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Parallel Generation and Evaluation of Weyl Sequences
, 1994
"... : 2 1 Introduction 2 2 Some measures of the quality of uniform distribution of sequences and parallel Weylsequences 3 3 Parallel Generation and Independence of Weyl Sequences 9 R5Z4/Rel 1.0/Oktober 31 1994 Introduction PACT 0 Abstract: The paper ist part of the NEWTON project. New Technology of ..."
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: 2 1 Introduction 2 2 Some measures of the quality of uniform distribution of sequences and parallel Weylsequences 3 3 Parallel Generation and Independence of Weyl Sequences 9 R5Z4/Rel 1.0/Oktober 31 1994 Introduction PACT 0 Abstract: The paper ist part of the NEWTON project. New Technology
FAST SORTING OF WEYL SEQUENCES USING COMPARISONS*
, 1981
"... Abstract. An algorithm is given which makes only O(log n) comparisons, and which will determine the ordering of the uniformly distributed (pseudo random) Weyl sequences given by {(kc)rood 1:1 _< k =< n}, where a is an unspecified irrational number. This result is shown to be best possible in ..."
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Abstract. An algorithm is given which makes only O(log n) comparisons, and which will determine the ordering of the uniformly distributed (pseudo random) Weyl sequences given by {(kc)rood 1:1 _< k =< n}, where a is an unspecified irrational number. This result is shown to be best possible
Binary search trees based on Weyl and Lehmer sequences
, 1998
"... This paper is based upon the presentation at the meeting in Salzburg. As a courtesy to those who attended the meeting, I will try to faithfully reproducewith minor omissions and additionswhat I said at that meeting. There are two basic background references for mathematical details, Devroye (1 ..."
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Cited by 3 (0 self)
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; b; m; xn all integer) derive their popularity from easily understood properties of Weyl and Lehmer sequences. As such generators produce integer sequences that are necessarily periodic, they can strictly speaking not be compared with aperiodic sequences such as fn`g for ` irrational. However
A Study Of Random Weyl Trees
, 1998
"... . We study binary search trees constructed from Weyl sequences fn`g; n 1, where ` is an irrational and f:g denotes "mod 1". We explore various properties of the structure of these trees, and relate them to the continued fraction expansion of `. If H n is the height of the tree with n nod ..."
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Cited by 1 (1 self)
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. We study binary search trees constructed from Weyl sequences fn`g; n 1, where ` is an irrational and f:g denotes "mod 1". We explore various properties of the structure of these trees, and relate them to the continued fraction expansion of `. If H n is the height of the tree with n
Weyl Group of
"... The Weyl groups are important for Lie algebras. Lie algebras arise in the study of Lie groups, coming from symmetries of differential equations, and of differentiable manifolds. The Weyl groups have been used to classify Lie algebras up to isomorphism. The Weyl group associated to a Lie algebra of t ..."
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The Weyl groups are important for Lie algebras. Lie algebras arise in the study of Lie groups, coming from symmetries of differential equations, and of differentiable manifolds. The Weyl groups have been used to classify Lie algebras up to isomorphism. The Weyl group associated to a Lie algebra
Weyl spectra and Weyl’s theorem
 Studia Math
, 2001
"... Abstract. “Weyl’s theorem ” for an operator on a Hilbert space is a statement that the complement in the spectrum of the “Weyl spectrum ” coincides with the isolated eigenvalues of finite multiplicity. In this paper we consider how Weyl’s theorem survives for polynomials of operators and under quas ..."
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Abstract. “Weyl’s theorem ” for an operator on a Hilbert space is a statement that the complement in the spectrum of the “Weyl spectrum ” coincides with the isolated eigenvalues of finite multiplicity. In this paper we consider how Weyl’s theorem survives for polynomials of operators and under
Generalised Weyl theorems and spectral pollution in the Galerkin method
 Journal of Spectral Theory
, 2012
"... Abstract. We consider a general framework for investigating spectral pollution in the Galerkin method. We show how this phenomenon is characterised via the existence of particular Weyl sequences which are singular in a suitable sense. For a semibounded selfadjoint operator A we identify relative c ..."
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Cited by 9 (2 self)
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Abstract. We consider a general framework for investigating spectral pollution in the Galerkin method. We show how this phenomenon is characterised via the existence of particular Weyl sequences which are singular in a suitable sense. For a semibounded selfadjoint operator A we identify relative
Fully commutative elements in the Weyl and affine Weyl groups
 J. Algebra
"... Abstract. Let W be a Weyl or an ane Weyl group and let Wc be the set of fully commutative elements in W. We associate each w 2 Wc to a digraph G(w). By using G(w), we give a graphtheoretic description for Lusztig's afunction on Wc and describe explicitly all the distinguished involutions of ..."
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Cited by 7 (2 self)
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Abstract. Let W be a Weyl or an ane Weyl group and let Wc be the set of fully commutative elements in W. We associate each w 2 Wc to a digraph G(w). By using G(w), we give a graphtheoretic description for Lusztig's afunction on Wc and describe explicitly all the distinguished involutions
Weyl groups, affine Weyl groups and reflection groups
"... This paper is a survey of some of the basic results pertaining to reflection groups. In x2, we start with the basic concepts and properties of Coxeter groups, such as the Exchange Lemma and in x4 we construct the geometric representation. Sections 3 and 5 are devoted to finite real reflection groups ..."
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groups and finite Coxeter groups and x6 concerns Weyl groups, which are crystallographic reflection groups. Weyl groups give rise to affine Weyl groups, studied in x7.
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