“惟一性”品格——谈语言的锤炼

曾在一篇谈写作的文章中读到这样的观点,写作至少必须具备五个重要的条件,其中之一是"个性鲜明的语言"。确实,写作最终是靠语言来完成的,就像绘画的物质表现形式是线条、色彩一样,写作的最主要的物质表现形式就是语言。语言"个性鲜明",除了要张扬作者的个性,有自身的语言风格外,更应表现在对语言的"惟一性"品格的锤炼。

CONSERVATIVE DIFFERENCE SCHEME BASED ON NUMERICAL ANALYSIS FOR NONLINEAR SCHRDINGER EQUATION WITH WAVE OPERATOR

A new conservative finite difference scheme is presented based on the numerical analysis for an initialboundary value problem of a class of Schroedinger equation with the wave operator. The scheme can be linear and implicit or explicit based on the parameter choice. The initial value after discretization has second-order accuracy that is consistent with the scheme accuracy. The existence and the uniqueness of the difference solution are proved. Based on the priori estimates and an inequality about norms, the stability and the convergence of difference solutions with the second-order are proved in the energy norm. Experimental results demonstrate the efficiency of the new scheme.

Weak solution for a fourth-order nonlinear wave equation

The existence and the nonexistence,the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation utt＋αΔ2 u-bΔut-βΔu＋ut｜ut｜^r＋g（u）=0 in Ω×（0,∞） are studied with the boundary condition u=（u）/（υ）=0 onΩ and the initial condition u（x,0）=u0（x）,ut（x,0）=u1（x,0） in bounded domain ΩR^n ,n≥1.The energy decay rate of the global solution is estimated by the multiplier method.The blow-up result of the solution in finite time is established by the ideal of a potential well theory,and the existence of the solution is gotten by the Galekin approximation method.

Anti-periodic solutions to a class of second-order evolution equations

In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.

Existence results for a class of parabolic evolution equations in Banach spaces

We discuss the existence results of the parabolic evolution equation d(x(t)+g(t,x(t)))/dt+A(t)x(t)=f(t,x(t)) in Banach spaces, where A(t) generates an evolution system and functions f,g are continuous. We get the theorem of existence of a mild solution, the theorem of existence and uniqueness of a mild solution and the theorem of existence and uniqueness of an S-classical (semi-classical) solution. We extend the cases when g(t)=0 or A(t)=A.

On existence and uniqueness of the solution of elastoplastic contact problems

Contact problems and elastoplastic problems are unified and described by the variational inequality formulation, in which the constraints of the constitutional relations for elastoplastic materials and the contact conditions are relaxed totally. First, the coerciveness of the functional is proved. Then the uniqueness of the solution of variational inequality for the elastoplastic contact problems is demonstrated. The existence of the solution is also demonstrated according to the sufficient conditions for the solution of the elliptic variational inequality. A mathematical foundation is developed for the variational extremum principle of elastoplastic contact problems. The developed variational extremum forms can give an effective and strict mathematical modeling to solve contact problems with mathematical programming.

Determination of pollution point source in parabolic system model

This paper considers an inverse problem for a partial differential equation to identify a pollution point source in a watershed. The mathematical model of the problem is a weakly coupled system of two linear parabolic equations for the concentrations u（x, t） and v（x, t） with an unknown point source F（x, t） = A（ t）δ（x- s） related to the concentration u（x, t）, where s is the point source location and A（t） is the amplitude of the pollution point source. Assuming that source F becomes inactive after time T＊, it is proved that it can be uniquely determined by the indirect measurements { v（0, t）, v（ a, t）, v（ b, t）, v（ l, t）, 0 〈 t ≤ T, T＊ 〈 T}, and, thus, the local Lipschitz stability for this inverse source problem is obtained. Based on the proof of its uniqueness, an inversion scheme is presented to determine the point source. Finally, two numerical examples are given to show the feasibility of the inversion scheme.

On meromorphic functions sharing one value

The uniqueness of meromorphic functions with one sharing value and an equality on deficiency is studied. We show that if two nonconstant meromorphic functions f(z) and g(z) satisfy δ(0,f)+δ(0,g)+δ(∞,f)+δ(∞,g)=3 or δ 2(0,f)+δ 2(0,g)+δ 2(∞,f)+δ 2(∞,g)=3, and E(1,f)=E(1,g) then f(z),g(z) must be one of five cases.

Weak solutions to one-dimensional quantum drift-diffusion equations for semiconductors

The weak solutions to the stationary quantum drift-diffusion equations （QDD） for semiconductor devices are investigated in one space dimension. The proofs are based on a reformulation of the system as a fourth-order elliptic boundary value problem by using an exponential variable transformation. The techniques of a priori estimates and Leray-Schauder＇s fixed-point theorem are employed to prove the existence. Furthermore, the uniqueness of solutions and the semiclassical limit δ→0 from QDD to the classical drift-diffusion （DD） model are studied.

On the uniqueness of entire functions

We study the uniqueness of entire functions and prove the following theorem: Let f(z) and g(z) be two nonconstant entire functions; n and k two positive integers with n>2k+4. If the zeros of both f(z) and g(z) are of multiplicity at least n, and f (k)(z) and g (k)(z) share 1 CM, then either f(z)=c 1e cz, g(z)= c 2e -cz, where c 1, c 2 and c are three constants satisfying (-1) kc 1c 2c 2k= 1, or f(z)≡g(z).