In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided int...In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided into,by the work of Amiot[Bull.Soc.Math.France,2007,135(3):435-474](see also[Adv.Math.,2008,217(6):2443-2484]and[J.Algebra,2016,446:426-449]),three classes:type A,type D and type E.展开更多
Aiming at exploring the excellent structural performance of the vein-stiffening membrane structure of dragonfly hind wings,we analyzed two planar computational models and three 3D computational models with cambered co...Aiming at exploring the excellent structural performance of the vein-stiffening membrane structure of dragonfly hind wings,we analyzed two planar computational models and three 3D computational models with cambered corrugation based on the finite element method.It is shown that the vein size in different zones is proportional to the magnitude of the vein internal force when the wing structure is subjected to uniform out-of-plane transverse loading.The membrane contributes little to the flexural stiffness of the planar wing models,while exerting an immense impact upon the stiffness of the 3D wing models with cambered corrugation.If a lumped mass of 10% of the wing is fixed on the leading edge close to the wing tip,the wing fundamental fre-quency decreases by 10.7%～13.2%;if a lumped mass is connected to the wing via multiple springs,the wing fundamental fre-quency decreases by 16.0%～18.0%.Such decrease in fundamental frequency explains the special function of the wing pterostigma in alleviating the wing quivering effect.These particular features of dragonfly wings can be mimicked in the design of new-style reticulately stiffening thin-walled roof systems and flapping wings in novel intelligent aerial vehicles.展开更多
Aloe dichotoma (Quiver tree) occurs in the arid regions of Namaqualand and Bushman land in South Africa, and in arid regions of southern Namibia. The Quiver trees are not only threatened by agricultural expansion, ove...Aloe dichotoma (Quiver tree) occurs in the arid regions of Namaqualand and Bushman land in South Africa, and in arid regions of southern Namibia. The Quiver trees are not only threatened by agricultural expansion, overgrazing, and mining;but also by climate changes and droughts. Previous studies show that Quiver trees are very sensitive to environmental changes, and do not respond well to extreme hot and dry conditions. This study investigates the current status of the Quiver tree within its existing environment, and also assesses the projected future changes of the Quiver tree habitat under different climatic scenarios. It provided evidence regarding the importance of the study to understanding the climate change impacts on the Quiver tree and its geographical response to climate changes.展开更多
In this paper, a sufficient and necessary condition for the indecomposable modules of the self injective algebra of finite representation type to be determined by their composition factors is presented by means of the...In this paper, a sufficient and necessary condition for the indecomposable modules of the self injective algebra of finite representation type to be determined by their composition factors is presented by means of the quiver with relations with the help of covering.展开更多
The model of the Coulomb dressed potential is applied to solving the problem of electron scattering for simplifying the calculation in the electrostatic field and the excimer laser field. The introduction and the appl...The model of the Coulomb dressed potential is applied to solving the problem of electron scattering for simplifying the calculation in the electrostatic field and the excimer laser field. The introduction and the application of the model are based on the electric dipole approximation, so the contribution of the electric multipole is neglected. In this paper, rigorous analysis and deduction are carried out for the introduction of the dressed Coulomb potential into the laser field. It is found that the introduction of the dressed potential in the fractional form is feasible only when the laser field （not including far ultraviolet field and x-ray） is a weak field, i.e. the quiver radius of the free electron is smaller than the atomic scale. In addition, the necessary analysis is also conducted of the limitation of the application of the Coulomb dressed potential.展开更多
For a field k and two finite groups G and X, when G acts on X from the right by group automorphisms, there is a Hopf algebra structure on k-space （kX°P）＊ kG （see Theorem 2.1）, called a non-balanced quantum ...For a field k and two finite groups G and X, when G acts on X from the right by group automorphisms, there is a Hopf algebra structure on k-space （kX°P）＊ kG （see Theorem 2.1）, called a non-balanced quantum double and denoted by Dx（G）. In this paper, some Hopf algebra properties of Dx （G） are given, the representation types of Dx （G） viewed as a k-algebra are discussed, the algebra structure and module category over Dx（G） are studied. Since the Hopf algebra structure of non-balanced quantum double DX （G） generMizes the usual quantum double D（G） for a finite group G, all results about Dx（G） in this paper can also be used to describe D（G） as a special case and the universal R-matrix of Dx （G） provides more solutions of Yang-Baxter equation.展开更多
Let K be an algebraically closed field and A be a finite dimensional algebra over K. In this paper we give a classification of biserial incidence algebras with quiver methods.
