Pub Date : 2021-08-19DOI: 10.21099/tkbjm/20224602153
F. Chapoton
This article introduces an algebra of functions in one variable $c$ defined by iterated integrals of two specific differential forms depending on $c$, where the product is the shuffle product. This algebra can be seen as a common deformation of multiple zeta values and of Kaneko-Tsumura's recent multiple $T$-values. The first few graded dimensions, assuming that a grading by the weight does hold, are computed.
{"title":"Multiple $T$-values with one parameter","authors":"F. Chapoton","doi":"10.21099/tkbjm/20224602153","DOIUrl":"https://doi.org/10.21099/tkbjm/20224602153","url":null,"abstract":"This article introduces an algebra of functions in one variable $c$ defined by iterated integrals of two specific differential forms depending on $c$, where the product is the shuffle product. This algebra can be seen as a common deformation of multiple zeta values and of Kaneko-Tsumura's recent multiple $T$-values. The first few graded dimensions, assuming that a grading by the weight does hold, are computed.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47803412","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 : 2021-07-01DOI: 10.21099/tkbjm/20214501069
M. Nagase, Takumi Shirakawa
Based on Getzler’s rescaling transformation, we obtain a formula for the heat kernel coefficients of the Dirac Laplacian on a spin manifold. One can compute them explicitly up to an arbitrarily high order by using only a basic knowledge of calculus added to the formula.
{"title":"A formula for the heat kernel coefficients of the Dirac Laplacians on spin manifolds","authors":"M. Nagase, Takumi Shirakawa","doi":"10.21099/tkbjm/20214501069","DOIUrl":"https://doi.org/10.21099/tkbjm/20214501069","url":null,"abstract":"Based on Getzler’s rescaling transformation, we obtain a formula for the heat kernel coefficients of the Dirac Laplacian on a spin manifold. One can compute them explicitly up to an arbitrarily high order by using only a basic knowledge of calculus added to the formula.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47558558","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 : 2020-12-01DOI: 10.21099/TKBJM/20204402235
D. Duverney, T. Kurosawa, I. Shiokawa
Let {xn} be a sequence of rational numbers greater than one such that xn+1 ≥ xn for all sufficiently large n and let εn ∈ {−1, 1}. Under certain growth conditions on the denominators of xn+1/x 2 n we prove that the irrationality exponent of the number ∑∞ n=1 εn/xn is equal to lim supn→∞(log xn+1/ log xn). 2010 Mathematics Subject Classification: 11A55, 11J70, 11J82, 11J91
{"title":"Irrationality exponents of certain fast converging series of\u0000 rational numbers","authors":"D. Duverney, T. Kurosawa, I. Shiokawa","doi":"10.21099/TKBJM/20204402235","DOIUrl":"https://doi.org/10.21099/TKBJM/20204402235","url":null,"abstract":"Let {xn} be a sequence of rational numbers greater than one such that xn+1 ≥ xn for all sufficiently large n and let εn ∈ {−1, 1}. Under certain growth conditions on the denominators of xn+1/x 2 n we prove that the irrationality exponent of the number ∑∞ n=1 εn/xn is equal to lim supn→∞(log xn+1/ log xn). 2010 Mathematics Subject Classification: 11A55, 11J70, 11J82, 11J91","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48209525","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 : 2020-12-01DOI: 10.21099/TKBJM/20204402271
Makoto Nakamura
{"title":"Remarks on the Navier-Stokes equations and the elastic wave\u0000 equations in homogeneous and isotropic spacetimes","authors":"Makoto Nakamura","doi":"10.21099/TKBJM/20204402271","DOIUrl":"https://doi.org/10.21099/TKBJM/20204402271","url":null,"abstract":"","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48598149","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 : 2020-12-01DOI: 10.21099/TKBJM/20204402309
Kenichiro Yamamoto
We prove that for all transitive piecewise monotonic maps, the following conditions are equivalent:(1) All ergodic measures on $[0,1]$ are approximated by periodic ones;(2) All invariant measures on coding spaces are approximated by periodic ones;(3) All ergodic measures on coding spaces are approximated by periodic ones.If we further assume that the map is piecewise increasing and either right or left continuous, then the following condition is also equivalent to (1)–(3).(4) All invariant measures on $[0,1]$ are approximated by periodic ones.We also construct an example of a piecewise decreasing and right continuous map which satisfies (1)–(3), but does not satisfy (4).
