Two-dimensional(2D)moirésuperlattices have emerged as a versatile platform for uncovering exotic quantum phases,many of which arise in bilayer systems exhibiting Archimedean tessellation patterns such as triangul...Two-dimensional(2D)moirésuperlattices have emerged as a versatile platform for uncovering exotic quantum phases,many of which arise in bilayer systems exhibiting Archimedean tessellation patterns such as triangular,hexagonal,and kagome lattices.Here,we propose a strategy to engineer semiregular tessellation patterns in untwisted bilayer graphene by applying anisotropic epitaxial tensile strain(AETS)along crystallographic directions.Through force-field and firstprinciples calculations,we demonstrate that AETS can induce a rich variety of semiregular tessellation geometries,including truncated hextille,prismatic pentagon,and brick-phase arrangements.Characteristic electronic Dirac and flat bands of the lattice models associated with these semiregular tessellations are observed near the Fermi level,arising from interlayer interactions generated by the spatial rearrangement of AB,BA,and SP domains.Furthermore,the real-space observations of electronic kagome,distorted Lieb,brick-like,and one-dimensional stripe lattices demonstrate that AETS enables tunable semiregular tessellation lattices.Our study identifies AETS as a promising new degree of freedom in moiréengineering,offering a reproducible and scalable platform for exploring exotic electronic lattices in moirésystems.展开更多
For a simple connected graph G, let A(G) and Q(G) be the adjacency matrix and signless Laplacian matrix, respectively of G. The principal eigenvector of A(G)(resp.Q(G)) is the unit positive eigenvector corresponding t...For a simple connected graph G, let A(G) and Q(G) be the adjacency matrix and signless Laplacian matrix, respectively of G. The principal eigenvector of A(G)(resp.Q(G)) is the unit positive eigenvector corresponding to the largest eigenvalue of A(G)(resp. Q(G)). In this paper, an upper bound and lower bound for the sum of the squares of the entries of the principal eigenvector of Q(G) corresponding to the vertices of an independent set are obtained.展开更多
The definition of principally pseudo injectivity motivates us to generalize tae notion of injectivity, noted SP pseudo injectivity. The aim of this paper is to investigate characterizations and properties of SP pseudo...The definition of principally pseudo injectivity motivates us to generalize tae notion of injectivity, noted SP pseudo injectivity. The aim of this paper is to investigate characterizations and properties of SP pseudo injective modules. Various results are devel- oped, many extending known results. As applications, we give some characterizations on Noetherian rings, QI rings, quasi-Frobenius rings.展开更多
Let R be a ring and I an ideal of R. A ring R is called I-semi-π--regular if R/I is π-regular and idempotents of R can be strongly lifted modulo I. Characterizations of I-semi-π-regular rings are given and relation...Let R be a ring and I an ideal of R. A ring R is called I-semi-π--regular if R/I is π-regular and idempotents of R can be strongly lifted modulo I. Characterizations of I-semi-π-regular rings are given and relations between semi-π-regular rings and semiregular rings are explored.展开更多
In this work,we explore a nonsmooth semi-infinite multiobjective fractional interval-valued optimization problem.Using an adequate constraint qualification,we establish necessary optimality conditions in terms of Kar...In this work,we explore a nonsmooth semi-infinite multiobjective fractional interval-valued optimization problem.Using an adequate constraint qualification,we establish necessary optimality conditions in terms of Karush–Kuhn–Tucker multipliers and upper semiregular convexificators.We do not assume that the interval-valued objective function is smooth or that it is convex.There are examples highlighting both our results and the limits of certain past studies.展开更多
