133 research outputs found
Zero-nonzero and real-nonreal sign determination
We consider first the zero–nonzero determination problem, which consists in determining the list of zero–nonzero conditions realized by a finite list of polynomials on a finite set Z⊂Ck with C an algebraic closed field. We describe an algorithm to solve the zero–nonzero determination problem and we perform its bit complexity analysis. This algorithm, which is in many ways an adaptation of the methods used to solve the more classical sign determination problem, presents also new ideas which can be used to improve sign determination. Then, we consider the real–nonreal sign determination problem, which deals with both the sign determination and the zero–nonzero determination problem. We describe an algorithm to solve the real–nonreal sign determination problem, we perform its bit complexity analysis and we discuss this problem in a parametric context.Fil: Perrucci, Daniel Roberto. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Oficina de Coordinacion Administrativa Ciudad Universitaria; ArgentinaFil: Roy, Marie Françoise. Universite de Rennes I. Institut de Recherche Mathematique de Rennes; Franci
The Controllability of Planar Bilinear Systems
endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. NOTE: At the time of publication, the author Daniel Koditschek was affiliated with Yale University. Currently, he is a faculty member of the School of Engineering at the University of Pennsylvania. This paper is posted at ScholarlyCommons
Limit distributions for large P\'{o}lya urns
We consider a two-color P\'{o}lya urn in the case when a fixed number of
balls is added at each step. Assume it is a large urn that is, the second
eigenvalue of the replacement matrix satisfies . After
drawings, the composition vector has asymptotically a first deterministic term
of order and a second random term of order . The object of
interest is the limit distribution of this random term. The method consists in
embedding the discrete-time urn in continuous time, getting a two-type
branching process. The dislocation equations associated with this process lead
to a system of two differential equations satisfied by the Fourier transforms
of the limit distributions. The resolution is carried out and it turns out that
the Fourier transforms are explicitly related to Abelian integrals over the
Fermat curve of degree . The limit laws appear to constitute a new family of
probability densities supported by the whole real line.Comment: Published in at http://dx.doi.org/10.1214/10-AAP696 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The Square Root Function of a Matrix
Having origins in the increasingly popular Matrix Theory, the square root function of a matrix has received notable attention in recent years. In this thesis, we discuss some of the more common matrix functions and their general properties, but we specifically explore the square root function of a matrix and the most efficient method (Schur decomposition) of computing it. Calculating the square root of a 2Ă—2 matrix by the Cayley-Hamilton Theorem is highlighted, along with square roots of positive semidefinite matrices and general square roots using the Jordan Canonical Form
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