Let $R$ be a commutative Noetherian ring, and let $I$ and $J$ be two ideals of $R$. Assume that $R$ is local with the maximal ideal ${mathfrak{m}}$, we mainly prove that (i) there exists an equality [{text{inf}}{i, mid H_{I,J}^i(M), {text{ is not Artinian}} }={text{inf}}{ {text{depth}}M_{mathfrak{p}} mid , {mathfrak{p}}in W(I, J)backslash {{mathfrak{m}}} }] for any finitely generated $R-$module $M$, where $W(I, J)={{mathfrak{p}} in {text{Spec}}(R) mid , I^n subseteq {mathfrak{p}}+J,, {text{for some positive integer}} ,n }$; (ii) for any finitely generated $R-$module $M$ with ${text{dim}}M=d$, $H_{I,J}^d(M)$ is Artinian. Also, we give a characterization to the supremum of all integers $r$ for which $H_{I,J}^r(M) neq 0$.
设$R$为可交换诺埃尔环，设$I$和$J$为$R$的两个理想。假设$R$是局部的，具有极大理想${mathfrak{m}}$，我们主要证明(i)对于任意有限生成的$R-$模块$M$存在一个等式[{text{inf}}{i, mid H_{I,J}^i(M), {text{ is not Artinian}} }={text{inf}}{ {text{depth}}M_{mathfrak{p}} mid , {mathfrak{p}}in W(I, J)backslash {{mathfrak{m}}} }]，其中$W(I, J)={{mathfrak{p}} in {text{Spec}}(R) mid , I^n subseteq {mathfrak{p}}+J,, {text{for some positive integer}} ,n }$;(ii)对于任何具有${text{dim}}M=d$的有限生成$R-$模块$M$, $H_{I,J}^d(M)$是Artinian。同时，我们给出了所有整数$r$的上极值的一个表征，其中$H_{I,J}^r(M) neq 0$。
{"title":"Some results on local cohomology modules defined by a pair of ideals","authors":"L. Chu, Qing Wang","doi":"10.1215/KJM/1248983036","DOIUrl":"https://doi.org/10.1215/KJM/1248983036","url":null,"abstract":"Let $R$ be a commutative Noetherian ring, and let $I$ and $J$ be two ideals of $R$. Assume that $R$ is local with the maximal ideal ${mathfrak{m}}$, we mainly prove that (i) there exists an equality [{text{inf}}{i, mid H_{I,J}^i(M), {text{ is not Artinian}} }={text{inf}}{ {text{depth}}M_{mathfrak{p}} mid , {mathfrak{p}}in W(I, J)backslash {{mathfrak{m}}} }] for any finitely generated $R-$module $M$, where $W(I, J)={{mathfrak{p}} in {text{Spec}}(R) mid , I^n subseteq {mathfrak{p}}+J,, {text{for some positive integer}} ,n }$; (ii) for any finitely generated $R-$module $M$ with ${text{dim}}M=d$, $H_{I,J}^d(M)$ is Artinian. Also, we give a characterization to the supremum of all integers $r$ for which $H_{I,J}^r(M) neq 0$.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1248983036","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087663","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}
{"title":"Free-fall and heteroclinic orbits to triple collisions in the isosceles three-body problem","authors":"M. Shibayama","doi":"10.1215/KJM/1265899480","DOIUrl":"https://doi.org/10.1215/KJM/1265899480","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66114237","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}
Let $G$ be a connected and simply connected, nilpotent Lie group. In this paper, we show that the cortex of $G$ is a semi-algebraic set by means of a geometric characterization. It is also shown that the cortex is the image under a linear projection of a countable union of a semi-algebraic sets lying in the tensor product $T$($mathfrak{g}$)$otimes$ $mathfrak{g}$*.
