scispace - formally typeset
Search or ask a question

Showing papers on "Generalization published in 1973"


Journal ArticleDOI
TL;DR: A generalization of information theory is presented with the aim of distinguishing the direction of information flow for mutually coupled statistical systems.
Abstract: A generalization of information theory is presented with the aim of distinguishing the direction of information flow for mutually coupled statistical systems. The bidirectional communication theory refers to two systems. Two directed transinformations are defined which are a measure of the statistical coupling between the systems. Their sum equals Shannon's transinformation. An information flow diagram explains the relation between the directed transinformations and the entropies of the sources. An extension to a group of such systems has also been proposed. The theory is able to describe the informational relationships between living beings and other multivariate complex systems as encountered in economy. An application example referring to group behavior with monkeys is given.

306 citations


Journal ArticleDOI
TL;DR: Two sufficient conditions of global observability of nonlinear systems are presented: the ratio condition which is the generalization of Fujisawa and Kuh's (1971) ratio condition of circuit theory and the strongly positive semidefinite condition.
Abstract: The purpose of this paper is to investigate the problem of observability of nonlinear systems. Two sufficient conditions of global observability of nonlinear systems are presented: (1) the ratio condition which is the generalization of Fujisawa and Kuh's (1971) ratio condition of circuit theory, (2) the strongly positive semidefinite condition. The relationships between these two conditions as well as the condition of positive definiteness of Fitts (1970) are given.

140 citations


Journal ArticleDOI
TL;DR: In this article, a non-linear second order dynamical system is replaced by a linear system in such a way that an average of the difference between the two systems is minimized.
Abstract: A method is presented whereby a non-linear second order dynamical system is replaced by a linear system in such a way that an average of the difference between the two systems is minimized. Provided the averaging operator possesses certain properties, it is shown that the replacement is unique and can be accomplished in a straightforward manner. The parameters of the replacement linear system are expressed in terms of averages of functions of the linearized solution.

138 citations


Journal ArticleDOI
TL;DR: In this paper, the Kemeny-Snell distance function is generalized to a distance function for the collection of all partial orderings of a set, and a new distance function defined by a set of axioms different from those given in Section 2.
Abstract: This paper generalizes the Kemeny‐Snell distance function for distances between weak orderings to a distance function for the collection of all partial orderings of a set. This generalization explains some of the seemingly strange properties of the Kemeny‐Snell distance, and extends it to such important classes of orderings as semiorders and interval orders. In section four I consider possible applications of the distance function and describe a number of problems that arise in attempts to apply the distance function. In section 3 I discuss the concept of a distance function in more general terms and introduce a new distance function defined by a set of axioms different from those given in Section 2.

133 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the linear differential equation, x = A(t) x, (1) x is a matrix function defined and continuous for all t on the real line R.

124 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present methods for estimating and testing hypotheses about linear functions of the unknown parameters in a generalization of the growth curve model which allows missing data, and the estimators proposed are best asymptotically normal (BAN).

104 citations



Proceedings Article
20 Aug 1973
TL;DR: A refutational system of logic for a language of order is presented, in the sense that a refutation of a set of sentences exists if and only if this set does not possess a general Henkin model.
Abstract: A refutational system of logic for a language of order w ia presented . This langage is a slight modification of Church's -calculus with types. The system is complete, in the sense that a refutation of a set of sentences exists if and only if this set does not possess a general Henkin model. The main rule of inference is a generalization of Robinson's resolution to type theory, which allows us to get rid of the substitution rule.

89 citations


Journal ArticleDOI
TL;DR: Criteria for the existance of observers for linear, time-invariant systems where some of the inputs are unmeasurable and statistically unknown are developed and an example is presented.

75 citations


Journal ArticleDOI
TL;DR: In this article, it is shown that the population balance equation derived by number balance is not always correct in the sense that the rates at which existing particles disappear and new particles appear as normally written are valid only under suitable (but not universally applicable) assumptions which are naturally brought to light by the framework presented herein.

