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The paper presents a stochastic approach to a Combat Model of tanks vs. tanks with emphasis of the following: A scheme for development of trail validation criteria; A useful procedure that can be expanded to a Semi-Markov model for combat; Approaches to data presentation; Insight into data analysis and data reduction. (Author)

The paper presents a stochastic approach to a Combat Model of tanks vs. tanks with emphasis of the following: A scheme for development of trail validation criteria; A useful procedure that can be expanded to a Semi-Markov model for combat; Approaches to data presentation; Insight into data analysis and data reduction. (Author), supported by Contract No. NR 042-286, U. S. Office of Naval Research, Probability and Statistics Branch, http://archive.org/details/statisticalproce00wang

This thesis reviews the allocation of Coast Guard district recruiting funds for five Coast Guard districts. An attempt is made to determine the marginal productivity of input factors, advertising, recruiting travel, and give away items. Financial data for the five districts reviewed is compared with the results of a questionnaire completed by 459 recruits, who v/ere enlisted from the districts studied. An attempt is also made to determine characteristic behavioral traits of Coast Guard enlistees to assist the district military procurement officer to allocate funds in an optimal manner.

A complete asymptotic development of the Stirling numbers S(N, K) of the second kind is obtained by the saddle point method previously employed by Moser and Wyman.

Renyi has considered an interesting model of traffic flow on a divided highway which extends to infinity in one direction without traffic lights or other inhomogeneities. It is assumed that each car travels at a constant speed which is a random variable and passing is always possible without delays. Among others, Renyi has obtained some results regarding mainly the spatial distribution of cars along the highway when the temporal distribution of cars is assumed to be described by a Poisson process. The purpose of the paper is to discuss a number of results that can be related to low density traffic flow models on an infinite highway. (Author)

A complete asymptotic development of the Stirling numbers S(N,K) of the second kind is obtained by the saddle point method. (Author)

Stochastic Models are developed to relate the statistics of sound speed fluctuations and bubble density variations as a function of sound frequency in the upper ocean. These predictions from the stochastic model have been compared with ocean experimental data of sound speed modulation in the frequency range 15 to 150 kHz, and show satisfactory agreement. Future experiments and further modification of this model are discussed. (Author)

Let X be a discrete random variable with parameter lambda = E(x)< infinity and denote B(n,r,a) = (sup n, sub r)(a to the power r)((1-a) to the power (m-r)). Let the distribution of X be compounded with B(n,r,a). If the resulting distribution is governed by the same law as X, then a characterization of the Poisson distribution is obtained. An alternative proof of the Rao-Rubin characterization is provided. (Author)

The problem of estimating the reliability characteristics of parallel systems with spares and/or repairable elements is investigated. A parallel system is such that the failure of all units causes failure of the entire system. Some bounds of higher moments are treated. (Author)

Given an m x n incidence matrix A(m,n), it is desired to 'squeeze' as many of its 1's as possible into its upper left-hand corner by a sequence of row and column permutations. Such problem arised in designing switches for computers. To establish criteria for the optimal matrix of matrix of the class of row and column permutations, we assign a weight W sub ij to each position in the original matrix where W sub ij is the weight assigned to the i-th row, j-th column position. The weight of matrix A(m,n) = (a sub ij) is taken to be summation, 1 = or < i = or < m, 1 = or < j = or < n, of (A sub ij W sub ij). Suppose W sub ij A(m,n) are given, then denote P(A) the permutation derived matrices of A, then the problem is to find max (A epsilon P(A)) summation, 1 = or < i = or < m, 1 = or < j = or

Characterization of the sign reverse rule of order 2 Markov matrix is given and totally positive and sign reverse rules are studied through a Markov process and its associated first passage probability distribution functions. (Author)

not available

Renyi has considered an interesting model of traffic flow on a divided highway which extends to infinity in one direction without traffic lights or other inhomogeneities. It is assumed that each car travels at a constant speed which is a random variable and passing is always possible without delays. Among others, Renyi has obtained some results regarding mainly the spatial distribution of cars along the highway when the temporal distribution of cars is assumed to be described by a Poisson process. The purpose of the paper is to discuss a number of results that can be related to low density traffic flow models on an infinite highway. (Author), Office of Naval Research Contract Number NR-042-286, http://archive.org/details/theoremongeometr00wang

A complete asymptotic development of the Stirling numbers S(N,K) of the second kind is obtained by the saddle point method previously employed by Moser and Wyman [Trans. Roy. Soc. Cannad., 49(1955) 49-54] and deBruijn [ Asymptotic Methods in Analysis, North-Holland Publishing Co., Amsterdam, (1958) 102-109] for the asymptotic representation of the related Bell numbers., Office of Naval Research, http://archive.org/details/asymptoticsofsti00blei, Office of Naval Research and the Naval Postgraduate School, Monterey, CA., NA

http://archive.org/details/uniquemaximumpro00blei, Approved for public release; distribution is unlimited.

The fact that Stirling Numbers of the Second Kind have arisen in various nonrelated fields, from microelectronics to topology, established the need for a more extensive study of the properties of those Stirling numbers. In order to study the properties, new identities and inequalities for Stirling Numbers if the Second Kind must be formed. In an attempt to deepen the understanding of Stirling Numbers, this paper first states and proves known identities and then establishes various new properties through the introduction of additional identities and inequalities.

A class of finite-memory deterministic algorithms is introduced and investigated, Optimiim algorithms are found for a small number of states (up to 21) and an asymptotic bound on error probability is obtained for a large number of states. The algorithms provide their own stopping rule.