Optimal linearization trajectories for tangent linear models

We examine differential equations where nonlinearity is a result of the advection part of the total derivative or the use of quadratic algebraic constraints between state variables (such as the ideal gas law). We show that these types of nonlinearity can be accounted for in the tangent linear model by a suitable choice of the linearization trajectory. Using this optimal linearization trajectory, we show that the tangent linear model can be used to reproduce the exact nonlinear error growth of perturbations for more than 200 days in a quasi-geostrophic model and more than (the equivalent of) 150 days in the Lorenz 96 model. We introduce an iterative method, purely based on tangent linear integrations, that converges to this optimal linearization trajectory. The main conclusion from this article is that this iterative method can be used to account for nonlinearity in estimation problems without using the nonlinear model. We demonstrate this by performing forecast sensitivity experiments in the Lorenz 96 model and show that we are able to estimate analysis increments that improve the two-day forecast using only four backward integrations with the tangent linear model. Copyright © 2011 Royal Meteorological Society

Femtosecond pulse shaping using differential evolutionary algorithm and wavelet operators

Evolutionary meta-algorithms for pulse shaping of broadband femtosecond duration laser pulses are proposed. The genetic algorithm searching the evolutionary landscape for desired pulse shapes consists of a population of waveforms (genes), each made from two concatenated vectors, specifying phases and magnitudes, respectively, over a range of frequencies. Frequency domain operators such as mutation, two-point crossover average crossover, polynomial phase mutation, creep and three-point smoothing as well as a time-domain crossover are combined to produce fitter offsprings at each iteration step. The algorithm applies roulette wheel selection; elitists and linear fitness scaling to the gene population. A differential evolution (DE) operator that provides a source of directed mutation and new wavelet operators are proposed. Using properly tuned parameters for DE, the meta-algorithm is used to solve a waveform matching problem. Tuning allows either a greedy directed search near the best known solution or a robust search across the entire parameter space.

A high frequency boundary element method for scattering by a class of nonconvex obstacles

In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched with carefully chosen oscillatory basis functions; these are selected via a study of the high frequency asymptotic behaviour of the solution. We demonstrate via a rigorous error analysis, supported by numerical examples, that to achieve any desired accuracy it is sufficient for the number of degrees of freedom to grow only in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods. This appears to be the first such numerical analysis result for any problem of scattering by a nonconvex obstacle. Our analysis is based on new frequency-explicit bounds on the normal derivative of the solution on the boundary and on its analytic continuation into the complex plane.

Evaluation of positioning error-induced pixel shifts on satellite linear push-broom imagery

Georeferencing is one of the major tasks of satellite-borne remote sensing. Compared to traditional indirect methods, direct georeferencing through a Global Positioning System/inertial navigation system requires fewer and simpler steps to obtain exterior orientation parameters of remotely sensed images. However, the pixel shift caused by geographic positioning error, which is generally derived from boresight angle as well as terrain topography variation, can have a great impact on the precision of georeferencing. The distribution of pixel shifts introduced by the positioning error on a satellite linear push-broom image is quantitatively analyzed. We use the variation of the object space coordinate to simulate different kinds of positioning errors and terrain topography. Then a total differential method was applied to establish a rigorous sensor model in order to mathematically obtain the relationship between pixel shift and positioning error. Finally, two simulation experiments are conducted using the imaging parameters of Chang’ E-1 satellite to evaluate two different kinds of positioning errors. The experimental results have shown that with the experimental parameters, the maximum pixel shift could reach 1.74 pixels. The proposed approach can be extended to a generic application for imaging error modeling in remote sensing with terrain variation.

Permanence of stability for a class of system of differential equations with two delays

The paper studies a class of a system of linear retarded differential difference equations with several parameters. It presents some sufficient conditions under which no stability changes for an equilibrium point occurs. Application of these results is given. (c) 2007 Elsevier Ltd. All rights reserved.

