The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattic...The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattice constant ratio of 1:2 as an example. For the symmetric nearest-neighbor intra-chain hopping two-leg ladder, the inversion symmetry protected topological insulator phase with two degenerate topological edge states appears. When the inversion symmetry is broken, the topological insulators with one or two topological edge states of different energies and topological metals with edge states embedded in the bulk states could emerge depending on the filling factor. The topological origin of these topological states in the two-leg ladders is the topological properties of the Chern insulators and Chern metals. According to the arrangement of two trivial quantum wires, we construct two types of three-leg ladders. Each type of the three-leg ladder could be divided into one trivial subspace and one topological nontrivial subspace by unitary transformation. The topological nontrivial subspace corresponds to the effective two-leg ladder model. As the filling factor changes, the system could be in topological insulators or topological metals phases. When the two-leg ladder is constructed by two trivial quantum wires with a lattice constant ratio of 1:3 and 2:3, the system could also realize rich topological states such as the topological insulators and topological metals with the topological edge states. These rich topological states in the two-leg and three-leg ladders could be confirmed by current experimental techniques.展开更多
By means of the method of torus knot theory, this paper gives the complete processes of obtaining the knotted pictures of four Bell b^es from the knotted pictures of four basic two qubit states.
A nonlocality distillation protocol for arbitrary high-dimensional systems is proposed. We study the nonlocality distillation in the 2-input d-output bi-partite case. Firstly, we give the one-parameter nonlocal boxes ...A nonlocality distillation protocol for arbitrary high-dimensional systems is proposed. We study the nonlocality distillation in the 2-input d-output bi-partite case. Firstly, we give the one-parameter nonlocal boxes and their correlated distilling protocol. Then, we generalize the one-parameter nonlocality distillation protocol to the twoparameter case. Furthermore, we introduce a contracting protocol testifying that the 2-input d-output nonlocal boxes make communication complexity trivial.展开更多
Let A be a basic hereditary artin algebra and R = A Q be the trivial extension of A by its minimal injective cogenerator Q. We construct some right （left） almost split morphisms and irreducible morphisms in modR thr...Let A be a basic hereditary artin algebra and R = A Q be the trivial extension of A by its minimal injective cogenerator Q. We construct some right （left） almost split morphisms and irreducible morphisms in modR through the corresponding morphisms in modA. Furthermore, we can determine its almost split sequences in modR.展开更多
We provide estimates on the degree of C l GV determinacy （ G is one of Mather’s groups R or K ） of function germs which are defined on analytic variety V and satisfies a non-degeneracy condition with respect to som...We provide estimates on the degree of C l GV determinacy （ G is one of Mather’s groups R or K ） of function germs which are defined on analytic variety V and satisfies a non-degeneracy condition with respect to some Newton polyhedron. The result gives an explicit order such that the C l geometrical structure of a function germ is preserved after higher order perturbations, which generalizes the result on C l G triviality of function germs given by M.A.S.Ruas.展开更多
Historically,re-selection,pedigree,and mass selection breeding methods have been used to develop open-pollinated cultivars of Upland cotton(Gossypium hirsutum L.). Due to the
The movie The Hours, adapted from Michael Cunningham's novel, presents us three different women's life in a day to reflect trivial people's struggle, contemplation of self-worth and death, with Philip Glas...The movie The Hours, adapted from Michael Cunningham's novel, presents us three different women's life in a day to reflect trivial people's struggle, contemplation of self-worth and death, with Philip Glass' scores and the well-designed settings. This paper focuses on Glass' scores and analyzes its connection with other elements, reflection of those people and coherence of the movie.展开更多
To Work for Tomorrow Liu Hong, General Manager of TUTTI Exhibition Service (Xiamen) Co., Ltd, has set up TUTTI Exhibition Service (Xiamen) Co., Ltd in 2001, when exhibition industry firstly appear in Xiamen. Furthermo...To Work for Tomorrow Liu Hong, General Manager of TUTTI Exhibition Service (Xiamen) Co., Ltd, has set up TUTTI Exhibition Service (Xiamen) Co., Ltd in 2001, when exhibition industry firstly appear in Xiamen. Furthermore, the company has developed rapidly in recent years. As Liu Hong regards, exhibition industry, as well as advertisement industry, is an industry filled with challenges and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).
A mid-infrared orbital angular momentum detector based on multilayer graphene has been successfully developed,overcoming the previous reliance on C_(2V) point group topological Weyl semimetals via the orbital photogal...A mid-infrared orbital angular momentum detector based on multilayer graphene has been successfully developed,overcoming the previous reliance on C_(2V) point group topological Weyl semimetals via the orbital photogalvanic effect.This CMOS-compatible two-dimensional material system is crucial for advancing the large-scale practical application of orbital angular momentum detectors.展开更多
In this paper we investigate a categorical aspect of n-trivial extension of a ring by a family of modules.Namely,we introduce the right(resp.,left)n-trivial extension of a category by a family of endofunctors.Among ot...In this paper we investigate a categorical aspect of n-trivial extension of a ring by a family of modules.Namely,we introduce the right(resp.,left)n-trivial extension of a category by a family of endofunctors.Among other results,projective,injective and flat objects of this category are characterized,and two applications are presented at the end of this paper.We characterize when an n-trivial extension ring is k-perfect and establish a result on the self-injective dimension of an n-trivial extension ring.展开更多
The structure of the trivial preference set of group decision making is studied, and the essential characters and generating reasons of the paradox of voting are revealed.
