分形插值函数的矩量及扰动误差估计

研究分形插值函数的矩量积分问题.对于一类分形插值函数,给出了它在各阶区间上的(p,q)阶矩量积分的计算公式.此外,考虑含有扰动项的迭代函数系所产生的分形插值函数的矩量,讨论了扰动项对于矩量的影响,给出扰动前后矩量的误差估计式.     

积分方程的ε复杂性

本文考虑积分方程的ε复杂性问题.问题的ε复杂性是在误差不超过ε的前提下解决问题所需的最小成本.对某些具各向异性核与自由项的第二类Fredholm方程,求得了ε复杂性的精确阶.同时,找到了解决该问题具最小成本的算法.     

积分方程的ε复杂性

本文考虑积分方程的ε复杂性问题问题的ε复杂性是在误差不超过ε的前提下解决问题所需的最小成本.对某些具各向异性核与自由项的第二类Fredbolm方程,求得了ε复杂性的精确阶.同时,找到了解决该问题具最小成本的算法。     

带弱耗散的两维非自治不可压Navier-Stokes方程拉回吸引子的上半连续性

该文研究了描述流体力学规律的一类带有弱耗散和扰动外力项的两维非自治不可压Navier-Stokes方程拉回吸引子的上半连续性.利用半群(过程族)的分解方法以及弱连续方法,可以得到自治系统全局吸引子和非自治系统拉回吸引子的存在性,进一步地,当ε0收敛到ε=0时候,非自治系统的拉回吸引子A_ε(t)可以连续收敛到自治系统的全局吸引子A.     

广义高维Klein-Gordon强迫扰动方程的孤子解

利用同伦映射方法研究了一类非线性广义强迫扰动Klein-Gordon方程.首先利用双曲正切待定系数法求得了无扰动项典型方程的孤子解.然后利用同伦映射原理得到了强迫扰动Klein-Gordon方程的任意次近似孤子解.最后叙述了得到的近似孤子解是一个解析展开式,还能对它进行解析运算.这对使用简单的模拟方法得到的近似解是达不到的.     

一类超前型微分差分方程的有界解及其渐近性质

本文考虑具有扰动项的超前型微分差分方程,证明了当退化方程具有负指数阶的有界解且扰动项满足一定条件时,扰动方程也具有负指数阶的有界解.     

二次自伴矩阵多项式阵特征值界的数值计算

在参数不确定性线性系统的鲁棒控制研究中,常用到的一个指标就是使不确定性系统在输出反馈或状态反馈控制下的闭环系统在H∞-范数界γ的条件下的二次稳定.是否二次稳定,一般要验证能否找到一个正常数,ε使相应的R iccati方程有正定解.而R iccati方程一般情况下求解相当困难.本文通过具体的分析,提出了一种在给定正定矩阵的条件下,找使此正定阵是R iccati方程的解相对应的正常数ε的可能范围的方法,即求解二次自伴矩阵多项式阵特征值界的方法.文中详细给出了所用理论及算法.给出了求正常数ε范围的一个实例.     

扰动Boussinesq方程的近似守恒律

构造了具有扰动项的Boussinesq方程的近似守恒向量和近似守恒律.在方程允许拉格朗日函数的情况下,利用欧拉方程的部分拉格朗日函数方法,研究了含有一阶线性组合扰动项的Boussineq方程的近似守恒律.给出了该方程的近似守恒向量及近似守恒律的分类结果.     

凸区域上拟线性椭圆型方程的尖峰解

本文讨论奇异扰动的拟线性椭圆型方程-ε△pu(x)=f(u(x)),u(x)≥0,x∈Ω;u=0,x∈Ω在Dirichlet边值条件下极小能量解的存在性和结构.其中ε＞0是小参数,p＞2,△pu=div(|Du|p-2Du),f(s)=sq-sp-1,p-1＜q＜Np/N-p-1.Ω RN(N≥2)是有界光滑区域.当ε→0时,方程存在一个极小能量解,应用移动平面方法可以证明此解在凸区域上会变成一个尖峰解.     

十一次Hamilton系统的Abelian积分零点个数的线性估计

本文研究一类十一次Hamilton系统在n次多项式扰动下的Abelian积分的零点个数问题.利用Picard-Fuchs方程法,得到这类扰动Hamilton系统的Abelian积分的零点个数的上界(计重数).     

Numerical methods for structured population models: The Escalator Boxcar Train

A numerical integration method is introduced for the class of hyperbolic partial differential equations that occur in physiologically structured population models. These equations describe the time evolution of the population density-function over the individual state-space Ω. Exploiting the biological interpretation of the equation, this density-function is represented by a set of moments over a collection of subdomains in Ω, moving along the characteristics of the partial differential equation (PDE). These moments are readily interpreted as numbers of individuals in a cohort, mean individual state in a cohort, etc. The numerical method consists of approximating the differential equations. The method appears to be very efficient for this special type of PDE. It combines such desirable properties as as lack of dispersion and dissipation and a preservation of monotonicity of the density function along the characteristics with a strong relation to the biological background of the equations for these moments to arrive at a closed system of ordinary differential equations. The method also allows one to incorporate the usual type of nonlinearities that occur in physiologically structured population models. A numerical example is presented as an illustration of the application of the method.     