A technique is provided to explicitly describe global dimensions of all An-type finite dimensional k-algebras for k an algebraic closed field. All possible global dimensions of all AN-type finite dimensional algebras ...A technique is provided to explicitly describe global dimensions of all An-type finite dimensional k-algebras for k an algebraic closed field. All possible global dimensions of all AN-type finite dimensional algebras are explicitly presented. In particular, it is pointed out that the maximum is n - 1, and the minimum is 1 for n 〉 1.展开更多
Non-isomorphic two dimensional indecomposable modules over infinite dimensional hereditary path algebras are described. We infer that none of them can be determined by their dimension vectors.
Let A be a basic,connected finite dimensional algebra over an algebraically closed field with finite representation type, α(A) be the maximum of set consisting of numbers of indecomposable summands in the middle term...Let A be a basic,connected finite dimensional algebra over an algebraically closed field with finite representation type, α(A) be the maximum of set consisting of numbers of indecomposable summands in the middle term of Auslander Reiten sequences in mod A. In this paper we show that if α(A)=1, then Γ A contains oriented cycles if and only if Γ A contains DT r periodic modules. When α(A)2 we give counterexamples to the assertion.展开更多
We introduce a non-standard quantum group Xq（Bn） of type Bn which is a Hopf algebra. Then we replace the group of grouplike elements of Xq（Bn）, and obtain a weak Hopf algebra wXq（Bn）. Finally, we describe the Ex...We introduce a non-standard quantum group Xq（Bn） of type Bn which is a Hopf algebra. Then we replace the group of grouplike elements of Xq（Bn）, and obtain a weak Hopf algebra wXq（Bn）. Finally, we describe the Ext-quiver of wXq（Bn） as a coalgebra.展开更多
Using the connection between McKay quiver and Loewy matrix, and the properties of characteristic polynomial of Loewy matrix, we give a generalized way to determine the McKay quiver for a finite subgroup of a generaliz...Using the connection between McKay quiver and Loewy matrix, and the properties of characteristic polynomial of Loewy matrix, we give a generalized way to determine the McKay quiver for a finite subgroup of a generalized linear group.展开更多
The goal of this paper is to investigate whether the Ext-groups of all pairs (M, N) of modules over Nakayama algebras of type (n,n,n) satisfy the condition ExtΛn(M,N)=0 for n >> 0 ? ExtΛn(M,N)=0 for n >>...The goal of this paper is to investigate whether the Ext-groups of all pairs (M, N) of modules over Nakayama algebras of type (n,n,n) satisfy the condition ExtΛn(M,N)=0 for n >> 0 ? ExtΛn(M,N)=0 for n >> 0. We achieve that by discussing the Ext-groups of Nakayama algebra with projectives of lengths 3n+1 and 3n+2 using combinations of modules of different lengths.展开更多
We study four-dimensional quiver gauge models from F-theory compactified on fourfolds with hyper-K¨ahler structure.Using intersecting complex toric surfaces,we derive a class of N =1 quivers with charged fundamen...We study four-dimensional quiver gauge models from F-theory compactified on fourfolds with hyper-K¨ahler structure.Using intersecting complex toric surfaces,we derive a class of N =1 quivers with charged fundamental matter placed on external nodes.The emphasis is on how local Calabi–Yau equations solve the corresponding physical constraints including the anomaly cancelation condition.Concretely,a linear chain of SU(N) groups with flavor symmetries has been constructed using polyvalent toric geometry.展开更多
As generalizations of quivers of type A,Igusa et al.introduced continuous quivers of type A.In this paper,we generalize BGP reflection functors to continuous quivers of type A,and we give another realization of the re...As generalizations of quivers of type A,Igusa et al.introduced continuous quivers of type A.In this paper,we generalize BGP reflection functors to continuous quivers of type A,and we give another realization of the reflection functor.展开更多
We classify the representation type of the descent algebras of type A in the positive characteristic case.The algebras have finite representation type only for a few small degrees;otherwise,they are wild.Our main redu...We classify the representation type of the descent algebras of type A in the positive characteristic case.The algebras have finite representation type only for a few small degrees;otherwise,they are wild.Our main reduction method relies on a surjective algebra homomorphism from a descent algebra of type A to another of lower degree.For small degree cases,we employ techniques from the representation theory of finite-dimensional algebras.展开更多
We provide a detailed description of inner and outer Poisson structures for the trivial extension A D(A),where A is a hereditary algebra of Dynkin type An and D(A)=Homk(A,K).