64 citations


Journal ArticleDOI
M. Elder1
TL;DR: In this paper, a method for using molecular symmetry properties to reduce the number of one and two-electron integrals that need to be calculated and stored in the course of a molecular SCF calculation is described.
Abstract: A method is described whereby molecular symmetry properties may be used to reduce the numbers of one- and two-electron integrals that need to be calculated and stored in the course of a molecular SCF calculation. The method is a generalization of a previously reported procedure, extending the earlier work to cover those molecules belonging to point groups which have complex representations. The practical application of the method is discussed and an illustrative example given. The quite extensive tables of molecular symmetry properties which the method uses may be computer generated in a straightforward manner. A procedure for doing this using a minimum amount of input data is presented.


Journal ArticleDOI
01 Jan 1973
TL;DR: Survival models arising in mathematical demography, in renewal and in replacement models lead to a generalization of the Gamma distribution function, which corresponds to the addition of random variables, generally dependent on reîevation product.
Abstract: — Survival models arising in mathematical demography, in renewal and in replacement models lead to a generalization of the Gamma distribution function. In these models the reîevation product corresponds to the addition of random variables, generally dependent. The reîevation product is non-commutative, non-associative, and only leftdistributive. In the case of auto-relevation, a reîevation product of two identically distributed random variables, a measure of renewal gain or life-extension is described by an expression akin to Shannori*s entropy. A common generalization of both the reîevation and convolution opérations is indicated in Section 8. Section l Définition. s(t) is a survivability function if 1 —s(t) is the cumulative distribution function of a non-negative random variable. s(t) is interpreted as the probability that a newborn individual will survive (at least) till age t; or that a new item will give at least t time units of service. The probability density that a newborn individual will die at age t is — s'(t)l cf. Appendix. Fpr simplicity of exposition we will assume, whenever needed, the differentiability of the functions considered. Theorenu Let ^4(0 and B(t) be survivability functions. Then

Journal ArticleDOI
TL;DR: In this article, the authors proposed a generalization of the minimum complementary energy principle of the classical linear theory of elasticity to the nonlinear case where t is not a constant.
Abstract: Until recently the famous principle of minimum complementary energy of the classical linear theory of elasticity has defied all attempts at an effective generalization to the nonlinear case where t...

Journal ArticleDOI
01 May 1973-Topology
TL;DR: In this paper, it was shown that for a foliation with one dimensional leaves, the volume of a segment in a leaf is just its length (in a fixed metric) whereas in higher dimensions the volume can grow exponentially in R. The authors also showed that in order to generalize the PoincarC-Bendixson theorem, they must make restrictions on the asymptotic behavior of the leaves of the foliation.

Journal ArticleDOI
TL;DR: In this article, a generalization of Kronecker's second limit formula to the setting of a general Fuchsian group of the first kind operating on the complex upper half-plane H is presented.
Abstract: In [1] we derived a generalization of Kronecker’s first limit formula. Our generalization was a limit formula for the Eisenstein series for an arbitrary cusp of a Fuchsian group Γ of the first kind operating on the complex upper half-plane H. In that work, we introduced Dedekind sums associated to the principal congruence subgroups Γ(N) of the elliptic modular group. The work of our preceding paper suggests a natural question: Is there a generalization of Kronecker’s second limit formula to the setting of a general Fuchsian group of the first kind? The answer to this question is the subject of this paper.


Journal ArticleDOI
TL;DR: A family T of k-subsets of an n-set such that no more than r have pairwise fewer than s elements in common is maximum (for sufficiently large n) only if T consists of all the k-sets containing at least one of r fixed disjoint s- Subsets.

Journal ArticleDOI
TL;DR: In this paper, a generalization of the theorems of Lindelof and Fatou in which approach to the boundary along complex tangential directions is allowed is shown. But this generalization is not applicable to the case of this paper.
Abstract: The author proves a generalization of the theorems of Lindelof and Fatou in which approach to the boundary along complex tangential directions is allowed.



