高阶Schr(o..)dinger方程的一族恒稳差分格式

A family of three-layer implicit difference schemes of high accuracy with two parameters for solving high order Schroedinger type equation au/at = i(-1)^m a^2mu/ax^2m are constructed(where i = √-1,m is positive integers). In the special case α =1/2,β = 0,we obtain a two-layer difference scheme. These schemes are proved to be absolutely stable for arbitrarily chosen non-negative parameters, and the order of the truncation error is O((△t)^2 (△x)^4). They are shown by numerical examples to be effective, and practice consistant with theoretical analysis.     

The Asymptotics of the Two-Dimensional Wave Equation for a General Multi-Connected Vibrating Membrane with Piecewise Smooth Robin Boundary Conditions

The asymptotic expansion for small |t| of the trace of the wave kernel ∧↑μ(t) =∑v=1^∞exp(-it μv^1/2), where i= √-1 and {μv}v=1^∞ are the eigenvalues of the negative Laplacian -△=-∑β=1^2(δ/δx^β)^2 in the (x^1, x^2)-plane, is studied for a multi-connected vibrating membrane Ω in R^2 surrounded by simply connected bounded domains Ωj with smooth boundaries δΩj(j=1,...,n), where a finite number of piecewise smooth Robin boundary conditions on the piecewise smooth components Гi(i=1 κj-1,...,κj) of the boundaries δΩj are considered, such that δΩj=∪i=1 κj-1^κj Гi and κ0=0. The basic problem is to extract information on the geometry of Ω using the wave equation approach. Some geometric quantities of Ω (e.g. the area of Ω, the total lengths of its boundary, the curvature of its boundary, the number of the holes of Ω, etc.) are determined from the asymptotic expansion of the trace of the wave kernel ∧↑μ(t) for small |t|.     

Extinction and Positivity for a Doubly Nonlinear Degenerate Parabolic Equation

The aims of this paper are to discuss the extinction and positivity for the solution of the initial boundary value problem and Cauchy problem of ut = div（[↓△u^m｜p-2↓△u^m）. It is proved that the weak solution will be extinct for 1 〈 p ≤ 1 ＋ 1/m and will be positive for p 〉 1 ＋ 1/m for large t, where m 〉 0.     

A Problem of Testing Homogeneity Against Order Constraints on Risk Differences

Consider I pairs of independent binomial variates x0i and x1i with corresponding parameters P0i and p1i and sample sizes n0i and n1i for i=1, …,I. Let △i = P1i-P0i be the difference of the two binomial parameters, where △i's are to be of interest and P0i's are nuisance parameters. The null hypothesis of homogeneity on the risk difference can be written as     

OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR DYNAMIC EQUATIONS WITH p-LAPLACIAN AND DAMPING

This paper concerns the oscillation of solutions of the second order nonlinear dynamic equation with p-Laplacian and damping（r（t）φ（x^△（t））^△＋p（t）φα（x^△α（t）＋q（t）f（xδ（t））=0on a time scale T which is unbounded above. Sign changes are allowed for the coefficient functions r, p and q. Several examples are given to illustrate the main results.     

A three level linearized compact difference scheme for the Cahn-Hilliard equation

This article is devoted to the study of high order accuracy difference methods for the Cahn-Hilliard equation.A three level linearized compact difference scheme is derived.The unique solvability and unconditional convergence of the difference solution are proved.The convergence order is O(τ 2 + h 4 ) in the maximum norm.The mass conservation and the non-increase of the total energy are also verified.Some numerical examples are given to demonstrate the theoretical results.     

A second order finite difference-spectral method for space fractional diffusion equations

A high order finite difference-spectral method is derived for solving space fractional diffusion equations,by combining the second order finite difference method in time and the spectral Galerkin method in space.The stability and error estimates of the temporal semidiscrete scheme are rigorously discussed,and the convergence order of the proposed method is proved to be O(τ2+Nα-m)in L2-norm,whereτ,N,αand m are the time step size,polynomial degree,fractional derivative index and regularity of the exact solution,respectively.Numerical experiments are carried out to demonstrate the theoretical analysis.     

一个关于风险差齐一性对序约束的检验问题

Consider I pairs of independent binomial variates X0i and X1i, with corresponding parameters P0i and P1i and sample sizes n0i and n1i for i = 1,…… , I. Let △i = P1i -P0i be the difference of the two binomial parameters, where △i‘s are to be of interest and Poi‘S are nuisance     

INVERSE PROBLEMS FOR A GENERAL MULTI－CONNECTED BOUNDED DRUM WITH APPLICATIONS IN PHYSICS

this paper studies the influence of a finite container on an ideal gas,The trace of the heat kernel Θ(t)=∑(μ=1)^∞ exp(-tλμ），where{λμ}(μ=1)^∞ are the eigenvalues of the negative Laplacian-△n=-∑(p=1)^n (a/axp)^2 in R^n(n=2 or 3) ,is studied for a general mult-connected bounded drum Ω which is surrounded by simply connected bounded domains Ωi with smooth boundaries aΩi(i=1,……,m) where the Dirichlet ,Neumann and Robin boundary Conditions on aΩi(i=1,……,m) are considered.Some geometrical properties of Ω are determined ,The theremodynamic quantities for an ideal gas encolosed in Ω are examined by using the asymptotic expansions of Θ(t) for short-sime t.It is shown that the ideal gas can not feel the shape of its container Ω，althought it can feel some geometrical properties of it.     

