Let X be a non-primary Hopf Surface with Abelian fundamental group π1 （X）（≌） Z Zm, L a line bundle on X, we give a formula for computing the dimension of cohomology H^q（X,Ω^P（L）） and the explicit results fo...Let X be a non-primary Hopf Surface with Abelian fundamental group π1 （X）（≌） Z Zm, L a line bundle on X, we give a formula for computing the dimension of cohomology H^q（X,Ω^P（L）） and the explicit results for non-primary exceptional Hopf surface.展开更多
An asymptotic algorithm is applied to the problem of a finite, thermo-elastic solid containing a surface breaking crack, when the exterior surface is subjected to oscillatory thermal loading. This algorithm involves t...An asymptotic algorithm is applied to the problem of a finite, thermo-elastic solid containing a surface breaking crack, when the exterior surface is subjected to oscillatory thermal loading. This algorithm involves the study of a model problem. An analytical and numerical study of this model problem of a thermo-elastic half space containing a surface breaking crack and subjected to oscillatory thermal loading is presented. The crack surface is traction free. In particular, the amplitude of the stress intensity factor at the crack vertex is found as a function of the crack depth and the frequency of thermal oscillation.展开更多
In this paper, we establish a rigidity theorem for compact constant mean curva- ture surfaces of the Berger sphere in terms of the surfaces＇ geometric invariants. This extends the previous similar result on compact m...In this paper, we establish a rigidity theorem for compact constant mean curva- ture surfaces of the Berger sphere in terms of the surfaces＇ geometric invariants. This extends the previous similar result on compact minimal surfaces of the Berger sphere.展开更多
The existence of the Hopf bifurcation of a complex ordinary differential equation system in the complex domain is studied in this paper by using the complex qualitative theory.In the complex domain,we conclude that th...The existence of the Hopf bifurcation of a complex ordinary differential equation system in the complex domain is studied in this paper by using the complex qualitative theory.In the complex domain,we conclude that the Hopf bifurcation appears for both directions of the parameter μ. The formulae of the Hopf bifurcation are also given in this paper.展开更多
Let X be a Hopf manifolds with Abelian fundamental group, L any flat line bundle on X, we give a formula for computing explicitly the cohomology Hq(X, Ωp(L) using the method of group action and the generalized Douady...Let X be a Hopf manifolds with Abelian fundamental group, L any flat line bundle on X, we give a formula for computing explicitly the cohomology Hq(X, Ωp(L) using the method of group action and the generalized Douady sequence.展开更多
The purpose of the present paper is to give an elementary method for the computation of the cohomology groups Hq（X,Ω^p X（L））, （0 ≤q ≤ n） of an n-dimensional non-primary Hopf manifold X with arbitrary fundamen...The purpose of the present paper is to give an elementary method for the computation of the cohomology groups Hq（X,Ω^p X（L））, （0 ≤q ≤ n） of an n-dimensional non-primary Hopf manifold X with arbitrary fundamental group. We use the method of Zhou to generalize the results for primary Hopf manifolds and non-primary Hopf manifold with an Abelian fundamental group.展开更多
The dynamical behavior of surface catalytic oxidation reaction of Pt(110)/CO+O2 modulated by colored noise, under the condition of specific temperature, has been investigated when the partial pressure of CO gas is nea...The dynamical behavior of surface catalytic oxidation reaction of Pt(110)/CO+O2 modulated by colored noise, under the condition of specific temperature, has been investigated when the partial pressure of CO gas is near the supercritical Hopf bifurcation point. By computer simulation the oscillation and stochastic resonance induced by colored noise are observed. The influences of the intensity and correlation time of colored noise on stochastic resonance are discussed. The range of sensitivity of the system to the environmental fluctuation is analyzed.展开更多
Under broad hypotheses we derive a scalar reduction of the generalized Kähler-Ricci soliton system.We realize solutions as critical points of a functional,analogous to the classical Aubin energy,defined on an orb...Under broad hypotheses we derive a scalar reduction of the generalized Kähler-Ricci soliton system.We realize solutions as critical points of a functional,analogous to the classical Aubin energy,defined on an orbit of the natural Hamiltonian action of diffeomorphisms,thought of as a generalized Kähler class.This functional is convex on a large set of paths in this space,and using this we show rigidity of solitons in their generalized Kähler class.As an application we prove uniqueness of the generalized Kähler-Ricci solitons on Hopf surfaces constructed in Streets and Ustinovskiy[Commun.Pure Appl.Math.74(9),1896-1914(2020)],finishing the classification in complex dimension 2.展开更多
基金Supported by NNSF(10171068)Supported by Beijing Excellent Talent Grant(20042D0500509)
文摘Let X be a non-primary Hopf Surface with Abelian fundamental group π1 （X）（≌） Z Zm, L a line bundle on X, we give a formula for computing the dimension of cohomology H^q（X,Ω^P（L）） and the explicit results for non-primary exceptional Hopf surface.
