THEORY AND APPLICATIONS OF MONOTONE SEMIFLOWS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS

The theory of monotone semiflows has been widely applied to functional differential equations (FDEs). The studies on the theory and applications of monotone semiflows for FDEs are very important and interesting. A brief des-cription of our recent works are as follows.By using general monotone semiflow theory, several results of positively invariant sets, monotone solutions and contracting rectangles of retarded functional differential equations(RFDEs) with infinite delay are gained under the assumption of quasimonotonicity; sufficient conditions for the existence, un-iqueness and global attractivity of periodic solutions are also established by combining the theory of monotone semiflows for neutral functional differential equations(NFDEs) and Krasnoselskii's fixed point theorem.     

Existence of two solutions of m-point boundary value problem for second order dynamic equations on time scales

In this paper, by means of a new twin fixed-point theorem in a cone, the existence of at least two positive solutions of m-point boundary value problem for second order dynamic equations on time scales is considered.     

标度系统一致性矩阵容量的计算方法

本文研究正互反矩阵的变换性质 ,提出一种保持正互反矩阵一致性程度的等价分类 ,为计算各种标度系统下的一致矩阵容量提供了计算方法     

小型企业规模的有效性分析

在当代企业纷纷追求规模的不断扩大的同时，统计数据却显示企业平均规模不断下降的事实趋势。论根据数学、经济学与博弈论的有关理论对企业规模小型化的内在要求进行了探讨，分析的结论一致证明：粘型化规模在当代经济环境中是充分有效的。     

Lorentz Invariant Decompositions of the State Vector Spaces and the Basis Problem

We consider a representation of the state reduction which depends neither on its reality nor on the details of when and how it emerges. Then by means of the representation we find necessary conditions, even if not the sufficient ones, for a decomposition of the state vector space to be a solution to the basis problem. The conditions are that the decomposition should be Lorentz invariant and orthogonal and that the associated projections should be continuous. They are shown to be able to determine a decomposition in each of a few examples considered if the other circumstances are taken into account together.     

Embedding of Dynamical Symmetry Groups U(1, 1) and U(2) of a Free Particle on AdS 2 and S 2 into Parasupersymmetry Algebra

Using two different types of the laddering equations realized simultaneously by the associated Gegenbauer functions, we show that all quantum states corresponding to the motion of a free particle on AdS ₂ and S ² are splitted into infinite direct sums of infinite-and finite-dimensional Hilbert subspaces which represent Lie algebras u(1, 1) and u(2) with infinite- and finite-fold degeneracies, respectively. In addition, it is shown that the representation bases of Lie algebras with rank 1, i.e., gl(2, C), realize the representation of nonunitary parasupersymmetry algebra of arbitrary order. The realization of the representation of parasupersymmetry algebra by the Hilbert subspaces which describe the motion of a free particle on AdS ₂ and S ² with the dynamical symmetry groups U(1, 1) and U(2) are concluded as well.     

On Quasiclassical Field Theories Invariant with Respect to a Lie Group

Mathematical Notes -     

Decentralized iterative learning control for a class of large scale interconnected dynamical systems

The problem of decentralized iterative learning control for a class of large scale interconnected dynamical systems is considered. In this paper, it is assumed that the considered large scale dynamical systems are linear time-varying, and the interconnections between each subsystem are unknown. For such a class of uncertain large scale interconnected dynamical systems, a method is presented whereby a class of decentralized local iterative learning control schemes is constructed. It is also shown that under some given conditions, the constructed decentralized local iterative learning controllers can guarantee the asymptotic convergence of the local output error between the given desired local output and the actual local output of each subsystem through the iterative learning process. Finally, as a numerical example, the system coupled by two inverted pendulums is given to illustrate the application of the proposed decentralized iterative learning control schemes.     

BRST invariance and the conical pendulum

The Hamiltonian formulation of the BRST method for quantizing constrained systems developed recently by Nemeschanskyet al is applied to the well-known problem of the conical pendulum in classical mechanics. The similarity of the system to a gauge theory wherein the two constraints serve as generators of local Abelian gauge transformations is also pointed out. The definition of the physical states of the system as a gauge theory and also as a BRST invariant theory is then discussed in some detail.     

Constrained control for uncertain linear systems

The linear state feedback synthesis problem for uncertain linear systems with state and control constraints is considered. We assume that the uncertainties are present in both the state and input matrices and they are bounded. The main goal is to find a linear control law assuring that both state and input constraints are fulfilled at each time. The problem is solved by confining the state within a compact and convex positively invariant set contained in the allowable state region.It is shown that, if the controls, the state, and the uncertainties are subject to linear inequality constraints and if a candidate compact and convex polyhedral set is assigned, a feedback matrix assuring that this region is positively invariant for the closed-loop system is found as a solution of a set of linear inequalities for both continuous and discrete time design problems.These results are extended to the case in which additive disturbances are present. The relationship between positive invariance and system stability is investigated and conditions for the existence of positively invariant regions of the polyhedral type are given.The author is grateful to Drs. Vito Cerone and Roberto Tempo for their comments.