STABLE RECOVERY OF SIGNALS WITH THE HIGH ORDER D-RIP CONDITION

This paper establishes a high order condition on the restricted isometry property adapted to a frame D(D-RIP) for the signal recovery.It is shown that if the measurement matrix A satisfies the D-RIP condition δ_(tk)(1/2)((t-1)/t) for t1,then all signals f which are sparse in terms of a tight frame D can be recovered stably or exactly via the l_1-analysis model based on y =Af+z in l_2 and Dantzig selector bounded noise setting.     

解高阶抛物型方程的高精度显式差分格式

1 引言 1960年,Saul’ev在文中讨论了如下的高阶(2m阶)抛物型方程 μ/t=(-1)~(m 1)~2mμ/x~(2m) (1)(其中m为正整数),提出了一类含极因子α的两层差分格式。当α=0时为显式格式,其稳定性条件为,r=△t/(△x)~(2m)<1/2~(2m-1),△t,△x分别为时间及空间步长。随后,文[2],[3]利用     

A COALITION APPROACH TO THE MANAGEMENT OF HIGH SEAS FISHERIES IN THE PRESENCE OF EXTERNALITIES

ABSTRACT. The current paper extends the coalition approach of the management of high seas fisheries to the presence of externalities. The coalition approach is set within the framework of a two‐stage game in which the payoffs depend on the entire coalition structure and are determined through a partition function. The relationship between the presence of externalities and the stability of the coalition structures is explored. The equilibrium coalition structures of the game are also examined. The application of the game to the Northern Atlantic bluefin tuna shows a typical picture of the high seas fisheries: the simultaneous presence of strong externalities in the coalition structures and the absence of stability of the grand coalition. A fundamental conclusion of this paper is that, generally, in order to guarantee the stability of the cooperative agreements it is not sufficient to implement a fair sharing rule for the distribution of the returns from cooperation. Stability requires a legal regime preventing the players that engage in noncooperative behavior from having access to the resource.     

开口弧上高阶奇异积分B—P型换序公式

利用单侧高阶奇异积分概念，把［４］和［１］中各型高阶奇异积分的Ｂｅｔｒａｎｄ－Ｐｏｉｎｃａｒｅ’换序公式推广到开口弧情况，其证明方法对封闭弧当然有效，但曲线开口时过程复杂得多。     

一类具有高阶奇性解的Hilbert核奇异积分方程

本文利用指数变换研究了一类解具高阶奇性的周期黎曼边值问题,通过转化法研究了一类解具有高阶奇性的Hilber核奇异积分方程,获得了相应的解和可解条件表达式.推广了Hilber核奇异积分方程的结果.     

一类核密度含高阶奇性Cauchy型积分的边值定理

本文推广「１」，「６」中的结果，讨论了一类开口弧核密度含高阶奇且情形更一般的Ｃａｕｃｈｙ型积分的边值定理，积分号下求导及Ｈ连续性。     

四阶杆振动方程的两类高精度辛格式

In this paper, we present two classes of symplectic schemes with high order accuracy for solving four-order rod vibration equation utt uxxxx=0 via the third type generating function method. First, the equation of four order rod vibration is written into the canonical Hamilton system; second, overcoming successfully the essential difficult on the calculus of high order variations derivative, we get the semi-discretization with arbitrary order of accuracy in time direction for the PDEs by the third type generating function method. Furthermore the discretization of the related modified equation of original equation is obtained. Finally, arbitrary order accuracy symplectic schemes are obtained. Numerical results are also presented to show the effectiveness of the scheme, high order accuracy and properties of excellent long-time numerical behavior.     

求解三维高次拉格朗日有限元方程的代数多重网格法

本文针对带有间断系数的三维椭圆问题,讨论任意四面体剖分下的二次拉格朗日有限元方程的代数多重网格法．通过分析线性和高次有限元空间之间的关系,我们给出了一种新的网格粗化算法和构造提升算子的代数途径．进一步,我们还对新的代数多重网格法给出了收敛性分析．数值实验表明这种代数多重网格法对求解二次拉格朗日有限元方程是健壮和有效的。     

含高次逆幂的矩阵方程对称解的双迭代算法

本文研究了在控制理论和随机滤波等领域中遇到的一类含高次逆幂的矩阵方程的等价矩阵方程对称解的数值计算问题.采用牛顿算法求等价矩阵方程的对称解,并采用修正共轭梯度法求由牛顿算法每一步迭代计算导出的线性矩阵方程的对称解或者对称最小二乘解,建立了求这类矩阵方程对称解的双迭代算法,数值算例验证了双迭代算法是有效的.     

MULTISYMPLECTIC COMPOSITION INTEGRATORS OF HIGH ORDER

A composition method for constructing high order multisymplectic integrators is presented in this paper. The basic idea is to apply composition method to both the time and the space directions. We also obtain a general formula for composition method.     

复合材料弹性结构的高精度多尺度算法与数值模拟

１．引言 由于复合材料结构物理参数的非均匀各向异性以及细部几何构形的复杂性,在计算它的位移场、应力、应变场时,传统的有限元法因网格生成困难和计算规模太大而难以实现．７０年代初,Ｉ．Ｂａｂｕｓｋａ,Ｊ．Ｌ．Ｌｉｏｎｓ等人针对复合材料弹性结构提出了均匀化方法,见文［１］,数值实验表明,均匀化方法对描述复合材料弹性结构的有效材料常数及刚度性质是有效的,但它不能刻画应力和应变场的局部变化,因而作为复合材料强度理论的判断依据,均匀化理论显然是不够的．为此,Ｊ．Ｌ．Ｌｉｏｎｓ,Ｏ．Ａ．Ｏｌｅｉｎｉｋ等分别就…