Journal ArticleDOI
TL;DR: A generalization of the Eberlein, de Leeuw and Glicksberg decomposition theorem for weakly almost periodic functions which does not rely on any fixed point theorem for its proof is given in this article.
Abstract: In this paper we present a generalization of the Eberlein, de Leeuw and Glicksberg decomposition theorem for weakly almost periodic functions which does not rely on any fixed point theorem for its proof. A generalization of the Ryll-Nardzewski fixed point theorem is given.

Journal ArticleDOI
TL;DR: In this article, a counterexample is given to a result of Perez which makes a statement about the convergence of a sequence of logarithms of Radon-Nikodym derivatives.
Abstract: A counterexample is given to a result of Perez which makes a statement about the convergence of a sequence of logarithms of Radon-Nikodym derivatives. The result, if true, would have been a generalization of the Shannon-McMillan theorem of information theory.

Journal ArticleDOI
TL;DR: In this article, a generalization of the common logistic function was developed, incorporating a nonunit saturation level, a nonzero intercept, and a non-symmetric shape, and the dependence of the three generalized characteristics on (estimated) parameter values was exhibited.
Abstract: A generalization of the common logistic function is developed, incorporating a non-unit saturation level, a non-zero intercept, and a non-symmetric shape. The dependence of the three generalized characteristics on (estimated) parameter values is exhibited. The statistical properties of the function are developed for the case where the dependent variable is a relative frequency. An empirical application shows that the effect of advertising on market share is best depicted by a curve which is everywhere concave to the origin.

Journal ArticleDOI
TL;DR: In this article, a generalization of minimum bias estimation was developed and applied to a setting in which the true model is assumed to be the ratio of real polynomials (rational function) while the approximating equation is a polynomial of low order.
Abstract: A generalization of minimum bias estimation as introduced in [6] is developed and applied to a setting in which the true model is assumed to be the ratio of real polynomials (rational function) while the approximating equation is assumed to be a polynomial of low order.

Journal ArticleDOI
TL;DR: The existence of an equilibrium point in discounted stochastic games was proved in this paper under assumptions of continuity and compactness, and the existence of the equilibrium point was proved under the assumption that the sets of states and actions are given by metric spaces.
Abstract: Nonzero-sum N-person stochastic games are a generalization of Shapley's two-person zero-sum terminating stochastic game. Rogers and Sobel showed that an equilibrium point exists when the sets of states, actions, and players are finite. The present paper treats discounted stochastic games when the sets of states and actions are given by metric spaces and the set of players is arbitrary. The existence of an equilibrium point is proven under assumptions of continuity and compactness. NONCOOPERATIVE STOCHASTIC GAME; DISCOUNTED MARKOVIAN DECISION PROCESS; EQUILIBRIUM POINT; DYNAMIC PROGRAMMING

Journal ArticleDOI
TL;DR: In this paper, a necessary and sufficient condition for the existence of covariance stabilizing transformations for the trinomial distribution is given. But it is conjectured that this non-existence of solutions is true for the general multinomial.
Abstract: After reviewing the asymptotic variance stabilizing transformations in one dimension, a generalization of these to multivariate cases is discussed. Results are given for the uniqueness of solutions when they exist, but unlike the one-dimensional case, covariance stabilizing transformations need not exist. In the two-dimensional case, a necessary and sufficient condition is given for the existence of solutions. It takes the form of a second-order partial differential equation that the elements of any square root of the inverse of the limiting covariance matrix must satisfy. This condition is applied to three examples with the conclusion that no covariance stabilizing transformation exists for the trinomial distribution. It is conjectured that this non-existence of solutions is true for the general multinomial.


Journal ArticleDOI
TL;DR: In the above correspondence, an algorithm has been described that allows the transposing of a 2n× 2nmatrix by reading and writing n times at the most via direct access rows of the matrix and by permuting its data elements.
Abstract: In the above correspondence,1an algorithm has been described that allows the transposing of a 2n× 2nmatrix by reading and writing n times at the most via direct access rows of the matrix and by permuting its data elements. The generalization to arbitrary square matrices has not been described, and the generalization to nonsquare matrices has been reported to be impossible.