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Tokyo Journal of Mathematics最新文献

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On Finite Type Invariants of Welded String Links and Ribbon Tubes 焊接串链和带状管的有限型不变量
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2022-01-01 DOI: 10.3836/tjm/1502179380
Adrien Casejuane, Jean-Baptiste Meilhan
{"title":"On Finite Type Invariants of Welded String Links and Ribbon Tubes","authors":"Adrien Casejuane, Jean-Baptiste Meilhan","doi":"10.3836/tjm/1502179380","DOIUrl":"https://doi.org/10.3836/tjm/1502179380","url":null,"abstract":"Welded knotted objects are a combinatorial extension of knot theory, which can be used as a tool for studying ribbon surfaces in 4-space. A finite type invariant theory for ribbon knotted surfaces was developped by Kanenobu, Habiro and Shima, and this paper proposes a study of these invariants, using welded objects. Specifically, we study welded string links up to wk-equivalence, which is an equivalence relation introduced by Yasuhara and the second author in connection with finite type theory. In low degrees, we show that this relation characterizes the information contained by finite type invariants. We also study the algebraic structure of welded string links up to wk-equivalence. All results have direct corollaries for ribbon knotted surfaces.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45537971","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: 1
Reconstruction of the Defect by the Enclosure Method for Inverse Problems of the Magnetic Schrödinger Operator 磁性Schrödinger算子逆问题的包体法缺陷重构
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2022-01-01 DOI: 10.3836/tjm/1502179363
K. Kurata, Ryusei Yamashita
{"title":"Reconstruction of the Defect by the Enclosure Method for Inverse Problems of the Magnetic Schrödinger Operator","authors":"K. Kurata, Ryusei Yamashita","doi":"10.3836/tjm/1502179363","DOIUrl":"https://doi.org/10.3836/tjm/1502179363","url":null,"abstract":"This study is based on the paper [1]. We give the formula to extract the position and the shape of the defect D generated in the object (conductor) Ω from the observation data on the boundary ∂Ω for the magnetic Schrödinger operator by using the enclosure method proposed by Ikehata [2]. We show a reconstruction formula of the convex hull of the defect D from the observed data, assuming certain higher regularity for the potentials of the magnetic Schrödinger operator, under the Dirichlet condition or the Robin condition on the boundary ∂D in the two and three dimensional case. Let Ω ⊂ R(n = 2, 3) be a bounded domain where the boundary ∂Ω is C and let D be an open set satisfying D ⊂ Ω and Ω D is connected. The defect D consists of the union of disjoint bounded domains {Dj}j=1, where the boundary of D is Lipschitz continuous. First, we define the DN map for the magnetic Schrödinger equation with no defect D in Ω. Here, let D Au := ∑n j=1 DA,j(DA,ju), where DA,j := 1 i ∂j +Aj and A = (A1, A2, · · · , An). Definition 1. Suppose q ∈ L∞(Ω), q ≥ 0, A ∈ C(Ω, R). For a given f ∈ H(∂Ω), we say u ∈ H(Ω) is a weak solution to the following boundary value problem for the magnetic Schrödinger equation { D Au+ qu = 0 in Ω, u = f on ∂Ω, (1.1)","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46564749","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: 1
On a Generalization of Monge–Ampère Equations and Monge–Ampère Systems 蒙日-安培方程及蒙日-安培系统的推广
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2022-01-01 DOI: 10.3836/tjm/1502179374
M. Kawamata, K. Shibuya
{"title":"On a Generalization of Monge–Ampère Equations and Monge–Ampère Systems","authors":"M. Kawamata, K. Shibuya","doi":"10.3836/tjm/1502179374","DOIUrl":"https://doi.org/10.3836/tjm/1502179374","url":null,"abstract":"We discuss Monge-Ampère equations from the view point of differential geometry. It is known that a Monge–Ampère equation corresponds to a special exterior differential system on a 1-jet space. In this paper, we generalize Monge–Ampère equations and prove that a (k+ 1)st order generalized Monge–Ampère equation corresponds to a special exterior differential system on a k-jet space. Then its solution naturally corresponds to an integral manifold of the corresponding exterior differential system. Moreover, we verify that the Korteweg-de Vries (KdV) equation and the Cauchy–Riemann equations are examples of our equation. 2010 Mathematics Subject Classification. Primary 58A15; Secondary 58A17.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47527732","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: 1
Virtual Knots with Properties of Kishino's Knot 具有岸野结性质的虚结
