Showing papers on "Generalization published in 1976"
TL;DR: A generalization of the Lax-Wendroff method is presented in this article, which bears the same relationship to the two-step Richtmyer method as the KreissOliger scheme does to the leapfrog method.
Abstract: A generalization of the Lax-Wendroff method is presented. This generalization bears the same relationship to the two-step Richtmyer method as the KreissOliger scheme does to the leapfrog method. Variants based on the MacCormack method are considered as well as extensions to parabolic problems. Extensions to two dimensions are analyzed, and a proof is presented for the stability of a Thommentype algorithm. Numerical results show that the phase error is considerably reduced from that of second-order methods and is similar to that of the Kreiss-Oliger method. Furthermore, the (2, 4) dissipative scheme can handle shocks without the necessity for an artificial viscosity.
319 citations
TL;DR: In this paper, a lower bound for the number of nodes in a cubature formula of degree 2s-1 is derived for two-fold integrals, and a generalization to then-dimensional case is given.
Abstract: For two-fold integrals, a lower bound is derived for the number of nodes in a cubature formula of degree 2s-1. There is a formula of degree 2s-1 for which the number of nodes attains this lower bound, iff a certain condition is fullfilled. By this condition, all formulas of degree 2s-1 with that minimal number of nodes can be constructed. Examples and a generalization to then-dimensional case are given.
142 citations
TL;DR: Through this transformational stage, the statistical approach to texture is shown to be a generalization of the structural approach in the same way that random variables are ageneralization of deterministic variables.
141 citations
TL;DR: In this paper, a generalization of the theory of distributions (adeles) on schemes of dimension 2 has been proposed, where the authors focus on the problem of finding the optimal distribution.
Abstract: This paper is devoted to the generalization of the theory of distributions (adeles) on schemes of dimension 2.Bibliography: 11 titles.
111 citations
TL;DR: It is proved that for large enough n (e.g. for n > 1000), the Sperner family consisting of subsets of a finite set X of cardinality n such that the union of any three sets belonging to F is different from X.
102 citations
TL;DR: In this article, a generalization of the well-poised concept for multidimensional series adapted to symmetry was proposed, and the analogue to Whipple's theorem was demonstrated for all $SU(n)$ series.
Abstract: By exploiting the known relationship between well-poised hypergeometric series and the combinatorial aspects of the representation theory of $SU(2)$, we define a generalization of the well-poised concept for multidimensional series adapted to $SU(n)$ symmetry. The analogue to Whipple’s theorem is demonstrated for $SU(3)$, and the analogue to the well-poised ${}_4 F_3 ( - 1)$ theorem is given for all $SU(n)$.
69 citations
TL;DR: A generalization of the quantifier elimination problem to finite fields is presented in this paper. But the generalization is not applicable to the problem of diophantine problems over finite fields.
Abstract: 0. Introduction 203 A. History and explanation of the problem 203 B. Background from logic and elimination theory 208 1. Generalizing the quantifier elimination problem . 210 A. Notations and terminology 210 B. The Frobenius symbol 212 C. Galois stratification and generalization of the diophantine problem .213 2. The intersection-union process 215 A. The intersection-union process over a finite field 215 B. The intersection-union process over a perfect field 217 3. A generalization of the theorems of Bertini and Noether . 219 4. Diophantine problems over all residue class fields of a number field . . .225 5. Diophantine problems over finite fields . 230 A. Over all extensions of a fixed finite field 230 B. Over all finite fields 231
55 citations
TL;DR: The most convenient numerical method for defining surfaces is by biparametric vectors, and the conditions for ensuring second order continuity are described in detail in the work of.
Abstract: The most convenient numerical method for defining surfaces is by biparametric vectors. The paper describes the conditions for ensuring second order continuity. A second definition of continuity is given which provides a mathematical generalization to order n between two surface patches.
55 citations
01 Jan 1976
TL;DR: In this article, it is shown that a logic of inductive generalization is obtained if this assumption is weakened in a natural way, in a way similar to the one in this paper.
