一般工艺假定及其投入产出模型的优化

根据供给表和使用表推算国家(地区)对称型投入产出表有两种方法,即:产品工艺假定方法和部门工艺假定方法.但是上述两种方法都属极端假设的方法,为此提出了一般工艺假定的概念和相应的优化模型,给出了国家(地区)对称型投入产出表编制的优化方法.     

一类具有到达损失、可选服务、反馈的M/G/1重试排队系统

考虑一个具有到达损失、可选服务、反馈的M/G/1重试排队系统.在假定重试区域中顾客具有相互独立的指数重试时间的情况下,得到了系统的转移概率矩阵和系统稳态的充分必要条件.列出微分方程,求得稳态时系统队长和重试区域中队长分布及相关指标.     

两大部类扩大再生产的充分必要条件与求解

两大部类扩大再生产的充分必要条件也就是马克思扩大再生产公式有解的充分必要条件.直到目前,由于还没有严谨地提出对于扩大再生产公式的一般求解方法,因而也没有严格地确定扩大再生产的充分必要条件.本文基于已经有研究获得的扩大再生产的一个必要条件,建立一种求解扩大再生产问题的一般方法,从而证明这个必要条件能够成为充分条件,由此确定它是充分必要条件.进而使用变量替换法,给出了通过直接求解两个部类的剩余价值积累率而求解扩大再生产问题的另一种方法.最后引用《资本论》中的两个实例,对所给出的两种求解扩大再生产问题的一般方法做了计算验证.     

广义几何规划最优解的条件

广义几何规划是一类特殊的非线性规划,通常依对偶定理求解,可是所得的点并不一定是最优解.本文提出一个必要条件和一个充分必要条件.许多例题表明,有时使用它们判断点 x~0 的最优性比使用一般非线性规划最优解的条件方便,而且可以得到更满意的结果.     

函数一致连续的一个充要条件

给出了一元函数在区间上一致连续的一个充分必要条件,举例说明了使用它来讨论函数在区间上的一致连续性将更为简单.     

集值上鞅可Doob分解的条件

假定(X,‖·‖)为实Banach空间,X*为其对偶空间,X*可分.给出了集值上鞅几种不同的Doob分解概念,利用支撑函数研究了集值上鞅在各种分解意义下可Doob分解的充分必要条件.     

带Lévy过程的正倒向对偶系统随机控制问题

讨论了一类控制系统是带Lévy过程的正倒向对偶随机微分方程的随机控制问题.本文假定控制区域为凸集,最优解是使目标函数达到最小的控制过程.使用带Lévy过程的Ito公式及Ekeland变分原理,作者建立了这类随机控制问题极值原理的一个必要条件.     

稠密语言关于析取语言的并分解

本文讨论了稠密语言与析取语言的关系.得到了稠密语言的两个充分必要条件:一个语言是稠密的充分必要条件是它为无限多个析取语言的无交并;一个语言是稠密的充分必要条件是它为两个析取语言的无交并.     

线性方程组解的有关问题

首先讨论了两个齐次线性方程组有非零公共解的充分必要条件并给出了非零公共解的一般形式,然后讨论了两个线性方程组同解的一个充分必要条件和非齐次线性方程组的线性无关解向量的个数以及非齐次线性方程组通解的表达式,最后证明了非齐次线性方程组有解的一个充分必要条件.     

导数在正项级数敛散性判定中的应用

作为正项级数敛散性的判别法,一般还没有一个充分必要条件.借助于导数理论,可给出一类级数收敛的充分必要条件     

强不变原理与完全收敛性的统一形式

本文建立了强不变原理与完全收效性的统一形式，得到了用强不变原理研究完全收敛性的方法，前人许多关于强不交原理和完全收敛性的结论是本文的推论．     

Movement of hot spots on the exterior domain of a ball under the Neumann boundary condition

We consider the Cauchy-Neumann problem of the heat equation in the exterior domain of a ball in R^N, and study the movement of hot spots of the solution as t→∞.     

