duality of One-variable Multiple Polylogarithms and Their $q$-analogues 一元多聚对数及其$q$-类似物的对偶性
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2020-10-12 DOI: 10.3836/tjm/1502179378
Shuji Yamamoto
{"title":"Duality of One-variable Multiple Polylogarithms and Their $q$-analogues","authors":"Shuji Yamamoto","doi":"10.3836/tjm/1502179378","DOIUrl":"https://doi.org/10.3836/tjm/1502179378","url":null,"abstract":"The duality relation of one-variable multiple polylogarithms was proved by Hirose, Iwaki, Sato and Tasaka by means of iterated integrals. In this paper, we give a new proof using the method of connected sums, which was recently invented by Seki and the author. Interestingly, the connected sum involves the hypergeometric function in its connector. Moreover, we introduce two kinds of $q$-analogues of the one-variable multiple poylogarithms and generalize the duality to them.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41767843","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}
引用次数: 2
On a Class of Singular Nonlinear First Order Partial Differential Equations 关于一类奇异非线性一阶偏微分方程
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2020-10-04 DOI: 10.3836/tjm/1502179352
H. Tahara
{"title":"On a Class of Singular Nonlinear First Order Partial Differential Equations","authors":"H. Tahara","doi":"10.3836/tjm/1502179352","DOIUrl":"https://doi.org/10.3836/tjm/1502179352","url":null,"abstract":"In this paper, we consider a class of singular nonlinear first order partial differential equations $t(partial u/partial t)=F(t,x,u, partial u/partial x)$ with $(t,x) in mathbb{R} times mathbb{C}$ under the assumption that $F(t,x,z_1,z_2)$ is a function which is continuous in $t$ and holomorphic in the other variables. Under suitable conditions, we determine all the solutions of this equation in a neighborhood of the origin.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47090105","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}
引用次数: 0
On 2-adic Lie Iterated Extensions of Number Fields Arising from a Joukowski Map 由Joukowski映射产生的数域的二次李迭代扩展
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2020-10-01 DOI: 10.3836/tjm/1502179321
Yasushi Mizusawa, Kota Yamamoto
{"title":"On 2-adic Lie Iterated Extensions of Number Fields Arising from a Joukowski Map","authors":"Yasushi Mizusawa, Kota Yamamoto","doi":"10.3836/tjm/1502179321","DOIUrl":"https://doi.org/10.3836/tjm/1502179321","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44719688","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}
引用次数: 2
Mean Square of Double Zeta-function 二重齐塔函数的均方
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2020-10-01 DOI: 10.3836/tjm/1502179322
D. Banerjee, T. Minamide, Y. Tanigawa
{"title":"Mean Square of Double Zeta-function","authors":"D. Banerjee, T. Minamide, Y. Tanigawa","doi":"10.3836/tjm/1502179322","DOIUrl":"https://doi.org/10.3836/tjm/1502179322","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45898474","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}
引用次数: 2
Fitting Ideals in Two-variable Equivariant Iwasawa Theory and an Application to CM Elliptic Curves 二变量等变Iwasawa理论的拟合理想及其在CM椭圆曲线上的应用
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2020-08-07 DOI: 10.3836/tjm/1502179347
T. Kataoka
{"title":"Fitting Ideals in Two-variable Equivariant Iwasawa Theory and an Application to CM Elliptic Curves","authors":"T. Kataoka","doi":"10.3836/tjm/1502179347","DOIUrl":"https://doi.org/10.3836/tjm/1502179347","url":null,"abstract":"We study equivariant Iwasawa theory for two-variable abelian extensions of an imaginary quadratic field. One of the main goals of this paper is to describe the Fitting ideals of Iwasawa modules using $p$-adic $L$-functions. We also provide an application to Selmer groups of elliptic curves with complex multiplication.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41480160","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}
引用次数: 3
Cauchy Theory for the Water Waves System in an Analytic Framework 解析框架下水波系的柯西理论
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2020-07-16 DOI: 10.3836/tjm/1502179355
T. Alazard, N. Burq, C. Zuily
{"title":"Cauchy Theory for the Water Waves System in an Analytic Framework","authors":"T. Alazard, N. Burq, C. Zuily","doi":"10.3836/tjm/1502179355","DOIUrl":"https://doi.org/10.3836/tjm/1502179355","url":null,"abstract":"In this paper we consider the Cauchy problem for gravity water waves, in a domain with a flat bottom and in arbitrary space dimension. We prove that if the data are of size $varepsilon$ in a space of analytic functions which have a holomorphic extension in a strip of size $sigma$, then the solution exists up to a time of size $C/varepsilon$ in a space of analytic functions having at time $t$ a holomorphic extension in a strip of size $sigma - C'varepsilon t$.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48845686","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}
引用次数: 6
Constructions of Smooth $SU(p,q)$-actions on the Projective Space ${mathbf P}^{p+q-1}_{mathbb C}$ with $m$ Closed and $m+1$ Open Orbits 具有$m$闭和$m+1$开轨道的投影空间${mathbf p}^{p+q-1}_{mathbb C}$上光滑$SU（p，q）$-作用的构造
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2020-06-01 DOI: 10.3836/TJM/1502179299
Kazuo Mukōyama, T. Ono, K. Takei
{"title":"Constructions of Smooth $SU(p,q)$-actions on the Projective Space ${mathbf P}^{p+q-1}_{mathbb C}$ with $m$ Closed and $m+1$ Open Orbits","authors":"Kazuo Mukōyama, T. Ono, K. Takei","doi":"10.3836/TJM/1502179299","DOIUrl":"https://doi.org/10.3836/TJM/1502179299","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48142226","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}
引用次数: 0
On Some Families of Certain Divisible Polynomials and Their Zeta Functions 关于某些可分多项式族及其Zeta函数
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2020-06-01 DOI: 10.3836/tjm/1502179317
K. Chinen
{"title":"On Some Families of Certain Divisible Polynomials and Their Zeta Functions","authors":"K. Chinen","doi":"10.3836/tjm/1502179317","DOIUrl":"https://doi.org/10.3836/tjm/1502179317","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46504741","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}
引用次数: 2
An Application of the Arithmetic of Elliptic Curves to the Class Number Problem for Quadratic Fields 椭圆曲线算法在二次域类数问题中的应用
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2020-06-01 DOI: 10.3836/tjm/1502179314
Yoshichika Iizuka, Yutaka Konomi, S. Nakano
{"title":"An Application of the Arithmetic of Elliptic Curves to the Class Number Problem for Quadratic Fields","authors":"Yoshichika Iizuka, Yutaka Konomi, S. Nakano","doi":"10.3836/tjm/1502179314","DOIUrl":"https://doi.org/10.3836/tjm/1502179314","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43826998","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}
引用次数: 8
Lifespan of Solutions for a Weakly Coupled System of Semilinear Heat Equations 一类弱耦合半线性热方程组解的寿命
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2020-06-01 DOI: 10.3836/TJM/1502179300
K. Fujiwara, M. Ikeda, Yuta Wakasugi
{"title":"Lifespan of Solutions for a Weakly Coupled System of Semilinear Heat Equations","authors":"K. Fujiwara, M. Ikeda, Yuta Wakasugi","doi":"10.3836/TJM/1502179300","DOIUrl":"https://doi.org/10.3836/TJM/1502179300","url":null,"abstract":"We introduce a straightforward method to analyze the blow-up of solutions to systems of ordinary differential inequalities, and apply it to study the blow-up of solutions to a weakly coupled system of semilinear heat equations. In particular, we give upper and lower estimates of the lifespan of the solution in the subcritical case.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41545986","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}
引用次数: 4
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