Showing papers on "Generalization published in 1974"

An Analytic Generalization of the Rogers-Ramanujan Identities for Odd Moduli

Abstract: A (k - 1)-fold Eulerian series expansion is given for II(1 - qn)-1, where the product runs over all positive integers n that are not congruent to 0,i or - i modulo 2k + 1. The Rogers-Ramanujan identities are the cases k = i = 2 and k = i + 1 = 2.

Subject and Predicate in Logic and Grammar

Abstract: Contents: Preface Introduction Part I The subject in logic: The 'basic combination': Some formal differences Spatio-temporal particulars and general concepts Propositional combination: a tripartition of function Formal differences explained for the basic case The generalization of the form An objection answered Proper Names - and others: What is the use of them? Names and identity Names in the framework of logic: proper names, variable names and descriptive names General names. Part II The subject in general: Language-types and perspicuous grammars: Essential grammar and variable grammar Language-types 1 and 2 Language-types 3: relations Further minor enrichments: space-time indication Substantiation and its modes: Special case and general function Some supporting evidence Modes of substantiation Further matters: existence negation scope The generalization of the subject: Derivative roles and derivative elements The generalization of the subject The fitting in of feature Further questions. Index.

A generalization of the FKG inequalities

Abstract: We generalize a theorem of Holley to include the case of continuous spins. Holley's theorem is itself a generalization of the inequalities due to Fortuin, Kastelyn and Ginibre.

A Generalized Cyclic Reduction Algorithm

Abstract: For the discrete Poisson equation, a generalization of cyclic reduction to arbitrary block size is given. A stable algorithm for accumulating the right sides is presented and results are given concerning optimal block size. Numerical experiments are also reported.

Transformation of Local Martingales Under a Change of Law

Abstract: Girsanov showed that under an absolutely continuous change in probability measure a Wiener process is transformed into the sum of a Wiener process and a second process with sample functions which are absolutely continuous. This result has a natural generalization in the context of local martingales. This generalization is derived in this paper, and some of its ramifications are examined. As a simple application, the likelihood ratio for a single-server queueing process with very general arrival and service characteristics is derived.

Positivity and stability tests for multidimensional filters (discrete-continuous)

Abstract: In this paper, a systematic procedure to test for stability of three-dimensional filters (discrete and continuous) is presented. The test is based on repeated applications of an extended Hermite or Schur-Cohn formulation, and use of Sturm's theorem to determine the content of a system of polynomial inequalities in a single indeterminate. The need for generating a constructive algorithm for stability tests for higher than three-dimensional filters using Tarski's generalization of Sturm's theorem is discussed. Application of certain combinatorial rules for transforming the multidimensional digital filter problem to the multidimensional continuous filter problem or vice versa) is made.

Entries, voices, exits : Towards a possible generalization of the Hirschman model

Abstract: Exit, voice and loj,altj, is an exciting and intriguing essay: exciting because of the keen insights it offers into the underlying similarities in the structures of decision-making options in the economy and in politics; intriguing because of the extraordinary range of questions it incites about further possibilities of model-building across other sectors of human life. Exit, voice starts you thinking in many directions: once you are caught in the magic of the model you keep on discovering parallels and analogues at all

Necessary and Sufficient Optimality Conditions for the Fritz John Problem with Linear Equality Constraints

Abstract: A generalization of Motzkin’s theorem of the alternative is developed, and is then used to obtain necessary optimality conditions for the Fritz John optimization problem with linear equality constraints. Under certain constraint qualifications and convexity assumptions these necessary conditions are also sufficient. An application of these results to the problem of Chebyshev approximation with interpolation is given.

The Role of Adaptation-Level In Stimulus Generalization

Abstract: Publisher Summary This chapter discusses the successes and failures of the Adaptation-level (AL) theory of stimulus generalization and provides an evaluation of its fruitfulness. The chapter describes the voluntary generalization experiments, which employs diverse stimulus dimensions such as lifted weight, wavelength, brightness, and line angle. Generally, the AL theory is extremely successful in predicting or interpreting the results of stimulus generalization experiments. With regard to the Central Tendency Effect, the central tendency shift occurs with reference to the psychological center (AL) of the generalization test series, which may not coincide with the physical center. In such cases, a shift of maximal responding from the training stimulus (TS) value may occur even when the test series is nominally symmetrical. In the choice paradigm, AL serves as the crossover point, such that stimuli above AL are to be responded to in one fashion and stimuli below AL are to be responded to in another. In the go/no-go situation, it appears that the TS are encoded not just with regard to their direction from, but also their distance from, the Prevailing AL.