Global solutions for impulsive abstract partial differential equations

In this paper, we study the existence of global solutions for a class of impulsive abstract functional differential equation. An application involving a parabolic system With impulses is considered. (c) 2008 Elsevier Ltd. All rights reserved.

A collocation method for solving singular integro-differential equations

This paper describes a collocation method for numerically solving Cauchy-type linear singular integro-differential equations. The numerical method is based on the transformation of the integro-differential equation into an integral equation, and then applying a collocation method to solve the latter. The collocation points are chosen as the Chebyshev nodes. Uniform convergence of the resulting method is then discussed. Numerical examples are presented and solved by the numerical techniques.

Large time behaviour for functional differential equations with dominant eigenvalues of arbitrary order

The spectral theory for linear autonomous neutral functional differential equations (FDE) yields explicit formulas for the large time behaviour of solutions. Our results are based on resolvent computations and Dunford calculus, applied to establish explicit formulas for the large time behaviour of solutions of FDE. We investigate in detail a class of two-dimensional systems of FDE. (C) 2009 Elsevier Inc. All rights reserved.

On the dominance of roots of characteristic equations for neutral functional differential equations

We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail. (C) 2009 Elsevier Inc. All rights reserved.

Prediction of the economic activity from the short and long-term interest rate differential: new evidences in Chile and the United States of America cases

The purpose of this work is to verify the stability of the relationship between real activity and interest rate spread. The test is based on Chen (1988) and Osorio and Galea (2006). The analysis is applied to Chile and the United States, from 1980 to 1999. In general, in both cases the relationship was statistically significant in early 80s, but a break point is found in both countries during that decades, suggesting that the relationship depends on the monetary rule follow by the Central Bank.

Simultaneous Differential Pulse Voltammetric Determination of Ascorbic Acid and Caffeine in Pharmaceutical Formulations Using a Boron-Doped Diamond Electrode

A cathodically pretreated boron-doped diamond electrode was used for the simultaneous anodic determination of ascorbic acid (AA) and caffeine (CAF) by differential pulse voltammetry Linear calibration curves (r = 0 999) were obtained from 1 9 x 10(-5) to 2 I x 10(-4) mol L(-1) for AA and from 9 7 x 10(-6) to 1 1 x 10-4 mol L(-1) for CAF. with detection limits of 19 wool L(-1) and 7 0 mu nol L(-1). respectively This method was successfully applied for the determination of AA and CAF in pharmaceutical formulations. with results equal to those obtained using a HPLC reference method

Differential pulse voltammetric determination of nitrite with gold ultramicroelectrode

The application of disk shaped gold ultramicroelectrode for nitrite determination with and without addition of supporting electrolyte was studied using the differential pulse voltammetric method. The well-defined peak for nitrite oxidation near 0.8V (vs. Ag/AgCl reference electrode) was used to obtain analytical plots in the concentration range from 0.1 to 0.6 mmol L-1 and from 10.0 to 50.0 mu mol.L-1. The calculated detection limit was 0.65 mu mol.L-1 in purified water, in the absence of supporting electrolyte, with relative standard deviation of 1.36% (n=6) for analyzing 10.0 mu mol L-1 nitrite solutions, and accuracy of 100.9 %, based on recovery studies. The application of this analytical method to mineral and river water samples of natural pH also showed improved sensitivity when compared with the linear sweep voltammetric method previously reported.

A solid paraffin-based carbon paste electrode modified with 2-aminothiazole organofunctionalized silica for differential pulse adsorptive stripping analysis of nickel in ethanol fuel

