We show that the Weyl group W = M 0 =M of a noncompact semisimple Lie group is obtained by taking xed point sets of smooth involutions in K=M. More precisely, one considers rst the xed point set X of the involutions deened on K=M by the elements of order 2 in exp ia. The Weyl group is either X , or the xed point set of the involutions deened on X by special elements of order 4 in exp ia.

The discretization of the multi{dimensional radiative transfer equation results in a very large linear system of equations. The standard solution method used by astrophysicists is a simpliied xed point iteration (called approximate {iteration) which becomes slow for problems most interesting in astrophysics. As an alternative, a class of (block) conjugate gradient{like methods is proposed, toge...

Let f be a quadratic polynomial which has an irrationally indi erent xed point Let z be a biaccessible point in the Julia set of f Then In the Siegel case the orbit of z must eventually hit the critical point of f In the Cremer case the orbit of z must eventually hit the xed point Siegel polynomials with biaccessible critical point certainly exist but in the Cremer case it is possible that biac...

Published in Agron. J. 103:76–84 (2011) Published online 3 Nov 2010 doi:10.2134/agronj2010.0189 Copyright © 2011 by the American Society of Agronomy, 5585 Guilford Road, Madison, WI 53711. All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrie...

We prove that the period doubling operator has an expanding di rection at the xed point We use the induced operator a Perron Frobenius type operator to study the linearization of the period dou bling operator at its xed point We then use a sequence of linear operators with nite ranks to study this induced operator The proof is constructive One can calculate the expanding direction and the rate ...

Di erent options for block oating point lter implementation are introduced and their e ciency determined. The e ciency is quanti ed by the additional number of operations over those required for xed point operation. Some of the implementations are new. It is shown that they are more e cient than the existing ones. Examples are given in which the processing time per recursion of a block oating p...

This paper presents an algorithm for solving Boolean xed-point equations containing one level of nesting of minimum and maximum xed points. The algorithm assumes that the equations of the inner xed point is of a certain restricted kind and has a worst-case time-and space-complexity that is linear in the size of the equation system. By observing that a range of behavioral relations { in particul...

We deene a value-based modal-calculus, built from rst-order formulas, modalities, and xed point operators parameterized by data variables, which allows to express temporal properties involving data. We interpret this logic over Crl terms deened by linear process equations. The satisfaction of a temporal formula by a Crl term is translated to the satisfaction of a rst-order formula containing pa...

We consider a perturbed nonlinear system with a xed point that is invariant under all perturbations. Under the assumption that this xed point is locally exponentially stable for the unperturbed system we propose a method for the approximation of the robust domain of attraction, that is, the set of points that are attracted to the xed point under all time-varying perturbations taking values in a...

in this paper is introduced a new type of generalization of metric spaces called sb metric space. for this new kind of spaces it has been proved a common xed point theorem for four mappings which satisfy generalized contractive condition. we also present example to conrm our theorem.