An extension of the invariance principle for dwell-time switched nonlinear systems

In this paper, we propose an extension of the invariance principle for nonlinear switched systems under dwell-time switched solutions. This extension allows the derivative of an auxiliary function V, also called a Lyapunov-like function, along the solutions of the switched system to be positive on some sets. The results of this paper are useful to estimate attractors of nonlinear switched systems and corresponding basins of attraction. Uniform estimates of attractors and basin of attractions with respect to time-invariant uncertain parameters are also obtained. Results for a common Lyapunov-like function and multiple Lyapunov-like functions are given. Illustrative examples show the potential of the theoretical results in providing information on the asymptotic behavior of nonlinear dynamical switched systems. (C) 2012 Elsevier B.V. All rights reserved.

Nonlinear (magnetic) correction to the field of a static charge in an external field

We find the first nonlinear correction to the field produced by a static charge at rest in a background constant magnetic field. It is quadratic in the charge and purely magnetic. The third-rank polarization tensor-the nonlinear response function-is written within the local approximation of the effective action in an otherwise model-and approximation-independent way within any P-invariant nonlinear electrodynamics, QED included. DOI: 10.1103/PhysRevD.86.125028

Estimation and diagnostics for heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions

An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. This novel class of models provides a useful generalization of the heteroscedastic symmetrical nonlinear regression models (Cysneiros et al., 2010), since the random term distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as skew-t, skew-slash, skew-contaminated normal, among others. A simple EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters is presented and the observed information matrix is derived analytically. In order to examine the performance of the proposed methods, some simulation studies are presented to show the robust aspect of this flexible class against outlying and influential observations and that the maximum likelihood estimates based on the EM-type algorithm do provide good asymptotic properties. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. Finally, an illustration of the methodology is given considering a data set previously analyzed under the homoscedastic skew-t nonlinear regression model. (C) 2012 Elsevier B.V. All rights reserved.

Error Upper Bounds for a Computational Method for Nonlinear Boundary and Initial-Value Problems

This work develops a computational approach for boundary and initial-value problems by using operational matrices, in order to run an evolutive process in a Hilbert space. Besides, upper bounds for errors in the solutions and in their derivatives can be estimated providing accuracy measures.

Delay nonlinear boundary conditions as limit of reactions concentrating in the boundary

In this work, we are interested in the dynamic behavior of a parabolic problem with nonlinear boundary conditions and delay in the boundary. We construct a reaction-diffusion problem with delay in the interior, where the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter epsilon goes to zero. We analyze the limit of the solutions of this concentrated problem and prove that these solutions converge in certain continuous function spaces to the unique solution of the parabolic problem with delay in the boundary. This convergence result allows us to approximate the solution of equations with delay acting on the boundary by solutions of equations with delay acting in the interior and it may contribute to analyze the dynamic behavior of delay equations when the delay is at the boundary. (C) 2012 Elsevier Inc. All rights reserved.

Simultaneous determination of dextromethorphan, dextrorphan and doxylamine in human plasma by HPLC coupled to electrospray ionization tandem mass spectrometry: Application to a pharmacokinetic study

In the present study, a fast, sensitive and robust method to quantify dextromethorphan, dextrorphan and doxylamine in human plasma using deuterated internal standards (IS) is described. The analytes and the IS were extracted from plasma by a liquid-liquid extraction (LLE) using diethyl-ether/hexane (80/20, v/v). Extracted samples were analyzed by high performance liquid chromatography coupled to electrospray ionization tandem mass spectrometry (HPLC-ESI-MS/MS). Chromatographic separation was performed by pumping the mobile phase (acetonitrile/water/formic acid (90/9/1, v/v/v) during 4.0 min at a flow-rate of 1.5 mL min(-1) into a Phenomenex Gemini (R) C18, 5 mu m analytical column (150 x 4.6 mm id.). The calibration curve was linear over the range from 0.2 to 200 ng mL(-1) for dextromethorphan and doxylamine and 0.05 to 10 ng mL(-1) for dextrorphan. The intra-batch precision and accuracy (%CV) of the method ranged from 2.5 to 9.5%, and 88.9 to 105.1%, respectively. Method inter-batch precision (%CV) and accuracy ranged from 6.7 to 10.3%, and 92.2 to 107.1%, respectively. The run-time was for 4 min. The analytical procedure herein described was used to assess the pharmacokinetics of dextromethorphan, dextrorphan and doxylamine in healthy volunteers after a single oral dose of a formulation containing 30 mg of dextromethorphan hydrobromide and 12.5 mg of doxylamine succinate. The method has high sensitivity, specificity and allows high throughput analysis required for a pharmacokinetic study. (C) 2012 Elsevier B.V. All rights reserved.