A graph Г is said to be G-locally primitive, where G is a subgroup of automorphisms of Г, if the stabiliser Ga of a vertex α acts primitively on the set Г( α ) of vertices of Г adjacent to α. For a finite non-a...A graph Г is said to be G-locally primitive, where G is a subgroup of automorphisms of Г, if the stabiliser Ga of a vertex α acts primitively on the set Г( α ) of vertices of Г adjacent to α. For a finite non-abelian simple group L and a Cayley subset S of L, suppose that L ? G ? Aut( L), and the Cayley graph Г = Cay ( L, S) is G-locally primitive. In this paper we prove that L is a simple group of Lie type, and either the valency of Г is an add prine divisor of |Out(L)|, orL =PΩ 8 + (q) and Г has valency 4. In either cases, it is proved that the full automorphism group of Г is also almost simple with the same socle L.展开更多
Let G be a finite group. A Cayley graph over G is a simple graph whose automorphism group has a regular subgroup isomorphic to G. A Cayley graph is called a CI-graph （Cayley iso- morphism） if its isomorphic images a...Let G be a finite group. A Cayley graph over G is a simple graph whose automorphism group has a regular subgroup isomorphic to G. A Cayley graph is called a CI-graph （Cayley iso- morphism） if its isomorphic images are induced by automorphisms of G. A well-known result of Babai states that a Cayley graph F of G is a CI-graph if and only if all regular subgroups of Aut（F） isomorphic to G are conjugate in Aut（F）. A semi-Cayley graph （also called bi-Cayley graph by some authors） over G is a simple graph whose automorphism group has a semiregular subgroup isomorphic to G with two orbits （of equal size）. In this paper, we introduce the concept of SCI-graph （semi-Cayley isomorphism） and prove a Babai type theorem for semi-Cayley graphs. We prove that every semi-Cayley graph of a finite group G is an SCI-graph if and only if G is cyclic of order 3. Also, we study the isomorphism problem of a special class of semi-Cayley graphs.展开更多
In this paper, the concept of generalized semiregular rings is extended to generalized weak semiregular rings. Some properties of these rings are studied and some results about semiregular rings and generalized semire...In this paper, the concept of generalized semiregular rings is extended to generalized weak semiregular rings. Some properties of these rings are studied and some results about semiregular rings and generalized semiregular rings are extended. We also give some equivalent characterizations of I-weak semiregular rings.展开更多
In this paper, the concept of right generalized semi-π-regular rings is defined. We prove that these rings are non-trival generalizations of both right GP-injective rings and semi- π-regular rings. Some properties o...In this paper, the concept of right generalized semi-π-regular rings is defined. We prove that these rings are non-trival generalizations of both right GP-injective rings and semi- π-regular rings. Some properties of these rings are studied and some results about generalized semiregular rings and GP-injective rings are extended.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.52461160327,92477205,12474173,and 12104313)the National Key R&D Program of China(Grant No.2023YFA1406500)+3 种基金the Department of Science and Technology of Guangdong Province(Grant No.2021QN02L820)Shenzhen Science and Technology Program(Grant No.RCYX20231211090126026,the Stable Support Plan Program 20220810161616001)the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.22XNKJ30)。
文摘Two-dimensional(2D)moirésuperlattices have emerged as a versatile platform for uncovering exotic quantum phases,many of which arise in bilayer systems exhibiting Archimedean tessellation patterns such as triangular,hexagonal,and kagome lattices.Here,we propose a strategy to engineer semiregular tessellation patterns in untwisted bilayer graphene by applying anisotropic epitaxial tensile strain(AETS)along crystallographic directions.Through force-field and firstprinciples calculations,we demonstrate that AETS can induce a rich variety of semiregular tessellation geometries,including truncated hextille,prismatic pentagon,and brick-phase arrangements.Characteristic electronic Dirac and flat bands of the lattice models associated with these semiregular tessellations are observed near the Fermi level,arising from interlayer interactions generated by the spatial rearrangement of AB,BA,and SP domains.Furthermore,the real-space observations of electronic kagome,distorted Lieb,brick-like,and one-dimensional stripe lattices demonstrate that AETS enables tunable semiregular tessellation lattices.Our study identifies AETS as a promising new degree of freedom in moiréengineering,offering a reproducible and scalable platform for exploring exotic electronic lattices in moirésystems.
