Effect of the Parameters of Three-Mirror Resonators on the Spectral Characteristics of Single-Pulse Laser Generation with Self-Injection of Priming Radiation

Based on a semiclassical theory, investigations were made of the dynamics and spectral composition of pulsed generation with self-injection of priming radiation from the active part of a three-mirror linear resonator, the passive part of which contains an active loss modulator and serves as the output reflector of the laser. It is shown that there exists a range of resonator parameters at which pulsed lasing has virtually a single frequency irrespective of the detuning of the frequencies of the priming radiation and of the nearest eigenmode of the composite resonator. Considering graphically the phase conditions of generation, it is established that among pulsed lasers with self-injection of priming radiation which are constructed on the basis of three-mirror linear and branched resonators, the most efficient for creating single-frequency generation are those in which the length of the main resonator, where generation of the pulse occurs, is larger than the length of the additional one intended for forming the priming radiation. With an inverse ratio of the lengths of the resonators, the conditions of single-frequency pulsed generation becomes dependent on the priming radiation frequency.     

Solving Problems with Min-Type Functions by Disjunctive Programming

We consider applications of disjunctive programming to global optimization and problems with equilibrium constraints. We propose a modification of the algorithm of F. Beaumont for disjunctive programming problems and show its numerical efficiency.     

A nilpotent Roth theorem

Let T and S be invertible measure preserving transformations of a probability measure space (X, ℬ, μ). We prove that if the group generated by T and S is nilpotent, then exists in L ²-norm for any u, v∈L ^∞(X, ℬ, μ). We also show that for A∈ℬ with μ(A)>0 one has . By the way of contrast, we bring examples showing that if measure preserving transformations T, S generate a solvable group, then (i) the above limits do not have to exist; (ii) the double recurrence property fails, that is, for some A∈ℬ, μ(A)>0, one may have μ(A∩T _-n A∩S ^{- n} A)=0 for all n∈ℕ. Finally, we show that when T and S generate a nilpotent group of class ≤c, in L ²(X) for all u, v∈L ^∞(X) if and only if T×S is ergodic on X×X and the group generated by T ^-1 S, T ^-2 S ²,..., T ^-c S ^c acts ergodically on X. Oblatum 19-V-2000 & 5-VII-2001?Published online: 12 October 2001     

On a class of new and practical performance indexes for approximation of fold bifurcations of nonlinear power flow equations

Efficient measurement of the performance index (the distance of a loading parameter from the voltage collapse point) is one of the key problems in power system operations and planning and such an index indicates the severity of a power system with regard to voltage collapse. There exist many interesting methods and ideas to compute this index. However, some successful methods are not yet mathematically justified while other mathematically sound methods are often proposed directly based on the bifurcation theory and they require the initial stationary state to be too close to the unknown turning point to make the underlying methods practical.This paper first gives a survey of several popular methods for estimating the fold bifurcation point including the continuation methods, bifurcation methods and the test function methods (Seydel's direct solution methods, the tangent vector methods and the reduced Jacobian method) and discuss their relative advantages and problems. Test functions are usually based on scaling of the determinant of the Jacobian matrix and it is generally not clear how to determine the behaviour of such functions. As the underlying nonlinear equations are of a particular type, this allows us to do a new analysis of the determinants of the Jacobian and its submatrices in this paper. Following the analysis, we demonstrate how to construct a class of test functions with a predictable analytical behaviour so that a suitable index can be produced. Finally, examples of two test functions from this class are proposed. For several standard IEEE test systems, promising numerical results have been achieved.     

一类机器人系统的最优控制

本文通过把结构阻尼系数当作控制变量来讨论一类弹性机器人系统的最优控制问题 ,并利用Banach空间几何性质证明了最优控制元的存在唯一性     

Instability in a delay-PDE model of earthquake occurrence

Summary Ductile deformation prior to brittle fracture in rocks causes fracture to take place with a time delay after the critical stress for fracture is reached, in the presence of an increasing load stress. We discuss the stability of a stochastic model of interactive earthquake occurrence under the influence of time delays resulting from the ductile process. A threshold for oscillatory behavior is found for large enough coupling and discrete time delays. The system is stable if the time delays are spread over a broad time interval, even for large coupling.     

Stabilizing management of fluctuating resources

We consider a resource management problem in which the management objective is to minimize fluctuations in resource stocks. Stabilizing management policies constitute the designing of memoryless state feedback control strategies for a discrete time resource model which contains unknown but bounded fluctuations. We also show that the problem of maximizing sustainable yield in an uncertain fishery can be considered as the problem of stabilizing of the stock level.The paper corresponds to an invited talk at the 14th Symposium on Operations Research, Ulm, September 6–8, 1989.The support by Yrjö Jahnsson Foundation is gratefully acknowledged.This work was supported by NSF and AFOSR under grant ECS 8602524.     

Sensitivity analysis for discrete optimal control problems

We present local sensitivity analysis for discrete optimal control problems with varying endpoints in the case when the customary regularity of boundary conditions can be violated. We study the behavior of the optimal solutions subject to parametric perturbations of the problem.     

理想气体在热力学中的作用

指出热力学理论是普遍的,不依赖于理想气体.理想气体为热力学理论提供了一个简单的实例,为测量热力学温度提供了一种简单的温度计.     

非完整系统Chetaev动力学和vakonomic动力学的等价条件

就一般非完整约束系统，从约束方程满足的变分恒等式出发，利用增广位形流形上的向量场定义三类非自由变分，即非完整变分：vakonomic变分、Hlder变分、Suslov变分，并讨论它们之间的关系以及它们成为自由变分的充要条件.利用非完整变分以及相应的积分变分原理建立两类动力学方程：vakonomic方程和Routh方程或Chaplygin方程.通过vakonomic方程分别与Routh方程和Chaplygin方程比较，得到它们具有共同解的两类充分必要条件.这些条件并不是约束的可积性条件. 关键词： 非完整约束 非完整变分 Chetaev条件 vakonomic动力学