In this paper, we obtained characterizations of a curve with respect to the Frenet frame of Ruled surfaces in the 3-dimensional Pseudo-Galilean space $ G_ 3^1$.
本文得到了三维伪伽利略空间$ G_ 3^1$中关于直纹曲面的Frenet坐标系的曲线的刻画。
{"title":"On characterizations of general helices for ruled surfaces in the pseudo-Galilean space G~3^1-(Part-I)","authors":"M. Bektaş","doi":"10.1215/KJM/1250283082","DOIUrl":"https://doi.org/10.1215/KJM/1250283082","url":null,"abstract":"In this paper, we obtained characterizations of a curve with respect to the Frenet frame of Ruled surfaces in the 3-dimensional Pseudo-Galilean space $ G_ 3^1$.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1250283082","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66090400","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 : 2012-01-01DOI: 10.1215/21562261-1550994
Y. Ando
We give two types of singularities of maps between 4 q -manifolds whose Thom polynomials with integer coefficients have nonvanishing coefficient of Pontrjagin class P q . We show that an element of the J -image of dimension 4 q − 1 has a fold map between S 4 q − 1 and can be detected by the leading terms of Thom polynomials of those singularities of an extended map between D 4 q of the fold map.
{"title":"Leading terms of Thom polynomials and $J$- images","authors":"Y. Ando","doi":"10.1215/21562261-1550994","DOIUrl":"https://doi.org/10.1215/21562261-1550994","url":null,"abstract":"We give two types of singularities of maps between 4 q -manifolds whose Thom polynomials with integer coefficients have nonvanishing coefficient of Pontrjagin class P q . We show that an element of the J -image of dimension 4 q − 1 has a fold map between S 4 q − 1 and can be detected by the leading terms of Thom polynomials of those singularities of an extended map between D 4 q of the fold map.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/21562261-1550994","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66024728","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 : 2011-04-29DOI: 10.1215/21562261-1625154
Radjesvarane Alexandre, Y. Morimoto, S. Ukai, Chao-Jiang Xu, Tong Yang
In this paper, we consider the spatially homogeneous Boltzmann equation without angular cutoff. We prove that every $L^1$ weak solution to the Cauchy problem with finite moments of all order acquires the $C^infty$ regularity in the velocity variable for the positive time.
{"title":"Smoothing effect of weak solutions for the spatially homogeneous Boltzmann Equation without angular cutoff","authors":"Radjesvarane Alexandre, Y. Morimoto, S. Ukai, Chao-Jiang Xu, Tong Yang","doi":"10.1215/21562261-1625154","DOIUrl":"https://doi.org/10.1215/21562261-1625154","url":null,"abstract":"In this paper, we consider the spatially homogeneous Boltzmann equation without angular cutoff. We prove that every $L^1$ weak solution to the Cauchy problem with finite moments of all order acquires the $C^infty$ regularity in the velocity variable for the positive time.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/21562261-1625154","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66024797","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 : 2011-02-02DOI: 10.1215/21562261-2642413
G. Tomasini, B. Orsted
In this paper we initiate a study of the relation between weight modules for simple Lie algebras and unitary representations of the corresponding simply-connected Lie groups. In particular we consider in detail from this point of view the universal covering group of SU(1,1), including new results on the discrete part of tensor products of irreducible representations. As a consequence of these results, we show that the set of smooth vectors of the tensor product intersects trivially some of the representations in the discrete spectrum.
{"title":"Unitary representations of the universal cover of SU(1,1) SU?(1,1) and tensor products","authors":"G. Tomasini, B. Orsted","doi":"10.1215/21562261-2642413","DOIUrl":"https://doi.org/10.1215/21562261-2642413","url":null,"abstract":"In this paper we initiate a study of the relation between weight modules for simple Lie algebras and unitary representations of the corresponding simply-connected Lie groups. In particular we consider in detail from this point of view the universal covering group of SU(1,1), including new results on the discrete part of tensor products of irreducible representations. As a consequence of these results, we show that the set of smooth vectors of the tensor product intersects trivially some of the representations in the discrete spectrum.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/21562261-2642413","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66026270","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 : 2011-01-01DOI: 10.1215/21562261-1424857
E. Bernardi, T. Nishitani
{"title":"On the Cauchy problem for noneffectively hyperbolic operators: The Gevrey 4 well-posedness","authors":"E. Bernardi, T. Nishitani","doi":"10.1215/21562261-1424857","DOIUrl":"https://doi.org/10.1215/21562261-1424857","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/21562261-1424857","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66024563","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 : 2011-01-01DOI: 10.1215/21562261-1299900
Kazuya Kato
We construct toroidal partial compactifications of p-adic period domains.
