一类非线性退化方程混合问题解的渐进性态

本文利用比较原理以及一种特殊变换研究了一类非线性退化方程的混合问题，得到了这类复杂问题解的渐进性质。     

ON THE EQUATION □φ = |vφ|2 IN FOUR SPACE DIMENSIONS

This paper considers the following Cauchy problem for semilinear wave equations in n spacedimensions□φ = F( φ),φ(0, x) = f(x), tφ(0, x) = g(x),The minimal value of s is determined such that the above Cauchy problem is locally well-posed in Hs. It turns out that for the general equation s must satisfyThis is due to Ponce and Sideris (when n = 3) and Tataru (when n ≥ 5). The purpose of thispaper is to supplement with a proof in the case n = 2, 4.     

高阶非线性时滞差分方程解的渐近性

研究如下的具强迫项的高阶非线性时滞差分方程△^my(n) u(n)l↑∑i=1 gi(y(n-τ))=v(n)其中，m≥1，u,v：N→R，gi：R→R且τ∈{0，1，2，3，…)，i=1，2，…，l，得到了使该方程的解具有某种渐近性态的充分条件。     

New Exact Solutions to the Combined KdV and mKdV Equation

The modified mapping method is developed to obtain new exact solutions to the combined KdV and mKdV equation. The method is applicable to a large variety of nonlinear evolution equations, as long as odd- and even-order derivative terms do not coexist in the equation under consideration.     

THE COUPLING OF NATURAL BOUNDARY ELEMENT AND FINITE ELEMENT METHOD FOR 2D HYPERBOLIC EQUATIONS

In this paper, we investigate the coupling of natural boundary element and finite element methods of exterior initial boundary value problems for hyperbolic equations. The governing equation is first discretized in time, leading to a time-step scheme, where an exterior elliptic problem has to be solved in each time step. Second, a circular artificial boundary FR consisting of a circle of radius R is introduced, the original problem in an unbounded domain is transformed into the nonlocal boundary value problem in abounded subdomain. And the natural integral equation and the Poisson integral formula are obtained in the infinite domainΩ2 outside circle of radius R. The coupled variational formulation is given. Only the function itself, not its normal derivative at artificial boundary ΓR, appears in the variational equation, so that the unknown numbers are reducedand the boundary element stiffness matrix has a few different elements. Such a coupled method is superior to the one based on direct boundary element method. This paper discusses finite element discretization for variational problem and its corresponding numerical technique, and the convergence for the numerical solutions. Finally, the numerical example is presented to illustrate feasibility and efficiency of this method.     

Lattice mechanical properties of some fcc f-shell metals

A pseudopotential depending on an effective core radius is proposed to study the binding energy, equation of state, ion-ion interaction, phonon dispersion curves (q-space and r-space analysis), mode Grüneisen parameters and dynamical elastic constants of some fcc f-shell metals La, Yb, Ce and Th. The contribution of the s-like electrons is calculated in the second-order perturbation theory for the potential while d and f-like electron is taken into account by introducing repulsive short-range Born-Mayer term. The parameter of the potential is evaluated by zero pressure condition. An excellent agreement between theoretical investigations and experimental findings is achieved which confirms the present formalism     

Analytical study of a flattened Gaussian beam through multi-apertured optical imaging systems of B = 0

By using the methods of the matrix decomposition and expansion of the hard-edged aperture function into a finite sum of complex Gaussian functions, the recurrence propagation expressions for a flattened Gaussian beam (FGB) through multi-apertured optical imaging systems of B = 0 are derived and illustrated with numerical examples. Comparisons with the straightforward numerical integration of the Collins formula and with the previous work are made. It is shown that the main advantages of our methods and results are the more accuracy and great reduction of computer time.     

On Quasiclassical Field Theories Invariant with Respect to a Lie Group

Mathematical Notes -     

三阶非线性时滞差分方程解的渐近性

研究了一类三阶非线性变滞量差分方程解的渐近性,给出了该类方程的非振动解当n→+∞时渐近趋于零或趋于某有限数值的几个充分条件.     

Constructing Solutions of an Ill-Posed Nonlinear Singularly Perturbed Problem for an Equation of Elliptic Type

Mathematical Notes -