Dynamical analysis of turbulence in fusion plasmas and nonlinear waves

Turbulence is one of the key problems of classical physics, and it has been the object of intense research in the last decades in a large spectrum of problems involving fluids, plasmas, and waves. In order to review some advances in theoretical and experimental investigations on turbulence a mini-symposium on this subject was organized in the Dynamics Days South America 2010 Conference. The main goal of this mini-symposium was to present recent developments in both fundamental aspects and dynamical analysis of turbulence in nonlinear waves and fusion plasmas. In this paper we present a summary of the works presented at this mini-symposium. Among the questions to be addressed were the onset and control of turbulence and spatio-temporal chaos. (C) 2011 Elsevier B. V. All rights reserved.

Assessment of variance components in nonlinear mixed-effects elliptical models

The issue of assessing variance components is essential in deciding on the inclusion of random effects in the context of mixed models. In this work we discuss this problem by supposing nonlinear elliptical models for correlated data by using the score-type test proposed in Silvapulle and Silvapulle (1995). Being asymptotically equivalent to the likelihood ratio test and only requiring the estimation under the null hypothesis, this test provides a fairly easy computable alternative for assessing one-sided hypotheses in the context of the marginal model. Taking into account the possible non-normal distribution, we assume that the joint distribution of the response variable and the random effects lies in the elliptical class, which includes light-tailed and heavy-tailed distributions such as Student-t, power exponential, logistic, generalized Student-t, generalized logistic, contaminated normal, and the normal itself, among others. We compare the sensitivity of the score-type test under normal, Student-t and power exponential models for the kinetics data set discussed in Vonesh and Carter (1992) and fitted using the model presented in Russo et al. (2009). Also, a simulation study is performed to analyze the consequences of the kurtosis misspecification.

Bartlett corrections in Birnbaum-Saunders nonlinear regression models

Lemonte and Cordeiro [Birnbaum-Saunders nonlinear regression models, Comput. Stat. Data Anal. 53 (2009), pp. 4441-4452] introduced a class of Birnbaum-Saunders (BS) nonlinear regression models potentially useful in lifetime data analysis. We give a general matrix Bartlett correction formula to improve the likelihood ratio (LR) tests in these models. The formula is simple enough to be used analytically to obtain several closed-form expressions in special cases. Our results generalize those in Lemonte et al. [Improved likelihood inference in Birnbaum-Saunders regressions, Comput. Stat. DataAnal. 54 (2010), pp. 1307-1316], which hold only for the BS linear regression models. We consider Monte Carlo simulations to show that the corrected tests work better than the usual LR tests.

Phase-Locked loops lock-in range in Frequency Modulated-Atomic Force Microscope nonlinear control system

Since the mid 1980s the Atomic Force Microscope is one the most powerful tools to perform surface investigation, and since 1995 Non-Contact AFM achieved true atomic resolution. The Frequency-Modulated Atomic Force Microscope (FM-AFM) operates in the dynamic mode, which means that the control system of the FM-AFM must force the micro-cantilever to oscillate with constant amplitude and frequency. However, tip-sample interaction forces cause modulations in the microcantilever motion. A Phase-Locked loop (PLL) is used to demodulate the tip-sample interaction forces from the microcantilever motion. The demodulated signal is used as the feedback signal to the control system, and to generate both topographic and dissipation images. As a consequence, a proper design of the PLL is vital to the FM-AFM performance. In this work, using bifurcation analysis, the lock-in range of the PLL is determined as a function of the frequency shift (Q) of the microcantilever and of the other design parameters, providing a technique to properly design the PLL in the FM-AFM system. (C) 2011 Elsevier B.V. All rights reserved.

