Time-periodic perturbation of a Liénard equation with an unbounded homoclinic loop

We consider a quadratic Liénard equation with an unbounded homoclinic loop, which is a solution tending in forward and backward time to a non-hyperbolic equilibrium point located at infinity. Under small time-periodic perturbation, this equilibrium becomes a normally hyperbolic line of singularities at infinity. We show that the perturbed system may present homoclinic bifurcations, leading to the existence of transverse intersections between the stable and unstable manifolds of such a normally hyperbolic line of singularities. The global study concerning the infinity is performed using the Poincaré compactification in polar coordinates, from which we obtain a system defined on a set equivalent to a solid torus in R³, whose boundary plays the role of the infinity. The transversality of the manifolds is proved using the Melnikov method and implies, via the Birkhoff-Smale Theorem, a complex dynamical behaviour of the perturbed system solutions in the finite part of the phase space. Numerical simulations are performed in order to illustrate this behaviour, which could be called “the chaos arising from infinity”, since it depends on the global structure of the Liénard equation, including the points at infinity. Although applied to a particular case, the analysis presented provides a geometrical approach to study periodic perturbations of homoclinic (or heteroclinic) loops to infinity of any planar polynomial vector field.     

Nonlinear perturbations of a ‐Laplacian equation with critical growth in

We prove the existence of solution for a class of ‐Laplacian equations where the nonlinearity has a critical growth. Here, we consider two cases: the first case involves the situation where the variable exponents are periodic functions. The second one involves the case where the variable exponents are nonperiodic perturbations.     

Stabilization of mixture of two rigid solids modeling temperature and porosity

In this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a mixture of two rigid solids modeling temperature and porosity. Our main result is to establish conditions which ensure the analyticity and the exponential stability of the corresponding semigroup.     

Kneading Theory: A Functorial Approach

We study the homology theory of ? - modal maps of the interval. We give another proof of the Milnor and Thurston results about zeta-functions and we give a functorial approach to kneading theory. Our results give explicit methods for computing the sequences of lap numbers ? (f ^k ) and the sequences of numbers of periodic points in an arbitrary interval [x,y]. Received: 25 February 1998 / Accepted: 15 January 1999     

Thermal and structural characterization of SrTi1-xNdxO3

Sr(Ti,Nd)O₃ was synthesized in order to evaluate the influence of the amount of neodymium on the thermal and structural properties of SrTiO₃. The synthesis was carried out using the polymeric precursor method. A small mass gain was observed for the SrTiO₃ and SrTi_0.98Nd_0.02O₃ samples accompanied by an exothermic peak in the DTA curves. Other steps at higher temperatures are assigned to the combustion of the organic material and carbonate. Elimination of defects by previous calcination of the precursors is responsible by the short and long range ordering of the perovskite. Cubic phase was obtained for undoped and doped SrTiO₃.     

Development and validation of a fast isocratic liquid chromatography method for the simultaneous determination of norfloxacin,lomefloxacin and ciprofloxacin in human plasma

A simple and fast liquid chromatographic method coupled with fluorescence detection (LC‐FD) is reported, for the first time, for the simultaneous quantification of norfloxacin (NOR), ciprofloxacin (CIP) and lomefloxacin (LOM) in human plasma, using levofloxacin as internal standard (IS). Sample preparation consists of a single‐step precipitation of plasma proteins followed by vortex‐mixing and centrifugation. Chromatographic separation was achieved within 7 min on a reversed‐phase C₁₈ column with a mobile phase consisting of 0.1% aqueous formic acid (pH = 3.0, triethylamine)–methanol (82:18, v/v) pumped isocratically at 1.2 mL/min. The detector was set at excitation/emission wavelengths of 278/450 nm. Calibration curves were linear (r² ≥ 0.994) in the range of 0.02–5.0 µg/mL, and the limit of quantification was established at 0.02 µg/mL for all analytes (NOR, CIP and LOM). The overall precision did not exceed 8.19% and accuracy was within ±10.91%. NOR, CIP and LOM were extracted from human plasma with an overall mean recovery ranged from 90.1 to 111.5%. No interferences were observed at the retention times of the analytes and IS. This novel LC‐FD method enables the reliable determination of NOR, CIP and LOM in a single chromatographic run, which may be suitable to support human pharmacokinetic‐based studies with those antimicrobial agents. Copyright © 2010 John Wiley & Sons, Ltd.     

Recent Emission Channeling Studies in Wide Band Gap Semiconductors

We present results of recent emission channeling experiments on the lattice location of implanted Fe and rare earths in wurtzite GaN and ZnO. In both cases the majority of implanted atoms are found on substitutional cation sites. The root mean square displacements from the ideal substitutional Ga and Zn sites are given and the stability of the Fe and rare earth lattice location against thermal annealing is discussed.