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The article presents abstracts of contributed papers submitted for presentation at the Chicago Meeting. "Some Recent Contributions to the Lanchester Theory of Combat," by Ralph E. Bach, Laislav Dolansky and Harlod L. Stubbs explains that since the original formulation of Lanchester's equations pertaining to the combat of two opposing forces, the theory has been extended, organized and applied by many scientists. Certain more recent extensions of this theory, which have been developed under Project Numerics, will be described in this paper. Another paper "Single-Shot Kill Probability As a Measure of Bombing Effectiveness," by Albert M. Johnson and Vincent A. Ciminera points out advantages of using single-shot kill probability as a measure of bombing effectiveness in evaluating weapon systems. Historically the circular probable error has been employed for this purpose. However, with compressed reaction tunes made possible by future systems and the large effective yields of nuclear weapons, it is more desirable to be able to predict the probability that a single bomb will impact within a lethal distance of its intended target. The computation of this statistic, the single shot kill probability, is accomplished for values of the lethal radius and parameters of the distribution which characterize the bombing system.

In this paper the traditional capital asset pricing model is reformulated as a system of simultaneous equations in which returns on similar securities are treated as endogenous variables and in which pertinent financial data for particular firms and a market factor are treated as exogenous variables. Such a system is estimated, and serious questions are raised concerning the tenability of the simple linear model so often used to explain capital asset prices under uncertainty. This paper offers a robust test of the capital asset pricing model (e.g., Sharpe [12] and [13] and Fama [3]) assumption which asserts that all of the inter- dependencies among security returns are accounted for solely by the relationship between a single security and a common market index. Also, it examines the relationship of security returns and corporate operating data to determine the extent to which the beta of the capital asset pricing model is simply a summary, surrogate measure for them. The proposed test is based on a simultaneous equation model. Two goals are sought through this research which, first, serves as a direct test of important implications of the capital asset pricing model and which, second, will provide approximations of the magnitude and direction of any biases that may exist in estimates of beta obtained from single index models. [ABSTRACT FROM AUTHOR]

This article presents a note on the paper "Optimal Growth Portfolios When Yields are Serially Correlated." The author offers a solution to finding the optimal amount of money to invest in a given investment opportunity when there is an optimal myopic policy. The author provides several equations that help in this determination process.

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The multi-index transportation problem is defined and a summary of the algorithm described in an earlier paper is given. This paper discusses the theorems justifying the use of the algorithm and gives a necessary condition for the existence of a solution. It also describes the formulation of three special-structure linear-programming problems as examples of multi-index problems. The three problems discussed are the capacitated Hitchcock problem, transportation where there is more than one method of transport available, and the transformation of one type of multi-index problem into another. A final section describes problems that have restrictions in the form of inequalities. [ABSTRACT FROM AUTHOR]

This paper develops solutions to extensions of F. W. LANCHESTER'S classical equations of 'modern warfare' (frequently referred to as aimed-fire equations) for combat between two homogeneous forces. In these extensions the lethality of the fire (as expressed by the Lanchester attrition-rate coefficient) depends on time. When the dependence is arbitrary, the solution is an infinite series of recursively related integrals; in special cases, more convenient representations (including representation in terms of tabulated functions) are available. Solutions are obtained in the following cases: (1) the lethality of each side's fire proportional to a power of time and both lethalities initially zero, and (2) the lethality of each side's fire linear with time, but only one side's lethality initially zero. The latter case models the constant-speed approach between forces whose weapons have different maximum effective ranges. [ABSTRACT FROM AUTHOR]

"Speed Words" uses an analogy between the psychomotive force of the dialectic field and the electromotive force of the magnetic field to formulate a conjecture which might be the subject of investigation. Using the term, "meaning time," which is explained, the paper introduces the time dimension as a function of word value. Accepted laws of an electric system are used to suggest parallel laws for the dialectic system. As a result, understanding speed of words is expressed by an equation WS = MT × WF, where WS is the relative speed of a word in terms of its understandability, MT is the meaning time in years of word use, and WF is the word frequency per million words used by a stated audience. Experimental use of this equation and method suggests that there may be as much meaning in a few dozen stable words, of greater meaning age than numbers, as there is in a few dozen digits in the decimal system - used as the basis of science and mathematics. This could lead to revealing an even more basic or universal language. If these points can be stressed, speed words are then only part of a larger concept. There could be a field of thought above, and yet related, to known physical fields. If such a field is postulated and searched for its analogical equivalents, language could, in a mean sense, become the thought field constant, the relationship of ideas, field units; time, the field denominator. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to extend the loop-technique of the stepping-stone algorithm to the generalized transportation problem. The main result (Theorem and Corollary of §6) is, that passing from a basic feasible solution to another one may always be carried out by constructing a simple symmetrical or a double loop (as defined in §2) and computing new values for the variables only along this path. The amount of computations needed for this turns out to be substantially reduced as compared to the usual way of solving the system of equations relating the new basis to the old one. [ABSTRACT FROM AUTHOR]

One of the problems which occupies the work study engineer is that of determining the number of observations necessary in order to estimate the work content of a job with a prescribed accuracy. A new equation is presented for this purpose. [ABSTRACT FROM AUTHOR]