Two Remarks on Independent Sets

In the first part we generalize the notion of strongly independent sets, introduced in [10] for polynomial ideals, to submodules of free modules and explain their computational relevance. We discuss also two algorithms to compute strongly independent sets that rest on the primary decomposition of squarefree monomial ideals.Usually the initial ideal in(I) of a polynomial ideal I is worse than I. In [9] the authors observed that nevertheless in(I) is not as bad as one should expect, showing that in(I) is connected in codimension one if I is prime.In the second part of the paper we add more evidence to that observation. We show that in(I) inherits (radically) unmixedness, connectedness in codimension one and connectedness outside a finite set of points from I and prove the same results also for initial submodules of free modules. The proofs use a deformation from I to in(I ).     

半导体瞬态问题特征变网格有限元法和分析

1 引 言考虑平面区域Ω　R2上的二维问题,其数学模型为[1]-△ψ=α（p-e+N（x））,（x,t）∈Ω×J,J（0,T],（1.1）     

On the iterative solution of the algebraic equations in fully implicit Runge-Kutta methods

This paper deals with the iterative solution of stage equations which arise when some fully implicit Runge-Kutta methods, in particular those based on Gauss, Radau and Lobatto points, are applied to stiff ordinary differential equations. The error behaviour in the iterates generated by Newton-type and, particularly, by single-Newton schemes which are proposed for the solution of stage equations is studied. We consider stiff systems y'(t) = f(t,y(t)) which are dissipative with respect to a scalar product and satisfy a condition on the relative variation of the Jacobian of f(t,y) with respect to y, similar to the condition considered by van Dorsselaer and Spijker in [7] and [17]. We prove new convergence results for the single-Newton iteration and derive estimates of the iteration error that are independent of the stiffness. Finally, some numerical experiments which confirm the theoretical results are presented. This revised version was published online in June 2006 with corrections to the Cover Date.     

n阶泛函微分方程边值问题

本文研究下列n阶RFDE边值问题:x⁽ⁿ⁾(t)=f(t,x_t,x(t),x′(t),…,x^(n-1)(t)),　t∈［0,T ］,x(t)=φ(t),t∈［-r,0］;x′(0)=η,x″(0)=η₂,…,x^(n-2) (0)=η_n-2,x^(j)(T)=A,其中j∈I={0,1,2,…,n-1},得到了解的存在性和唯一性新的结果.     

ON THE CONVERGENCE OF KING-WERNER ITERATION METHOD IN BANACH SPACE ON THE CONVERGENCE OF KING-WERNER ITERATION METHOD IN BANACH SPACE

1. IntroductionLetf(x) = 0 (1.1)where j: X - Y is a norilineax operator which maps Banach space X into Baaedspace Y. The well-known iteration methods for solving (1.1) are the Nixon methodaam very ldnds of its improvement methods. One of them is the so called King-Wernerm6thod denned bykw(p, x03 yo):which is established by King in [7], Werner in [12] in d~nt formulas, respectively.It is interesting that the method (1.2) is of order 1 fi with the same functioncompotatinn coSt and twO ti…     

Dynamics of a higher-order rational difference equation

We consider a higher order rational difference equation. Firstly, we skillfully give a sufficient and necessary condition for the existence and uniqueness of the initial value problem. And then we investigate the local stability, asymptotic behavior, periodicity and oscillation of solutions for the difference equation. Finally, we give some numerical simulations to illustrate our results.     

Fractional model and solution for the Black‐Scholes equation

This work presents a new model of the fractional Black‐Scholes equation by using the right fractional derivatives to model the terminal value problem. Through nondimensionalization and variable replacements, we convert the terminal value problem into an initial value problem for a fractional convection diffusion equation. Then the problem is solved by using the Fourier‐Laplace transform. The fundamental solutions of the derived initial value problem are given and simulated and display a slow anomalous diffusion in the fractional case.     

一类强阻尼非线性波动方程的广义解

用Galerkin方法研究了一类非线性波动方程的初边值问题,证明其在一定条件下强解的存在性.     

A Fokas approach to the coupled modified nonlinear Schrödinger equation on the half‐line

In this work, we discuss the coupled modified nonlinear Schrödinger (CMNLS) equation, which describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. By use of the Fokas approach, the initial‐boundary value problem for the CMNLS equation related to a 3×3 matrix Lax pair on the half‐line is to be analyzed. Assuming that the solution {u(x,t),v(x,t)} of CMNLS equation exists, we will prove that it can be expressed in terms of the unique solution of a 3×3 matrix Riemann‐Hilbert problem formulated in the plane of the complex spectral parameter λ. Moreover, we also get that some spectral functions s(λ) and S(λ) are not independent of each other but meet a global relationship.     

The existence of global solutions for the fourth-order nonlinear Schrodinger equations

In this paper, the problem of a class of multidimensional fourth-order nonlinear Schr\"{o}dinger equation including the derivatives of the unknown function in the nonlinear term is studied, and the existence of global weak solutions of nonlinear Schr\"{o}dinger equation is proved by the Galerkin method according to the different values of $\lambda$.