Boundary element solution of the two-dimensional groundwater flow equation with stochastic free surface boundary condition

An innovative approach to the approximate solution of stochastic partial differential equations in groundwater flow is presented. The method uses a formulation of the Ito's lemma in Hilbert spaces to derive partial differential equations satisfying the moments of the solution process. Since the moments equations are deterministic, they could be solved by any analytical or numerical method existing in the literature. This permits the analysis and solution of stochastic partial differential equations occurring in two-dimensional or three-dimensional domains of any geometrical shape. The method is tested for the first time in the present paper through a practical application in a sandy phreatic aquifer at the Chalk River Nuclear Laboratories, Ontario, Canada. The equation solved is the two-dimensional LaPlace equation with a dynamic, randomly perturbed, free surface boundary condition. The moments equations are derived and solved by using the boundary integral equation method. A comparison is made with a previous analytical solution obtained by applying the randomly forced one-dimensional Boussinesq equation, and some observations on modeling procedures are given.     

Principal and nonprincipal solutions of impulsive differential equations with applications

We introduce the concept of principal and nonprincipal solutions for second order differential equations having fixed moments of impulse actions is obtained. The arguments are based on Polya and Trench factorizations as in non-impulsive differential equations, so we first establish these factorizations. Making use of the existence of nonprincipal solutions we also establish new oscillation criteria for nonhomogeneous impulsive differential equations. Examples are provided with numerical simulations to illustrate the relevance of the results.     

Nonstationary queues with Interrrupted Poisson arrivals and unreliable/repairable servers

A queueing model having a nonstationary Interrupted Poisson arrival process (IPP(t)),s time-dependent exponential unreliable/repairable servers and finite capacityc is introduced, and an approximation method for analysis of it is developed and tested. Approximations are developed for the time-dependent queue length moments and the system viewpoint waiting time distributions and moments. The approximation involves state-space partitioning and numerically integrating partial-moment differential equations (PMDEs). Surrogate distribution approximations (SDA's) are used to close the system of PMDEs. The approximations allow for analysis using only (s + 1)(s + 6) differential equations for the queue length moments rather than the 2(c + 1)(s +1) equations required by the classic method of numerically integrating the full set of Kolmogorov-forward equations. Effectively hours of cpu time are reduced to minutes for even modest capacity systems. Approximations for waiting time distributions and moments are developed.This research was partially funded by National Science Foundation grant ECS-8404409.     

Moments of claims in a Markovian environment

This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace–Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.     

Generalized moment estimation of stochastic differential equations

We study the semiparametric estimation of stochastic differential equations employing methods based on moment conditions, comparing the finite sample and robustness properties of generalized method of moments, empirical likelihood and minimum contrast methods using unconditional and conditional formulations of moment conditions. The results obtained indicate that the estimators proposed, particularly, the estimators based on exponential tilting, obtain better results than those of the generalized methods of moments normally used to estimate stochastic differential equations. This conclusion is mainly derived from the robustness properties of this method in the presence of problems of incorrect specification.     

Picone type formula for half‐linear impulsive differential equations with discontinuous solutions

Picone type formula for half‐linear impulsive differential equations with discontinuous solutions having fixed moments of impulse actions is derived. Employing the formula, Leighton and Sturm–Picone type comparison theorems as well as several oscillation criteria for impulsive differential equations are obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

A Peano-Like Theorem for Stochastic Differential Equations with Nonlocal Sample Dependence

The existence of a not-necessarily-unique strong solution for a stochastic differential equations with nonlocal sample dependence is established under the assumption that the coefficients satisfy an asymptotically local boundedness condition in addition to continuity. The proof is by an Euler-like construction of approximations. These equations include mean-field stochastic differential equations, but the nonlocal sample dependence can be more general than just the dependence on moments of the solution.     

CONTINUOUS DEPENDENCE OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS ON THE INITIAL CONDITIONS AND BARRIER CURVES＊

The basic objects of investigation in this article are nonlinear impulsive differential equations.The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-cal...     

Parameter and moment bounds for a nonlinear stochastic ecology model

A differential equation model of a marine ecosystem is formulated as a stochastic process. The ecosystem is modeled by considering the random exchange of a chemical nutrient between three components of the ecosystem. The Chapman-Kolmogorov equations and the moment or cumulant generating functions for the process are derived to examine analytically the behavior of the moments of the process. Through the use of differential inequalities, bounds on the exchange rate parameters are derived to reflect component extinction. Bounds on the moments of the process are also obtained.