文摘In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided into,by the work of Amiot[Bull.Soc.Math.France,2007,135(3):435-474](see also[Adv.Math.,2008,217(6):2443-2484]and[J.Algebra,2016,446:426-449]),three classes:type A,type D and type E.
基金Project supported by the National Natural Science Foundation of China(No. 50408022)the Visiting Scholarship from the Future Academic Star Project of Zhejiang Universitythe Scientific Research Foundation for the Returned Overseas Chinese Scholars,MOE and Zhejiang Province,China
文摘Aiming at exploring the excellent structural performance of the vein-stiffening membrane structure of dragonfly hind wings,we analyzed two planar computational models and three 3D computational models with cambered corrugation based on the finite element method.It is shown that the vein size in different zones is proportional to the magnitude of the vein internal force when the wing structure is subjected to uniform out-of-plane transverse loading.The membrane contributes little to the flexural stiffness of the planar wing models,while exerting an immense impact upon the stiffness of the 3D wing models with cambered corrugation.If a lumped mass of 10% of the wing is fixed on the leading edge close to the wing tip,the wing fundamental fre-quency decreases by 10.7%～13.2%;if a lumped mass is connected to the wing via multiple springs,the wing fundamental fre-quency decreases by 16.0%～18.0%.Such decrease in fundamental frequency explains the special function of the wing pterostigma in alleviating the wing quivering effect.These particular features of dragonfly wings can be mimicked in the design of new-style reticulately stiffening thin-walled roof systems and flapping wings in novel intelligent aerial vehicles.
文摘Aloe dichotoma (Quiver tree) occurs in the arid regions of Namaqualand and Bushman land in South Africa, and in arid regions of southern Namibia. The Quiver trees are not only threatened by agricultural expansion, overgrazing, and mining;but also by climate changes and droughts. Previous studies show that Quiver trees are very sensitive to environmental changes, and do not respond well to extreme hot and dry conditions. This study investigates the current status of the Quiver tree within its existing environment, and also assesses the projected future changes of the Quiver tree habitat under different climatic scenarios. It provided evidence regarding the importance of the study to understanding the climate change impacts on the Quiver tree and its geographical response to climate changes.
文摘In this paper, a sufficient and necessary condition for the indecomposable modules of the self injective algebra of finite representation type to be determined by their composition factors is presented by means of the quiver with relations with the help of covering.
基金Project supported by the National Natural Science Foundation of China （Grant No 10575140） and the Natural Science Foundation of Chongqing Science and Technology Committee （Grant No 2005BB8267） and The Basic Research Foundation of Chongqing Education Committee （Grant No KJ060813）.
文摘The model of the Coulomb dressed potential is applied to solving the problem of electron scattering for simplifying the calculation in the electrostatic field and the excimer laser field. The introduction and the application of the model are based on the electric dipole approximation, so the contribution of the electric multipole is neglected. In this paper, rigorous analysis and deduction are carried out for the introduction of the dressed Coulomb potential into the laser field. It is found that the introduction of the dressed potential in the fractional form is feasible only when the laser field （not including far ultraviolet field and x-ray） is a weak field, i.e. the quiver radius of the free electron is smaller than the atomic scale. In addition, the necessary analysis is also conducted of the limitation of the application of the Coulomb dressed potential.
