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Recurrence Relation (recurrence + relation)

Distribution by Scientific Domains
Mathematics and Statistics66%

Selected Abstracts

A GENERALIZED EMERSON RECURRENCE RELATION

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2008
J. C. W. Rayner
Summary The Emerson (1968, Biometrics 24, 695,701) recurrence relation has many important applications in statistics. However, the original derivation applied only to discrete distributions. In the following, a simple derivation is given that generalizes the Emerson recurrence relation to any distribution for which the necessary expectations exist. A modern application is outlined. [source]

Topological torsion related to some recursive sequences of integers

MATHEMATISCHE NACHRICHTEN, Issue 7 2008
Giuseppina Barbieri
Abstract For a recursively defined sequence u: = (un) of integers, we describe the subgroup tu (,,) of the elements x of the circle group ,, satisfying limnunx = 0. More attention is dedicated to the sequences satisfying a secondorder recurrence relation. In this case, we show that the size and the free-rank of tu (,,) is determined by the asymptotic behaviour of the ratios qn = (un /un ,1) and we extend previous results of G. Larcher, C. Kraaikamp, and P. Liardet obtained from continued fraction expansion. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

A Lanczos-type algorithm for the QR factorization of regular Cauchy matrices

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2002
Dario Fasino
Abstract We present a fast algorithm for computing the QR factorization of Cauchy matrices with real nodes. The algorithm works for almost any input matrix, does not require squaring the matrix, and fully exploits the displacement structure of Cauchy matrices. We prove that, if the determinant of a certain semiseparable matrix is non-zero, a three term recurrence relation among the rows or columns of the factors exists. Copyright © 2002 John Wiley & Sons, Ltd. [source]

A GENERALIZED EMERSON RECURRENCE RELATION

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2008
J. C. W. Rayner
Summary The Emerson (1968, Biometrics 24, 695,701) recurrence relation has many important applications in statistics. However, the original derivation applied only to discrete distributions. In the following, a simple derivation is given that generalizes the Emerson recurrence relation to any distribution for which the necessary expectations exist. A modern application is outlined. [source]

The one-level functional equation of multi-rate loss systems

EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS, Issue 2 2003
Harro L. Hartmann
Motivated by the discrete multi-rate Kaufmann,Roberts recurrence relations, we derive a functional equation (FE), which covers nonintegral states. This FE implies a unique effective step parameter d, which defines an equivalent one-level recurrence depth, or bit-rate, at each state under progress. This state-dependent depth results from the equality requirement of the multi-rate and the one-level model in the moment-generating function transform domain. By this method it is possible to model d by a few moments of the original multi-rate statistic. In this case we obtain an explicit FE solution covering the entire (global) state space. Next we verify that the resulting state probability density incorporates iteratively enumerated discrete state probabilities, including the state-dependent depth. With a system capacity C the iterations then need time complexities between O(C) and O(C2). In contrast to this each FE state, is performed at a time complexity O(1). By the efficient coverage of the whole state space, fast optimizations of multi-rate networks and multi-resource systems can be improved. Copyright © 2003 AEI. [source]

Erratum: On the calculation of arbitrary multielectron molecular integrals over slater-type orbitals using recurrence relations for overlap integrals.

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2008

No abstract is available for this article. [source]

Auxiliary functions for molecular integrals with Slater-type orbitals.

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 9 2006

Abstract Many types of molecular integrals involving Slater functions can be expressed, with the ,-function method in terms of sets of one-dimensional auxiliary integrals whose integrands contain two-range functions. After reviewing the properties of these functions (including recurrence relations, derivatives, integral representations, and series expansions), we carry out a detailed study of the auxiliary integrals aimed to facilitate both the formal and computational applications of the ,-function method. The usefulness of this study in formal applications is illustrated with an example. The high performance in numerical applications is proved by the development of a very efficient program for the calculation of two-center integrals with Slater functions corresponding to electrostatic potential, electric field, and electric field gradient. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source]

Weakening arcs in tournaments,

JOURNAL OF GRAPH THEORY, Issue 2 2004
Denis Hanson
Abstract A weakening arc of an irreducible tournament is an arc whose reversal creates a reducible tournament. We consider properties of such arcs and derive recurrence relations for enumerating strong tournaments with no such arcs, one or more such arcs, and exactly one such arc. We also give some asymptotic results on the numbers of such tournaments, among other things. © 2003 Wiley Periodicals, Inc. J Graph Theory 45: 142,162, 2004 [source]