GLOBAL TOPOLOGICAL PROPERTIES OF HOMOGENEOUS VECTOR FIELDS IN {\tf R}$^{^{\hbox{\normal 3}}}$

In this paper, the authors prove that the flows of homogeneous vector field $Q(x)$ at infinity are topologically equivalent to the flows of the tangent vector field $Q_T(u)$ $(u\in S^2)$ on the sphere $S^2$, and show the theorems for the global topological classification of $Q(x)$. They derive the necessary and sufficient conditions for the global asymptotic stability and the boundedness of vector field $Q(x),$ and obtain the criterion for the global topological equivalence of two homogeneous vector fields.     

An analytical approach to global optimization

Global optimization problems with a few variables and constraints arise in numerous applications but are seldom solved exactly. Most often only a local optimum is found, or if a global optimum is detected no proof is provided that it is one. We study here the extent to which such global optimization problems can be solved exactly using analytical methods. To this effect, we propose a series of tests, similar to those of combinatorial optimization, organized in a branch-and-bound framework. The first complete solution of two difficult test problems illustrates the efficiency of the resulting algorithm. Computational experience with the programbagop, which uses the computer algebra systemmacsyma, is reported on. Many test problems from the compendiums of Hock and Schittkowski and others sources have been solved.The research of the first and the third authors has been supported by AFOSR grants #0271 and #0066 to Rutgers University. Research of the second author has been supported by NSERC grant #GP0036426 and FCAR grants #89EQ4144 and #90NC0305.     

A two-class discrete-time queueing model with two dedicated servers and global FCFS service discipline

This paper considers a simple discrete-time queueing model with two types (classes) of customers (types 1 and 2) each having their own dedicated server (servers A and B resp.). New customers enter the system according to a general independent arrival process, i.e., the total numbers of arrivals during consecutive time slots are i.i.d. random variables with arbitrary distribution. Service times are deterministically equal to 1 slot each. The system uses a “global FCFS” service discipline, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their types. As a consequence of the “global FCFS” rule, customers of one type may be blocked by customers of the other type, in that they may be unable to reach their dedicated server even at times when this server is idle, i.e., the system is basically non-workconserving. One major aim of the paper is to estimate the negative impact of this phenomenon on the queueing performance of the system, in terms of the achievable throughput, the system occupancy, the idle probability of each server and the delay. As it is clear that customers of different types hinder each other more as they tend to arrive in the system more clustered according to class, the degree of “class clustering” in the arrival process is explicitly modeled in the paper and its very direct impact on the performance measures is revealed. The motivation of our work are systems where this kind of blocking is encountered, such as input-queueing network switches or road splits.     

三维地磁流方程的整体吸引子

在本文中,我们通过引入一类Ｆｒｅｃｈｅｔ空间,得到了三维有界光滑区域上的地磁流方程的弱解的整体吸引子的存在性。     

变分方法对具有Stark势非线性Schr(o)dinger方程的应用

本文讨论一类具有Stark势的非线性Schr(o)dinger方程,通过构造一个交叉强制变分问题和发展流的所谓不变流形,得到一个解爆破和整体存在的最佳准则.同时证明了驻波的不稳定性.     

一类具阻尼非线性波动方程的Cauchy问题

本文研究一类具阻尼非线性波动方程Cauchy问题整体广义解和整体古典解的存在唯一性,并用凸性方法给出解爆破的充分条件.     

Global existence and time decay of the non-cutoff Boltzmann equation with hard potential

This paper is concerned with the Cauchy problem on the Boltzmann equation without angular cutoff assumption for hard potential in the whole space. When the initial data is a small perturbation of a global Maxwellian, the global existence of solution to this problem is proved in unweighted Sobolev spaces $H^N\left({\mathbb{R}}_{x,v}^6\right)$ with $N\ge 2$. But if we want to obtain the optimal temporal decay estimates, we need to add the velocity weight function, in this case the global existence and the optimal temporal decay estimate of the Boltzmann equation are all established. Meanwhile, we further gain a more accurate energy estimate, which can guarantee the validity of the assumption in Chen et al. (0000).     

Optimal weighting scheme and the role of coupling strength against load failures in degree-based weighted interdependent networks

The optimal weighting scheme and the role of coupling strength against load failures on symmetrically and asymmetrically coupled interdependent networks were investigated. The degree-based weighting scheme was extended to interdependent networks, with the flow dynamics dominated by global redistribution based on weighted betweenness centrality. Through contingency analysis of one-node removal, we demonstrated that there still exists an optimal weighting parameter on interdependent networks, but it might shift as compared to the case in isolated networks because of the break of symmetry. And it will be easier for the symmetrically and asymmetrically coupled interdependent networks to achieve robustness and better cost configuration against the one-node-removal-induced cascade of load failures when coupling strength was weaker. Our findings might have great generality for characterizing load-failure-induced cascading dynamics in real-world degree-based weighted interdependent networks.     

模糊优选（优化）理论与模型

本文提出的多目标系统模糊优选(优化)理论与计算模型,是处理多目标系统的一个新的优化方法。