超精密铣削的三维微加工工艺

本研究旨在对用于获取有雕刻表面金属工件的超精密微加工工艺进行探讨。研究中使用的是车床型的超精密铣床,由分辨率为1nm的X和Z向运动工作台及分辨率为0.0001度的可定位的C轴组成。作为一种铣削工具,一种改进型的由一颗水晶钻构成的“仿球尖铣刀”被放置在X轴的高速气浮轴承之上。这样一来,X轴和C轴的协调运动就可产生三维铣削的效果。为提高表面粗糙度,通过模拟我们研究的刀具边沿和工件表面的接触情况,结果发现,刀具低速进给时切削比较有效。作为三维微加工工艺的一个例子,运用数字仪提供的扫描数据在一个直径为3mm的铜表面上制作一个传统的NOH面罩。经证明,超精密铣床有潜力加工出表面粗糙度为69nm(P—V值)的工件。     

Extrapolation of the mean lifetime of a large population from its preliminary survival history

A large population of independent identical units having finite mean lifetime T is observed. From the history A(y) of cumulative arrivals and the history B(y) of cumulative removals in the interval 0 ≦ y ≦ τ one must predict at time τ the desired T . Two lifetime predictors X(τ) and Y(τ) and related simple predictors obtained from A(y) and B(y) are shown to converge to T with a rate of convergence dependent on the structure of the failure rate function of the units. This dependence is studied theoretically and numerically.     

A method for reducing coefficients in integer linear inequalities

Approaches are considered for the reduction of coefficients in linear integer inequalities. It is shown that coefficients may be reduced easily in many practical examples. The (0-1) problem is also reconsidered and certain areas of exploration developed.     

Some limiting distributions associated with sequences of multinomial trials

A series of independent trials is considered in which one of k ≥ 2 mutually exclusive and exhaustive outcomes occurs at each trial. The series terminates when m outcomes of any one type have occurred. The limiting distribution (as m → ∞) of the number of trials performed until termination is found with particular attention to the situation where a Dirichlet distribution is assigned to the k vector of probabilities for each outcome. Applications to series of races involving k runners and to spares problems in reliability modeling are discussed. The problem of selecting a stopping rule so that the probability of the series terminating on outcome i is k^?1 (i.e., a “fair” competition) is also studied. Two generalizations of the original asymptotic problem are addressed.     

Exact first and second order moments of order statistics from the truncated exponential distribution

Exact expressions for the first and second order moments of order statistics from the truncated exponential distribution, when the proportion 1–P of truncation is known in advance, are presented in this paper. Tables of expected values and variances-covariances are given for P = 0.5 (0.1) 0.9 and n = 1 (1) 10.     

A game theoretic approach to a two firm bidding problem

In this paper a model is developed for determining optimal strategies for two competing firms which are about to submit sealed tender bids on K contracts. A contract calls for the winning firm to supply a specific amount of a commodity at the bid price. By the same token, the production of that commodity involves various amounts of N different resources which each firm possesses in limited quantities. It is assumed that the same two firms bid on each contract and that each wants to determine a bidding strategy which will maximize its profits subject to the constraint that the firm must be able to produce the amount of products required to meet the contracts it wins. This bidding model is formulated as a sequence of bimatrix games coupled together by N resource constraints. Since the firms' strategy spaces are intertwined, the usual quadratic programming methods cannot be used to determine equilibrium strategies. In lieu of this a number of theorems are given which partially characterize such strategies. For the single resource problem techniques are developed for determining equilibrium strategies. In the multiple resource problem similar methods yield subequilibrium strategies or strategies that are equilibrium from at least one firm's point of view.     

Comparison of stochastic processes used in sonar detection models

In any model for a sonar detection process, some assumption must be made about the nature of the acoustic fluctuation process. Two processes that are widely used in this role are the jump process and the Gauss-Markov process. These processes are similar in that they are both stationer) Markov processes and have autocovariance functions of the form s?²exp(—γt). For these reasons, it might be believed that one could use either of these processes and get comparable results if all one is interested in is computing cumulative detection probabilities or mean time to gain or lose contact. However, such is not the case in that vastly different results can be obtained in some applications. An application of this sort is presented. We also present necessary and sufficient conditions for a threshold to have the property that it is almost surely crossed by the jump process, or by the Gauss-Markov process. This affords another method of comparison.     

Bayes adaptive control of two-echelon inventory systems,II: The multistation case

The present paper extends the results of [7] to cases of multistation lower echelon. For this purpose an algorithm for the optimal allocation of the upper echelon stock among the lower echelon stations is developed. The policy of ordering for the upper echelon is an extension of the Bayes prediction policy developed in [7]. Explicit formulae are presented for the execution of this policy. Several simulation runs are presented and analyzed for the purpose of obtaining information on the behavior of the system, under the above control policy, over short and long periods.     

An iterative procedure for nondiscounted discrete-time markov decisions

This paper considers the problem of computing, by iterative methods, optimal policies for Markov decision processes. The policies computed are optimal for all sufficiently small interest rates.