时间尺度上二阶拟线性阻尼动力方程的振动性分析

研究二阶拟线性时滞阻尼动力方程[a(t)|x^Δ(t)|^λ-1x^Δ(t)]^Δ+b(t)|x^Δ(t)|^λ-1x^Δ(t)+p(t)|x(δ(t))|^λ-1x(δ(t))=0的振动性,其中t ₀∈T,而T为任意时间尺度,考虑方程是非正则情形,即$\int^{∞}_{t_0}$[a^-1(s)e_-b/a(s,t₀)]^1/λ Δs < ∞。 通过引入广义Riccati变换,借助时间尺度上的有关理论,并结合不等式技巧,建立了该方程振动的一些新的充分条件,推广、改进并丰富了现有文献中的结果。     

若干高维可积和不可积模型的严格解

可积和不可积模型可以描述自然科学中的诸多现象, 寻找高维非线性模型的严格解已成为可积系统的一个重要研究内容. 结合达布变换法和多线性分离变量法, 可以得到多个(2+1)维非线性模型包含任意函数的严格解, 通过选取不同的任意函数, 构造这些非线性模型新的相互激发模式. 进一步推广了形变映射理论, 建立了变系数 场和sine-Gordon以及双sine-Gordon场的形变映射关系, 从而得到高维不可积模型包含任意函数的新严格解. 对任意函数的不同选择, 构造了sine-Gordon和双sine-Gordon可积模型丰富的局域解和周期解, 如多solitoff解及其周期波推广、周期形变的蛇形孤波解以及变模的拟周期解等.     

基于流率入树枝向量行列式算法的循环经济系统增长反馈分析

设计了江西省萍乡市兰坡村“猪-沼-粮”循环经济系统工程的流率入树模型,并利用流率入树枝向量行列式算法得到了系统的反馈环,在反馈环基础上,构造了系统增长基模,得到结论,以沼气工程（沼肥）为纽带,发展养殖业能实现生猪养殖、稻谷种植和蔬菜种植之间的良性循环,能够达到稻谷增产和收入增长,在微观层面上实现粮食安全和农民增收双赢。     

线性函数的性质及其应用 线性函数的性质及其应用

给出了线性函数、部分线性函数和线性变量的定义,提出了它们的性质.根据上述定义,利用布尔代数中的基本定理和公式以及自双反函数和对称函数的定义对这些性质给出了证明.最后讨论了它们在逻辑综合以及计算逻辑函数的布尔差分中的应用.     

检测线性函数与线性变量的表格方法

讨论了线性函数、部分线性函数和线性变量的定义、性质和定理,提出了检测基于最小项展开的逻辑函数的线性变量与线性函数的表格方法.提出了直接从RM型逻辑函数的Reed-Muller展开出发以及直接从OC型OC展开出发检测RM型逻辑函数和OC型逻辑函数的线性变量及线性函数的表格方法.文中提出的表格方法具有简单、方便和易于计算机编程操作等优点.     

随机变量相等的一个充要条件

本文证得分布于有限区间上的随机变量相等的充要条件为其各阶原点矩相等．     

One‐step boundary knot method for discontinuous coefficient elliptic equations with interface jump conditions

This study makes the first attempt to apply the boundary knot method (BKM), a meshless collocation method, to the solution of linear elliptic problems with discontinuous coefficients, also known as the elliptic interface problems. The additional jump conditions are usually required to be prescribed at the interface which is used to maintain the well‐posedness of the considered problem. To solve the problem efficiently, the original governing equation is first transformed into an equivalent inhomogeneous modified Helmholtz equation in the present numerical formulation. Then the computational domain is divided into several subdomains, and the solution on each subdomain is approximated using the BKM approach. Unlike the conventional two‐step BKM, this study presents a one‐step BKM formulation which possesses merely one influence matrix for inhomogeneous problems. Several benchmark examples with various discontinuous coefficients have been tested to demonstrate the accuracy and efficiency of the present BKM scheme. © 2016Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1509–1534, 2016     

Functionally separable solutions to nonlinear wave equations by group foliation method

We apply functional separation of variables within the approach of the group foliation method to the nonlinear wave equation with variable speed and external force: utt=A(x)(Dx(u)ux)+B(x)Q(u), Ax≠0. A classification of these equations admitting functionally separable solutions is performed and the resulting solutions are obtained in explicit form in many cases.     

A Comparison of Splittings and Integral Equation Solvers for a Nonseparable Elliptic Equation

Iterative numerical schemes for solving the electrostatic partial differential equation with variable conductivity, using fast and high-order accurate direct methods for preconditioning, are compared. Two integral method schemes of this type, based on previously suggested splittings of the equation, are proposed, analyzed, and implemented. The schemes are tested for large problems on a square. Particular emphasis is paid to convergence as a function of geometric complexity in the conductivity. Differences in performance of the schemes are predicted and observed in a striking manner. AMS subject classification (2000) 31A10, 35C15, 65R20.Received May 2004. Accepted September 2004. Communicated by Anders Szepessy.Johan Helsing: This work was supported by the Swedish Science Research Council under contract 621-2001-2799.