Classification of Proper Holomorphic Mappings between Hartogs Domains over Homogeneous Siegel Domains

The Hartogs domain over homogeneous Siegel domain D_N,s(s > 0) is defined by the inequality ■, where D is a homogeneous Siegel domain of type Ⅱ,(z, ζ) ∈ D × C^N and KD(z, z) is the Bergman kernel of D. Recently, Seo obtained the rigidity result that proper holomorphic mappings between two equidimensional domains D_N,s and D’_N’,s’ are biholomorphisms for N ≥ 2. In this article, we find a counter-example to show that the rigidity result is not true for D...     

Difference Independence of the Euler Gamma Function*

In this paper,the authors established a sharp version of the difference analogue of the celebrated Holder’s theorem concerning the differential independence of the Euler gamma function Г. More precisely,if P is a polynomial of n+1 variables in C[X,Y₀,…,Y_n-1] such that P(s,Г(s+a₀),…,Г(s+a_n-1))≡0 for some(a₀,…,a_n-1) ∈ Cⁿ and a_i-a_j ■ Z for any 0≤i相似文献   

Brake Orbits of a Reversible Even Hamiltonian System Near an Equilibrium

In this paper,we consider the brake orbits of a reversible even Hamiltonian system near an equilibrium.Let the Hamiltonian system(H S)x=J H(x)satisfies H(0)=0,H(0)=0,reversible and even conditions H(Nx)=H(x)and H(-x)=H(x)for all x∈R²ⁿ.Suppose the quadratic form Q(x)=1/2 is non-degenerate.Fixτ₀>0 and assume that R²ⁿ=E⊕F decomposes into linear subspaces E and F which are invariant under the flow associated to the linear system x=J H'(0)x and such that each solution of the above linear system in E isτ₀-periodic whereas no solution in F{0}isτ₀-periodic.Writeσ(τ₀)=σ_Q(τ₀)for the signature of Q|E.Ifσ(τ₀)≠=0,we prove that either there exists a sequence of brake orbits x_k→0 withτk-periodic on the hypersurface H^-1(0)whereτ_k→τ₀;or for eachλclose to 0 withλ_σ(τ₀)>0 the hypersurface H-1(λ)contains at least 1/2|σ(τ₀)|distinct brake orbits of the Hamiltonian system(HS)near 0 with periods nearτ₀.Such result for periodic solutions was proved by Bartsch in 1997.     

Anick Resolution and the Minimal Projective Resolution of Uq+(C3)

In this paper,from the Anick’s resolution and Grobner-Shirshov basis for quantized enveloping algebra of type C₃, we compute the minimal projective resolution of the trivial module U_q⁺(C₃)and as an application,we obtain that the global dimension of U_q⁺(C₃) is 9.     

THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS

In this paper, we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations -(ε²a + εb∫_R³|?u|²)?u + V(x)u = u^p, u > 0 in R³,which concentrate at non-degenerate critical points of the potential function V(x), where a, b >0, 1 < p < 5 are constants, and ε > 0 is a parameter. Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity, we establish the existe...     

DYNAMICS OF A NONLOCAL DISPERSAL FOOT-AND-MOUTH DISEASE MODEL IN A SPATIALLY HETEROGENEOUS ENVIRONMENT

Foot-and-mouth disease is one of the major contagious zoonotic diseases in the world.It is caused by various species of the genus Aphthovirus of the family Picornavirus,and it always brings a large number of infections and heavy financial losses.The disease has become a major public health concern.In this paper,we propose a nonlocal foot-and-mouth disease model in a spatially heterogeneous environment,which couples virus-to-animals and animals-to-animals transmission pathways,and investigate the dynamics of the disperal.The basic reproduction number R₀is defined as the spectral radius of the next generation operator R(x)by a renewal equation.The relationship between R₀and a principal eigenvalue of an operator L₀is built.Moreover,the proposed system exhibits threshold dynamics in terms of R₀,in the sense that R₀determines whether or not foot-and-mouth disease invades the hosts.Through numerical simulations,we have found that increasing animals'movements is an effective control measure for preventing prevalence of the disease.     