Given a finite dimensional special biserial algebra A with normed basis we obtain the dimension formulae of the first Hochschild homology groups of A and the vector space Alt(DA). As a consequence, an explicit dimensi...Given a finite dimensional special biserial algebra A with normed basis we obtain the dimension formulae of the first Hochschild homology groups of A and the vector space Alt(DA). As a consequence, an explicit dimension formula of the first Hochschild cohomology group of trivial extension TA = A × DA in terms of the combinatorics of the quiver and relations is determined.展开更多
Let T(A)=A?D(A) be a representation-finite trivial extension algebra. We haveproved: (i) every indecomposable module of T(A) is determined by its top and socle, (ii)every indecomposable module of T(A) is determined by...Let T(A)=A?D(A) be a representation-finite trivial extension algebra. We haveproved: (i) every indecomposable module of T(A) is determined by its top and socle, (ii)every indecomposable module of T(A) is determined by its Loewy factors and socal factorsrespectively.展开更多
Let A be a finite-dimensional algebra over an algebraically closed field. An indecomposable (right) ,4-module M is called generic provided M is infinite k-dimensional but finite length as (left) EndA(M)-module. Let R ...Let A be a finite-dimensional algebra over an algebraically closed field. An indecomposable (right) ,4-module M is called generic provided M is infinite k-dimensional but finite length as (left) EndA(M)-module. Let R = A DA be the trivial extension algebra of A- Generic R-modules are constructed from generic A-modules using some functors between Mod A and Mod R. it is also proved that if A is a tame hereditary algebra, then R has only two generic modules.展开更多
Let A be a Koszul algebra, and let M be a graded A-bimodule. We prove that the trivial extension algebra of A by M is also a Koszul algebra whenever M is Koszul as a left A-module. Applications and examples are also p...Let A be a Koszul algebra, and let M be a graded A-bimodule. We prove that the trivial extension algebra of A by M is also a Koszul algebra whenever M is Koszul as a left A-module. Applications and examples are also provided.展开更多
We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbit...We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbitrary field of characteristic p. The proof uses Auslander-Reiten theory.展开更多
In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point bo...In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point boundary problems of ordinary differential system of equations.展开更多
We showed in [G. H], if f is a Cr-topologically mixing map of the circle (r ≥0),then its rotation set will be non-trivial. But this statement is only satisfied for generic(open and dense) subset of all Cr-topological...We showed in [G. H], if f is a Cr-topologically mixing map of the circle (r ≥0),then its rotation set will be non-trivial. But this statement is only satisfied for generic(open and dense) subset of all Cr-topologically mixing maps of the circle (r≥0). Here,we present another proof of the above statement. Moreover, we introduce a topologicallymixing map of the circle with trivial rotation set.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12074101 and 11604081)sponsored by the Natural Science Foundation of Henan Province, China (Grant No. 212300410040)。
文摘The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattice constant ratio of 1:2 as an example. For the symmetric nearest-neighbor intra-chain hopping two-leg ladder, the inversion symmetry protected topological insulator phase with two degenerate topological edge states appears. When the inversion symmetry is broken, the topological insulators with one or two topological edge states of different energies and topological metals with edge states embedded in the bulk states could emerge depending on the filling factor. The topological origin of these topological states in the two-leg ladders is the topological properties of the Chern insulators and Chern metals. According to the arrangement of two trivial quantum wires, we construct two types of three-leg ladders. Each type of the three-leg ladder could be divided into one trivial subspace and one topological nontrivial subspace by unitary transformation. The topological nontrivial subspace corresponds to the effective two-leg ladder model. As the filling factor changes, the system could be in topological insulators or topological metals phases. When the two-leg ladder is constructed by two trivial quantum wires with a lattice constant ratio of 1:3 and 2:3, the system could also realize rich topological states such as the topological insulators and topological metals with the topological edge states. These rich topological states in the two-leg and three-leg ladders could be confirmed by current experimental techniques.
文摘By means of the method of torus knot theory, this paper gives the complete processes of obtaining the knotted pictures of four Bell b^es from the knotted pictures of four basic two qubit states.
基金Supported by the National Basic Research Program of China under Grant No 2012CB921900the National Natural Science Foundation of China under Grant Nos 11175089 and 11475089
文摘A nonlocality distillation protocol for arbitrary high-dimensional systems is proposed. We study the nonlocality distillation in the 2-input d-output bi-partite case. Firstly, we give the one-parameter nonlocal boxes and their correlated distilling protocol. Then, we generalize the one-parameter nonlocality distillation protocol to the twoparameter case. Furthermore, we introduce a contracting protocol testifying that the 2-input d-output nonlocal boxes make communication complexity trivial.