Abstract: One of the most interesting viewpoints from which inductive logic can be looked at is to ask what the different factors are that must be taken into account in singular inductive inference, i.e., in the usual technical jargon, what the arguments of the representative functions of one’s system of inductive methods are. It is well known that Carnap’s λ-continuum of inductive methods can be derived from essentially one single assumption concerning these arguments of the representative function.1 It is shown in this paper that a logic of inductive generalization is obtained if this assumption is weakened in a natural way.
44 citations
TL;DR: A generalization of a theorem of Geman and Horowitz concerning random measures is obtained in this paper, which in turn is used to extend a well-known theorem for random measures.
Abstract: A generalization of a theorem of Geman and Horowitz concerning random measures is obtained. Their theorem in turn is used to extend a well-known
40 citations
TL;DR: In this article, a preschool boy was taught by a peer-tutor to label five printed three-letter words in a tutoring room and a generalization setting, which was a work area.
TL;DR: A new upper bound for Vi(n) improves the bound given by the standard Hadian-Sobel algorithm by a generalization of the Kirkpatrick-Hadian-SOBel algorithm, and extends Kirkpatrick's method to a much wider range of application.
Abstract: The worst-case, minimum number of comparisons complexity Vi(n) of the i-th selection problem is considered. A new upper bound for Vi(n) improves the bound given by the standard Hadian-Sobel algorithm by a generalization of the Kirkpatrick-Hadian-Sobel algorithm, and extends Kirkpatrick's method to a much wider range of application. This generalization compares favorably with a recent algorithm by Hyafil.
TL;DR: Using Schauder's fixed point theorem, sufficient conditions for global relative controllability are given and the results obtained are a generalization of Davison, and Klamka.
TL;DR: In this paper, it was shown that a sequence of such tests is statistically independent when the model remains unchanged under the null hypothesis that both sets of observations are generated by the same regression model.
Abstract: where SS, is the residual sum of squares (RSS) from a regression based on the original n observations and SS2 is the RSS from a regression based on all n + m observations. Under the null hypothesis that both sets of observations are generated by the same regression model, in which the disturbances are normally distributed and obey the classical assumptions, the test statistic (1) has an F distribution with (m, n k) degrees of freedom. If m > k the test is still valid although in such circumstances the analysis of covariance test is usually to be preferred'; see Chow (1960, p. 598). The proof that the statistic (1) follows an F distribution under the null hypothesis may be found in Chow (1960) and also in Fisher (1970). The present note sets out an alternative proof, which follows almost immediately given certain results on "recursive residuals." As well as providing fresh insight into the Chow test this approach leads to a useful generalization, namely that a sequence of such tests is statistically independent when the model remains unchanged. This result has important implications for the construction of procedures designed to detect structural change. It may also be useful in connection with testing for outliers.
01 Dec 1976
TL;DR: In this paper, new criteria as a generalization of the resultant of two polynomials are given for relative primeness of polynomial matrices together with system theoretic interpretations and unification of the existing and new criteria.
Abstract: New criteria as a generalization of the resultant of two polynomials are given for relative primeness of polynomial matrices together with system theoretic interpretations and unification of the existing and new criteria.
TL;DR: A multidimensional Tauberian theorem is established in this article, which generalizes the one-dimensional Tauberians of Hardy and Littlewood, and is used in the present paper.
Abstract: A multidimensional Tauberian theorem is established which generalizes the one-dimensional Tauberian theorem of Hardy and Littlewood.Bibliography: 6 titles.
01 Mar 1976
TL;DR: A hierarchy of global flow problem classes, each solvable by an appropriate generalization of the "node listing" method of Kennedy, are defined, and it is shown that each of these generalized methods is optimum, among all iterative algorithms, for solving problems within its class.
