On hyperbolicity cones associated with elementary symmetric polynomials

Elementary symmetric polynomials can be thought of as derivative polynomials of . Their associated hyperbolicity cones give a natural sequence of relaxations for . We establish a recursive structure for these cones, namely, that the coordinate projections of these cones are themselves hyperbolicity cones associated with elementary symmetric polynomials. As a consequence of this recursion, we give an alternative characterization of these cones, and give an algebraic characterization for one particular dual cone associated with together with its self-concordant barrier functional.     

Solvability and Stability for Singular Fractional (p,q)-difference Equation

In this paper, we initiate the solvability and stability for a class of singular fractional $(p,q)$-difference equations. First, we obtain an existence theorem of solution for the fractional $(p,q)$-difference equation. Then, by using a fractional $(p,q)$-Gronwall inequality, some stability criteria of solution are established, which also implies the uniqueness of solution.     

一类二阶线性变系数微分方程通解的解法

采用特解和常数变易法,给出一类二阶线性变系数齐次和非齐次微分方程的通解公式,实例说明如何运用此通解公式.     

Maccari's方程组新的精确行波解

利用多项式的完全判别系统和初等积分法求出了Maccari's方程组的许多新的精确行波解.此方法与其它方法相比更简洁.     

Strong solutions to the equations of electrically conductive magnetic fluids

We study the equations of flow of an electrically conductive magnetic fluid, when the fluid is subjected to the action of an external applied magnetic field. The system is formed by the incompressible Navier–Stokes equations, the magnetization relaxation equation of Bloch type and the magnetic induction equation. The system takes into account the Kelvin and Lorentz force densities. We prove the local-in-time existence of the unique strong solution to the system equipped with initial and boundary conditions. We also establish a blow-up criterion for the local strong solution.     

A uniqueness theorem of radially symmetric positive stationary solutions for a competition–diffusion system

In this paper, as a first step to study the global structure of solution, we treat a class of reaction–diffusion systems with competitive interaction, and discuss a uniqueness theorem of radially symmetric solutions for the system. To do this, the comparison principle and the shooting method are employed, and the spatial profile is investigated.     

R3中一类Kirchhoff型方程变号解的存在性及集中性

本文研究了一类Kirchhoff型方程。利用极大极小原理及惩罚函数方法,证明了上述方程变号解的存在性及集中性,我们的结果推广了文献[4]的结果。     

线性半向量二层规划问题的全局优化方法

研究了线性半向量二层规划问题的全局优化方法. 利用下层问题的对偶间隙构造了线性半向量二层规划问题的罚问题, 通过分析原问题的最优解与罚问题可行域顶点之间的关系, 将线性半向量二层规划问题转化为有限个线性规划问题, 从而得到线性半向量二层规划问题的全局最优解. 数值结果表明所设计的全局优化方法对线性半向量二层规划问题是可行的.     

一类Riccati矩阵方程广义自反解的双迭代算法

本文研究了一类Riccati矩阵方程广义自反解的数值计算问题.利用牛顿算法将Riccati矩阵方程的广义自反解问题转化为线性矩阵方程的广义自反解或者广义自反最小二乘解问题,再利用修正共轭梯度法计算后一问题,获得了求Riccati矩阵方程的广义自反解的双迭代算法.拓宽了求解非线性矩阵方程的迭代算法.数值算例表明双迭代算法是有效的.     

两大部类持续扩大再生产的优化

基于经典的马克思两大部类社会再生产公式,建立了离散确定型的持续扩大再生产的优化问题的动态规划模型.在生产资料部类的不变资本产出率高于另一部类的条件下,动态规划的指标函数是作为决策变量的生产资料部类积累率的单调函数,因而可以使用逆序解法或者顺序解法,获得唯一的最优策略和最优指标函数.借助《资本论》中的一个举例,计算验证了最优解.