A new technique to generate independent periodic attractors in the state space of nonlinear dynamic systems

This paper proposes a method to generate several independent periodic attractors, in continuous-time nonchaotic systems (with an equilibrium point or a limit cycle), based on a switching piecewise-constant controller. We demonstrate here that the state space equidistant repartition of these attractors is on a precise zone of a precise curve that depends on the parameters of the system. We determine the state space domains where the attractors are generated from different initial conditions. A mathematical formula giving their maximal number in function of the controller piecewise-constant values is then deduced. Throughout this study, the proposed methodology is illustrated with several examples.     

Existence, localization and multiplicity results for positive radial solutions of semilinear elliptic systems

Existence, localization and multiplicity results of positive solutions to a system of singular second-order differential equations are established by means of the vector version of Krasnoselskii's cone fixed point theorem. The results are then applied for positive radial solutions to semilinear elliptic systems.     

Low power cross-flow atmospheric pressure Ar + He plasma jet : Spectroscopic diagnostic and excitation capabilities

A cross-flow atmospheric plasma jet with distilled water or analyte solution nebulization has been investigated. The plasma gas flows perpendicularly to the RF powered electrode (11.21 MHz) and a grounded electrode was added for plasma stabilization. The working parameters of the plasma generator can be controlled in order to maximize either the plasma power (75 W) or the voltage on the RF powered electrode (plasma power, 40 W). The plasma gas, pure argon (0.4 l min⁻¹) or a mixture of argon (0.3–0.4 l min⁻¹) and helium (0–0.2 l min⁻¹), was also used for liquid nebulization. Optical emission of the plasma, collected in the normal viewing mode, was used for plasma diagnostics and for evaluating its excitation capabilities. The influence of helium content in the mixed-gas plasma on the plasma characteristics and on the emission axial profiles of the plasma gas constituents and of the analytes originate from the wet aerosol was studied. The addition of helium to the argon plasma, generally determines decreases in the emission of the plasma gas constituents (with the exception of molecular nitrogen), in the rotational temperature and in the electron number density and increases in the excitation temperatures and in the emission of easily excitable analytes. Based on the determined electron number densities, it was concluded that in the plasma zone which presents interest from analytical point of view the plasma is not very far from the partial thermodynamic equilibrium. In function of the helium content in the plasma gas and of the axial distance from the powered electrode the excitation temperatures are in the range of 2420–3340 K for argon, 2500–5450 K for oxygen and 900–2610 K for ionic calcium and the electron number densities are in the range of 1.2 10¹²–1.25 10¹³ cm⁻³. Some elements with excitation energy lower than 6 eV were excited in the plasma. The plasma excitation capability depends on the working conditions of the plasma generator (maximum power or maximum voltage on the RF powered electrode) and on the helium content in the mixed-gas plasma. The estimated detection limits for the studied elements (Na, Li, K, Ca, Cu, Ag, Cd, Hg and Zn) are in the range of 7 ng ml⁻¹ to 28 μg ml⁻¹.     

A Generalization of the Hutchinson Measure

The Hutchinson measure is the invariant measure associated with an iterated function system with probabilities. Generalized iterated function systems (GIFS) are generalizations of iterated function systems which are obtained by considering contractions from X × X to X, rather than contractions from a metric space X to itself. Along the lines of this generalization we consider GIFS with probabilities. In this paper we prove the existence of an analogue of Hutchinson measure associated with a GIFS with probabilities and present some of its properties. The work was supported by CNCSIS grant 8A;1067/2006.     

A Γ-convergence result for Néel walls in micromagnetics

Three reduced models are considered for Néel walls which are dominant transition layers in thin-film micromagnetics. Each model comes as a nonlocal and nonconvex variational principle for one-dimensional magnetizations and it depends on a small parameter ε > 0. Our aim is to study the Γ-convergence of these models as eˉ 0{\varepsilon \downarrow 0} . We prove that the limiting magnetization patterns are piecewise constant functions that correspond to a finite number of walls of the same angle. The Γ-limit energy is proportional to the number of walls of these configurations and the energetic cost of each wall is quartic for small wall angles.     