THE BALL-COVERING PROPERTY ON DUAL SPACES AND BANACH SEQUENCE SPACES

In this paper,we prove that(X,p)is separable if and only if there exists a w^*-lower semicontinuous norm sequence{p_n}_n=1^∞of(X^*,p)such that(1)there exists a dense subset G_nof X^*such that p_nis Gateaux differentiable on G_nand dp_n(Gn_n)■X for all n∈N;(2)p_n≤p and p_n→p uniformly on each bounded subset of X^*;(3)for anyα∈(0,1),there exists a ball-covering{B(x^*i,n,Ti,n)}∞i=1 of(X^*,p_n)such that it isα-off the origin and x_i,n^*∈Gn_n.Moreover,we also prove that if Xi is a Gateaux differentiability space,then there exist a real numberα>0 and a ball-covering(B)i of Xi such that(B)i isα-off the origin if and only if there exist a real numberα>0 and a ball-covering B of l^∞(X_i)such that(B)isα-off the origin.     

加权Baouendi-Grushin型算子的基本解与一类加权Hardy不等式(英文)

In this paper we obtain the fundamental solution for a class of weighted BaouendiGrushin type operator L_p,γ,αu = ▽_γ·(|▽_γu|^p-2ρ^α▽_γu) on R^m+n with singularity at the origin,where ▽_γ is the gradient operator defined by ▽_γ =（▽_x,|x|^γ▽_y） and ρ is the distance function.As an application,we get some Hardy type inequalities associated with ▽_γ.     

BLOW-UP SOLUTIONS OF TWO-COUPLED NONLINEAR SCHR?DINGER EQUATIONS IN THE RADIAL CASE

We consider the blow-up solutions to the following coupled nonlinear Schrodinger equations■.On the basis of the conservation of mass and energy,we establish two sufficient conditions to obtain the existence of a blow-up for radially symmetric solutions.These results improve the blow-up result of Li and Wu [10] by dropping the hypothesis of finite variance((|x|u₀,|x|v₀) ∈L²(R^N) × L²(R^N)).     

Existence of Positive Solutions to a Fractional-Kirchhoff System

Let Ω be a bounded smooth domain in R^N(N≥3).Assuming that 0 0 are constants,we consider the existence results for positive solutions of a class of fractional elliptic system below,■Under some assumptions of h_i(x,u,v,▽u,▽v)(i=1,2),we get a priori bounds of the positive solutions to the problem(1.1) by the blow-up methods and rescaling argument.Based on these estimates and degree theory,we establis...     

Reliability of a Multicomponent Stress-strength Model Based on a Bivariate Kumaraswamy Distribution with Censored Data

In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type-Ⅱ censored scheme.These elements(X₁,Y₁),(X₂,Y₂),…,(X_k,Y_k) follow a bivariate Kumaraswamy distribution and each element is exposed to a common random stress T which follows a Kumaraswamy distribution.The system is reg...     

THE GLOBAL EXISTENCE OF BV SOLUTIONS OF THE ISENTROPIC p-SYSTEM WITH LARGE INITIAL DATA

In this paper,we study the global existence of BV solutions of the initial value problem for the isentropic p-system,where the state equation of the gas is given by P=Av^-γ.For γ> 1,the general existence result for large initial data has not been obtained.By using the Glimm scheme,Nishida,Smoller and Diperna successively obtained the global existence results for(γ-1)TV(v₀(x),u₀(x)) being small.In the present paper,by adopting a rescaling technique,we improve th...     

NATURALLY REDUCTIVE(α1, α2) METRICS

Letting F be a homogeneous(α₁, α₂) metric on the reductive homogeneous manifold G/H, we first characterize the natural reductiveness of F as a local f-product between naturally reductive Riemannian metrics. Second, we prove the equivalence among several properties of F for its mean Berwald curvature and S-curvature. Finally, we find an explicit flag curvature formula for G/H when F is naturally reductive.     

