On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences

In this work we consider the dynamic consequences of the existence of infinite heteroclinic cycle in planar polynomial vector fields, which is a trajectory connecting two saddle points at infinity. It is stated that, although the saddles which form the cycle belong to infinity, for certain types of nonautonomous perturbations the perturbed system may present a complex dynamic behavior of the solutions in a finite part of the phase plane, due to the existence of tangencies and transversal intersections of their stable and unstable manifolds. This phenomenon might be called the chaos arising from infinity. The global study at infinity is made via the Poincare Compactification and the argument used to prove the statement is the Birkhoff-Smale Theorem. (c) 2004 WILEY-NCH Verlag GmbH & Co. KGaA, Weinheim.

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

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

The Noether theorem for geometric actions and area preserving diffeomorphisms on the torus

We find that within the formalism of coadjoint orbits of the infinite dimensional Lie group the Noether procedure leads, for a special class of transformations, to the constant of motion given by the fundamental group one-cocycle S. Use is made of the simplified formula giving the symplectic action in terms of S and the Maurer-Cartan one-form. The area preserving diffeomorphisms on the torus T2=S1⊗S1 constitute an algebra with central extension, given by the Floratos-Iliopoulos cocycle. We apply our general treatment based on the symplectic analysis of coadjoint orbits of Lie groups to write the symplectic action for this model and study its invariance. We find an interesting abelian symmetry structure of this non-linear problem.

Fermionic analysis of Davey-Stewartson dromions

Dromion solutions of the Davey-Stewartson equation are analysed from the point of view of the bilinear formalism. The corresponding τ-functions are expressed in terms of vacuum expectation values of Clifford operators and their group-theoretical content is provided. Explicit computation performed with the help of Wick's theorem allows us to characterize the dromion interaction. © 1990.

Neural network detection of grinding burn from acoustic emission

An artificial neural network (ANN) approach is proposed for the detection of workpiece `burn', the undesirable change in metallurgical properties of the material produced by overly aggressive or otherwise inappropriate grinding. The grinding acoustic emission (AE) signals for 52100 bearing steel were collected and digested to extract feature vectors that appear to be suitable for ANN processing. Two feature vectors are represented: one concerning band power, kurtosis and skew; and the other autoregressive (AR) coefficients. The result (burn or no-burn) of the signals was identified on the basis of hardness and profile tests after grinding. The trained neural network works remarkably well for burn detection. Other signal-processing approaches are also discussed, and among them the constant false-alarm rate (CFAR) power law and the mean-value deviance (MVD) prove useful.

On computing discriminants of subfields of ℚ (ζp r)

The conductor-discriminant formula, namely, the Hasse Theorem, states that if a number field K is fixed by a subgroup H of Gal(ℚ(ζn)/ℚ), the discriminant of K can be obtained from H by computing the product of the conductors of all characters defined modulo n which are associated to K. By calculating these conductors explicitly, we derive a formula to compute the discriminant of any subfield of ℚ(ζpr), where p is an odd rime and r is a positive integer. © 2002 Elsevier Science USA.

PI Stabilization of a Class of Time Delay Systems

In this paper we use the Hermite-Biehler theorem to establish results for the design of proportional plus integral (PI) controllers for a class of time delay systems. We extend results of the polynomial case to quasipolynomials using the property of interlacing in high frequencies of the class of time delay systems considered. A signature for the quasipolynomials in this class is derived and used in the proposed approach which yields the complete set of the stabilizing PI controllers.

Reversible Hamiltonian Liapunov center theorem

We study the existence of periodic solutions in the neighbourhood of symmetric (partially) elliptic equilibria in purely reversible Hamiltonian vector fields. These are Hamiltonian vector fields with an involutory reversing symmetry R. We contrast the cases where R acts symplectically and anti-symplectically. In case R acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point. In case R acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions.

PID stabilization of a class of time delay systems

In this paper we use the Hermite-Biehler theorem to establish results for the design of proportional plus integral plus derivative (PID) controllers concerning a class of time delay systems. Using the property of interlacing at high frequencies of the class of systems considered and linear programming we obtain the set of all stabilizing PID controllers. © 2005 IEEE.

A Bayesian approach to estimate the accuracy of in-house ELISA assay to measure rabies antibodies from compulsory vaccinated dogs and cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Lower-semicontinuity and optimization of convex functionals

The result that we treat in this article allows to the utilization of classic tools of convex analysis in the study of optimality conditions in the optimal control convex process for a Volterra-Stietjes linear integral equation in the Banach space G([a, b],X) of the regulated functions in [a, b], that is, the functions f : [a, 6] → X that have only descontinuity of first kind, in Dushnik (or interior) sense, and with an equality linear restriction. In this work we introduce a convex functional Lβf(x) of Nemytskii type, and we present conditions for its lower-semicontinuity. As consequence, Weierstrass Theorem garantees (under compacity conditions) the existence of solution to the problem min{Lβf(x)}. © 2009 Academic Publications.

Liouville's theorem and power series for quaternionic functions

In recent years quaternionic functions have been an intense and prosperous object of research, and important results were determined [1]-[6]. Some of these results are similar to well known cases in one complex variable, op. cit. [5], [6]. In this paper the hypercomplex expansion of a function in a power series as well as determination of a Liouville's type theorem have been investigated to the quaternionic functions. In this case, it is observed that the Liouville's type theorem is true for second order derivatives, which differs from its classical version. © 2011 Academic Publications, Ltd.

A comparison of performance indexes in DC-DC converters under different stabilizing state-dependent switching laws

This paper deals with the problem of establishing stabilizing state-dependent switching laws in DC-DC converters operating at continuous conduction mode (CCM) and comparing their performance indexes. Firstly, the nature of the problem is defined, that is, the study of switched affine systems, which may not share a common equilibrium point. The concept of stability is, therefore, broadened. Then, the central theorem is proposed, from which a family of switching laws can be derived, namely the minimum law and the hold state law. Some of these are proved to stabilize the basic DC-DC converters and then, their performances are compared to another law, from a previous work, by simulation, where a great reduction in overshoot is obtained. © 2011 IEEE.

Geometrical wave equation and the cauchy-like theorem for octonions

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyper-string with initial conditions similar to the one-dimensional case.

Detection of Paracoccidioides spp. in environmental aerosol samples

Taking into account that paracoccidioidomycosis infection occurs by inhalation of the asexual conidia produced by Paracoccidioides spp. in its saprobic phase, this work presents the collection of aerosol samples as an option for environmental detection of this pathogen, by positioning a cyclonic air sampler at the entrance of armadillo burrows. Methods included direct culture, extinction technique culture and Nested PCR of the rRNA coding sequence, comprising the ITS1-5.8S-ITS2 region. In addition, we evaluated one armadillo (Dasypus novemcinctus) as a positive control for the studied area. Although the pathogen could not be isolated by the culturing strategies, the aerosol sampling associated with molecular detection through Nested PCR proved the best method for discovering Paracoccidioides spp. in the environment. Most of the ITS sequences obtained in this investigation proved to be highly similar with the homologous sequences of Paracoccidioides lutzii from the GenBank database, suggesting that this Paracoccidioides species may not be exclusive to mid-western Brazil as proposed so far. © 2013 ISHAM.