Infinity Behavior of Bounded Subharmonic Functions on Ricci Non-negative Manifolds

In this paper,we study the infinity behavior of the bounded subharmonic functions on a Ricci non-negative Riemannian manifold M.We first show that limr→∞r^2/V(r)∫B(r)△hdv=0if h is a bounded subharmonic function.If we further assume that the Laplacian decays pointwisely faster than quadratically we show that h approaches its supremun pointwisely at infinity,under certain auxiliary conditions on the volume growth of M.In particular,our result applies to the case when the Riemannian manifold has maximum volume growth.We also derive a representation formula in our paper,from which one can easily derive Yau‘s Liouville theorem on bounded harmonic functions.     

求极限的等价无穷大代换

给出等价无穷大代换的法则,并由此得到求某些未定式极限的计算方法.     

Axisymmetric free vibrations of infinite thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

ASYMPTOTIC PROPERTIES OF THE MOMENT CONVERGENCE FOR NA SEQUENCES

It is well-known that the complete convergence theorem for i.i.d. random variables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4]obtained a moment version of Hsu and Robbins series. However, the series tends to infinity whenever ∈ goes to zero, so it is of interest to investigate the asymptotic behavior of the series as ∈ goes to zero. This note gives some limit theorems of the series generated by moments for NA random variables.     

半线性摄动电报方程的渐近理论及应用

对二阶半线性摄动电报方程的初值问题.本交给出了一个渐近方法.证明了渐近理论及形式近似解的合理性都在时间变量无穷大时(即0≤t≤O(|ε|-1)成立.作为浙近理论的应用,我们对一个带初问题的特殊电报方程进行了研究,得到了两个|ε|-1阶渐近近似解.     

有限与无限

举例说明在有限情况下成立的结论,在无限情况下不一定成立。     

Attractor for lattice system of dissipative Zakharov equation

We consider the asymptotic behavior of solutions of an infinite lattice dynamical system of dissipative Zakharov equation. By introducing new weight inner product and norm in the space and establishing uniform estimate on ＂Tail End＂ of solutions, we overcome some difficulties caused by the lack of Sobolev compact embedding under infinite lattice system, and prove the existence of the global attractor; then by using element decomposition and the covering property of a polyhedron in the finite-dimensional space, we obtain an upper bound for the Kolmogorov ε-entropy of the global attractor; finally, we present the upper semicontinuity of the global attractor.     

A method for classifying orbits near asteroids

A method for classifying orbits near asteroids under a polyhedral gravitational field is presented, and may serve as a valuable reference for spacecraft orbit design for asteroid exploration. The orbital dynamics near aster- oids are very complex. According to the variation in orbit characteristics after being affected by gravitational perturbation during the periapsis passage, orbits near an as- teroid can be classified into 9 categories： （1） surrounding- to-surrounding, （2） surrounding-to-surface, （3） surrounding- to-infinity, （4） infinity-to-infinity, （5） infinity-to-surface, （6） infinity-to-surrounding, （7） surface-to-surface, （8） surface- to-surrounding, and （9） surface-to- infinity. Assume that the orbital elements are constant near the periapsis, the gravitation potential is expanded into a harmonic series. Then, the influence of the gravitational perturbation on the orbit is studied analytically. The styles of orbits are dependent on the argument of periapsis, the periapsis radius, and the periapsis velocity. Given the argument of periapsis, the orbital energy before and after perturbation can be derived according to the periapsis radius and the periapsis velocity. Simulations have been performed for orbits in the gravitational field of 216 Kleopatra. The numerical results are well consistent with analytic predictions.     

具有以双曲线与赤道弧为边界的周期环域的二次系统的Poincare分支及其应用

本文讨论了一类具有以双曲线与赤道弧为边界的周期环域的二次系统的Pincare分支．分别举出了此系统在一个奇点外围恰好存在两个单重环；恰好存在一个二重环；恰好存在一个单重环和一个无穷大分界线环等例子。