Generalized Grötzsch ring function and generalized elliptic integrals

In this paper, we study the quotient of hypergeometric functions μ_a(r) in the theory of Ramanujan's generalized modular equation for a ∈(0, 1/2]. Several new inequalities are given for this and related functions. Our main results complement and generalize some known results in the literature.     

Blowing up of solutions to the Cauchy problem for the generalized Zakharov system with combined power-type nonlinearities

This paper deals with blowing up of solutions to the Cauchy problem for a class of general- ized Zakharov system with combined power-type nonlinearities in two and three space dimensions. On the one hand, for c0 = +∞ we obtain two finite time blow-up results of solutions to the aforementioned system. One is obtained under the condition α≥ 0 and 1 + 4/N ≤ p N +2/N-2 or α 0 and 1 p 1 + 4/N (N = 2, 3); the other is established under the condition N = 3, 1 p N +2/N-2 and α(p-3) ≥ 0. On the other hand, for c0 +∞ and α(p-3) ≥ 0, we prove a blow-up result for solutions with negative energy to the Zakharov system under study.     

Gradient Flow of the Lβ-Functional

In this paper,we start to study the gradient flow of the functional L_β introduced by Han-Li-Sun in[8].As a first step,we show that if the initial surface is symplectic in a K?hler surface,then the symplectic property is preserved along the gradient flow.Then we show that the singularity of the flow is characterized by the maximal norm of the second fundamental form.When β=1,we derive a monotonicity formula for the flow.As applications,we show that the l-tangent cone of the flow consists of the finite flat planes.     

THE EXISTENCE AND CONCENTRATION OF GROUND STATE SIGN-CHANGING SOLUTIONS FOR KIRCHHOFF-TYPE EQUATIONS WITH A STEEP POTENTIAL WELL

In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well■ in R³,where a,b> 0 are constants,λ is a positive parameter,V ∈ C(R³,R) is a steep potential well and the nonlinearity f ∈ C(R,R) satisfies certain assumptions.By applying a signchanging Nehari manifold combined with the method of constructing a sign-changing(PS)_C sequence,we obtain the existence of ground state sign-changing solutions with precisely two nodal domains w...     

Large m asymptotics for minimal partitions of the Dirichlet eigenvalue

In this paper,we study large m asymptotics of the l 1 minimal m-partition problem for the Dirichlet eigenvalue.For any smooth domainΩ?Rⁿsuch that|Ω|=1,we prove that the limit lim_m→∞l¹_m(Ω)=c 0 exists,and the constant c 0 is independent of the shape ofΩ.Here,l¹_m(Ω)denotes the minimal value of the normalized sum of the first Laplacian eigenvalues for any m-partition ofΩ.     

A Universal Inequality for Stability of Coarse Lipschitz Embeddings

Let X and Y be two pointed metric spaces.In this article,we give a generalization of the Cheng-Dong-Zhang theorem for coarse Lipschitz embeddings as follows:If f:X→Y is a standard coarse Lipschitz embedding,then for each x^*∈Lip₀(X) there exist α,γ> 0 depending only on f and Q_x*G Lip₀(Y) with ‖Q_x*‖_Lip ≤α‖x^*‖_Lip such that ■,for all x∈X.Coarse stability for a pair of metric spaces is studied.This can be consi...     

On the values of representation functions

For a set A of nonnegative integers, the representation functions R2(A,n) and R3(A,n) are defined as the numbers of solutions to the equation n = a + a′ with a,a′∈ A, a < a′ and a a′, respectively. Let N be the set of nonnegative integers. Given n0 > 0, it is known that there exist A,A′■ N such that R2(A′,n) = R2(N \ A′,n) and R3(A,n) = R3(N \ A,n) for all n n0. We obtain several related results. For example, we prove that: If A ■ N such that R3(A,n) = R3(N \ A,n) for all n n0, then (1) for any n n0 we have...