A new model shift mapping was given in bilateral symbol space. It is topologically conjugate with the traditional shift mapping. Similar to Smale Horseshoe, a model was constructed correspondent to the model shift map...A new model shift mapping was given in bilateral symbol space. It is topologically conjugate with the traditional shift mapping. Similar to Smale Horseshoe, a model was constructed correspondent to the model shift mapping, i.e., a class of mapping on Mbius strip was given. Its attractors' structure and dynamical behaviour were described.展开更多
A vertex-colored graph G is said to be rainbow vertex-connected if every two vertices of G are connected by a path whose internal vertices have distinct colors, such a path is called a rainbow path. The rainbow vertex...A vertex-colored graph G is said to be rainbow vertex-connected if every two vertices of G are connected by a path whose internal vertices have distinct colors, such a path is called a rainbow path. The rainbow vertex-connection number of a connected graph G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainbow vertex-connected. If for every pair u, v of distinct vertices, G contains a rainbow u-v geodesic, then G is strong rainbow vertex-connected. The minimum number k for which there exists a k-vertex-coloring of G that results in a strongly rainbow vertex-connected graph is called the strong rainbow vertex-connection number of G, denoted by srvc(G). Observe that rvc(G) ≤ srvc(G) for any nontrivial connected graph G. In this paper, for a Ladder L_n,we determine the exact value of srvc(L_n) for n even. For n odd, upper and lower bounds of srvc(L_n) are obtained. We also give upper and lower bounds of the(strong) rainbow vertex-connection number of Mbius Ladder.展开更多
There are many results on the flexibility of(general) embeddings of graphs,but few are known about that of strong embeddings.In this paper,we study the flexibility of strong embeddings of circular and Mbius ladders on...There are many results on the flexibility of(general) embeddings of graphs,but few are known about that of strong embeddings.In this paper,we study the flexibility of strong embeddings of circular and Mbius ladders on the projective plane and the Klein bottle by using the joint tree model of embeddings.The numbers of(nonequivalent) general embeddings and strong embeddings of circular and Mbius ladders on these two nonorientable surfaces are obtained,respectively.And the structures of those strong embeddings are described.展开更多
The convergence of linear fractional transformations is an important topic in mathematics.We study the pointwise convergence of p-adic Mbius maps,and classify the possibilities of limits of pointwise convergent sequen...The convergence of linear fractional transformations is an important topic in mathematics.We study the pointwise convergence of p-adic Mbius maps,and classify the possibilities of limits of pointwise convergent sequences of Mbius maps acting on the projective line P1(C p),where C p is the completion of the algebraic closure of Q p.We show that if the set of pointwise convergence of a sequence of p-adic Mbius maps contains at least three points,the sequence of p-adic Mbius maps either converges to a p-adic Mbius map on the projective line P1(C p),or converges to a constant on the set of pointwise convergence with one unique exceptional point.This result generalizes the result of Piranian and Thron(1957)to the non-archimedean settings.展开更多
Mbius container molecules C64H8,C60N4H4,and C58N6H2 with topological one-sided characteristics were constructed at the first time by imitating natural trumpet shells.The structure is an open cage with an inner hexagon...Mbius container molecules C64H8,C60N4H4,and C58N6H2 with topological one-sided characteristics were constructed at the first time by imitating natural trumpet shells.The structure is an open cage with an inner hexagonal bridge.The bridge joints the outer and inner surfaces of the cage to form a new one-sided Mbius structure.The optimized structures of the three molecules in the singlet(the ground state),triplet and quintet states are obtained using the density functional theory(B3LYP).For the ground state structures of the three Mbius molecules,their oxidizabilities are weaker than that of the C60 and reducibilities are close to that of the stable C80 cage and slightly stronger than that of the C60.These may show that the unusual Mbius structures have some stability.Their potential properties were predicted,for example,the special aromaticity of the bridge ring due to the unique interaction between the bridge and the cage wall.These findings enlarge the knowledge of Mbius molecules. The idea of bionic and topological imitating in chemistry may promote the design of new complex-shaped nano-molecules and molecular devices.展开更多
