Showing papers on "Generalization published in 1978"
263 citations
TL;DR: In this paper, a method for implementing any system by a network of processes so it continues to function properly despite the failure or malfunction of individual processes and communication arcs; where "malfunction" is doing something incorrectly, and "failure" means doing nothing.
240 citations
TL;DR: In this article, it is shown that the notion of cone-compactness (a generalization of compactness) is sufficient to guarantee the existence of an efficient point and the relationship between the set of efficient points and the optimal sets of certain linear functions is elucidated.
Abstract: The properties of efficient (admissible) points of subsets of $R^n $ are discussed in the case when the space is ordered by a convex cone. It is demonstrated that the notion of cone-compactness (a generalization of compactness) is sufficient to guarantee the existence of an efficient point. The relationship between the set of efficient points and the optimal sets of certain linear functions is elucidated in a series of theorems extending previous results, when the underlying set satisfies a weakened convexity assumption (cone-convexity). Geoffrion’s concept of proper efficiency is generalized and after showing that our definition is a valid generalization, the appropriate characterization theorem is established.
189 citations
TL;DR: In this paper, the authors extend the affine case of a theorem of Cheney and Goldstein on proximity maps of convex sets to show that a generalization of the symmetrization technique of Powell always generates least change updates.
Abstract: In many problems involving the solution of a system of nonlinear equations, it is necessary to keep an approximation to the Jacobian matrix which is updated at each iteration. Computational experience indicates that the best updates are those that minimize some reasonable measure of the change to the current Jacobian approximation subject to the new approximation obeying a secant condition and perhaps some other approximation properties such as symmetry. In this paper we extend the affine case of a theorem of Cheney and Goldstein on proximity maps of convex sets to show that a generalization of the symmetrization technique of Powell always generates least change updates. This generalization has such broad applicability that we obtain an easy unified derivation of all the most successful updates. Furthermore, our techniques apply to interesting new cases such as when the secant condition might be inconsistent with some essential approximation property like sparsity. We also offer advice on how to choose the properties which are to be incorporated into the approximations and how to choose the measure of changes to be minimized.
180 citations
TL;DR: Two types of graph-theoretic representations of psychological distances or dissimilarities are proposed: weighted free trees and weighted bidirectional trees.
104 citations
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TL;DR: In this paper, a variety of equivalent definitions and theorems concerning the mixing distance are presented that are of use for further applications, and a theorem is deduced which is a generalization of a fundamental theorem by Hardy, Littlewood, and Polya on inequalities.
Abstract: Mixing character denotes a property concerning the composition of sets. It was first used in order to present criteria for ligand systems in molecules that assure the existence of chiral isomers. Since then the concept of mixing character has been found to have further fields of applications in physics and pure mathematics. Various theorems have been given in the meantime that are reviewed here mostly in the form of equivalent definitions. The mixing distance is another, still more general concept suggested by a study of the time dependent behaviour of nonisolated thermodynamical systems. It describes a dissimilarity of probability distributions, the decrease of which characterizes irreversible phenomena. In the present paper a variety of equivalent definitions and theorems concerning the mixing distance are presented that are of use for further applications. Moreover, a theorem is deduced which is a generalization of a fundamental theorem by Hardy, Littlewood, and Polya on inequalities. Applications of the results given in the present paper will be explored in a subsequent publication that is mostly concerned with the concept of statistical information.
98 citations
TL;DR: In this article, the authors generalized MA to ℵ1-complete forcing by strengthening the ℴ2-C.C. condition, which occurs in many proofs.
Abstract: We generalized MA e.g., to ℵ1-complete forcing, by strengthening the ℵ2-C.C. condition which occurs in many proofs. We show some consequences of MA generalized, and show that we get a model of ZFC in which the modadic theory ofω 2 is decidable.
94 citations
TL;DR: In this article, a generalization of matrix elements of composite operators, called cut vertices, is introduced, and the Bogalubov-Parasink-Hepp-Zimmermann method of renormalization is discussed.
Abstract: Cut vertices, a generalization of matrix elements of composite operators, are introduced. Their renormalization is discussed. The Bogalubov-Parasink-Hepp-Zimmermann method of renormalization of cut vertices allows one to obtain a generalization of the Wilson expansion where cut vertices multiplied by singular functions appear rather than local operators times singular functions. A Callan-Symanzik equation for the moments of the structure function in e/sup +/ + e/sup -/ ..-->.. hadron (p) + anything is derived. This equation is valid to all orders of perturbation theory in both gauge and nongauge theories. Expamples of renormalization through the two-loop level are given.
