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The article discusses the pattern in vegetation, in which the peaks in the graph of mean square against block size are interpreted. To analyze the peaks in the graph, a logarithmic transformation to both the variance and the spacing is applied, and fitted a polynomial regression of log-variance on log-spacing. The apparent fit by linear regressions results from failure to allow for the occurence of overall trends in representation of species, the rising curve to be expected for random distribution, and the application of logarithmic transformation to the variance data.

The results of empirical studies by Friedman, Laidler, Chow, and others indicate that a weighted average of current and past values of measured income is a better explanatory variable in the demand function for money than is current measured income. There is also some empirical evidence to the effect that weighted averages of current and past interest rates (see Hamburger and Starleaf) and weighted averages of current and past values of a price index (Friedman) have more explanatory power in the demand function for money than do current interest rates and current prices. In nearly all of the empirical studies of the efficacy of distributed-lagged independent variables in the demand function for money, standard families of J-shaped weight structures have been used for the generation of the weighted-average independent variables. In fact, in most cases, a geometrically decaying weight structure has been used, and it has frequently been transformed by the method of Koyck. The purpose of this paper is to report the results of an empirical study of lag structures in the demand function for money which involved the use of Almon's technique. We also present some evidence concerning money illusion in the demand for money and the empirical appropriateness of defining money inclusive of time deposits. [ABSTRACT FROM AUTHOR]

This paper presents an active RC synthesis of rational transfer functions using unity gain controlled sources. The denominator polynomial of the transfer function is decomposed in such a way that the pole sensitivity can be optimized to a prescribed value, the modulus and the argument of which can be easily controlled. The basic configuration can be used to realize the right-half (R.H.) s-plane transmission zeros. The present method is compared with those of Hakim and Cheung. The paper includes one design example. [ABSTRACT FROM AUTHOR]

This paper defines a problem type, called the transportation-location problem, that can be considered a generalization of the Hitchcock transportation problem in which, in addition to seeking the amounts to be shipped from origins to destinations, it is also necessary to find, at the same time, the optimal locations of these sources with respect to a fixed and known set of destinations. This new problem is characterized mathematically, and exact and approximate methods are presented for its solution. [ABSTRACT FROM AUTHOR]

A number of special-purpose computers have been built in the past for the solution of polynomial equations. Most of the computers are expensive and their design is based on the principle of harmonic synthesis. This paper describes the development, design, and construction of a transformer analog polynomial equation solver (TAPES). The operation of this special-purpose analog computer depends on the well-known techniques of harmonic synthesis. The basic principles of 'transformer analog computation' first suggested by Blackburn (1937), have been extended to yield a compact, accurate and inexpensive computer for the solution of algebraic equations. The computer uses only tapped transformers and ganged switches as its building elements. A unique feature of the computer is that coefficients greater than unity can be set very easily, thereby increasing the accuracy to which a root can be evaluated. As built, the computer can handle equations up to the sixth degree, but the method could be extended to build computers for solving equations of higher degree, without appreciable loss of accuracy in computation.
An isograph designed completely on the transformer analog principle is described in this paper. To our knowledge the equipment described in this paper is the simplest of all isographs constructed so far. As constructed, the computer is capable of solving sixth-degree equations but the method could be extended for solving higher-degree equations without appreciable loss of accuracy. It is possible to find the roots with the computer in a short time, provided the roots are fairly well separated. If the roots are closely spaced the minima obtained on the null meters are rather broad and the accuracy suffers in respect of these roots as is the case with similar isographs. Though the inherent accuracy is high, the accuracy to which a root, can be determined is limited to 1degrees in the argument and this is only a design feature which is introduced deliberately.... [ABSTRACT FROM AUTHOR]

The purpose of this paper is two fold: first to provide a method for evaluating projects which have an income pattern describable by a polynomial function of time, and to provide a means for evaluating projects which exhibit a yearly growth or decline in earnings while maintaining the ability to account for the time pattern of earnings, and second to bring forth ah assessment technique which will reflect the possibility of attaining various levels of income for each of the periods of interest. Methods utilized in developing the various models are based on the concept of dynamic return. The future and present worth of a project are calculated for the case in which the earnings follow a pattern of the form given by either Ct[m] or C(1 - t)m. Two types of growth patterns, geometric, in which earnings increase or decline by a fixed percentage each year, and arithmetic, in which earnings increase or decrease by a fixed amount each year, are analyzed. Finally, an income model based on the binomial distribution is developed for evaluating projects which could have two income levels, each having an associated probability. Upper and lower confidence limits for the present and future worths of the project are calculated. Extensions are noted which will permit the inclusion of any of a number of levels of profit for each year of the project. [ABSTRACT FROM AUTHOR]

In reporting an experiment that includes a factor applied at many levels one may be willing to neglect certain terms of an assumed polynomial response curve. E.g. if there are 7 levels one may assume a cubic curve and neglect the quartic, quintic and sextic terms. If the block size is less than a replicate a "best" confounding mm be selected by use of a standard computer program. "Best" here means "with minimum loss of information on (say) linear, quadratic and cubic terms". The analysis of such an experiment involves covariance on a few simple dummy variates. The procedure for design and analysis for 7 or 8 levels in blocks of 4 is given in detail and the method of extension to other cases is indicated. The paper is presented as a modest example of the possible use of electronic computers to scan many possible designs and to indicate which of them are best using simple criteria, but without making exact orthngonality a sine qua non. [ABSTRACT FROM AUTHOR]

Geometric programming is a mathematical programming technique that is designed to determine the constrained minimum value of a generalized polynomial objective function. To date, most applications of the technique have been restricted to certain classes of engineering problems. This paper presents a brief summary of geometric programming and then illustrates its application to managerial problems by applying it to three well-known inventory models. [ABSTRACT FROM AUTHOR]

This paper gives rules that enable the transformation of a 0–1 polynomial programming problem into a 0–1 linear programming problem to be effected with reduced numbers of constraints. Rules are also given that provide reduced numbers of variables when the true variables of interest are not individual cross-product terms, but sums of such terms or polynomials of the form (∑Xj)p. [ABSTRACT FROM AUTHOR]

This paper extends the Sequential Unconstrained Minimization Technique for nonlinear programming to include problems where the constraints are a mixture of inequalities and equalities. Theorems indicating the dual nature of the method and the solution of a subproblem are given. Finally, the theoretical basis for a k-point extrapolation procedure is established. [ABSTRACT FROM AUTHOR]