文摘For a simple connected graph G, let A(G) and Q(G) be the adjacency matrix and signless Laplacian matrix, respectively of G. The principal eigenvector of A(G)(resp.Q(G)) is the unit positive eigenvector corresponding to the largest eigenvalue of A(G)(resp. Q(G)). In this paper, an upper bound and lower bound for the sum of the squares of the entries of the principal eigenvector of Q(G) corresponding to the vertices of an independent set are obtained.
基金Supported by the Ph.D.Programs Foundation of Ministry of Education of China(200803570003)
文摘The definition of principally pseudo injectivity motivates us to generalize tae notion of injectivity, noted SP pseudo injectivity. The aim of this paper is to investigate characterizations and properties of SP pseudo injective modules. Various results are devel- oped, many extending known results. As applications, we give some characterizations on Noetherian rings, QI rings, quasi-Frobenius rings.
基金Foundation item:This work is partially supported by the NNSF(10171011)of Chinathe NNSF(10571026)of Chinathe Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutes of MOE,P.R.C.
文摘Let R be a ring and I an ideal of R. A ring R is called I-semi-π--regular if R/I is π-regular and idempotents of R can be strongly lifted modulo I. Characterizations of I-semi-π-regular rings are given and relations between semi-π-regular rings and semiregular rings are explored.
文摘In this work,we explore a nonsmooth semi-infinite multiobjective fractional interval-valued optimization problem.Using an adequate constraint qualification,we establish necessary optimality conditions in terms of Karush–Kuhn–Tucker multipliers and upper semiregular convexificators.We do not assume that the interval-valued objective function is smooth or that it is convex.There are examples highlighting both our results and the limits of certain past studies.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 69873002).
文摘A graph Г is said to be G-locally primitive, where G is a subgroup of automorphisms of Г, if the stabiliser Ga of a vertex α acts primitively on the set Г( α ) of vertices of Г adjacent to α. For a finite non-abelian simple group L and a Cayley subset S of L, suppose that L ? G ? Aut( L), and the Cayley graph Г = Cay ( L, S) is G-locally primitive. In this paper we prove that L is a simple group of Lie type, and either the valency of Г is an add prine divisor of |Out(L)|, orL =PΩ 8 + (q) and Г has valency 4. In either cases, it is proved that the full automorphism group of Г is also almost simple with the same socle L.
文摘Let G be a finite group. A Cayley graph over G is a simple graph whose automorphism group has a regular subgroup isomorphic to G. A Cayley graph is called a CI-graph （Cayley iso- morphism） if its isomorphic images are induced by automorphisms of G. A well-known result of Babai states that a Cayley graph F of G is a CI-graph if and only if all regular subgroups of Aut（F） isomorphic to G are conjugate in Aut（F）. A semi-Cayley graph （also called bi-Cayley graph by some authors） over G is a simple graph whose automorphism group has a semiregular subgroup isomorphic to G with two orbits （of equal size）. In this paper, we introduce the concept of SCI-graph （semi-Cayley isomorphism） and prove a Babai type theorem for semi-Cayley graphs. We prove that every semi-Cayley graph of a finite group G is an SCI-graph if and only if G is cyclic of order 3. Also, we study the isomorphism problem of a special class of semi-Cayley graphs.
基金the National Natural Science Foundation of China (No.10571085)
文摘In this paper, the concept of generalized semiregular rings is extended to generalized weak semiregular rings. Some properties of these rings are studied and some results about semiregular rings and generalized semiregular rings are extended. We also give some equivalent characterizations of I-weak semiregular rings.
文摘In this paper, the concept of right generalized semi-π-regular rings is defined. We prove that these rings are non-trival generalizations of both right GP-injective rings and semi- π-regular rings. Some properties of these rings are studied and some results about generalized semiregular rings and GP-injective rings are extended.
