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
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
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
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
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.
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.
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.
