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.

On the periodic solutions of a class of duffing differential equations

In this work we study the periodic solutions, their stability and bifurcation for the class of Duffing differential equation mathematical equation represented where C > 0, ε > 0 and Λ are real parameter, A(t), b(t) and h(t) are continuous T periodic functions and ε is sufficiently small. Our results are proved using the averaging method of first order.

Tilings induced by a class of cubic Rauzy fractals

We study aperiodic and periodic tilings induced by the Rauzy fractal and its subtiles associated with beta-substitutions related to the polynomial x3-ax2-bx-1 for a≥b≥1. In particular, we compute the corresponding boundary graphs, describing the adjacencies in the tilings. These graphs are a valuable tool for more advanced studies of the topological properties of the Rauzy fractals. As an example, we show that the Rauzy fractals are not homeomorphic to a closed disc as soon as a≤2b-4. The methods presented in this paper may be used to obtain similar results for other classes of substitutions.© 2012 Elsevier B.V. All rights reserved.

Effective synchronization of a class of chua's chaotic systems using an exponential feedback coupling

A robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory. Computer simulations are given to illustrate and verify the method. © 2013 Patrick Louodop et al.

Simultaneous linearization of a class of pairs of involutions with normally hyperbolic composition

In this paper we obtain a result on simultaneous linearization for a class of pairs of involutions whose composition is normally hyperbolic. This extends the corresponding result when the composition of the involutions is a hyperbolic germ of diffeomorphism. Inside the class of pairs with normally hyperbolic composition, we obtain a characterization theorem for the composition to be hyperbolic. In addition, related to the class of interest, we present the classification of pairs of linear involutions via linear conjugacy. © 2012 Elsevier Masson SAS.

Existence of solutions for a class of degenerate quasilinear elliptic equation in R-N with vanishing potentials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On Global Attractors for a Class of Parabolic Problems

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

Positive Solution for a Class of Degenerate Quasilinear Elliptic Equations in R-N

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On a class of abstract neutral functional differential equations

By using the theory of semigroups of growth α, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered.

On the Limit Cycles for a Class of Continuous Piecewise Linear Differential Systems with Three Zones

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

A class of cubic Rauzy fractals

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the zeros of a class of generalized hypergeometric polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Solvability in the large for a class of complex vector fields on the cylinder

This work deals with global solvability of a class of complex vector fields of the form L = partial derivative/partial derivative t + (a(x, t)+ ib(x, t))partial derivative/partial derivative x, where a and b are real-valued C-infinity functions, defined on the cylinder Omega = R x S-1. Relatively compact (Sussmann) orbits are allowed. The connection with Malgrange's notion of L-convexity for supports is investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.