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Showing papers on "Generalization published in 1972"



Journal ArticleDOI
TL;DR: A constructive existence proof for equilibria of polymatrix games is given in this paper, which is based on a generalization of the almost complementary paths used for the linear complementarity problem.
Abstract: A constructive existence proof is given for equilibria of polymatrix games. The construction is based on a generalization of the almost-complementary paths used for the linear complementarity problem.

115 citations


Journal ArticleDOI
TL;DR: This paper presents a generalization of results of Hakimi and Goldman on optimum locations of centers (warehouses) in a network leading to a proof of a stronger version of Goldman's conjecture.
Abstract: This paper presents a generalization of results of Hakimi and Goldman on optimum locations of centers (warehouses) in a network. This generalization is achieved by a conceptual simplification of the previous results leading to a proof of a stronger version of Goldman's conjecture.

65 citations


Journal ArticleDOI
TL;DR: This paper considers the degrees a such that the recursive sets are uniformly of degree ≦a and characterize them by the condition a’ ≦ 0, which will be used to study the relationship between Turing and many-one reducibility on the r.e. sets.
Abstract: One of the most fundamental and characteristic features of recursion theory is the fact that the recursive sets are not uniformly recursive. In this paper we consider the degrees a such that the recursive sets are uniformly of degree ≦a and characterize them by the condition a’ ≦ 0". A number of related results will be proved, and one of these will be combined with a theorem of Yates to show that there is no r.e. degree a < 0’ such that the r.e. sets of degree ≦a are uniformly of degree ≦a. This result and a generalization will be used to study the relationship between Turing and many-one reducibility on the r.e. sets.

64 citations


Journal ArticleDOI
TL;DR: In this article, it is shown that an obvious generalization of the subjective metrics model by Bloxom, Horan, Carroll and Chang has a very simple algebraic solution which was previously considered by Meredith in a different context.
Abstract: It is shown that an obvious generalization of the subjective metrics model by Bloxom, Horan, Carroll and Chang has a very simple algebraic solution which was previously considered by Meredith in a different context. This solution is readily adapted to the special case treated by Bloxom, Horan, Carroll and Chang. In addition to being very simple, this algebraic solution also permits testing the constraints of these models explicitly. A numerical example is given.

59 citations



Journal ArticleDOI
Bernard Saperstein1
TL;DR: In this article, a 1's and b 0's are randomly arranged in a row, and the largest number of 1's appearing within any m consecutive points in the arrangement is defined.
Abstract: Let a 1's and b 0's be randomly arranged in a row; k is defined to be the largest number of 1's appearing within any m consecutive points in the arrangement. We find Pk*(k) = Pr{k a/2, and give upper 5% points on k for some choices of a, b, and m. This generalization of the classical birthday problem corresponds to a test for nonrandom clustering that is a discrete analogue to a scan test for clustering of points on the line discussed by Nous [4].

52 citations


Journal ArticleDOI
TL;DR: In this paper, a generalization of Erdos and Turan's inequality on B 2 -sequences of integers to B 2 −sequences with integer components is presented. But the result is only applicable to the case when the dimension tends to infinity.

51 citations


Journal ArticleDOI
TL;DR: In this paper, a model accompanied performance of correct responses with no verbalization, with provision of a weak verbal code, a strong verbal code or the strong code plus a rule to guide correct response.

49 citations



Journal ArticleDOI
TL;DR: The investigation of the formal systems obtained by extending well-known connectives to continuous arguments, called ''soft algebras,'' are investigated and it is shown that every soft algebra is a bounded, distributive and symmetric lattice.

01 Jul 1972
TL;DR: In this article, a class of bilinear estimation problems involving single-degree-of-freedom rotation is formulated and resolved, and both continuous and discrete time estimation problems are considered.
Abstract: : A class of bilinear estimation problems involving single-degree-of- freedom rotation is formulated and resolved. Both continuous and discrete time estimation problems are considered. Error criteria, probability distributions, and optimal estimates on the circle are studies. An effective synthesis procedure for continuous time estimation is provided, and a generalization to estimation on arbitrary abelian Lie groups is included. An intrinsic difference between the discrete and continuous problems is discussed, and the complexity of the equations in the discrete time case is analyzed in this setting. Applications of these results to a number of practical problems including FM demodulation and frequency stability are examined.

Journal ArticleDOI
TL;DR: In this paper, the problem of estimating the slope of a polynomial regression at a fixed point of the experimental region such that the variance of the least-square estimate of the slope at the fixed point is a minimum and the average variance of a least-squares estimator of the estimate is the minimum is discussed.
Abstract: The problem of estimating the slope of a polynomial regression at a fixed point of the experimental region such that (a) the variance of the least-square estimate of the slope at the fixed point is a minimum and (b) the average variance of the least-square estimate of the slope is a minimum is discussed in this paper. In general these designs can be obtained using Kiefer-Wolfowitz [5] characterization of c-optimal designs, Federov [2] characterization of L-optimal designs, and Studden's [10] generalization of the Elfving Theorem [1]. After presenting a brief review of these characterization theorems, specific illustrations for the quadratic and cubic regressions are presented in detail.

Book
29 Jun 1972
TL;DR: A priori estimates for solutions of linear elliptic functional equations with constant coefficients are given in this article, where a representation for continuous linear functionals on W o m,p (G) (1?) and its applications: a generalization of Garding's inequality and existence theorems.
Abstract: Outline.- A priori estimates for solutions of linear elliptic functional equations with constant coefficients.- A representation for continuous linear functionals on W o m,p (G) (1 ?) and its applications: A generalization of Garding's inequality and existence theorems.- Regularity and existence theorems for uniformly elliptic functional equations.

