We first prove that for a finite dimensional non-semisimple Hopfalgebra H, the trivial H-module is not projective and so the almost split sequence ended with k exists. By this exact sequence, for all indecomposable H-...We first prove that for a finite dimensional non-semisimple Hopfalgebra H, the trivial H-module is not projective and so the almost split sequence ended with k exists. By this exact sequence, for all indecomposable H-module X, we can construct a special kind of exact sequence ending with it. The main aim of this paper is to determine when this special exact sequence is an almost split one. For this aim, we restrict H to be tmimodular and the square of its antipode to be an inner automorphism. As a special case, we give an application to the quantum double D（H）=（H^op）^＊∞ H） of any non-semisimple Hopf algebra.展开更多
大地震能够同时激发出许多的地球自由振荡简正模,且地球的椭率、自转和内部的各向异性也会引起简正模的分裂,使各单线态之间的频率更接近(仅为几个μHz),这对地球自由振荡模型的检测提出更高的要求。本文以标准时频变换为基础,推导并验...大地震能够同时激发出许多的地球自由振荡简正模,且地球的椭率、自转和内部的各向异性也会引起简正模的分裂,使各单线态之间的频率更接近(仅为几个μHz),这对地球自由振荡模型的检测提出更高的要求。本文以标准时频变换为基础,推导并验证一种自由振荡模型检测的新方法。以3 S 1模型的检测为例,与经典的FT谱方法和最新的OSE方法相比,该方法具有更高的频率分辨率。展开更多
The concept of the splitting ring of the polynomial over ring Z(pe) is introduced and the factomation of polynomials and the properties df polynomial roots are discussed. By using these results and the structure of se...The concept of the splitting ring of the polynomial over ring Z(pe) is introduced and the factomation of polynomials and the properties df polynomial roots are discussed. By using these results and the structure of sequence families, it is shown that the terms of a linear recurring sequence over Z/(pe) may be represented by the roots of its characteristic polynomial and the representation is uniquely determined by the sequence.展开更多
Let A be an Artinian algebra and F an additive subbifunctor of Ext,（-, -） having enough projectives and injectives. We prove that the dualizing subvarieties of mod A closed under F-extensions have F-almost split seq...Let A be an Artinian algebra and F an additive subbifunctor of Ext,（-, -） having enough projectives and injectives. We prove that the dualizing subvarieties of mod A closed under F-extensions have F-almost split sequences. Let T be an F-cotilting module in mod A and S a cotilting module over F = End（T）. Then Horn（-, T） induces a duality between F-almost split sequences in ⊥FT and almost sl31it sequences in ⊥S, where addrS = Hom∧（f（F）, T）. Let A be an F-Gorenstein algebra, T a strong F-cotilting module and 0→A→B→C→0 and F-almost split sequence in ⊥FT.If the injective dimension of S as a Г-module is equal to d, then C≌（ΩCM^-dΩ^dDTrA^＊）^＊,where（-）^＊=Hom（g,T）.In addition, if the F-injective dimension of A is equal to d, then A≌ΩMF^-dDΩFop^-d TrC≌ΩCMF^-d ≌F^d DTrC.展开更多
Let l be a line in a projective space Pn.We consider the blowing up P^(n)(l)of Pnalong l.Assume that X is a smooth closed subvariety of P^(n).If the strict transform of X in P^(n)(l)has a splitting tangent sequence an...Let l be a line in a projective space Pn.We consider the blowing up P^(n)(l)of Pnalong l.Assume that X is a smooth closed subvariety of P^(n).If the strict transform of X in P^(n)(l)has a splitting tangent sequence and dim X is at least 2,then X is a linear subspace of P^(n).展开更多
基金Project (No. 10371107) supported by the National Natural ScienceFoundation of China
文摘We first prove that for a finite dimensional non-semisimple Hopfalgebra H, the trivial H-module is not projective and so the almost split sequence ended with k exists. By this exact sequence, for all indecomposable H-module X, we can construct a special kind of exact sequence ending with it. The main aim of this paper is to determine when this special exact sequence is an almost split one. For this aim, we restrict H to be tmimodular and the square of its antipode to be an inner automorphism. As a special case, we give an application to the quantum double D（H）=（H^op）^＊∞ H） of any non-semisimple Hopf algebra.
文摘大地震能够同时激发出许多的地球自由振荡简正模,且地球的椭率、自转和内部的各向异性也会引起简正模的分裂,使各单线态之间的频率更接近(仅为几个μHz),这对地球自由振荡模型的检测提出更高的要求。本文以标准时频变换为基础,推导并验证一种自由振荡模型检测的新方法。以3 S 1模型的检测为例,与经典的FT谱方法和最新的OSE方法相比,该方法具有更高的频率分辨率。
基金Project supported by the State Key Laboratory of Information Security,Graduate School of Academia Sinica.
文摘The concept of the splitting ring of the polynomial over ring Z(pe) is introduced and the factomation of polynomials and the properties df polynomial roots are discussed. By using these results and the structure of sequence families, it is shown that the terms of a linear recurring sequence over Z/(pe) may be represented by the roots of its characteristic polynomial and the representation is uniquely determined by the sequence.
基金Partially supported by the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20060284002)National Natural Science Foundation of China (Grant No. 10771095)National Natural Science Foundation of Jiangsu Province of China (Grant No. BK2007517)
文摘Let A be an Artinian algebra and F an additive subbifunctor of Ext,（-, -） having enough projectives and injectives. We prove that the dualizing subvarieties of mod A closed under F-extensions have F-almost split sequences. Let T be an F-cotilting module in mod A and S a cotilting module over F = End（T）. Then Horn（-, T） induces a duality between F-almost split sequences in ⊥FT and almost sl31it sequences in ⊥S, where addrS = Hom∧（f（F）, T）. Let A be an F-Gorenstein algebra, T a strong F-cotilting module and 0→A→B→C→0 and F-almost split sequence in ⊥FT.If the injective dimension of S as a Г-module is equal to d, then C≌（ΩCM^-dΩ^dDTrA^＊）^＊,where（-）^＊=Hom（g,T）.In addition, if the F-injective dimension of A is equal to d, then A≌ΩMF^-dDΩFop^-d TrC≌ΩCMF^-d ≌F^d DTrC.
基金Supported by National Natural Science Foundation of China(Grant No.12001547)Guangdong Basic and Applied Basic Research Foundation(Grant No.2019A1515110907)。
文摘Let l be a line in a projective space Pn.We consider the blowing up P^(n)(l)of Pnalong l.Assume that X is a smooth closed subvariety of P^(n).If the strict transform of X in P^(n)(l)has a splitting tangent sequence and dim X is at least 2,then X is a linear subspace of P^(n).