{"title":"Sur le Cortex d'un groupe de Lie nilpotent","authors":"Imed Kédim, Megdiche Hatem","doi":"10.1215/KJM/1248983034","DOIUrl":"https://doi.org/10.1215/KJM/1248983034","url":null,"abstract":"Let $G$ be a connected and simply connected, nilpotent Lie group. In this paper, we show that the cortex of $G$ is a semi-algebraic set by means of a geometric characterization. It is also shown that the cortex is the image under a linear projection of a countable union of a semi-algebraic sets lying in the tensor product $T$($mathfrak{g}$)$otimes$ $mathfrak{g}$*.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1248983034","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087279","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}
We consider a Markov chain with values in [0,$infty$)$^{mathbb{z}d}$. The Markov chain includes some interesting examples such as the oriented site percolation, the directed polymers in random environment, and a time discretization of the binary contact process. We prove a central limit theorem for �the spatial distribution of population� when $dgeq 3$ and a certain square-integrability condition for the total population is satisfied. This extends a result known for the directed polymers in random environment to a large class of models.
{"title":"Central Limit Theorem for Linear Stochastic Evolutions","authors":"M. Nakashima","doi":"10.1215/KJM/1248983037","DOIUrl":"https://doi.org/10.1215/KJM/1248983037","url":null,"abstract":"We consider a Markov chain with values in [0,$infty$)$^{mathbb{z}d}$. The Markov chain includes some interesting examples such as the oriented site percolation, the directed polymers in random environment, and a time discretization of the binary contact process. We prove a central limit theorem for �the spatial distribution of population� when $dgeq 3$ and a certain square-integrability condition for the total population is satisfied. This extends a result known for the directed polymers in random environment to a large class of models.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087681","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}
We use a projective groups representation ρ of the unimodular group G× ˆ G on L 2 ( G ) to define Gabor wavelet transform of a function f with respect to a window function g , where G is a locally compact abelian group and ˆ G its dual group. Using these transforms, we define a weighted Banach H 1 , ρ w ( G ) and its antidual space H 1 ∼ , ρ w ( G ) , w being a moderate weight function on G × ˆ G . These spaces reduce to the well known Feichtinger algebra S 0 ( G ) and Banach space of Feichtinger distribution S (cid:2) 0 ( G ) respectively for w ≡ 1. We obtain an atomic decomposition of H 1 , ρ w ( G ) and study some properties of Gabor multipliers on the spaces L 2 ( G ) , H 1 , ρ w ( G ) and H 1 ∼ , ρ w ( G ). Finally, we prove a theorem on the compactness of Gabor multiplier operators on L 2 ( G ) and H 1 , ρ w ( G ), which reduces to an earlier result of Feichtinger [Fei 02, Theorem 5.15 (iv)] for w = 1 and G = R d .
利用l2 (G)上的单模群gx * G的一个射影群表示ρ定义了函数f关于窗函数G的Gabor小波变换，其中G是一个局部紧阿贝尔群，G是它的对偶群。利用这些变换，我们定义了一个加权的Banach h1， ρ w (G)和它的反对偶空间h1 ~， ρ w (G)，其中w是G × G上的一个中等权函数。当w≡1时，这些空间分别化为众所周知的Feichtinger代数s0 (G)和Feichtinger分布S (cid:2) 0 (G)的Banach空间。我们得到了h1， ρ w (G)的原子分解，并研究了l2 (G)， h1， ρ w (G)和h1 ~， ρ w (G)空间上Gabor乘子的一些性质。最后，我们证明了l2 (G)和h1， ρ w (G)上的Gabor乘子算子的紧性定理，它简化为Feichtinger [Fei 02，定理5.15 (iv)]对于w = 1和G = R d的早期结果。
{"title":"Gabor multipliers for weighted Banach spaces on locally compact abelian groups","authors":"S. S. Pandey","doi":"10.1215/KJM/1256219154","DOIUrl":"https://doi.org/10.1215/KJM/1256219154","url":null,"abstract":"We use a projective groups representation ρ of the unimodular group G× ˆ G on L 2 ( G ) to define Gabor wavelet transform of a function f with respect to a window function g , where G is a locally compact abelian group and ˆ G its dual group. Using these transforms, we define a weighted Banach H 1 , ρ w ( G ) and its antidual space H 1 ∼ , ρ w ( G ) , w being a moderate weight function on G × ˆ G . These spaces reduce to the well known Feichtinger algebra S 0 ( G ) and Banach space of Feichtinger distribution S (cid:2) 0 ( G ) respectively for w ≡ 1. We obtain an atomic decomposition of H 1 , ρ w ( G ) and study some properties of Gabor multipliers on the spaces L 2 ( G ) , H 1 , ρ w ( G ) and H 1 ∼ , ρ w ( G ). Finally, we prove a theorem on the compactness of Gabor multiplier operators on L 2 ( G ) and H 1 , ρ w ( G ), which reduces to an earlier result of Feichtinger [Fei 02, Theorem 5.15 (iv)] for w = 1 and G = R d .","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113524","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}
In this paper we generalize some results, obtained by Shimura, Yoshida on critical values of L-functions of l-adic representations attached to tensor product of Hilbert modular forms, to the critical values of L-functions of arbitrary base change to totally real number elds of l-adic representations attached to tensor product of Hilbert modular forms.
