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http://hdl.handle.net/10092/1
Sat, 03 Oct 2015 00:02:32 GMT2015-10-03T00:02:32ZDepth of idempotent-generated subsemigroups of a regular ring
http://hdl.handle.net/10092/11059
Title: Depth of idempotent-generated subsemigroups of a regular ring
Authors: Hannah, J.; O'Meara, K.C.
Abstract: If S is an idempotent-generated semigroup, its depth is the minimum number of idempotents needed to express a general element
as a product of idempotents. Here we study the depth of S where
S is the semigroup generated by all the idempotents of a von
Neumann regular ring, and the depth of various subsemigroups of S.
For example, if R is directly finite, the depth of S equals the
index of nilpotence of R, which considerably extends a result of
Ballantine (1978) for matrices over a field. We also answer a
query of Professor Howie by supplying a ring-theoretic explanation
of Reynolds and Sullivan's (1985) result that the depth is 3 for
certain subsemigroups in the infinite-dimensional full linear case.Fri, 01 Jan 1988 00:00:00 GMThttp://hdl.handle.net/10092/110591988-01-01T00:00:00ZPfaffians and determinants for Schur Q-functions
http://hdl.handle.net/10092/11058
Title: Pfaffians and determinants for Schur Q-functions
Authors: Hamel, A. M.
Abstract: Schur Q-functions were originally introduced by Schur in relation to projective representations of the symmetric group and they can be defined combinatorially
in terms of shifted tableaux. In this paper we describe planar decompositions
of shifted tableaux into strips and use the shapes of these strips
to generate pfaffians and determinants that are equal to Schur Q-functions. As
special cases we obtain the classical pfaffian associated with Schur Q-functions,
a pfaffian for skew Q-functions due to Jozefiak and Pragacz, and some determinantal
expressions of Okada. We also obtain results for Schur P-functions,
results for supersymmetric Schur functions, and generalizations to variable sets
subscripted by arbitrarily ordered alphabets.Sat, 01 Jan 1994 00:00:00 GMThttp://hdl.handle.net/10092/110581994-01-01T00:00:00ZCurve fitting with nonlinear spiral splines
http://hdl.handle.net/10092/11057
Title: Curve fitting with nonlinear spiral splines
Authors: Coope, I. D.
Abstract: Collocating spiral splines are derived as an approximation to the curve of least energy. The defining equations, although nonlinear, are easily solved because the
Jacobian matrix has banded structure. A simple but effective iterative scheme for the
solution of these equations is described together with a useful scheme for determining
initial approximations for nonlinear splines. The resulting curve is invariant with respect
to translation and rotation of axes and is usually much smoother than is possible with
polynomial splines because the curvature of the spiral spline varies linearly with respect
to arc length.Tue, 01 Jan 1991 00:00:00 GMThttp://hdl.handle.net/10092/110571991-01-01T00:00:00ZAn adaptive scheme for the derivation of harmonic impedance contours
http://hdl.handle.net/10092/11056
Title: An adaptive scheme for the derivation of harmonic impedance contours
Authors: Dominguez, M.; Coope, I.D.; Arrillaga, J.; Watson, N.R.
Abstract: The aim of this paper is to make the calculation of harmonic impedances accurate and efficient. An adaptive scheme is proposed which minimises the number of
frequency samples to be used in the derivation of the impedance/frequency loci. The
scheme is then used to derive three-phase harmonic impedance contours which take into
account any specified range of fundamental frequency variation.Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/10092/110561993-01-01T00:00:00Z