For an immersed submanifold x ： M^m→ Sn in the unit sphere S^n without umbilics, an eigenvalue of the Blaschke tensor of x is called a Blaschke eigenvalue of x. It is interesting to determine all hypersurfaces in Sn...For an immersed submanifold x ： M^m→ Sn in the unit sphere S^n without umbilics, an eigenvalue of the Blaschke tensor of x is called a Blaschke eigenvalue of x. It is interesting to determine all hypersurfaces in Sn with constant Blaschke eigenvalues. In this paper, we are able to classify all immersed hypersurfaces in S^m＋1 with vanishing MSbius form and constant Blaschke eigenvalues, in case （1） x has exact two distinct Blaschke eigenvalues, or （2） m = 3. With these classifications, some interesting examples are also presented.展开更多
An immersed umbilic-free submanifold in the unit sphere is called Blaschke isoparametric if its Mobius form vanishes identically and all of its Blaschke eigenvalues are constant. In this paper, we give a complete clas...An immersed umbilic-free submanifold in the unit sphere is called Blaschke isoparametric if its Mobius form vanishes identically and all of its Blaschke eigenvalues are constant. In this paper, we give a complete classification for all Blaschke isoparametric hypersurfaces with three distinct Blaschke eigenvalues.展开更多
Let x ： M^n→S^n＋1 be an immersed hypersurface in the （n ＋1）-dimensional sphere S^n＋1. If, for any points p,q ∈ M^n, there exists a Mobius transformation Ф ： S^n＋l →S^n＋1 such that Ф o x（M^n） = x（M^n）...Let x ： M^n→S^n＋1 be an immersed hypersurface in the （n ＋1）-dimensional sphere S^n＋1. If, for any points p,q ∈ M^n, there exists a Mobius transformation Ф ： S^n＋l →S^n＋1 such that Ф o x（M^n） = x（M^n） and Ф o x（p） = x（q）, then the hypersurface is called a Mobius homogeneous hypersurface. In this paper, the Mobius homogeneous hypersurfaces with three distinct principal curvatures are classified completely up to a Mobius transformation.展开更多
Let x be an m-dimensional umbilic-free hypersurface in an （m＋1）-dimensional unit sphere Sm＋l （m≥3）. In this paper, we classify and explicitly express the hypersurfaces with two distinct princi- pal curvatures a...Let x be an m-dimensional umbilic-free hypersurface in an （m＋1）-dimensional unit sphere Sm＋l （m≥3）. In this paper, we classify and explicitly express the hypersurfaces with two distinct princi- pal curvatures and closed MSbius form, and then we characterize and classify conformally flat hypersurfaces of dimension larger than 3.展开更多
An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under th...An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under the condition of having constant MSbius principal curvatures, we show that the hypersurface is of vanishing MSbius form if and only if its MSbius form is parallel with respect to the Levi-Civita connection of its MSbius metric. Moreover, typical examples are constructed to show that the condition of having constant MSbius principal curvatures and that of having vanishing MSbius form are independent of each other.展开更多
In this paper, we study the combinatorial properties ol words m chscrete dynamical systems from antisymmetric cubic maps. We also discuss the relationship of primitive kneading sequences of length n and period-doublin...In this paper, we study the combinatorial properties ol words m chscrete dynamical systems from antisymmetric cubic maps. We also discuss the relationship of primitive kneading sequences of length n and period-doubling kneading sequences of length 2n, and then determine the number of all kneading sequences of length n.展开更多
In this paper, a general algorithm for the computation of the Fourier coefficients of 2π-periodic （continuous） functions is developed based on Dirichlet characters, Gauss sums and the generalized MSbius transform. ...In this paper, a general algorithm for the computation of the Fourier coefficients of 2π-periodic （continuous） functions is developed based on Dirichlet characters, Gauss sums and the generalized MSbius transform. It permits the direct extraction of the Fourier cosine and sine coefficients. Three special cases of our algorithm are presented. A VLSI architecture is presented and the error estimates are given.展开更多
In this paper, we present a new proof of the uniqueness of Koebe-Andreev-Thurston theorem. Our method is based on the argument principle in complex analysis and reviews the connection between the circle packing theore...In this paper, we present a new proof of the uniqueness of Koebe-Andreev-Thurston theorem. Our method is based on the argument principle in complex analysis and reviews the connection between the circle packing theorem and complex analysis.展开更多
