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      By UW Authors

      Recent articles by authors in Math, Applied Math, and Statistics.

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      *Record 1 of 5.
      *Click Here to View Full Record
      Title: PISOT FAMILY SELF-AFFINE TILINGS, DISCRETE SPECTRUM, AND THE MEYER PROPERTY

      Author Full Names: Lee, Jeong-Yup; Solomyak, Boris

      Source: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 32 (3): 935-959 10.3934/dcds.2012.32.935 MAR 2012
      Abstract: We consider self-affine tilings in the Euclidean space and the associated tiling dynamical systems, namely, the translation action on the orbit closure of the given tiling. We investigate the spectral properties of the system.Itturnsoutthatthepresenceofthediscretecomponentdependsonthe algebraic properties of the eigenvalues of the expansion matrix phi for the tiling. Assuming that phi is diagonalizable over C and all its eigenvalues are algebraic conjugates of the same multiplicity, we show that the dynamical system has a relatively dense discrete spectrum if and only if it is not weakly mixing, and if and only if the spectrum of phi is a "Pisot family." Moreover, this is equivalent to the Meyer property of the associated discrete set of "control points" for the tiling.

      *Record 2 of 5.
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      Title: On the subdifferential regularity of max root functions for polynomials

      Author Full Names: Burke, James V.; Eaton, Julia

      Source: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 75 (3): 1168-1187 10.1016/j.na.2011.01.021 FEB 2012
      Abstract: In 2001, Burke and Overton showed that the abscissa mapping on polynomials is subdifferentially regular on the monic polynomials of degree n. We extend this result to the class of max polynomial root functions which includes both the polynomial abscissa and the polynomial radius mappings. The approach to the computation of the subgradient simplifies that given by Burke and Overton and provides new insight into the variational properties of these functions. (C) 2011 Elsevier Ltd. All rights reserved.