Relaxive Hilbert Ports

Abstract: The completely monotonic behavior of the transient responses of RC n-ports to certain pulses of finite duration is used to characterize a more general kind of system, which we call the relaxive Hilbert port. This generalization encompasses networks having an infinite number of lumped and distributed elements as well as an infinite number of ports.A primary result of this work is the generalization of Bernstein’s theorem on completely monotonic functions to operator-valued functions. This in turn leads to a representation theorem, which states that the frequency-domain system function for a relaxive Hilbert port is the Stieltjes transform of a positive-operator measure. The approximation of the unit-impulse response by a finite sum of damped exponentials is discussed. For n-ports, this provides a means of synthesizing a relaxive Hilbert port as an RC network with perhaps ideal transformers.Meixner’s concept of a relaxation system of the second kind is also extended to operator-valued functions, and relaxiv...

The kinetic theory of polyatomic liquids. II. The rough sphere, rigid ellipsoid, and square‐well ellipsoid models

Abstract: The generalized moment method presented in the first paper of this series is applied here to three model systems. These models—rough spheres, rigid ellipsoids, and square‐well ellipsoids—have been selected not only because they are more tractable than others from a computational point of view but also because they mimic with varying degrees of success several characteristics of real polyatomic fluids. Formulas are derived for the transport coefficients and relaxation times descriptive of the establishment and maintenance of a steady state of transport of energy and of linear and angular momentum. To the approximation of Enskog these phenomenological coefficients can be expressed in terms of integrals of the same type as occur in the dilute gas theory. The integrands of these (which are trivial to evaluate in the rough sphere case) are complicated by the fact that they include the polyatomic generalization of the equilibrium pair distribution function. The formulas given here also include contributions (based upon the theories of Severne, of Prigogine, Nicolis and Misguich, and of Davis) from dynamical correlations that are not included in the Enskog approximations. These are more difficult to evaluate numerically.

Two-variable rational approximants: a new method

Abstract: A new generalization of Pade approximants to power series in two (or more) variables is given, along with an example of its application.

Validity Generalization of Holland's Hexagonal Model

Abstract: Holland's hexagonal model for six occupational groups (Realistic, Investigative, Artistic, Social, Enterprising, and Conventional) was tested with data on estimated occupational rewards. Data on ra...

On quotients of manifolds: A generalization of the closed subgroup theorem

Abstract: Let M be a (C, Hausdorff, paracompact) manifold, and let R be an equivalence relation on M. Then R is called regular if the quotient M/R is a (not necessarily Hausdorff) manifold in such a way that the canonical projection TTR : M-+M/R is a submersion. For results on regular relations cf. Palais [1], Serre [2]. The following characterization of regularity is wellknown (cf. Serre [2, LG, Chapter 3, §12]): R is regular if and only if it is a submanifold (with the subspace topology) of M X Afin such a way that the map (m, m')-+m from R onto M is a submersion. The purpose of this note is to announce a different characterization of regularity. Proofs will appear elsewhere (Sussmann [3]). Our condition is motivated in a natural way by Systems Theory. As will be shown in [4], Theorem 2 is precisely what is needed to show that, under fairly general conditions, every finite-dimensional \"controllable\" nonlinear system has a realization which is both \"controllable\" and observable. Here we shall not pursue this line. Rather, we shall state our condition and show that it is a rather natural generalization of the closed subgroup theorem. Let X be a vector field on an open subset of M. We say that X is a symmetry vector field of R if, whenever (m, m') e R9 it follows that (Xt(m), Xt{m')) e R for every real t for which Xt(m) and Xt(m) are both defined (here t-+Xt(m) is the integral curve of X which passes through m when t=0). Let S°°CR, M) denote the set of all C vector fields X defined on open subsets of M that are symmetry vector fields for R. It is not difficult to show that S°°(R, M) is a presheaf of Lie algebras of vector fields. If L is a set of vector fields defined on open subsets of M, we say that L is transitive if, for every me M, the vectors X(m), X e L, span the tangent space of M at m. If A is a subset ofAfxM, we call L A-transitive if, for every (m, m') e A, the tangent space of M at m is spanned by the

Compensation and Combinatorial Systems in the Acquisition and Generalization of Conservation

Abstract: SHEPPARD, JOHN L. Compensation and Combinatorial Systems in the Acquisition and Generalization of Conservation. CHGm DEVELOPrENTr, 1974, 45, 717-730. A training study of conservation investigated whether learning of compensation could be used to develop conservation and lead to generalization. From a sample of 174 children, 2 experimental and 2 control groups totaling 80 5-6-year-old Ss were selected on the basis of low scores on a conservation pretest. The experimental groups were given training sessions, 1 with water containers 1 with plasticine, while 1 control group had experiences with multiplication of relations in a matrix of beakers without water, and another had no training. A significant number of experimental Ss acquired the conservation involved and generalized in posttests to other conservations, but in almost all instances control Ss did not change. Practice in the anticipationof-levels type of task leading to compensation in a structural system such as a groupoid for conservation was effective in producing concept acquisition.

A Preliminary View of Generalization in Language Training

Abstract: Through modeling, eight language-handicapped children were trained in the use of two syntactic structures in an effort to examine the nature and extent of generalization in language training. Compa...