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This note presents some comments on BONDER'S paper on the Lanchester attrition-rate coefficient, which indicate that a valid prediction of average attrition is obtained by using the harmonic mean of the variable attrition rates rather than the arithmetic mean. This change results in a constant Lanchester attrition-rate coefficient being defined as the reciprocal of the expected time to kill a target. An alternate and more general method for obtaining the constant coefficient is presented and some comparative results are displayed. An appendix indicates the conditions for which it is appropriate to use the harmonic and arithmetic means of rates in general. [ABSTRACT FROM AUTHOR]

Some discrepancies in an earlier paper describing a bulk service queuing situation with customer balking or reneging are pointed out. Necessary modifications to make the model more valid are incorporated in a reformulation and an approach for developing the state-time probabilities of the system is suggested. [ABSTRACT FROM AUTHOR]

Léon Wairas' "Correspondence and Related Papers," edited by W. Jaffé is the source book on the birth of mathematical economics. He himself was first to succeed in breaching the wall of the scornful opposition to the application of mathematics to economics, only at the high cost of forty years of a much-resented exile and of endless struggles with this correspondence as a weapon. Still more important, "Correspondence" provides a fascinating example of the social process of discovery with feedbacks through colleagues engaged in similar endeavors. Such records are of special interest for those blessed periods in the history of a science when ideas have ripened to the point where several scientists discover the same things at the same time. This was certainly the case of economics around the 1870's when ten persons independently discovered marginal utility and its relation to relative prices, and around the 1880's when only a slightly smaller number of economists discovered the similar relation for marginal productivities.

Optimization is rightly claimed to be the most significant factor distinguishing the modern approach to machining processes from the orthodox one. Practical results can be obtained from the application of mathematical modelling and optimization techniques.
The paper presents a procedure for solution of machining process optimization problems, with the use of theory of graphs and Bellman's optimum principle.
The finite graph G=(N, A) (where N denoted a set of nodes and A the set of arcs) here presents the set of feasible solutions. Each arc represents a corresponding machining operation and each path the feasible machining process.
A number can be associated with each are the increment of criterion for optimality. Using the optimum principle we can find the shortest possible path in the graph, thus solving given problems of choice for the optimal machining process.
There is a variety of ways in which the performance criterion can be formulated. In this paper only those performance measures having sufficient economical justification are considered. We may minimize the costs of machining processes, or optimize economical effectiveness of capital engaged.
The method presented can be applied with every additive criterion, as well as with some non-additive ones. A practical example illustrates the field of possible application of this method. [ABSTRACT FROM AUTHOR]

The primary objectives of this article will be to reconcile the several lease or buy models and identify points where different choices will lead to different conclusions. However, the immediate motivation is the recent article by Johnson and Lewellen on the lease-or-buy decision in this journal. They state, "We will first indicate our disaffections with extant models of this process and then suggest an alternative--allegedly superior--model." For ease in comparing the results of this paper with those of Johnson and Lewellen (hereafter referred to as J & L), to the extent it is feasible, the same set of symbols and equations will be used. [ABSTRACT FROM AUTHOR]

The author comments on the article "A Simultaneous Equation Approach to Financial Planning." He states that in terms of mathematical connotations, "Simultaneous Equation" is an overstatement and that it is pretentious to call a series of equations "simultaneous" because they are accounting identities. He suggests that the authors should have compared their pro forma model with other models in more details. He states that other pro forma models allow for greater flexibility and have users specify several categories of cost separately a function of variables and fixed values.

This paper presents a review of the exact formulae for control limits for P charts and C charts. Also presented are appropriate graphical methods so that these limits may be easily evaluated. The use of the exact methods, given appropriate tables and/or curves, is no more difficult than the approximate methods which are prevalent in the literature. This note is not intended to criticize the approximate techniques which have been used; rather it is intended to illustrate the use of existing theory whereby the errors of approximation may be eliminated. [ABSTRACT FROM AUTHOR]

The article focuses on the random walk theory of stock price behavior which posits that past stock-price movements cannot be used to predict future market prices that would allow traders to profit from the predictions. If stock price movements were to become predictable enough that a profit were possible, proponents of the random walk theory argue that enough market participants would quickly recognize and exploit the pattern. These market participants compete enough to make all non-random fluctuations so small that they cannot be exploited for a profit. As a result, the trader would be as well off with a buy and hold strategy as he would with a mechanical decision rule based upon past price changes.

The article presents a discussion about dialectic materialism and modern science. It discusses the conditions in which dialectic materialism creates for scientists and for scientific pursuits. Dialectic materialism holds that internal contradiction are inherent in all things and phenomena of nature, and treats reality being in constant flux and change. The relationship and the contributions of dialectic materialism in physics, theory of relativity, mathematics, and quantum theory are also discussed.