{"title":"On the density of periodic measures for piecewise monotonic\u0000 maps and their coding spaces","authors":"Kenichiro Yamamoto","doi":"10.21099/TKBJM/20204402309","DOIUrl":"https://doi.org/10.21099/TKBJM/20204402309","url":null,"abstract":"We prove that for all transitive piecewise monotonic maps, the following conditions are\u0000 equivalent:(1) All ergodic measures on $[0,1]$ are approximated by periodic ones;(2) All invariant measures on coding spaces are approximated by periodic ones;(3) All ergodic measures on coding spaces are approximated by periodic ones.If we further assume that the map is piecewise increasing and either right or left\u0000 continuous, then the following condition is also equivalent to (1)–(3).(4) All invariant measures on $[0,1]$ are approximated by periodic ones.We also construct an example of a piecewise decreasing and right continuous map which\u0000 satisfies (1)–(3), but does not satisfy (4).","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48968375","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 : 2020-12-01DOI: 10.21099/TKBJM/20204402213
M. Kaneko, Hirofumi Tsumura
We study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is regarded as the ‘shuffle counterpart’ of Hoffman’s ‘odd variant’, exhibits nice properties such as duality, shuffle product, parity results, etc., like ordinary multiple zeta values. We also give some conjectures on relations between our values, Hoffman’s values, and multiple zeta values.
{"title":"On multiple zeta values of level two","authors":"M. Kaneko, Hirofumi Tsumura","doi":"10.21099/TKBJM/20204402213","DOIUrl":"https://doi.org/10.21099/TKBJM/20204402213","url":null,"abstract":"We study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is regarded as the ‘shuffle counterpart’ of Hoffman’s ‘odd variant’, exhibits nice properties such as duality, shuffle product, parity results, etc., like ordinary multiple zeta values. We also give some conjectures on relations between our values, Hoffman’s values, and multiple zeta values.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42287774","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 : 2020-09-24DOI: 10.21099/tkbjm/20214501001
R. Laterveer
Garbagnati has constructed certain surfaces of general type that are bidouble planes as well as double covers of K3 surfaces. In this note, we study the Chow groups (and Chow motive) of these surfaces.
{"title":"Zero-cycles on Garbagnati surfaces","authors":"R. Laterveer","doi":"10.21099/tkbjm/20214501001","DOIUrl":"https://doi.org/10.21099/tkbjm/20214501001","url":null,"abstract":"Garbagnati has constructed certain surfaces of general type that are bidouble planes as well as double covers of K3 surfaces. In this note, we study the Chow groups (and Chow motive) of these surfaces.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49540313","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 : 2020-09-22DOI: 10.21099/tkbjm/20214501051
Atsufumi Honda, S. Izumiya, K. Saji, Keisuke Teramoto
A surface in the Lorentz-Minkowski $3$-space is generally a mixed type surface, namely, it has the lightlike locus. We study local differential geometric properties of such a locus on a mixed type surface. We define a frame field along a lightlike locus, and using it, we define two lightlike ruled surfaces along a lightlike locus which can be regarded as lightlike approximations of the surface along the lightlike locus. We study a relationship of singularities of these lightlike surfaces and differential geometric properties of the lightlike locus. We also consider the intersection curve of two lightlike approximations, which gives a model curve of the lightlike locus.
{"title":"Geometry of lightlike locus on mixed type surfaces in Lorentz-Minkowski 3-space from a contact viewpoint","authors":"Atsufumi Honda, S. Izumiya, K. Saji, Keisuke Teramoto","doi":"10.21099/tkbjm/20214501051","DOIUrl":"https://doi.org/10.21099/tkbjm/20214501051","url":null,"abstract":"A surface in the Lorentz-Minkowski $3$-space is generally a mixed type surface, namely, it has the lightlike locus. We study local differential geometric properties of such a locus on a mixed type surface. We define a frame field along a lightlike locus, and using it, we define two lightlike ruled surfaces along a lightlike locus which can be regarded as lightlike approximations of the surface along the lightlike locus. We study a relationship of singularities of these lightlike surfaces and differential geometric properties of the lightlike locus. We also consider the intersection curve of two lightlike approximations, which gives a model curve of the lightlike locus.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43460289","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 : 2020-07-01DOI: 10.21099/tkbjm/20204401203
Mayuko Kon
{"title":"3-Dimensional real hypersurfaces with transversal $eta$-Killing Ricci tensor field of a complex space form","authors":"Mayuko Kon","doi":"10.21099/tkbjm/20204401203","DOIUrl":"https://doi.org/10.21099/tkbjm/20204401203","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":"45028741","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 : 2020-07-01DOI: 10.21099/tkbjm/20204401121
B. Cahen
{"title":"The complex Weyl calculus as a Stratonovich-Weyl correspondence for the real diamond group","authors":"B. Cahen","doi":"10.21099/tkbjm/20204401121","DOIUrl":"https://doi.org/10.21099/tkbjm/20204401121","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":"46448481","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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