Journal ArticleDOI
TL;DR: In this paper, a statistical generalization of the model is proposed, which allows one to separate the multi-paripheral and diffractive contributions to then-particle production cross-sections.
Abstract: The discussion of the multiperipheral bootstrap model in its one-dimensional version leads one to consider some experimental and theoretical inconsistencies, which are expected to be crucial at very high energies. A statistical generalization of the model is proposed; the new model allows one to separate the multiperipheral and diffractive contributions to then-particle production cross-sections. The general properties of the model are investigated.

Journal ArticleDOI
TL;DR: In this article, a generalization of the results of [4], [5] to the case of noncommutative formal groups is presented. But this generalization is restricted to groups with non-commutativity.
Abstract: We prove and extend the results of [7], thereby obtaining a generalization of [4], [5] to the case of noncommutative formal (co)groups.

Journal ArticleDOI
TL;DR: In this paper, the concept of α, β-elementary equivalence of two relational structures is defined and sufficient and necessary conditions are given for this notion by generalizing Ehrenfeucht's game in algebraic terms.
Abstract: The concept of α, β-elementary equivalence of two relational structures is defined. Sufficient and necessary conditions are given for this notion by generalizing Ehrenfeucht’s game in algebraic terms. Some results, in a first order language with generalized quantifier, are obtained.

Journal ArticleDOI
TL;DR: In this article, a generalization of the hyperstability criterion given in the literature is discussed, which is directly applicable for the synthesis of hyperstable adaptation algorithms for various applications.
Abstract: A generalization of the hyperstability criterion given in the literature is discussed. The new hyperstability conditions were obtained by utilizing the properties of the positive definite kernels. The results presented here are directly applicable for the synthesis of hyperstable adaptation algorithms for various applications.

Journal ArticleDOI
TL;DR: This paper proves the following result and transfinite extensions of it: If the cardinalities |I| = f and |S| = n are finite and f > n(r − 1), then one can find r disjoint subsets Iυ(υ = 1,…,r) of I for which ⋃ i∈I 1 M i = … = ⋁ i∈�I r M i


Journal ArticleDOI
TL;DR: In this article, a linear transformation which is used in the unified analysis of electrical machines without and without a commutator is considered and a generalization of Park's transformation to an arbitrary polyphase machine is presented.
Abstract: In this paper the linear transformation which is used in the unified analysis of electrical machines without & commutator is considered. It is shown that, a very straightforward derivation of the so-called commutator transformation is obtained if the underlying mathematical problem is well defined and linear system theory techniques are used to reduce a set of time-varying linear differential equations to a set of time-invariant ones. This leads to a generalization of Park's transformation to an arbitrary polyphase machine, and also yields a better insight into why the usual assumptions of unified machine theory are necessary

01 Mar 1972
TL;DR: A generalization of the Lanczos algorithm for reducing the problem to a symmetric tridiagonal eigenproblem is given and a numerically stable variant of the algorithm is described.
Abstract: The problem of computing the eigensystem of Ax = $\lambda$Bx when A and B are symmetric and B is positive definite is considered. A generalization of the Lanczos algorithm for reducing the problem to a symmetric tridiagonal eigenproblem is given. A numerically stable variant of the algorithm is described. The new algorithm depends heavily upon the computation of elementary Hermitian matrices. An ALGOL W procedure and a numerical example are also given.

Journal ArticleDOI
TL;DR: In this article, a generalization of the variational theorem of Leighton was proposed for the non-linear case, where the negative sign of the functional and the condition imply the vanishing of all solutions on [α, β] on some sub-interval of the subinterval.
Abstract: This paper offers the following generalization of the well known variational theorem of Leighton. Considering the non-linear equation , we show that following an arbitrary choice of function u(x)∊C2 and of G(u(x)), G(u(α)) = G(u(β)) = 0; G(u(x)) > 0 for all x in [α, β] the negative sign of the functional implies that all solutions of our equation will be bounded in absolute value by the number (m/K)1/(K-1), where on some sub-interval of [α, β]. In the linear case, K= 1, we show that the negative sign of the above functional and the condition imply the vanishing of all solutions on [α, β]


Journal ArticleDOI
TL;DR: Zimmerman et al. as mentioned in this paper compared ethnicity x modeling or non-modeling training x repetition or nonrepetition of a rule summary and found that both modeling and repetition improved performance.
Abstract: ZIMMERMAN, BARRY J., and ROSENTHAL, TED L. Observation, Repetition, and Ethnic Background in Concept Attainment and Generalization. CHILD DEVELOPMENT, 1972, 43, 605-613. Attaining and generalizing a new concept were studied in Mexicanand Anglo-American fifth graders. The design factorially compared ethnicity x modeling or nonmodeling training x repetition or nonrepetition of a rule summary. All children received feedback on correct responses during performance-phase trials. Both modeling and repetition improved performance. Prior-modeling groups reduced errors faster than nonmodeling groups, whose errors decreased in the last block of trials. Concept generalization was aided by modeling and, especially, by repetition which mainly determined later verbalization of the rule. Anglooutperformed Mexican-American children, but the major results held for both ethnic groups.

Journal ArticleDOI
TL;DR: The algorithm presented here works by eliminating all off-diagonal variables in terms of the diagonal ones, and then specifying values for the diagonal variables for tridiagonal problems in n steps for an n-origin, n-destination problem.
Abstract: Some transportation problems are such that, when origins and destinations are suitably indexed, the cost matrix contains elements along the main diagonal, a band above it, and a band below it, whil...