93 citations
TL;DR: In this article, the supersymmetric generalization of the 't Hooft-Polyakov magnetic monopole and of the Julia-Zee dyon was constructed, and it was shown that the quantum corrections to the monopole mass are vanishing as a consequence of supersymmetry of the theory.
92 citations
01 Jan 1978
TL;DR: A theorem for the global asymptotic stability of a class of feedback systems is established and it is shown that the equivalent feedback representation of the equation associated with the generalized error of the model reference adaptive system (MRAS) belongs to this class.
Abstract: A theorem for the global asymptotic stability of a class of feedback systems is established. It is shown that the equivalent feedback representation of the equation associated with the generalized error of the model reference adaptive system (MRAS) belongs to this class. A general form of the parameter adaptation algorithm which contains as particular forms various known adaptation algorithma is introduced. Explicit stability conditions are obtained for the case of this general type algorithm. The usefulness of the results is illustrated by their application to the straightforward generalization of some recent MRAS designs.
90 citations
TL;DR: In this paper, the most general linear form of a Neville-Aitken-algorithm for interpolation of functions by linear combinations of functions forming a Cebysev-system is presented.
Abstract: In this note we will present the most general linear form of a Neville-Aitken-algorithm for interpolation of functions by linear combinations of functions forming a Cebysev-system. Some applications are given. Expecially we will give simple new proofs of the recurrence formula for generalized divided differences [5] and of the author's generalization of the classical Neville-Aitkena-algorithm[8]applying to complete Cebysev-systems. Another application of the general Neville-Aitken-algorithm deals with systems of linear equations. Also a numerical example is given.
01 Mar 1978
TL;DR: Methodological lessons are drawn from a broad analysis of the World3 model and certain general attitudes are recommended that may be useful in many phases of model analysis.
Abstract: Methodological lessons are drawn from a broad analysis of the World3 model. It is argued that model understanding is a crucial part of the modeling approach. Generalization of the experiences with World3 leads to a proposal for a general approach to understanding complicated models. First, certain general attitudes are recommended. Subsequently, a strategy for model analysis is presented in algorithmic form and illustrated by reference to the World3 study. Finally, an extensive list of tools and techniques is given that may be useful in many phases of model analysis.
TL;DR: In this article, a continued fraction expansion in two variables is described and shown to correspond to a double power series, which is a natural generalization of the S-fraction and can be truncated to form a sequence of rational approximants.
Proceedings Article•
13 Sep 1978
TL;DR: Mutual dependency appears as a generalization of functional and multivalued ones and provides a necessary and sufficient condition for a relation to be nonloss decomposable into three of its projections.
Abstract: In this paper the new concept of mutual dependency in data base relations is introduced. Mutual dependency appears as a generalization of functional and multivalued ones. Furthermore, it provides a necessary and sufficient condition for a relation to be nonloss decomposable into three of its projections. Then, attention is paid to more general decompositions and a necessary and sufficient condition for a relation to be undecomposable is proven.
01 Jan 1978
TL;DR: An operational theory for the generalization of productions for before-and-after situation pairs and situation sequences is developed, based on previous work in concept induction, and this theory has been computer implemented.
Abstract: Relational productions provide a mathematically tractable formal model for operators in discrete systems. Two paradigms for the inductive learning of such operators are considered: before-and-after situation pairs and situation sequences. An operational theory for the generalization of productions for these paradigms is then developed, based on previous work in concept induction. This theory has been computer implemented. In examples three “blocks world” operators are learned from six before-and-after pairs and also from a sequence of fifteen blocks world situations. A transformational grammar learning example of Hayes-Roth is repeated with an improvement in speed of two orders of magnitude.
TL;DR: In this paper, a group-theoretic study of the quasi-intelligent states is presented, which are a generalization of the intelligent states satisfying equality in the Heisenberg uncertainty relation ΔJ12ΔJ22? (1/4) ‖〈J3〉
Abstract: In this first of a series of papers, a group‐theoretic study is presented of the quasi‐intelligent states which are a generalization of the intelligent states satisfying equality in the Heisenberg uncertainty relation ΔJ12ΔJ22? (1/4) ‖〈J3〉‖2. A method based on the knowledge of a certain generating function is given for the calculation of matrix elements of polynomials in the infinitesimal generators of the rotation group between quasi‐intelligent states. Examples of such computations are also included to exhibit the improvement and efficiency of the present methods.
TL;DR: In this article, the problem is reduced via invariance considerations and a new test statistic is proposed, which is shown to be a unique locally best invariant test and locally minimax.
