A generalization of Ramsey theory for graphs, with stars and complete graphs as forbidden subgraphs /

Includes bibliographical references.

A generalization of Ramsey theory for graphs /

Bibliography: p. 16.

Learning and generalization of structural descriptions : evaluation criteria and comparative review of selected methods /

"February 1980."

Interval generalization of switching theory,

Includes bibliographical references.

A generalization of Ramsey theory for graphs /

Includes bibliographical references.

Situational specificity and validity generalization results for apprentice occupations /

Bibliography: p. 25.

On a generalization of the Oberwolfach problem

Let e(1),e(2),... e(n) be a sequence of nonnegative integers Such that the first non-zero term is not one. Let Sigma(i=1)(n) e(i) = (q - 1)/2, where q = p(n) and p is an odd prime. We prove that the complete graph on q vertices can be decomposed into e(1) C-pn-factors, e(2) C-pn (1)-factors,..., and e(n) C-p-factors. (C) 2004 Elsevier Inc. All rights reserved.

Generalization by symbolic abstraction in cascaded recurrent networks

Generalization performance in recurrent neural networks is enhanced by cascading several networks. By discretizing abstractions induced in one network, other networks can operate on a coarse symbolic level with increased performance on sparse and structural prediction tasks. The level of systematicity exhibited by the cascade of recurrent networks is assessed on the basis of three language domains. (C) 2004 Elsevier B.V. All rights reserved.

Differential impact of posterior lesions in the left and right hemisphere on visual category learning and generalization to contrast reversal

Hemispheric differences in the learning and generalization of pattern categories were explored in two experiments involving sixteen patients with unilateral posterior, cerebral lesions in the left (LH) or right (RH) hemisphere. In each experiment participants were first trained to criterion in a supervised learning paradigm to categorize a set of patterns that either consisted of simple geometric forms (Experiment 1) or unfamiliar grey-level images (Experiment 2). They were then tested for their ability to generalize acquired categorical knowledge to contrast-reversed versions of the learning patterns. The results showed that RH lesions impeded category learning of unfamiliar grey-level images more severely than LH lesions, whereas this relationship appeared reversed for categories defined by simple geometric forms. With regard to generalization to contrast reversal, categorization performance of LH and RH patients was unaffected in the case of simple geometric forms. However, generalization to of contrast-reversed grey-level images distinctly deteriorated for patients with LH lesions relative to those with RH lesions, with the latter (but not the former) being consistently unable to identify the pattern manipulation. These findings suggest a differential use of contrast information in the representation of pattern categories in the two hemispheres. Such specialization appears in line with previous distinctions between a predominantly lefthemispheric, abstract-analytical and a righthemispheric, specific-holistic representation of object categories, and their prediction of a mandatory representation of contrast polarity in the RH. Some implications for the well-established dissociation of visual disorders for the recognition of faces and letters are discussed.

Constructive updating/downdating of oblique projectors:a generalization of the Gram-Schmidt process

A generalization of the Gram-Schmidt procedure is achieved by providing equations for updating and downdating oblique projectors. The work is motivated by the problem of adaptive signal representation outside the orthogonal basis setting. The proposed techniques are shown to be relevant to the problem of discriminating signals produced by different phenomena when the order of the signal model needs to be adjusted. © 2007 IOP Publishing Ltd.

On a New Approach to Williamson's Generalization of Pólya's Enumeration Theorem

Pólya’s fundamental enumeration theorem and some results from Williamson’s generalized setup of it are proved in terms of Schur- Macdonald’s theory (S-MT) of “invariant matrices”. Given a permutation group W ≤ Sd and a one-dimensional character χ of W , the polynomial functor Fχ corresponding via S-MT to the induced monomial representation Uχ = ind|Sdv/W (χ) of Sd , is studied. It turns out that the characteristic ch(Fχ ) is the weighted inventory of some set J(χ) of W -orbits in the integer-valued hypercube [0, ∞)d . The elements of J(χ) can be distinguished among all W -orbits by a maximum property. The identity ch(Fχ ) = ch(Uχ ) of both characteristics is a consequence of S-MT, and is equivalent to a result of Williamson. Pólya’s theorem can be obtained from the above identity by the specialization χ = 1W , where 1W is the unit character of W.

Further Generalization of Kobayashi's Gamma Function

In this paper, we introduce a further generalization of the gamma function involving Gauss hypergeometric function 2F1 (a, b; c; z)

Generalization of a Conjecture in the Geometry of Polynomials

In this paper we survey work on and around the following conjecture, which was first stated about 45 years ago: If all the zeros of an algebraic polynomial p (of degree n ≥ 2) lie in a disk with radius r, then, for each zero z1 of p, the disk with center z1 and radius r contains at least one zero of the derivative p′ . Until now, this conjecture has been proved for n ≤ 8 only. We also put the conjecture in a more general framework involving higher order derivatives and sets defined by the zeros of the polynomials.

Generalization of Ehrlich-Kjurkchiev Method for Multiple Roots of Algebraic Equations

In this paper a new method which is a generalization of the Ehrlich-Kjurkchiev method is developed. The method allows to find simultaneously all roots of the algebraic equation in the case when the roots are supposed to be multiple with known multiplicities. The offered generalization does not demand calculation of derivatives of order higher than first simultaneously keeping quaternary rate of convergence which makes this method suitable for application from practical point of view.