Slow-fast systems on algebraic varieties bordering piecewise-smooth dynamical systems

This article extends results contained in Buzzi et al. (2006) [4], Llibre et al. (2007, 2008) [12,13] concerning the dynamics of non-smooth systems. In those papers a piecewise C-k discontinuous vector field Z on R-n is considered when the discontinuities are concentrated on a codimension one submanifold. In this paper our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets. In order to do this we first consider F :U -> R a polynomial function defined on the open subset U subset of R-n. The set F-1 (0) divides U into subdomains U-1, U-2,...,U-k, with border F-1(0). These subdomains provide a Whitney stratification on U. We consider Z(i) :U-i -> R-n smooth vector fields and we get Z = (Z(1),...., Z(k)) a discontinuous vector field with discontinuities in F-1(0). Our approach combines several techniques such as epsilon-regularization process, blowing-up method and singular perturbation theory. Recall that an approximation of a discontinuous vector field Z by a one parameter family of continuous vector fields is called an epsilon-regularization of Z (see Sotomayor and Teixeira, 1996 [18]; Llibre and Teixeira, 1997 [15]). Systems as discussed in this paper turn out to be relevant for problems in control theory (Minorsky, 1969 [16]), in systems with hysteresis (Seidman, 2006 [17]) and in mechanical systems with impacts (di Bernardo et al., 2008 [5]). (C) 2011 Elsevier Masson SAS. All rights reserved.

On the first nu(6) anti-aligned librating asteroid family of Tina

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Molecular and crystal structure of trans-(dicyanato)-bis(triphenylphosphine)palladium(II)

The triphenylphosphine (PPh3) displaces the acetonitrile from [PdCl2(CH3CN)2], and subsequent addition of the potassium cyanate causes substitution of the chloro ligand by NCO- to yield trans-[Pd(NCO)2(PPh3)2]. The complex was characterized by elemental analysis, IR spectroscopy and single-crystal X-ray diffraction. The title compound was crystallized in a triclinic system, space group P1 with a = 9.213(3)Å, b = 9.781(7)Å, c = 10.483(5)Å, α = 111.39(5)°, β = 93.49(3)°, γ = 103.81(4)°, V = 845.0(1)Å3, Z = 1. The coordination geometry around Pd(II) in this complex is nearly square-planar, with the ligands in a trans relationship. 2008 © The Japan Society for Analytical Chemistry.

A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1,1). We also give the associated Gaussian type quadrature formulas. © 2012 IMACS.

Orthogonal polynomials on the unit circle and chain sequences

Szego{double acute} has shown that real orthogonal polynomials on the unit circle can be mapped to orthogonal polynomials on the interval [-1,1] by the transformation 2x=z+z-1. In the 80's and 90's Delsarte and Genin showed that real orthogonal polynomials on the unit circle can be mapped to symmetric orthogonal polynomials on the interval [-1,1] using the transformation 2x=z1/2+z-1/2. We extend the results of Delsarte and Genin to all orthogonal polynomials on the unit circle. The transformation maps to functions on [-1,1] that can be seen as extensions of symmetric orthogonal polynomials on [-1,1] satisfying a three-term recurrence formula with real coefficients {cn} and {dn}, where {dn} is also a positive chain sequence. Via the results established, we obtain a characterization for a point w(|w|=1) to be a pure point of the measure involved. We also give a characterization for orthogonal polynomials on the unit circle in terms of the two sequences {cn} and {dn}. © 2013 Elsevier Inc.

Limitantes para os zeros de polinômios gerados por uma relação de recorrência de três termos

Pós-graduação em Matemática - IBILCE

Estudo de sistemas lineares por parte com três zonas e aplicação na análise de um circuito elétrico envolvendo um memristor

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Caracterização venosa central em crianças internadas em Unidades de Terapia Intensiva pediátrica

Pós-graduação em Pediatria - FMB

Search for narrow resonances and quantum black holes in inclusive and b-tagged dijet mass spectra from pp collisions at root s=7 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Favard type theorem for orthogonal polynomials on the unit circle from a three term recurrence formula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Palindromic and perturbed polynomials: zeros location

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Geometric singular perturbartion theory for non-smooth dynamical systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

CYCLIC CODES THROUGH B[X], B[X; 1/kp Z(0)] and B[X; 1/p(k) Z(0)]: A COMPARISON

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Constructions of codes through the semigroup ring B[X; 1/2(2)Z(0)] and encoding

For any finite commutative ring B with an identity there is a strict inclusion B[X; Z(0)] subset of B[X; Z(0)] subset of B[X; 1/2(2)Z(0)] of commutative semigroup rings. This work is a continuation of Shah et al. (2011) [8], in which we extend the study of Andrade and Palazzo (2005) [7] for cyclic codes through the semigroup ring B[X; 1/2; Z(0)] In this study we developed a construction technique of cyclic codes through a semigroup ring B[X; 1/2(2)Z(0)] instead of a polynomial ring. However in the second phase we independently considered BCH, alternant, Goppa, Srivastava codes through a semigroup ring B[X; 1/2(2)Z(0)]. Hence we improved several results of Shah et al. (2011) [8] and Andrade and Palazzo (2005) [7] in a broader sense. Published by Elsevier Ltd

Search for particles decaying into a Z boson and a photon in p(p)over-bar collisions at root s=1.96 TeV

We present the results of a search for a new particle X produced in p (p) over bar collisions at root s- = 1.96 TeV and subsequently decaying to Z gamma. The search uses 0.3 fb(-1) of data collected with the DO detector at the Fermilab Tevatron Collider. We set limits on the production cross section times the branching fraction sigma(p (p) over bar -> X) x B(X -> Z gamma) that range from 0.4 to 3.5 pb at the 95% C.L. for X with invariant masses between 100 and 1000 GeV/c(2), over a wide range of X decay widths. (c) 2006 Elsevier B.V. All rights reserved.