2,590 research outputs found
A study of the significance of family inter-relationships in a selected long-term public assistance case involving an incapacitated father
Thesis (M.S.)--Boston University, 1948. This item was digitized by the Internet Archive
On the spectral distribution of large weighted random regular graphs
McKay proved that the limiting spectral measures of the ensembles of
-regular graphs with vertices converge to Kesten's measure as
. In this paper we explore the case of weighted graphs. More
precisely, given a large -regular graph we assign random weights, drawn from
some distribution , to its edges. We study the relationship
between and the associated limiting spectral distribution
obtained by averaging over the weighted graphs. Among other results, we
establish the existence of a unique `eigendistribution', i.e., a weight
distribution such that the associated limiting spectral
distribution is a rescaling of . Initial investigations suggested
that the eigendistribution was the semi-circle distribution, which by Wigner's
Law is the limiting spectral measure for real symmetric matrices. We prove this
is not the case, though the deviation between the eigendistribution and the
semi-circular density is small (the first seven moments agree, and the
difference in each higher moment is ). Our analysis uses
combinatorial results about closed acyclic walks in large trees, which may be
of independent interest.Comment: Version 1.0, 19 page
Frequency combs in quadratically nonlinear resonators
We describe the physics and modelling of frequency combs and corresponding temporal patterns in coherently driven, quadratically nonlinear resonators
Ariel - Volume 3 Number 8
Editors
Richard J. Bonanno
Robin A. Edwards
Associate Editors
Steven Ager
Tom Williams
Lay-out Editor
Eugenia Miller
Contributing Editors
Paul Bialas
Robert Breckenridge
David Jacoby
Mike LeWitt
Terry Burt
Michael Leo
Editors Emeritus
Delvyn C. Case, Jr.
Paul M. Fernhof
On the convergence of Regge calculus to general relativity
Motivated by a recent study casting doubt on the correspondence between Regge
calculus and general relativity in the continuum limit, we explore a mechanism
by which the simplicial solutions can converge whilst the residual of the Regge
equations evaluated on the continuum solutions does not. By directly
constructing simplicial solutions for the Kasner cosmology we show that the
oscillatory behaviour of the discrepancy between the Einstein and Regge
solutions reconciles the apparent conflict between the results of Brewin and
those of previous studies. We conclude that solutions of Regge calculus are, in
general, expected to be second order accurate approximations to the
corresponding continuum solutions.Comment: Updated to match published version. Details of numerical calculations
added, several sections rewritten. 9 pages, 4 EPS figure
Fast algorithms for computing defects and their derivatives in the Regge calculus
Any practical attempt to solve the Regge equations, these being a large
system of non-linear algebraic equations, will almost certainly employ a
Newton-Raphson like scheme. In such cases it is essential that efficient
algorithms be used when computing the defect angles and their derivatives with
respect to the leg-lengths. The purpose of this paper is to present details of
such an algorithm.Comment: 38 pages, 10 figure
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