Global entropy solutions to the compressible Euler equations in the isentropic nozzle flow for large data: Application of the generalized invariant regions and the modified Godunov scheme

We study the motion of isentropic gas in nozzles. This is a major subject in fluid dynamics. In fact, the nozzle is utilized to increase the thrust of rocket engines. Moreover, the nozzle flow is closely related to astrophysics. These phenomena are governed by the compressible Euler equations, which are one of crucial equations in inhomogeneous conservation laws.In this paper, we consider its unsteady flow and devote to proving the global existence and stability of solutions to the Cauchy problem for the general nozzle. The theorem has been proved in Tsuge (2013). However, this result is limited to small data. Our aim in the present paper is to remove this restriction, that is, we consider large data. Although the subject is important in Mathematics, Physics and engineering, it remained open for a long time. The problem seems to rely on a bounded estimate of approximate solutions, because we have only method to investigate the behavior with respect to the time variable. To solve this, we first introduce a generalized invariant region. Compared with the existing ones, its upper and lower bounds are extended constants to functions of the space variable. However, we cannot apply the new invariant region to the traditional difference method. Therefore, we invent the modified Godunov scheme. The approximate solutions consist of some functions corresponding to the upper and lower bounds of the invariant regions. These methods enable us to investigate the behavior of approximate solutions with respect to the space variable. The ideas are also applicable to other nonlinear problems involving similar difficulties.     

Integrable fermionic extensions of the Garnier system and the anharmonic oscillator

We first derive a fermionic extension of the Garnier system by applying the method of binary nonlinearization of spectral problem to the supersymmetric KdV equation of Kupershmidt and then a fermionic extension of the anharmonic oscillator by a simple reduction. The integrable properties of resulting systems such as Lax representations, corresponding r-matrices and conversed integrals of motion are established.     

容斥原理在汉密尔顿问题中的应用

容斥原理是组合数学中的经典的计数方法,该原理的基本思想是:先不排除重叠的情况,把包含于某种性质的所有对象的数目先计算出来,然后再把重复计算的数目排斥出去.针对汉密尔顿问题,[15]利用邻接矩阵给出了判断一个图是否为汉密尔顿图的充要条件.本文将结合容斥原理给出汉密尔顿路径存在性的一个判别条件,并给出汉密尔顿路径的计算公式.     

The coincidences among the semicore and the dominance core

We propose the semicore and the dominance core, and provide the coincidences between the semicore and the dominance core.     

On synchronization of chaotic systems based on the Thau observer design

In this paper we revisit the Thau observer design and concern its application to the synchronization problem of two Lorenz name related systems in the master-slave formalism. The first one is the Lorenz-Stenflo system possessing a positively invariant ellipsoid while another one is the hyperchaotic Lorenz system possessing a positively invariant cylinder. Information about loci of these invariant domains is applied for the observer design. Further, we present one assertion related to one spectral inequality arisen in the process of assigning stable spectrum to the observer matrix and show its use in the observer design. We demonstrate the efficiency of synchronization schemes for the both of systems with help of numerical simulation.     

On some applications of the Briot-Bouquet differential subordination

Recently Srivastava et al. [J. Dziok, H.M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct. 14 (2003) 7-18; J. Dziok, H.M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999) 1-13; Y.C. Kim, H.M. Srivastava, Fractional integral and other linear operators associated with the Gaussian hypergeometric function, Complex Var. Theory Appl. 34 (1997) 293-312] introduced and studied a class of analytic functions associated with the generalized hypergeometric function. In the present paper, by using the Briot-Bouquet differential subordination, new results in this class are obtained.     

Speeding up the Floyd-Warshall algorithm for the cycled shortest path problem

On a network with a cycle, where at least one cycle exists, the Floyd-Warshall algorithm is one of the algorithms most used for determining the least cost path between every pair of nodes. In this work a new algorithm for this problem is developed that requires less computational effort than the Floyd-Warshall algorithm. Furthermore, we show that the basis of our algorithm is much easier to understand, which might be an advantage for educational purposes. A small example validates our algorithm and shows its implementation.     

关于Delta算子的广义Taylor公式的余项估计

本文对哑演算中Ｒｏｔａ提出的至今尚未解决的广义Ｔａｌｏｒ公式的余项估计问题进行了研究。获得了Ｄｅｌｔａ算子关于一般函数的一个不同于Ｌａｇｒａｎｇｅ型的结果,并解决了二阶Ｄｅｌｔａ算子的余项估计问题。