{"title":"On the critical values of $L$-functions of tensor product of base change for Hilbert modular forms","authors":"Cristian Virdol","doi":"10.1215/KJM/1256219161","DOIUrl":"https://doi.org/10.1215/KJM/1256219161","url":null,"abstract":"In this paper we generalize some results, obtained by Shimura, Yoshida on critical values of L-functions of l-adic representations attached to tensor product of Hilbert modular forms, to the critical values of L-functions of arbitrary base change to totally real number elds of l-adic representations attached to tensor product of Hilbert modular forms.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1256219161","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113712","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}
{"title":"The rationality problem for four-dimensional linear actions","authors":"H. Kitayama, A. Yamasaki","doi":"10.1215/KJM/1256219162","DOIUrl":"https://doi.org/10.1215/KJM/1256219162","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113757","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}
In this paper, we give a characterization of the direct product of balls by its holomorphic automorphism group. Using a result on the standardization of certain compact group actions on complex manifolds, we show that, for a connected Stein manifold M of dimension n , if its holomorphic automorphism group contains a topological subgroup that is isomorphic to the holomorphic automorphism group of the direct product B of balls in C n , then M itself is biholomorphically equivalent to B .
{"title":"An intrinsic characterization of the direct product of balls","authors":"A. Kodama, S. Shimizu","doi":"10.1215/KJM/1260975042","DOIUrl":"https://doi.org/10.1215/KJM/1260975042","url":null,"abstract":"In this paper, we give a characterization of the direct product of balls by its holomorphic automorphism group. Using a result on the standardization of certain compact group actions on complex manifolds, we show that, for a connected Stein manifold M of dimension n , if its holomorphic automorphism group contains a topological subgroup that is isomorphic to the holomorphic automorphism group of the direct product B of balls in C n , then M itself is biholomorphically equivalent to B .","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1260975042","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66114116","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}
W.Kirsch and I.Veseli´c proved a generalized Wegner estimate for Schr¨odinger operators with generalized alloy type potentials at negative energies for each fixed position of impurities. In this paper, a similar estimate is proven treating also the position of impurities as random variables.
{"title":"Wegner estimate for a generalized alloy type potential","authors":"Jyunichi Takahara","doi":"10.1215/KJM/1256219155","DOIUrl":"https://doi.org/10.1215/KJM/1256219155","url":null,"abstract":"W.Kirsch and I.Veseli´c proved a generalized Wegner estimate for Schr¨odinger operators with generalized alloy type potentials at negative energies for each fixed position of impurities. In this paper, a similar estimate is proven treating also the position of impurities as random variables.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113570","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}
The invariant Cantor set of Smale’s horseshoe map is imbedded into a connented and not arcwise connected, invariant, compact set with zero Lebesgue measure.
{"title":"Connected and not arcwise connected invariant sets for some 2-dimmensional dynamical systems","authors":"F. Nakajima","doi":"10.1215/kjm/1256219160","DOIUrl":"https://doi.org/10.1215/kjm/1256219160","url":null,"abstract":"The invariant Cantor set of Smale’s horseshoe map is imbedded into a connented and not arcwise connected, invariant, compact set with zero Lebesgue measure.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113698","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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