Fixed points of asymptotic contractions

Let be a contractive gauge function in the sense that φ is continuous, φ(s)<s for s>0, and if f:M→M satisfies d(f(x),f(y))?φ(d(x,y)) for all x,y in a complete metric space (M,d), then f always has a unique fixed point. It is proved that if T:M→M satisfies

     

On positive radial entire solutions of second-order quasilinear elliptic systems

We study positive radial entire solutions of second-order quasilinear elliptic systems of the form

(∗)     

Multiplicity and asymptotic behavior of positive solutions for a singular semilinear elliptic problem

The following singular elliptic boundary value problem is studied:

     

截断平顶高斯光束M2因子的比较研究

使用熵束宽、渐近分析和环围功率法对截断平顶高斯光束的束腰宽度w、远场发散角θ0和M²因子作了比较研究.结果表明:按不同束宽定义得到的截断平顶高斯光束的w、θ0和M²因子不同,且与截断参量a/w0(a为光阑半宽度,w0为平顶高斯光束初始束腰宽度)有关.随a/w0的增加,三种方法计算得到的w、θ0和M²都分别趋于某常量.     

Dissipation in Turbulent Shear Flows: A Wall Function Approach for High Reynolds Numbers

Dissipation effects that are neglected in almost all numerical codes when it comes to turbulent flows are analysed systematically. It is shown how the direct and the indirect dissipation can be implemented into the codes when asymptotic considerations about the flow behaviour close to a wall are taken into account. As an example, adiabatic pipe flow is analysed with special emphasis on the distribution of energy between the mechanical and thermal part of the total energy.     

Asymptotic exponential cones of Metzler matrices and their use in the solution of an algebraic problem

The aim of this paper is that of investigating the asymptotic exponential cone of a single Metzler matrix, introduced in [23], and of defining and analysing the new concept of asymptotic exponential cone of a family of Metzler matrices (along a certain direction). These results will provide necessary and/or sufficient conditions for the solvability of an interesting algebraic problem that arises in the context of continuous-time positive switched systems and, specifically, in the investigation of the reachability property [21,22,25].     

Asymptotic behavior of solutions of second-order nonlinear impulsive differential equations

In this work, the asymptotic behavior of all solutions of second-order nonlinear ordinary differential equations with impulses is investigated. By impulsive differential inequality and Riccati transformation, sufficient conditions of asymptotic behavior of all solutions of second-order nonlinear ordinary differential equations with impulses are obtained. An example is also inserted to illustrate the impulsive effect.     

The E-theoretic descent functor for groupoids

The paper establishes, for a wide class of locally compact groupoids Γ, the E-theoretic descent functor at the C^∗-algebra level, in a way parallel to that established for locally compact groups by Guentner, Higson and Trout. Section 2 shows that Γ-actions on a C₀(X)-algebra B, where X is the unit space of Γ, can be usefully formulated in terms of an action on the associated bundle B^?. Section 3 shows that the functor B→C^∗(Γ,B) is continuous and exact, and uses the disintegration theory of J. Renault. Section 4 establishes the existence of the descent functor under a very mild condition on Γ, the main technical difficulty involved being that of finding a Γ-algebra that plays the role of Cbcont(T,B) in the group case.     

Global existence and exponential stability for a contact problem between two thermoelastic beams

In this paper we analyze a dynamic unilateral contact problem between two thermoelastic beams. We establish the existence of a weak global-in-time solution, by a penalization method. Moreover, we study the asymptotic behavior of such a solution proving that the energy associated to the system decays exponentially to zero, as time goes to infinity.     

一类非线性奇摄动Robin问题解的渐近性态

利用渐近理论和微分不等式的方法,该文研究了一类非线性奇摄动Robin问题. 证明了其解的存在性,并得到了解的任意n 阶一致有效渐近展开式.