构造了p进周期域的环向部分紧化。
{"title":"$p$-Adic period domains and toroidal partial compactifications, I","authors":"Kazuya Kato","doi":"10.1215/21562261-1299900","DOIUrl":"https://doi.org/10.1215/21562261-1299900","url":null,"abstract":"We construct toroidal partial compactifications of p-adic period domains.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/21562261-1299900","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66024481","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 : 2011-01-01DOI: 10.1215/21562261-1424866
J. Asadollahi, Shokrollah Salarian, R. Sazeedeh
{"title":"On the local cohomology and support for triangulated categories","authors":"J. Asadollahi, Shokrollah Salarian, R. Sazeedeh","doi":"10.1215/21562261-1424866","DOIUrl":"https://doi.org/10.1215/21562261-1424866","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/21562261-1424866","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66024571","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 : 2010-08-19DOI: 10.1215/21562261-1299909
Abel Castorena, C. Ciliberto
In this paper we prove a theorem stated by Castelnuovo which bounds the dimension of linear systems of plane curves in terms of two invariants, one of which is the genus of the curves in the system. This extends a previous result of Castelnuovo and Enriques.We classify linear systems whose dimension belongs to certain intervals which naturally arise from Castelnuovo’s theorem. Then we make an application to the followingmoduli problem: what is themaximu mnumber ofmoduli of curves of geometric genus g varying in a linear system on a surface? It turns out that, for g ≥ 22, theanswer is 2g+1, and it is attained by trigonal canonical curves varying on a balanced rational normal scroll.
{"title":"On a theorem of Castelnuovo and applications to moduli","authors":"Abel Castorena, C. Ciliberto","doi":"10.1215/21562261-1299909","DOIUrl":"https://doi.org/10.1215/21562261-1299909","url":null,"abstract":"In this paper we prove a theorem stated by Castelnuovo which bounds the \u0000dimension of linear systems of plane curves in terms of two invariants, one of which is \u0000the genus of the curves in the system. This extends a previous result of Castelnuovo and \u0000Enriques.We classify linear systems whose dimension belongs to certain intervals which \u0000naturally arise from Castelnuovo’s theorem. Then we make an application to the followingmoduli \u0000problem: what is themaximu mnumber ofmoduli of curves of geometric genus \u0000g varying in a linear system on a surface? It turns out that, for g ≥ 22, theanswer is 2g+1, \u0000and it is attained by trigonal canonical curves varying on a balanced rational normal \u0000scroll.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/21562261-1299909","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66024508","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 : 2010-03-01DOI: 10.1215/0023608X-2009-008
J. Itoh, S. Sabau, H. Shimada
We prove a Gauss-Bonnet type formula for Riemann-Finsler surfaces of non-constant indicatrix volume and with regular piecewise smooth boundary. We give a Hadamard type theorem for N-parallels of a Landsberg surface.
{"title":"A Gauss-Bonnet-type formula on Riemann-Finsler surfaces with nonconstant indicatrix volume","authors":"J. Itoh, S. Sabau, H. Shimada","doi":"10.1215/0023608X-2009-008","DOIUrl":"https://doi.org/10.1215/0023608X-2009-008","url":null,"abstract":"We prove a Gauss-Bonnet type formula for Riemann-Finsler surfaces of non-constant indicatrix volume and with regular piecewise smooth boundary. We give a Hadamard type theorem for N-parallels of a Landsberg surface.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/0023608X-2009-008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66040389","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 : 2010-02-16DOI: 10.1215/21562261-1214375
B. Feigin, E. Feigin, M. Jimbo, T. Miwa, E. Mukhin
We begin a study of the representation theory of quantum continuous $mathfrak{gl}_infty$, which we denote by $mathcal E$. This algebra depends on two parameters and is a deformed version of the enveloping algebra of the Lie algebra of difference operators acting on the space of Laurent polynomials in one variable. Fundamental representations of $mathcal E$ are labeled by a continuous parameter $uin {mathbb C}$. The representation theory of $mathcal E$ has many properties familiar from the representation theory of $mathfrak{gl}_infty$: vector representations, Fock modules, semi-infinite constructions of modules. Using tensor products of vector representations, we construct surjective homomorphisms from $mathcal E$ to spherical double affine Hecke algebras $Sddot H_N$ for all $N$. A key step in this construction is an identification of a natural bases of the tensor products of vector representations with Macdonald polynomials. We also show that one of the Fock representations is isomorphic to the module constructed earlier by means of the $K$-theory of Hilbert schemes.
{"title":"Quantum continuous $mathfrak{gl}_{infty}$: Semiinfinite construction of representations","authors":"B. Feigin, E. Feigin, M. Jimbo, T. Miwa, E. Mukhin","doi":"10.1215/21562261-1214375","DOIUrl":"https://doi.org/10.1215/21562261-1214375","url":null,"abstract":"We begin a study of the representation theory of quantum continuous $mathfrak{gl}_infty$, which we denote by $mathcal E$. This algebra depends on two parameters and is a deformed version of the enveloping algebra of the Lie algebra of difference operators acting on the space of Laurent polynomials in one variable. Fundamental representations of $mathcal E$ are labeled by a continuous parameter $uin {mathbb C}$. The representation theory of $mathcal E$ has many properties familiar from the representation theory of $mathfrak{gl}_infty$: vector representations, Fock modules, semi-infinite constructions of modules. Using tensor products of vector representations, we construct surjective homomorphisms from $mathcal E$ to spherical double affine Hecke algebras $Sddot H_N$ for all $N$. A key step in this construction is an identification of a natural bases of the tensor products of vector representations with Macdonald polynomials. We also show that one of the Fock representations is isomorphic to the module constructed earlier by means of the $K$-theory of Hilbert schemes.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2010-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/21562261-1214375","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66024823","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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