Runge–Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments

In this paper we deal with the numerical solutions of Runge–Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments. The numerical solution is given by the numerical Green’s function. It is shown that Runge–Kutta methods preserve their original order for first-order periodic boundary value differential equations with piecewise constant arguments. We give the conditions under which the numerical solutions preserve some properties of the analytic solutions, e.g., uniqueness and comparison theorems. Finally, some experiments are given to illustrate our results.     

三维可压等熵Euler方程光滑解的整体存在性

研究了三维可压等熵Euler方程Cauchy问题光滑解的整体存在性.如果初值是一个常状态的小扰动并且初速度的旋度等于零,证明了三维可压等熵Euler方程Cauchy问题光滑解的整体存在性.     

高阶脉冲中立型偏泛函微分方程的强迫振动性

研究一类具高阶Laplace算子的高阶脉冲非线性中立型偏泛函微分方程的强迫振动性,利用Green公式和微分不等式方法将所讨论的脉冲中立型偏微分方程转化为脉冲中立型微分不等式的问题,获得了这类方程在三类不同边值条件下所有解强迫振动的若干充分条件.     

配送量不定的供应链协调

本文研究供应链管理中配送量不确定时，制造商和分销商之间的协调问题。通过建立惩罚和奖励机制模型来协调供应链各部分的运作，使得分散系统就如一个整体。同时分析供应链的利润分配问题，分别得出各个机制下分销商的最优决策。     

关于离散HJB方程的下解与上解

本文讨论HJB方程上、下解的几个性质,并讨论了从上解出发的一个迭代法的收敛性.     

关于不含k-C-圈的n阶r-一致超图的若干结果

主要讨论了不含k-C-圈的n阶r-一致超图,对不同的k,分别得出了它的极大边数的一个下界,并且得出在有些情况下它的下界是最大的.另外,我们得到了Krn含k-C-圈的一个充分必要条件.     

一类具有非线性发生率的传染病模型的稳定性

建立和研究一类具有非线性发生率的传染病模型,得到该模型基本再生数R_0的表达式,运用Lyapunov函数和第二加性复合矩阵理论证明了当R_0<1时无病平衡点全局渐近稳定,此时疾病消失,当R_0>1时地方病平衡点全局渐近稳定,此时疾病在人群中流行.     

Cauchy Integral Formulae in Quaternionic Hermitean Clifford Analysis

The theory of complex Hermitean Clifford analysis was developed recently as a refinement of Euclidean Clifford analysis; it focusses on the simultaneous null solutions, called Hermitean monogenic functions, of two Hermitean Dirac operators constituting a splitting of the traditional Dirac operator. In this function theory, the fundamental integral representation formulae, such as the Borel?CPompeiu and the Clifford?CCauchy formula have been obtained by using a (2 ×?2) circulant matrix formulation. In the meantime, the basic setting has been established for so-called quaternionic Hermitean Clifford analysis, a theory centred around the simultaneous null solutions, called q-Hermitean monogenic functions, of four Hermitean Dirac operators in a quaternionic Clifford algebra setting. In this paper we address the problem of establishing a quaternionic Hermitean Clifford?CCauchy integral formula, by following a (4?× 4) circulant matrix approach.     

A study of nonlinear Langevin equation involving two fractional orders in different intervals

This paper studies a nonlinear Langevin equation involving two fractional orders α∈(0,1] and β∈(1,2] with three-point boundary conditions. The contraction mapping principle and Krasnoselskii’s fixed point theorem are applied to prove the existence of solutions for the problem. The existence results for a three-point third-order nonlocal boundary value problem of nonlinear ordinary differential equations follow as a special case of our results. Some illustrative examples are also discussed.     

Quantitative Local Bounds for Subcritical Semilinear Elliptic Equations

The purpose of this paper is to prove local upper and lower bounds for weak solutions of semilinear elliptic equations of the form ???u =?cu ^p , with 0 < p < p _s = (d + 2)/(d - 2), defined on bounded domains of ${{\mathbb{R}^d}, d \geq 3}$ , without reference to the boundary behaviour. We give an explicit expression for all the involved constants. As a consequence, we obtain local Harnack inequalities with explicit constants, as well as gradient bounds.