文摘An asymptotic algorithm is applied to the problem of a finite, thermo-elastic solid containing a surface breaking crack, when the exterior surface is subjected to oscillatory thermal loading. This algorithm involves the study of a model problem. An analytical and numerical study of this model problem of a thermo-elastic half space containing a surface breaking crack and subjected to oscillatory thermal loading is presented. The crack surface is traction free. In particular, the amplitude of the stress intensity factor at the crack vertex is found as a function of the crack depth and the frequency of thermal oscillation.
文摘In this paper, we establish a rigidity theorem for compact constant mean curva- ture surfaces of the Berger sphere in terms of the surfaces＇ geometric invariants. This extends the previous similar result on compact minimal surfaces of the Berger sphere.
文摘The existence of the Hopf bifurcation of a complex ordinary differential equation system in the complex domain is studied in this paper by using the complex qualitative theory.In the complex domain,we conclude that the Hopf bifurcation appears for both directions of the parameter μ. The formulae of the Hopf bifurcation are also given in this paper.
文摘Let X be a Hopf manifolds with Abelian fundamental group, L any flat line bundle on X, we give a formula for computing explicitly the cohomology Hq(X, Ωp(L) using the method of group action and the generalized Douady sequence.
基金supported by 973 Project Foundation of China and Outstanding Youth science Grant of NSFC(Grant No.19825105)
文摘The purpose of the present paper is to give an elementary method for the computation of the cohomology groups Hq（X,Ω^p X（L））, （0 ≤q ≤ n） of an n-dimensional non-primary Hopf manifold X with arbitrary fundamental group. We use the method of Zhou to generalize the results for primary Hopf manifolds and non-primary Hopf manifold with an Abelian fundamental group.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.20173052 and 2020301).
文摘The dynamical behavior of surface catalytic oxidation reaction of Pt(110)/CO+O2 modulated by colored noise, under the condition of specific temperature, has been investigated when the partial pressure of CO gas is near the supercritical Hopf bifurcation point. By computer simulation the oscillation and stochastic resonance induced by colored noise are observed. The influences of the intensity and correlation time of colored noise on stochastic resonance are discussed. The range of sensitivity of the system to the environmental fluctuation is analyzed.
基金V.A.was supported in part by an NSERC Discovery Grant and a Connect Talent Grant of the Région Pays de la Loire.
文摘Under broad hypotheses we derive a scalar reduction of the generalized Kähler-Ricci soliton system.We realize solutions as critical points of a functional,analogous to the classical Aubin energy,defined on an orbit of the natural Hamiltonian action of diffeomorphisms,thought of as a generalized Kähler class.This functional is convex on a large set of paths in this space,and using this we show rigidity of solitons in their generalized Kähler class.As an application we prove uniqueness of the generalized Kähler-Ricci solitons on Hopf surfaces constructed in Streets and Ustinovskiy[Commun.Pure Appl.Math.74(9),1896-1914(2020)],finishing the classification in complex dimension 2.
