Pub Date : 2020-07-01DOI: 10.21099/tkbjm/20204401063
Masaya Kawamura
{"title":"Regularity results for the almost Hermitian curvature flow","authors":"Masaya Kawamura","doi":"10.21099/tkbjm/20204401063","DOIUrl":"https://doi.org/10.21099/tkbjm/20204401063","url":null,"abstract":"","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48399522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-13DOI: 10.21099/tkbjm/20214502097
Yuichiro Sato
A totally umbilical submanifold in pseudo-Riemannian manifolds is a fundamental notion, which is characterized by the fact that the second fundamental form to be proportional to the metric. And, it is also a generalization of a notion of a totally geodesic submanifold. In this paper, we classify congruent classes of full totally umbilical submanifolds in non-flat pseudo-Riemannian space forms, and consider its moduli spaces. As a consequence, we obtain that some moduli spaces of isometric immersions between space forms whose curvatures have the same constant are non-Hausdorff.
{"title":"Totally umbilical submanifolds in pseudo-Riemannian space forms","authors":"Yuichiro Sato","doi":"10.21099/tkbjm/20214502097","DOIUrl":"https://doi.org/10.21099/tkbjm/20214502097","url":null,"abstract":"A totally umbilical submanifold in pseudo-Riemannian manifolds is a fundamental notion, which is characterized by the fact that the second fundamental form to be proportional to the metric. And, it is also a generalization of a notion of a totally geodesic submanifold. In this paper, we classify congruent classes of full totally umbilical submanifolds in non-flat pseudo-Riemannian space forms, and consider its moduli spaces. As a consequence, we obtain that some moduli spaces of isometric immersions between space forms whose curvatures have the same constant are non-Hausdorff.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46849534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-13DOI: 10.21099/tkbjm/20214501013
Ryusuke Sugawara
We prove that linear groups over rings of non-commutative Laurent polynomials $D_{tau}$ have Tits systems with the corresponding affine Weyl groups and have universal central extensions if $|Z(D)|geq 5$ and $|Z(D)|neq 9$. We also determine structures of $K_1$-groups and identify generators of $K_2$-groups.
{"title":"Universal central extensions of linear groups over rings of non-commutative Laurent polynomials, associated $K_1$-groups and $K_2$-groups","authors":"Ryusuke Sugawara","doi":"10.21099/tkbjm/20214501013","DOIUrl":"https://doi.org/10.21099/tkbjm/20214501013","url":null,"abstract":"We prove that linear groups over rings of non-commutative Laurent polynomials $D_{tau}$ have Tits systems with the corresponding affine Weyl groups and have universal central extensions if $|Z(D)|geq 5$ and $|Z(D)|neq 9$. We also determine structures of $K_1$-groups and identify generators of $K_2$-groups.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48290372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-22DOI: 10.21099/tkbjm/20214501037
Y. Okada, H. Yamane
We consider the Neumann version of the spherical mean value operator and its variants in the space of smooth functions, distributions and compactly supported ones. Surjectivity and range characterization issues are addressed from the viewpoint of convolution equations.
{"title":"Generalized spherical mean value operators on Euclidean space","authors":"Y. Okada, H. Yamane","doi":"10.21099/tkbjm/20214501037","DOIUrl":"https://doi.org/10.21099/tkbjm/20214501037","url":null,"abstract":"We consider the Neumann version of the spherical mean value operator and its variants in the space of smooth functions, distributions and compactly supported ones. Surjectivity and range characterization issues are addressed from the viewpoint of convolution equations.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42448234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-01DOI: 10.21099/tkbjm/20234702207
A. Patkowski
We extend Salem's Integral equation to the non-homogenous form, and offer the associated criteria for the Riemann Hypothesis. Explicit solutions for the non-homogenous case are given, which in turn give further insight into Salem's criteria for the RH. As a conclusion, we show these results follow from a corollary relating the uniqueness of solutions of the non-homogenous form with Wiener's theorem.
{"title":"ON SALEM’S INTEGRAL EQUATION AND RELATED CRITERIA","authors":"A. Patkowski","doi":"10.21099/tkbjm/20234702207","DOIUrl":"https://doi.org/10.21099/tkbjm/20234702207","url":null,"abstract":"We extend Salem's Integral equation to the non-homogenous form, and offer the associated criteria for the Riemann Hypothesis. Explicit solutions for the non-homogenous case are given, which in turn give further insight into Salem's criteria for the RH. As a conclusion, we show these results follow from a corollary relating the uniqueness of solutions of the non-homogenous form with Wiener's theorem.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141228227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-03DOI: 10.21099/TKBJM/20204402251
Neil Mañibo, E. Miro, D. Rust, Gwendolyn S. Tadeo
We use generalised Zeckendorf representations of natural numbers to investigate mixing properties of symbolic dynamical systems. The systems we consider consist of bi-infinite sequences associated with so-called random substitutions. We focus on random substitutions associated with the Fibonacci, tribonacci and metallic mean numbers and take advantage of their respective numeration schemes.
{"title":"Zeckendorf representations and mixing properties of\u0000 sequences","authors":"Neil Mañibo, E. Miro, D. Rust, Gwendolyn S. Tadeo","doi":"10.21099/TKBJM/20204402251","DOIUrl":"https://doi.org/10.21099/TKBJM/20204402251","url":null,"abstract":"We use generalised Zeckendorf representations of natural numbers to investigate mixing properties of symbolic dynamical systems. The systems we consider consist of bi-infinite sequences associated with so-called random substitutions. We focus on random substitutions associated with the Fibonacci, tribonacci and metallic mean numbers and take advantage of their respective numeration schemes.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46374753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-01DOI: 10.21099/tkbjm/1585706453
Takayuki Kobayashi, M. Misawa, Kenji Nakamura
{"title":"Time-space $L^2$-boundedness for the 2D Navier-Stokes equations and hyperbolic Navier-Stokes equations","authors":"Takayuki Kobayashi, M. Misawa, Kenji Nakamura","doi":"10.21099/tkbjm/1585706453","DOIUrl":"https://doi.org/10.21099/tkbjm/1585706453","url":null,"abstract":"","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43852651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-01DOI: 10.21099/tkbjm/1585706451
M. Pandey, B. Ramakrishnan, Anup Kumar Singh
{"title":"Shimura and Shintani liftings of certain cusp forms of half-integral and integral weights","authors":"M. Pandey, B. Ramakrishnan, Anup Kumar Singh","doi":"10.21099/tkbjm/1585706451","DOIUrl":"https://doi.org/10.21099/tkbjm/1585706451","url":null,"abstract":"","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47228511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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