We show that,assisted by the Peierls transition of lattice,as a quasi-one dimensional(Q1D) tight binding system,a M¨obius molecular device can behave as a simple topological insulator.With the Peierls phase trans...We show that,assisted by the Peierls transition of lattice,as a quasi-one dimensional(Q1D) tight binding system,a M¨obius molecular device can behave as a simple topological insulator.With the Peierls phase transition to form a domain wall,the solitonary zero modes exist as the ground state of this electron-phonon hybrid system,which is protected by the Z_2 topology of the M¨obius strip.The robustness of the ground state prevents these degenerate zero modes from their energy spectrum splitting caused by any perturbation.展开更多
Presents the counting of the counts number of primitive elements of finite dimensional field extension GF(p nm )/GF(p n) using (1) the principle of inclusion exclusion, (2) the Mbius inversion, (3) the Euler ...Presents the counting of the counts number of primitive elements of finite dimensional field extension GF(p nm )/GF(p n) using (1) the principle of inclusion exclusion, (2) the Mbius inversion, (3) the Euler function, and the new identity obtained ∑t｜p nm-1 , t p nmq j -1(t)=p nm -∑jp nmq j +∑j 1<j 2p nmqj 1qj 2 -…+(-1) kp nmq 1…q k where, m>1, p is a prime, (·) is Euler function, and q 1,…,q k are the all distinct prime divisors of m.展开更多
This paper deals with representations of groups by "affine" automorphisms of compact, convex spaces, with special focus on "irreducible" representations: equivalently"minimal" actions. Wh...This paper deals with representations of groups by "affine" automorphisms of compact, convex spaces, with special focus on "irreducible" representations: equivalently"minimal" actions. When the group in question is P SL(2, R), the authors exhibit a oneone correspondence between bounded harmonic functions on the upper half-plane and a certain class of irreducible representations. This analysis shows that, surprisingly, all these representations are equivalent. In fact, it is found that all irreducible affine representations of this group are equivalent. The key to this is a property called "linear Stone-Weierstrass"for group actions on compact spaces. If it holds for the "universal strongly proximal space"of the group(to be defined), then the induced action on the space of probability measures on this space is the unique irreducible affine representation of the group.展开更多
文摘A new model shift mapping was given in bilateral symbol space. It is topologically conjugate with the traditional shift mapping. Similar to Smale Horseshoe, a model was constructed correspondent to the model shift mapping, i.e., a class of mapping on Mbius strip was given. Its attractors' structure and dynamical behaviour were described.
基金Supported by the National Natural Science Foundation of China(11551001,11061027,11261047,11161037,11461054)Supported by the Science Found of Qinghai Province(2016-ZJ-948Q,2014-ZJ-907)
文摘A vertex-colored graph G is said to be rainbow vertex-connected if every two vertices of G are connected by a path whose internal vertices have distinct colors, such a path is called a rainbow path. The rainbow vertex-connection number of a connected graph G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainbow vertex-connected. If for every pair u, v of distinct vertices, G contains a rainbow u-v geodesic, then G is strong rainbow vertex-connected. The minimum number k for which there exists a k-vertex-coloring of G that results in a strongly rainbow vertex-connected graph is called the strong rainbow vertex-connection number of G, denoted by srvc(G). Observe that rvc(G) ≤ srvc(G) for any nontrivial connected graph G. In this paper, for a Ladder L_n,we determine the exact value of srvc(L_n) for n even. For n odd, upper and lower bounds of srvc(L_n) are obtained. We also give upper and lower bounds of the(strong) rainbow vertex-connection number of Mbius Ladder.