Femtosecond third-order nonlinear spectra of lead-germanium oxide glasses containing silver nanoparticles

This work reports on the spectral dependence of both nonlinear refraction and absorption in lead-germanium oxide glasses (PbO-GeO2) containing silver nanoparticles. We have found that this material is suitable for all-optical switching at telecom wavelengths but at the visible range it behaves either as a saturable absorber or as an optical limiter. (C) 2012 Optical Society of America

Enhancement of the Nonlinear Optical Absorption of the E7 Liquid Crystal at the Nematic-Isotropic Transition

We present an experimental study of the nonlinear optical absorption of the eutectic mixture E7 at the nematic-isotropic phase transition by the Z-scan technique, under continuous-wave excitation at 532 nm. In the nematic region, the effective nonlinear optical coefficient beta, which vanishes in the isotropic phase, is negative for the extraordinary beam and positive for an ordinary beam. The parameter , whose definition in terms of the nonlinear absorption coefficient follows the definition of the optical-order parameter in terms of the linear dichroic ratio, behaves like an order parameter with critical exponent 0.22 +/- 0.05, in good agreement with the tricritical hypothesis for the nematic-isotropic transition.

Development of Nanoinjector Devices for Electrospray Ionization - Tandem Mass Spectrometry (ESI-MSn)

In mass spectrometric (MS) systems with electrospray ionization (ESI), the sample can be analyzed coupled to separation systems (such as liquid chromatography or capillary electrophoresis) or simply by direct infusion. The greatest benefit of the type of injection is the possibility of continuous use of small amounts of samples over a long period of time. This extended analysis time allows a complete study of fragmentation by mass spectrometry, which is critical for structure elucidation of new compounds, or when using an ion trap mass analyzer. The injector filled with the sample is placed at the ESI source inlet creating an electric field suitable for the continuous formation of a spray (solvent and sample) and consequently, the gradual and even release of the sample. For the formation of the spray, is necessary that the injector end is metalized. The formation of a bilayer of titanium and gold provided an excellent attachment of the film, resulting in a nanoinjector for ionization/spray formation in the system for MS. The nanoinjectors showed high repeatability and stability over 100 min by continuous sampling with 10 mu L of sample.

Electrospray Ionization Mass Spectrometry Fingerprinting of Extracts of the Leaves of Arrabidaea chica

Arrabidaea chica (crajiru) is an important Amazonian plant. Its extracts are used as red pigments, antimicrobial agents and astringents. Three different varieties of this species are cultivated in the Amazon region. In this work, direct infusions of A. chica extracts from these three varieties were analyzed via electrospray ionization mass spectrometry (ESI(+)-MS) fingerprinting. Derived data from the spectra were classified by using a multivariate method (PLS-DA, partial least squares-discriminant analysis). The direct method that is herein presented relies on extraction of dry, powdered leaves with acidified methanol/water solution with no further sample preparation. The resulting supernatants were analyzed by direct infusion ESI(+)-MS, which provides characteristic fingerprints of the sample composition. 3-Deoxyanthocyanidins are important substances in A. chica, their ions were used as markers in the PLS-DA data treatment. PLS-DA was able to differentiate the three varieties. ESI(+)-MS fingerprinting works as a simple and fast method to differentiate varieties of A. chica.

A nonlinear elliptic problem with terms concentrating in the boundary

In this paper, we investigate the behavior of a family of steady-state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a e-neighborhood of a portion G of the boundary. We assume that this e-neighborhood shrinks to G as the small parameter e goes to zero. Also, we suppose the upper boundary of this e-strip presents a highly oscillatory behavior. Our main goal here was to show that this family of solutions converges to the solutions of a limit problem, a nonlinear elliptic equation that captures the oscillatory behavior. Indeed, the reaction term and concentrating potential are transformed into a flux condition and a potential on G, which depends on the oscillating neighborhood. Copyright (C) 2012 John Wiley & Sons, Ltd.