基金Supported by Doctoral Foundation of Qingdao University of Science and Technology (20080022398)the National Natural Science Foundation of China (11271318, 11171296)the Specialized Research Fund for the Doctoral Program of Higher Education of China (20110101110010)
文摘For a field k and two finite groups G and X, when G acts on X from the right by group automorphisms, there is a Hopf algebra structure on k-space （kX°P）＊ kG （see Theorem 2.1）, called a non-balanced quantum double and denoted by Dx（G）. In this paper, some Hopf algebra properties of Dx （G） are given, the representation types of Dx （G） viewed as a k-algebra are discussed, the algebra structure and module category over Dx（G） are studied. Since the Hopf algebra structure of non-balanced quantum double DX （G） generMizes the usual quantum double D（G） for a finite group G, all results about Dx（G） in this paper can also be used to describe D（G） as a special case and the universal R-matrix of Dx （G） provides more solutions of Yang-Baxter equation.
基金Foundation item： Supported by the National Natural Science Foundation of China（11271119） Supported by the Natural Science Foundation of Beijing（1122002）
文摘Let K be an algebraically closed field and A be a finite dimensional algebra over K. In this paper we give a classification of biserial incidence algebras with quiver methods.
基金Supported by the National Natural Science Foundation of China(Grant No.11371307)
文摘A technique is provided to explicitly describe global dimensions of all An-type finite dimensional k-algebras for k an algebraic closed field. All possible global dimensions of all AN-type finite dimensional algebras are explicitly presented. In particular, it is pointed out that the maximum is n - 1, and the minimum is 1 for n 〉 1.
基金The NSF(11371307)of ChinaResearch Culture Funds(2014xmpy11)of Anhui Normal University
文摘Non-isomorphic two dimensional indecomposable modules over infinite dimensional hereditary path algebras are described. We infer that none of them can be determined by their dimension vectors.
文摘Let A be a basic,connected finite dimensional algebra over an algebraically closed field with finite representation type, α(A) be the maximum of set consisting of numbers of indecomposable summands in the middle term of Auslander Reiten sequences in mod A. In this paper we show that if α(A)=1, then Γ A contains oriented cycles if and only if Γ A contains DT r periodic modules. When α(A)2 we give counterexamples to the assertion.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11671024 11471186)the Natural Science Foundation of Beijing(Grant No.1162002)
文摘We introduce a non-standard quantum group Xq（Bn） of type Bn which is a Hopf algebra. Then we replace the group of grouplike elements of Xq（Bn）, and obtain a weak Hopf algebra wXq（Bn）. Finally, we describe the Ext-quiver of wXq（Bn） as a coalgebra.
基金Foundation item:This work is partly supported by NSF(103710036)of Chinakey project(02A024)of provincial Ministry of Foundation of Hunan.
文摘Using the connection between McKay quiver and Loewy matrix, and the properties of characteristic polynomial of Loewy matrix, we give a generalized way to determine the McKay quiver for a finite subgroup of a generalized linear group.
文摘The goal of this paper is to investigate whether the Ext-groups of all pairs (M, N) of modules over Nakayama algebras of type (n,n,n) satisfy the condition ExtΛn(M,N)=0 for n >> 0 ? ExtΛn(M,N)=0 for n >> 0. We achieve that by discussing the Ext-groups of Nakayama algebra with projectives of lengths 3n+1 and 3n+2 using combinations of modules of different lengths.
文摘We study four-dimensional quiver gauge models from F-theory compactified on fourfolds with hyper-K¨ahler structure.Using intersecting complex toric surfaces,we derive a class of N =1 quivers with charged fundamental matter placed on external nodes.The emphasis is on how local Calabi–Yau equations solve the corresponding physical constraints including the anomaly cancelation condition.Concretely,a linear chain of SU(N) groups with flavor symmetries has been constructed using polyvalent toric geometry.
基金Supported by National Natural Science Foundation of China(No.11771445).
文摘As generalizations of quivers of type A,Igusa et al.introduced continuous quivers of type A.In this paper,we generalize BGP reflection functors to continuous quivers of type A,and we give another realization of the reflection functor.
基金the Edinburgh Napier University for their support at thebeginning of this project
文摘We classify the representation type of the descent algebras of type A in the positive characteristic case.The algebras have finite representation type only for a few small degrees;otherwise,they are wild.Our main reduction method relies on a surjective algebra homomorphism from a descent algebra of type A to another of lower degree.For small degree cases,we employ techniques from the representation theory of finite-dimensional algebras.
文摘We provide a detailed description of inner and outer Poisson structures for the trivial extension A D(A),where A is a hereditary algebra of Dynkin type An and D(A)=Homk(A,K).
