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Convex Sets (convex + set)

Distribution by Scientific Domains
Mathematics and Statistics28%

Selected Abstracts

Restoration of PSD from Chord Length Distribution Data using the Method of Projections onto Convex Sets

PARTICLE & PARTICLE SYSTEMS CHARACTERIZATION, Issue 2 2005
Jörg Worlitschek
Abstract The interpretation of chord length distributions (CLDs) is essential in many fields and has been discussed by various authors. Here, the technique of the Focused Beam Reflectance Measurement (FBRM) is considered as on-line and in-situ measurement device of the CLD of particle dispersions and emulsions. Though useful in general, this measurement cannot be converted directly into a particle size distribution (PSD), unless the physics of the measurement method is described and accounted for. In this work we present a new tool to carry out such a conversion once the particle shape is known a priori and can be fixed, which is based on a two step procedure: (1) the computation of a matrix that converts the PSD of a population of particles with given shape into the corresponding CLD using a 3-dimensional geometric model; (2) the calculation of the PSD from the resulting linear matrix equation for the measured CLD. Here, the method of Projections onto Convex Sets (POCS) is applied to solve the PSD restoration problem, which is a mathematically ill-posed inverse problem. We study the effect of particle shape and matrix dimension on the ill-posed character of the inverse problem. A detailed error analysis of the CLD allows for a predictive description of a posteriori constraints in the POCS framework. We discuss the application of this method to the characterization of simulated test cases and experimentally obtained data. [source]

Intermediate Preferences and Behavioral Conformity in Large Games

JOURNAL OF PUBLIC ECONOMIC THEORY, Issue 1 2009
GUILHERME CARMONA
Motivated by Wooders, Cartwright, and Selten (2006), we consider games with a continuum of players and intermediate preferences. We show that any such game has a Nash equilibrium that induces a partition of the set of attributes into a bounded number of convex sets with the following property: all players with an attribute in the interior of the same element of the partition play the same action. We then use this result to show that all sufficiently large, equicontinuous games with intermediate preferences have an approximate equilibrium with the same property. Our result on behavior conformity for large finite game generalizes Theorem 3 of Wooders et al. (2006) by allowing both a wider class of preferences and a more general attribute space. [source]

Image-based EPI ghost correction using an algorithm based on projection onto convex sets (POCS)

MAGNETIC RESONANCE IN MEDICINE, Issue 4 2002
K.J. Lee
Abstract This work describes the use of a method, based on the projection onto convex sets (POCS) algorithm, for reduction of the N/2 ghost in echo-planar imaging (EPI). In this method, ghosts outside the parent image are set to zero and a model k -space is obtained from the Fourier transform (FT) of the resulting image. The zeroth- and first-order phase corrections for each line of the original k -space are estimated by comparison with the corresponding line in the model k -space. To overcome problems of phase wrapping, the first-order phase corrections for the lines of the original k -space are estimated by registration with the corresponding lines in the model k -space. It is shown that applying these corrections will result in a reduction of the ghost, and that iterating the process will result in a convergence towards an image in which the ghost is minimized. The method is tested on spin-echo EPI data. The results show that the method is robust and remarkably effective, reducing the N/2 ghost to a level nearly comparable to that achieved with reference scans. Magn Reson Med 47:812,817, 2002. © 2002 Wiley-Liss, Inc. [source]

Phase-field systems for multi-dimensional Prandtl,Ishlinskii operators with non-polyhedral characteristics

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2002
Jürgen Sprekels
Abstract Hysteresis operators have recently proved to be a powerful tool in modelling phase transition phenomena which are accompanied by the occurrence of hysteresis effects. In a series of papers, the present authors have proposed phase-field models in which hysteresis non-linearities occur at several places. A very important class of hysteresis operators studied in this connection is formed by the so-called Prandtl,Ishlinskii operators. For these operators, the corresponding phase-field systems are in the multi-dimensional case only known to admit unique solutions if the characteristic convex sets defining the operators are polyhedrons. In this paper, we use approximation techniques to extend the known results to multi-dimensional Prandtl,Ishlinskii operators having non-polyhedral convex characteristicsets. Copyright © 2002 John Wiley & Sons, Ltd. [source]

On the boundedness of some potential-type operators with oscillating kernels

MATHEMATISCHE NACHRICHTEN, Issue 5 2005
Denis N. Karasev
Abstract We consider a class of multidimensional potential-type operators with kernels that have singularities at the origin and on the unit sphere and that are oscillating at infinity. We describe some convex sets in the (1/p, 1/q)-plane for which these operators are bounded from Lp into Lq and indicate domains where they are not bounded. We also reveal some effects which show that oscillation and singularities of the kernels may strongly influence on the picture of boundedness of the operators under consideration. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]