Optimal intensity control of a multi-class queue

We study a mixed problem of optimal scheduling and input and output control of a single server queue with multi-classes of customers. The model extends the classical optimal scheduling problem by allowing the general point processes as the arrival and departure processes and the control of the arrival and departure intensities. The objective of our scheduling and control problem is to minimize the expected discounted inventory cost over an infinite horizon, and the problem is formulated as an intensity control. We find the well-knownc is the optimal solution to our problem.Supported in part by NSF under grant ECS-8658157, by ONR under contract N00014-84-K-0465, and by a grant from AT&T Bell Laboratories.The work was done while the author was a postdoctoral fellow in the Division of Applied Sciences, Harvard University, Cambridge, Massachusetts 02138.     

Solution of a class of stochastic linear-convex control problems using deterministic equivalents

In this paper, we identify a new class of stochastic linearconvex optimal control problems, whose solution can be obtained by solving appropriate equivalent deterministic optimal control problems. The term linear-convex is meant to imply that the dynamics is linear and the cost function is convex in the state variables, linear in the control variables, and separable. Moreover, some of the coefficients in the dynamics are allowed to be random and the expectations of the control variables are allowed to be constrained. For any stochastic linear-convex problem, the equivalent deterministic problem is obtained. Furthermore, it is shown that the optimal feedback policy of the stochastic problem is affine in its current state, where the affine transformation depends explicitly on the optimal solution of the equivalent deterministic problem in a simple way. The result is illustrated by its application to a simple stochastic inventory control problem.This research was supported in part by NSERC Grant A4617, by SSHRC Grant 410-83-0888, and by an INRIA Post-Doctoral Fellowship.     

Prophet inequalities for parallel processes

Generalizations of prophet inequalities for single sequences are obtained for optimal stopping of several parallel sequences of independent random variables. For example, if {X_{i, j}, 1 ≤ i ≤ n, 1 ≤ j < ∞} are independent non-negative random variables, then

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and this bound is best possible. Applications are made to comparisons of the optimal expected returns of various alternative methods of stopping of parallel processes.     

Hereditary optimal control problems: Numerical method based upon a padé approximation

In this paper, we consider a particular approximation scheme which can be used to solve hereditary optimal control problems. These problems are characterized by variables with a time-delayed argumentx(t – ). In our approximation scheme, we first replace the variable with an augmented statey(t) x(t - ). The two-sided Laplace transform ofy(t) is a product of the Laplace transform ofx(t) and an exponential factor. This factor is approximated by a first-order Padé approximation, and a differential relation fory(t) can be found. The transformed problem, without any time-delayed argument, can then be solved using a gradient algorithm in the usual way. Four problems are solved to illustrate the validity and usefulness of this technique.This research was supported in part by the National Aeronautics and Space Administration under NASA Grant NCC-2-106.     

Evidence for the poisson distribution for quasi-energies in the quantum kicked-rotator model

A transformation on the two-dimensional torus which is related to the problem of limit distribution for the distance between the levels in the kicked-rotator model is considered. The first four moments of the r.w. which describe the numbers of visits of a point in a rectangle of measure are calculated. It is shown that when 0 they converge to the first four moments of a Poisson r.w.     

安装误差对正交弧齿锥齿轮副接触区影响的分析

本文从理论上分析了正交弧齿锥齿轮副的各种安装误差对啮合接触区的单独影响和综合影响,建立了安装误差作用下齿面接触区的数学模型,并通过具体实例讨论了各项安装误差对啮合接触区单独影响和综合影响的程度以及综合影响的“叠加效应”和“互补效应”,提出了满足接触要求前提下降低安装要求的措施.     

A novel method for synthesizing diorganylphosphinous acids from red phosphorus and arylalkenes

The reaction of styrene and -methylstyrene with P in aprotic polar solvents in the presence of KOH affords diorganylphosphinous acids.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1680–1681, September, 1994.     

An unusual new reaction of α-olefins with magnesiumn-alkyl derivatives catalyzed by Cp2ZrCl2

The reaction of organomagnesium compounds (OMC) containing alkyl radicals of normal structure with -olefins, resulting in the formation of alkenylorganomagnesium compounds and accompanied by hydride transfer was discovered and systematically investigated. A scheme providing for the formation of zirconacyclopentane complexes was proposed for the mechanism of the reaction.Institute of Organic Chemistry, Ural Branch, Russian Academy of Sciences, 450054 Ufa. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 5, pp. 1187–1196, May, 1992.     

N-取代苯并咪唑和N-取代-2-硫代噻唑烷酮类化合物的质谱研究

本文所研究的7种N-取代苯并咪唑和硫代噻唑烷酮类化合物是一类新合成的具有较高杀菌活性的化合物。本文利用电子轰击质谱技术对表中所列的化合物进行了研究。在高分辨精确质量测量和亚稳离子测定的基础上着重讨论了分子内3、4位C—C键的断裂和与杂环