Abstract: This paper studies iterative methods for the global flow analsis of computer programs. We define a hierarchy of global flow problem classes, each solvable by an appropriate generalization of the "node listing" method of Kennedy. We show that each of these generalized methods is optimum, among all iterative algorithms, for solving problems within its class. We give lower bounds on the time required by iterative algorithms for each of the problem classes.
01 Jan 1976
TL;DR: In this article, a nonlinear generalization of the well-known integral inequality due to Bihari is presented. This generalization is useful in obtaining pointwise estimates of solutions of nonlinear Volterra integral equations.
Abstract: The aim of the present note is to prove a nonlinear generalization of the well-known integral inequality due to Bihari. This generalization is useful in obtaining pointwise estimates of solutions of nonlinear Volterra integral equations.
TL;DR: In this paper, a generalization of the Kuhn-Tucker necessary conditions is developed where neither the objective function nor the constraint functions are required to be differentiable, and a new constraint qualification is imposed in order to validate the optimality criteria.
Abstract: The problem under consideration is a maximization problem over a constraint set defined by a finite number of inequality and equality constraints over an arbitrary set in a reflexive Banach space. A generalization of the Kuhn-Tucker necessary conditions is developed where neither the objective function nor the constraint functions are required to be differentiable. A new constraint qualification is imposed in order to validate the optimality criteria. It is shown that this qualification is the weakest possible in the sense that it is necessary for the optimality criteria to hold at the point under investigation for all families of objective functions having a constrained local maximum at this point
01 Jan 1976
Abstract: It is proved that if a Hausdorff continuum X can be approximated by finite trees (see the text for definition) then there exists a (generalized) arc L and a continuous surjection
01 Jan 1976
TL;DR: In this paper, it was shown that the moment condition tß(t) e Ü may be omitted from the hypotheses of the WienerLévy theorem for nonintegrable functions.
Abstract: Recently, Shea and Wainger obtained a variant of the WienerLévy theorem for nonintegrable functions of the form a(t) = b(t) + ß(t), where b(t) is nonnegative, nonincreasing, convex and locally integrable, and ß(t), tß(t) e L1 (0, oo). It is shown here that the moment condition tß(t) e Ü may be omitted from the hypotheses of this theorem. These results are useful in the study of stability problems for some Volterra integral and integrodifferential equations. Introduction. It is well known that under rather weak hypotheses (see [9, Chapter 4] and [3]) the solutions of the linear Volterra equations (1) uii) = fit) /J ait s)uis) ds (0 < t < oo), (2) u'it) = fit) /J ait s)uis) ds (M(0) = u0 ; 0 < t < oo)
TL;DR: Several weak base (in the sense of A V Arhangel'skit) metrization theorems are established, including a weak base generalization of the Nagata-Smirnov Metrization Theorem.
Abstract: Several weak base (in the sense of A V Arhangel'skit) metrization theorems are established, including a weak base generalization of the Nagata-Smirnov Metrization Theorem
TL;DR: In this article, Weyl's ''unitary trick'' is generalized to the context of semisimple symmetric Lie algebras with Cartan subspaces, over fields of characteristic zero.
Abstract: H. Weyl's \"unitary trick\" is generalized to the context of semisimple symmetric Lie algebras with Cartan subspaces, over fields of characteristic zero. As an illustration of its usefulness, the result is used to transfer to characteristic zero an important theorem in the representation theory of real semisimple Lie algebras.
TL;DR: In this paper, the construction of a complete system of basic invariants for the sixteen-vertex model on an M x N lattice is repeated by means of an alternative method based on the theory of algebraic invariants.
Abstract: The construction of a complete system of basic invariants for the sixteen-vertex model on an M x N lattice as described in part I is repeated by means of an alternative method based on the theory of algebraic invariants. We use a generalization of a theorem by Cayley and Sylvester to determine the characteristics of the covariants belonging to the basic system. In this way we arrive at the same set of 21 invariants that was found in part I. The present method offers the possibility of a generalization to the three-dimensional 64-vertex model and the vertex model on a triangular lattice.