基金supported by National Natural Science Foundation of China (Grant No.10571013)
文摘There are many results on the flexibility of(general) embeddings of graphs,but few are known about that of strong embeddings.In this paper,we study the flexibility of strong embeddings of circular and Mbius ladders on the projective plane and the Klein bottle by using the joint tree model of embeddings.The numbers of(nonequivalent) general embeddings and strong embeddings of circular and Mbius ladders on these two nonorientable surfaces are obtained,respectively.And the structures of those strong embeddings are described.
基金supported by National Natural Science Foundation of China(Grant Nos.10831004 and 11301510)
文摘The convergence of linear fractional transformations is an important topic in mathematics.We study the pointwise convergence of p-adic Mbius maps,and classify the possibilities of limits of pointwise convergent sequences of Mbius maps acting on the projective line P1(C p),where C p is the completion of the algebraic closure of Q p.We show that if the set of pointwise convergence of a sequence of p-adic Mbius maps contains at least three points,the sequence of p-adic Mbius maps either converges to a p-adic Mbius map on the projective line P1(C p),or converges to a constant on the set of pointwise convergence with one unique exceptional point.This result generalizes the result of Piranian and Thron(1957)to the non-archimedean settings.
基金supported by the National Natural Science Foundation of China (20773046)
文摘Mbius container molecules C64H8,C60N4H4,and C58N6H2 with topological one-sided characteristics were constructed at the first time by imitating natural trumpet shells.The structure is an open cage with an inner hexagonal bridge.The bridge joints the outer and inner surfaces of the cage to form a new one-sided Mbius structure.The optimized structures of the three molecules in the singlet(the ground state),triplet and quintet states are obtained using the density functional theory(B3LYP).For the ground state structures of the three Mbius molecules,their oxidizabilities are weaker than that of the C60 and reducibilities are close to that of the stable C80 cage and slightly stronger than that of the C60.These may show that the unusual Mbius structures have some stability.Their potential properties were predicted,for example,the special aromaticity of the bridge ring due to the unique interaction between the bridge and the cage wall.These findings enlarge the knowledge of Mbius molecules. The idea of bionic and topological imitating in chemistry may promote the design of new complex-shaped nano-molecules and molecular devices.
基金Supported by the National Natural Science Foundation of China under Grant No.11504241the Natural Science Foundation of Shenzhen University under Grant No.201551
文摘We show that,assisted by the Peierls transition of lattice,as a quasi-one dimensional(Q1D) tight binding system,a M¨obius molecular device can behave as a simple topological insulator.With the Peierls phase transition to form a domain wall,the solitonary zero modes exist as the ground state of this electron-phonon hybrid system,which is protected by the Z_2 topology of the M¨obius strip.The robustness of the ground state prevents these degenerate zero modes from their energy spectrum splitting caused by any perturbation.
文摘Presents the counting of the counts number of primitive elements of finite dimensional field extension GF(p nm )/GF(p n) using (1) the principle of inclusion exclusion, (2) the Mbius inversion, (3) the Euler function, and the new identity obtained ∑t｜p nm-1 , t p nmq j -1(t)=p nm -∑jp nmq j +∑j 1<j 2p nmqj 1qj 2 -…+(-1) kp nmq 1…q k where, m>1, p is a prime, (·) is Euler function, and q 1,…,q k are the all distinct prime divisors of m.
文摘This paper deals with representations of groups by "affine" automorphisms of compact, convex spaces, with special focus on "irreducible" representations: equivalently"minimal" actions. When the group in question is P SL(2, R), the authors exhibit a oneone correspondence between bounded harmonic functions on the upper half-plane and a certain class of irreducible representations. This analysis shows that, surprisingly, all these representations are equivalent. In fact, it is found that all irreducible affine representations of this group are equivalent. The key to this is a property called "linear Stone-Weierstrass"for group actions on compact spaces. If it holds for the "universal strongly proximal space"of the group(to be defined), then the induced action on the space of probability measures on this space is the unique irreducible affine representation of the group.