Abstract: This paper treats a generalization of the classical MANOVA testing problem. The problem is reduced via invariance considerations and a new test statistic is proposed. This new test is shown to be a unique locally best invariant test and locally minimax.
TL;DR: In generalization of a purely probabilistic result, the general form of symmetric, β -recursive entropies of randomized systems of events is determined in the framework of the mixed theory of information.
Abstract: In generalization of a purely probabilistic result ( Daroczy, 1970 , Information and Control 16 , 36–41), the general form of. symmetric, β -recursive entropies of randomized systems of events is determined in the framework of the mixed theory of information.
TL;DR: Two composition theorems are proved that yield the existence of new (ordinary) difference families and thus of new block designs with a point regular abelian automorphism group.
TL;DR: Results suggest that the generahzatmn of the resolutton prmctple for theorem-proving is a more efficient method for treating equahty than prewously proposed schemes.
Abstract: This paper defines a generahzatmn of the resolutton prmctple for theorem-proving, which permRs a hterarchtcal orgamzatton within the theorem-prover The generahzatton corresponds to an cxtenston of the usual umficatmn procedures A graph-theoreUc categonzaUon of sets of clauses with input or umt refutatmns is given, and completeness theorems are proved m th~s category In the case of sets of clauses which include the equahty predicate, the generahzatmn gives a new techmque for treating equahty, for which a completeness theorem Ls proved An maplementatmn of these tdeas gives results which suggest that this ~s a more efficient method for treating equahty than prewously proposed schemes
TL;DR: In this article, the relative controllability of non-linear time-varying systems with distributed delays in the control is investigated using Schauder's fixed-point theorem.
Abstract: Relative controllability of non-linear time-varying systems with distributed delays in the control is considered. Using Schauder's fixed-point theorem, sufficient conditions for global relative controllability are given. The results obtained are a generalization of the results given by Davison and Ball (1972), Davison and Kunze (1970) and Klamka (1975 c, 1976 a, b).
31 May 1978
TL;DR: A more detailed representation of a generalization abstraction which consists of a hybrid between a (graphical) network and a predicate calculus formalism is presented.
Abstract: This paper examines the notion of a generalization abstraction proposed by Smith and Smith and considers the properties of a collection of generalizations as a unit called a 'generalization hierarchy'. Presented here is a more detailed representation which consists of a hybrid between a (graphical) network and a predicate calculus formalism.
TL;DR: In this paper, a single first-order, state-determined differential equation is used to relate five postulational models of survival (mortality), population growth, and autocatalysis.
Abstract: A single first-order, state-determined differential equation is used to relate five postulational models of survival (mortality), population growth, and autocatalysis. Generalization is made to a case of a state-varying fundamental rate parameter.
TL;DR: In this article, Cheng and Pearson showed that the conditions obtained under certain assumptions in [1] are valid under more general assumptions and obtained the solution to a more general linear multivariable regulator problem than that previously solved by Wonham and Pearson.
Abstract: This paper presents a generalization of some recent results of Cheng and Pearson [1]. It is shown that the conditions obtained under certain assumptions in [1] are valid under more general assumptions. We therefore obtain the solution to a more general linear multivariable regulator problem than that previously solved by Wonham and Pearson [2].
TL;DR: A class of finite-state Markov processes evolving on finite groups is defined and a pair of "dual" filtering algorithms are defined by introducing some concepts from the theory of representations of finite groups to derive an efficient nonlinear filtering algorithm.
Abstract: We consider a class of nonlinear estimation problems possessing certain algebraic properties, and we exploit these properties in order to study the computational complexity of nonlinear estimation algorithms. Specifically, we define a class of finite-state Markov processes evolving on finite groups and consider noisy observations of these processes. By introducing some concepts from the theory of representations of finite groups, we are able to define a pair of "dual" filtering algorithms. We then study several specific classes of groups in detail, and, by developing a generalization of the fast Fourier transform algorithm, we derive an efficient nonlinear filtering algorithm. A continuous-time version of these ideas is developed for cyclic groups.
TL;DR: In this article, a priori error estimates are derived for the discretization error which results when the linear Navier-Stokes equations are solved by a method which closely resembles the MAC-method of Harlow and Welch.
Abstract: In this paper a priori error estimates are derived for the discretization error which results when the linear Navier-Stokes equations are solved by a method which closely resembles the MAC-method of Harlow and Welch. General boundary conditions are permitted and the estimates are in terms of the discreteL 2 norm. A solvability result is given which also applies to a generalization of the method to the nonlinear case. This generalization is used in the last section to produce a numerical solution to the problem of flow around an obstacle.