基金The NSF (11271119) of Chinathe NSF (1122002) of Beijing
文摘Let A be a basic hereditary artin algebra and R = A Q be the trivial extension of A by its minimal injective cogenerator Q. We construct some right （left） almost split morphisms and irreducible morphisms in modR through the corresponding morphisms in modA. Furthermore, we can determine its almost split sequences in modR.
基金supported by the National Nature Science Foundation of China(10671009 10871149)
文摘We provide estimates on the degree of C l GV determinacy （ G is one of Mather’s groups R or K ） of function germs which are defined on analytic variety V and satisfies a non-degeneracy condition with respect to some Newton polyhedron. The result gives an explicit order such that the C l geometrical structure of a function germ is preserved after higher order perturbations, which generalizes the result on C l G triviality of function germs given by M.A.S.Ruas.
文摘Historically,re-selection,pedigree,and mass selection breeding methods have been used to develop open-pollinated cultivars of Upland cotton(Gossypium hirsutum L.). Due to the
文摘The movie The Hours, adapted from Michael Cunningham's novel, presents us three different women's life in a day to reflect trivial people's struggle, contemplation of self-worth and death, with Philip Glass' scores and the well-designed settings. This paper focuses on Glass' scores and analyzes its connection with other elements, reflection of those people and coherence of the movie.
文摘To Work for Tomorrow Liu Hong, General Manager of TUTTI Exhibition Service (Xiamen) Co., Ltd, has set up TUTTI Exhibition Service (Xiamen) Co., Ltd in 2001, when exhibition industry firstly appear in Xiamen. Furthermore, the company has developed rapidly in recent years. As Liu Hong regards, exhibition industry, as well as advertisement industry, is an industry filled with challenges and
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).
文摘A mid-infrared orbital angular momentum detector based on multilayer graphene has been successfully developed,overcoming the previous reliance on C_(2V) point group topological Weyl semimetals via the orbital photogalvanic effect.This CMOS-compatible two-dimensional material system is crucial for advancing the large-scale practical application of orbital angular momentum detectors.
基金Dirar Benkhadra's research reported in this publication was supported by a scholarship from the Graduate Research Assis taut ships in Developing Countries Program of the Commission for Developing Countries of the International Mathematical UnionThe third author was partially supported by the grant MTM2014-54439-P from Ministerio de Economia y Competitividad.
文摘In this paper we investigate a categorical aspect of n-trivial extension of a ring by a family of modules.Namely,we introduce the right(resp.,left)n-trivial extension of a category by a family of endofunctors.Among other results,projective,injective and flat objects of this category are characterized,and two applications are presented at the end of this paper.We characterize when an n-trivial extension ring is k-perfect and establish a result on the self-injective dimension of an n-trivial extension ring.
文摘The structure of the trivial preference set of group decision making is studied, and the essential characters and generating reasons of the paradox of voting are revealed.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10201004).
文摘Given a finite dimensional special biserial algebra A with normed basis we obtain the dimension formulae of the first Hochschild homology groups of A and the vector space Alt(DA). As a consequence, an explicit dimension formula of the first Hochschild cohomology group of trivial extension TA = A × DA in terms of the combinatorics of the quiver and relations is determined.
基金Project supported by the National Natural Science Foundation of China.
文摘Let T(A)=A?D(A) be a representation-finite trivial extension algebra. We haveproved: (i) every indecomposable module of T(A) is determined by its top and socle, (ii)every indecomposable module of T(A) is determined by its Loewy factors and socal factorsrespectively.
文摘Let A be a finite-dimensional algebra over an algebraically closed field. An indecomposable (right) ,4-module M is called generic provided M is infinite k-dimensional but finite length as (left) EndA(M)-module. Let R = A DA be the trivial extension algebra of A- Generic R-modules are constructed from generic A-modules using some functors between Mod A and Mod R. it is also proved that if A is a tame hereditary algebra, then R has only two generic modules.
基金The author is very grateful to the referees for helpful comments. He thanks Professor Yu Ye for numerous discussion and suggestions. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11471017）, Doctoral Research Foundation, and the Research Culture Foundation of Anhui Normal University （No. 2014xmpyll）.
文摘Let A be a Koszul algebra, and let M be a graded A-bimodule. We prove that the trivial extension algebra of A by M is also a Koszul algebra whenever M is Koszul as a left A-module. Applications and examples are also provided.
基金the Japan Society for Promotion of Science （JSPS）, Grant-in-Aid for Scientific Research （C）15K04776, 2015-2018, and by the CIB in EPFL. The second author was supported by the German Science Foundation （DFG） Scientific Priority Programme SPP-1489 ＂Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory＂.
文摘We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbitrary field of characteristic p. The proof uses Auslander-Reiten theory.
文摘In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point boundary problems of ordinary differential system of equations.
文摘We showed in [G. H], if f is a Cr-topologically mixing map of the circle (r ≥0),then its rotation set will be non-trivial. But this statement is only satisfied for generic(open and dense) subset of all Cr-topologically mixing maps of the circle (r≥0). Here,we present another proof of the above statement. Moreover, we introduce a topologicallymixing map of the circle with trivial rotation set.