We investigate the approximate solution of the Dirac equation for a combination of Mobius square and Mie type potentials under the pseudospin symmetry limit by using supersymmetry quantum mechanics. We obtain the boun...We investigate the approximate solution of the Dirac equation for a combination of Mobius square and Mie type potentials under the pseudospin symmetry limit by using supersymmetry quantum mechanics. We obtain the bound-state energy equation and the corresponding spinor wave functions in an approximate analytical manner. We comment on the system via various useful figures and tables.展开更多
Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the socalled DDVV inequality which relates the scalar curvature,the mean curvature and the normal scalar curvature.This pro...Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the socalled DDVV inequality which relates the scalar curvature,the mean curvature and the normal scalar curvature.This property is conformal invariant;hence we study them in the framework of Mbius geometry,and restrict to three-dimensional Wintgen ideal submanifolds in S5.In particular,we give Mbius characterizations for minimal ones among them,which are also known as(3-dimensional)austere submanifolds(in 5-dimensional space forms).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
In this paper, we construct a new integrable equation called Mobius-Toda equation which is a generalization of q-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further ...In this paper, we construct a new integrable equation called Mobius-Toda equation which is a generalization of q-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of the Mobius-Toda equation and a whole integrable MSbius-Toda hierarchy are also constructed. To show the integrability, the bi-Hamiltonian structure and tau symmetry of the MSbius-Toda hierarchy are given and this leads to the existence of the tau function.展开更多
The atomic and electronic structures of Pb bilayer/Pt（111） are investigated with two theoretical calculations. We find that the stable （2 × 2）/（3 × 3） Pb/Pt（lll） structure is a promising candidate fo...The atomic and electronic structures of Pb bilayer/Pt（111） are investigated with two theoretical calculations. We find that the stable （2 × 2）/（3 × 3） Pb/Pt（lll） structure is a promising candidate for being used as a template with self-organized ordered Pb semi-cluster array on the first Pb monolayer. This stable structure can realize the ordered Au single-atom array around the Pb semi-clusters that can cause selective adsorption of noble atoms. The size of Pb magic number semi-cluster plays a more important role in determining the periodicity of the template than the lattice constant misfit between the substrate and the overlayer. This leads to quite a different periodicity between the two stable templates, which are （2 × 2）/（3 × 3） Pb/Pt（111） and Pb/Cu（111）. Therefore, by considering the size of the stable semi-clusters and carefully selecting different substrate materials, we can tune the density of Pb semi-clusters as the nucleation points and then tune the periodicity of the stable template.展开更多
文摘For an immersed submanifold x ： M^m→ Sn in the unit sphere S^n without umbilics, an eigenvalue of the Blaschke tensor of x is called a Blaschke eigenvalue of x. It is interesting to determine all hypersurfaces in Sn with constant Blaschke eigenvalues. In this paper, we are able to classify all immersed hypersurfaces in S^m＋1 with vanishing MSbius form and constant Blaschke eigenvalues, in case （1） x has exact two distinct Blaschke eigenvalues, or （2） m = 3. With these classifications, some interesting examples are also presented.
基金supported by National Natural Science Foundation of China (Grant Nos. 10671181, 11071225)
文摘An immersed umbilic-free submanifold in the unit sphere is called Blaschke isoparametric if its Mobius form vanishes identically and all of its Blaschke eigenvalues are constant. In this paper, we give a complete classification for all Blaschke isoparametric hypersurfaces with three distinct Blaschke eigenvalues.
基金supported by the National Natural Science Foundation of China(Nos.11571037,11471021)
文摘Let x ： M^n→S^n＋1 be an immersed hypersurface in the （n ＋1）-dimensional sphere S^n＋1. If, for any points p,q ∈ M^n, there exists a Mobius transformation Ф ： S^n＋l →S^n＋1 such that Ф o x（M^n） = x（M^n） and Ф o x（p） = x（q）, then the hypersurface is called a Mobius homogeneous hypersurface. In this paper, the Mobius homogeneous hypersurfaces with three distinct principal curvatures are classified completely up to a Mobius transformation.