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2022-01-01 DOI: 10.3836/tjm/1502179365
Y. Ohyama, Migiwa Sakurai
{"title":"Virtual Knots with Properties of Kishino's Knot","authors":"Y. Ohyama, Migiwa Sakurai","doi":"10.3836/tjm/1502179365","DOIUrl":"https://doi.org/10.3836/tjm/1502179365","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43419315","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
Predual of Weak Orlicz Spaces and its Applications to Fefferman-Stein Vector-valued Maximal Inequality 弱Orlicz空间的预偶及其在Fefferman-Stein向量值极大不等式上的应用
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2022-01-01 DOI: 10.3836/tjm/1502179373
N. Hatano, Ryota Kawasumi, Takahiro Ono
{"title":"Predual of Weak Orlicz Spaces and its Applications to Fefferman-Stein Vector-valued Maximal Inequality","authors":"N. Hatano, Ryota Kawasumi, Takahiro Ono","doi":"10.3836/tjm/1502179373","DOIUrl":"https://doi.org/10.3836/tjm/1502179373","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42575822","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
Base Change Theorems for Log Analytic Spaces 对数分析空间的基变定理
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2022-01-01 DOI: 10.3836/tjm/1502179376
Chikara Nakayama
{"title":"Base Change Theorems for Log Analytic Spaces","authors":"Chikara Nakayama","doi":"10.3836/tjm/1502179376","DOIUrl":"https://doi.org/10.3836/tjm/1502179376","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48185294","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: 1
A Note on Equivalence Classes of SO0(p,q)-actions on Sp+q−1 whose Restricted SO(p)×SO(q)-action is the Standard Action 关于限制SO（p）×SO（q）-作用为标准作用的Sp+q−1上SO0（p，q）-动作等价类的一个注记
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2022-01-01 DOI: 10.3836/tjm/1502179370
T. Ono
{"title":"A Note on Equivalence Classes of SO0(p,q)-actions on Sp+q−1 whose Restricted SO(p)×SO(q)-action is the Standard Action","authors":"T. Ono","doi":"10.3836/tjm/1502179370","DOIUrl":"https://doi.org/10.3836/tjm/1502179370","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42676081","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
Preduals of Sobolev Multiplier Spaces for End Point Cases 端点情况下Sobolev乘子空间的预公数
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2022-01-01 DOI: 10.3836/tjm/1502179383
Keng Hao Ooi
{"title":"Preduals of Sobolev Multiplier Spaces for End Point Cases","authors":"Keng Hao Ooi","doi":"10.3836/tjm/1502179383","DOIUrl":"https://doi.org/10.3836/tjm/1502179383","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43223187","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
Anisotropic Sobolev Spaces with Weights 具有权重的各向异性Sobolev空间
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2021-12-03 DOI: 10.3836/tjm/1502179386
G. Metafune, L. Negro, C. Spina
{"title":"Anisotropic Sobolev Spaces with Weights","authors":"G. Metafune, L. Negro, C. Spina","doi":"10.3836/tjm/1502179386","DOIUrl":"https://doi.org/10.3836/tjm/1502179386","url":null,"abstract":"We study Sobolev spaces with weights in the half-space $mathbb{R}^{N+1}_+={(x,y): x in mathbb{R}^N, y>0}$, adapted to the singular elliptic operators begin{equation*} mathcal L =y^{alpha_1}Delta_{x} +y^{alpha_2}left(D_{yy}+frac{c}{y}D_y -frac{b}{y^2}right). end{equation*}","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46056074","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
A Generalization of Bauer's Identical Congruence 鲍尔同余的一个推广
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2021-09-01 DOI: 10.3836/tjm/1502179350
Boaz Cohen
{"title":"A Generalization of Bauer's Identical Congruence","authors":"Boaz Cohen","doi":"10.3836/tjm/1502179350","DOIUrl":"https://doi.org/10.3836/tjm/1502179350","url":null,"abstract":"In this paper we generalize Bauer's Identical Congruence appearing in Hardy and Wright's book [6], Theorems 126 and 127. Bauer's Identical Congruence asserts that the polynomial $prod_t(x-t)$, where the product runs over a reduced residue system modulo a prime power $p^a$, is congruent (mod $p^a$) to the “simple” polynomial $(x^{p-1}-1)^{p^{a-1}}$ if $p>2$ and $(x^2-1)^{2^{a-2}}$ if $p=2$ and $ageqslant2$. Our article generalizes these results to a broader context, in which we find a “simple” form of the polynomial $prod_t(x-t)$, where the product runs over the solutions of the congruence $t^nequiv 1pmod{mathrm{P}^a}$ in the framework of the ring of algebraic integers of a given number field $mathbb{K}$, and where $mathrm{P}$ is a prime ideal.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45384480","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
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