Painless Reconstruction from Magnitudes of Frame Coefficients

The goal of this paper is to develop fast algorithms for signal reconstruction from magnitudes of frame coefficients. This problem is important to several areas of research in signal processing, especially speech recognition technology, as well as state tomography in quantum theory. We present linear reconstruction algorithms for tight frames associated with projective 2-designs in finite-dimensional real or complex Hilbert spaces. Examples of such frames are two-uniform frames and mutually unbiased bases, which include discrete chirps. The number of operations required for reconstruction with these frames grows at most as the cubic power of the dimension of the Hilbert space. Moreover, we present a very efficient algorithm which gives reconstruction on the order of d operations for a d-dimensional Hilbert space.     

Self-assembling diblock copolymers of poly[N-(2-hydroxypropyl)methacrylamide] and a beta-sheet peptide

The self-assembly of hybrid diblock copolymers composed of poly(HPMA) and beta-sheet peptide P11 (CH(3)CO-QQRFQWQFEQQ-NH(2)) blocks was investigated. Copolymers were synthesized via thiol-maleimide coupling reaction, by conjugation of semitelechelic poly(HPMA)-SH with maleimide-modified beta-sheet peptide. As expected, CD and CR binding studies showed that the peptide block imposed its beta-sheet structural arrangement on the structure of diblock copolymers. TEM and AFM proved that peptide and these copolymers had the ability to self-assemble into fibrils.     

A new Fenchel dual problem in vector optimization

We introduce a new Fenchel dual for vector optimization problems inspired by the form of the Fenchel dual attached to the scalarized primal multiobjective problem. For the vector primal-dual pair we prove weak and strong duality. Furthermore, we recall two other Fenchel-type dual problems introduced in the past in the literature, in the vector case, and make a comparison among all three duals. Moreover, we show that their sets of maximal elements are equal.     

A two-component polymeric optode membrane based on a multifunctional ionic liquid

This work details the use of a 2-component optode membrane which is capable of generating three distinct colours in the presence of Cu(2+) and Co(2+) ions. It has been found that the ionic liquid (IL) trihexyltetradecylphosphonium dicyanamide [P(6,6,6,14)][DCA] can act as plasticizer, ligand and transducer dye when used in poly(vinyl chloride) (PVC) membranes, which significantly simplifies the optode membrane cocktail. Upon exposure to an aqueous Cu(2+) solution, a yellow colour is generated within the membrane, while exposure to an aqueous Co(2+) solution generates a blue colour. Exposure to a solution containing both ions produces a green colour. Vibrational spectroscopy has been used to investigate the molecular basis of the IL-metal ion the binding mechanism. Analytical characteristics of the membranes including the effect of interfering ions, binding constants and the limit of detection for both ions have been estimated. Finally the case of simultaneous dual-analyte recognition is presented based on two distinct absorption maxima.     

Global Jacobian and Γ-convergence in a two-dimensional Ginzburg-Landau model for boundary vortices

In the theory of 2D Ginzburg-Landau vortices, the Jacobian plays a crucial role for the detection of topological singularities. We introduce a related distributional quantity, called the global Jacobian that can detect both interior and boundary vortices for a 2D map u. We point out several features of the global Jacobian, in particular, we prove an important stability property. This property allows us to study boundary vortices in a 2D Ginzburg-Landau model arising in thin ferromagnetic films, where a weak anchoring boundary energy penalising the normal component of u at the boundary competes with the usual bulk potential energy. We prove an asymptotic expansion by Γ-convergence at the second order for this mixed boundary/interior energy in a regime where boundary vortices are preferred. More precisely, at the first order of the limiting expansion, the energy is quantised and determined by the number of boundary vortices detected by the global Jacobian, while the second order term in the limiting energy expansion accounts for the interaction between the boundary vortices.