基金supported by National Natural Science Foundation of China (Grant Nos.10561010, 10861013)
文摘Let x be an m-dimensional umbilic-free hypersurface in an （m＋1）-dimensional unit sphere Sm＋l （m≥3）. In this paper, we classify and explicitly express the hypersurfaces with two distinct princi- pal curvatures and closed MSbius form, and then we characterize and classify conformally flat hypersurfaces of dimension larger than 3.
基金Supported by National Natural Science Foundation of China (Grant No.10671181)
文摘An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under the condition of having constant MSbius principal curvatures, we show that the hypersurface is of vanishing MSbius form if and only if its MSbius form is parallel with respect to the Levi-Civita connection of its MSbius metric. Moreover, typical examples are constructed to show that the condition of having constant MSbius principal curvatures and that of having vanishing MSbius form are independent of each other.
文摘In this paper, we study the combinatorial properties ol words m chscrete dynamical systems from antisymmetric cubic maps. We also discuss the relationship of primitive kneading sequences of length n and period-doubling kneading sequences of length 2n, and then determine the number of all kneading sequences of length n.
基金Supported by National Natural Science Foundation of China(11201370)the Science and Technology Program of Shaanxi Province of China(2013JM1017,2014JM1007,2014KJXX-61)the Natural Science Foundation of the Education Department of Shaanxi Province of China(2013JK0558)
文摘In this paper, a general algorithm for the computation of the Fourier coefficients of 2π-periodic （continuous） functions is developed based on Dirichlet characters, Gauss sums and the generalized MSbius transform. It permits the direct extraction of the Fourier cosine and sine coefficients. Three special cases of our algorithm are presented. A VLSI architecture is presented and the error estimates are given.
基金Supported by National Natural Science Foundation of China (Grant No. 10701084)
文摘In this paper, we present a new proof of the uniqueness of Koebe-Andreev-Thurston theorem. Our method is based on the argument principle in complex analysis and reviews the connection between the circle packing theorem and complex analysis.
文摘We investigate the approximate solution of the Dirac equation for a combination of Mobius square and Mie type potentials under the pseudospin symmetry limit by using supersymmetry quantum mechanics. We obtain the bound-state energy equation and the corresponding spinor wave functions in an approximate analytical manner. We comment on the system via various useful figures and tables.
基金supported by National Natural Science Foundation of China (Grant Nos. 10901006,11171004 and 11331002)
文摘Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the socalled DDVV inequality which relates the scalar curvature,the mean curvature and the normal scalar curvature.This property is conformal invariant;hence we study them in the framework of Mbius geometry,and restrict to three-dimensional Wintgen ideal submanifolds in S5.In particular,we give Mbius characterizations for minimal ones among them,which are also known as(3-dimensional)austere submanifolds(in 5-dimensional space forms).
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.
基金supported by the National Natural Science Foundation of China(11571192)the Natural Science Foundation of Ningbo(2015A610157)K.C.Wong Magna Fund in Ningbo University
文摘In this paper, we construct a new integrable equation called Mobius-Toda equation which is a generalization of q-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of the Mobius-Toda equation and a whole integrable MSbius-Toda hierarchy are also constructed. To show the integrability, the bi-Hamiltonian structure and tau symmetry of the MSbius-Toda hierarchy are given and this leads to the existence of the tau function.
基金supported by the National Natural Science Foundation of China (Grant No. 50531050)the National Basic Research Program of China (Grant No. 2006CB605100)+1 种基金the Natural Science Foundation for Postdoctoral Scientists of China (GrantNo. 20090450426)the CRI of UNC-Charlotte
文摘The atomic and electronic structures of Pb bilayer/Pt（111） are investigated with two theoretical calculations. We find that the stable （2 × 2）/（3 × 3） Pb/Pt（lll） structure is a promising candidate for being used as a template with self-organized ordered Pb semi-cluster array on the first Pb monolayer. This stable structure can realize the ordered Au single-atom array around the Pb semi-clusters that can cause selective adsorption of noble atoms. The size of Pb magic number semi-cluster plays a more important role in determining the periodicity of the template than the lattice constant misfit between the substrate and the overlayer. This leads to quite a different periodicity between the two stable templates, which are （2 × 2）/（3 × 3） Pb/Pt（111） and Pb/Cu（111）. Therefore, by considering the size of the stable semi-clusters and carefully selecting different substrate materials, we can tune the density of Pb semi-clusters as the nucleation points and then tune the periodicity of the stable template.