A solid paraffin-based carbon paste electrode modified with 2-aminothiazole organofunctionalized silica (SiAt-SPCPE) was applied to Ni2+ determination in commercial ethanol fuel samples. The proposed method comprised four steps: (1) Ni2+ preconcentration at open circuit potential directly in the ethanol fuel sample, (2) transference of the electrode to an electrochemical cell containing DMG, (3) differential pulse voltammogram registering and (4) surface regeneration by polishing the electrode. The proposed method combines the high Ni2+ adsorption capacity presented by 2-aminothiazole organofunctionalized silica with the electrochemical properties of the Ni(DMG)2 complex, whose electrochemical reduction provides the analytical signal.All experimental parameters involved in the proposed method were optimized. Using a preconcentration time of 20 min, it was obtained a linear range from 7.5 x 10(-9) to 1.0 x 10(-6) mol L-1 with detection limit of 2.0 x 10(-9) mol L-1. Recovery values between 96.5 and 102.4% were obtained for commercial samples spiked with 1.0 mu mol L-1 Ni2+ and the developed electrode was totally stable in ethanolic solutions. The contents of Ni2+ found in the commercial samples using the proposed method were compared to those obtained by graphite furnace atomic absorption spectroscopy by using the F- and t-test. Neither the F- nor t-values exceeded the critical values at 95% confidence level, confirming that there are not statistical differences between the results obtained by both methods. These results indicate that the developed electrode can be successfully employed to reliable Ni2+ determination in commercial ethanol fuel samples without any sample pretreatment or dilution step. (c) 2006 Elsevier B.V. All rights reserved.

Copper determination in ethanol fuel by differential pulse anodic stripping voltammetry at a solid paraffin-based carbon paste electrode modified with 2-aminothiazole organofunctionalized silica

Solid paraffin-based carbon paste electrodes modified with 2-aminothiazole organofunctionalized silica have been applied to the anodic stripping determination of copper ions in ethanol fuel samples without any sample treatment. The proposed method comprised four steps: (1) copper ions preconcentration at open circuit potential directly in the ethanol fuel sample; (2) exchange of the solution and immediate cathodic reduction of the absorbate at controlled potential; (3) differential pulse anodic stripping voltammetry; (4) electrochemical surface regeneration by applying a positive potential in acid media. Factors affecting the preconcentration, reduction and stripping steps were investigated and the optimum conditions were employed to develop the analytical procedure. Using a preconcentration time of 20 min and reduction time of 120 s at -0.3 V versus Ag/AgCl(sat) a linear range from 7.5 x 10(-8) to 2.5 x 10(-6) mol L(-1) with detection limit of 3.1 x 10(-8) mol L(-1) was obtained. Interference studies have shown a decrease in the interference effect according to the sequence: Ni > Zn > Cd > Pb > Fe. However, the interference effects of these ions have not forbidden the application of the proposed method. Recovery values between 98.8 and 102.3% were obtained for synthetic samples spiked with known amounts of Cu(2+) and interfering metallic ions. The developed electrode was successfully applied to the determination of Cu(2+) in commercial ethanol fuel samples. The results were compared to those obtained by flame atomic absorption spectroscopy by using the F-test and t-test. Neither F-value nor t-value have exceeded the critical values at 95% confidence level, confirming that there are no significant differences between the results obtained by both methods. (c) 2006 Elsevier B.V. All rights reserved.

Investigation of the H tau tau and Hbb coupling constants for a scalar (Pseudoscalar) higgs Boson at a future linear electron-positron collider

The possibility of setting constraints on the Couplings of a scalar (pseudoscalar) Higgs boson to the tau lepton and the b quark in the reactions e(+)e(-)-->v (v) over bar tau(+)tau(-) and e(+)e(-)-->v (v) over barb (b) over bar at a future linear electron-positron collider of total energy roots = 500 GeV is studied. The admixture of a new hypothetical pseudoscalar state of the Higgs boson in the Hf (f) over bar vertex is parametrized in the form (mf/v)(a+igamma(5)b). on the basis of an analysis of differential distributions for the processes under study, it is shown that data from the future linear collider TESLA will make it possible to constrain the parameters a and b as -0.32 less than or equal to Deltaa less than or equal to 0.24 and -0.73 less than or equal to b less than or equal to 0.73 in the case of the reaction e(+)e(-)-->v (v) over bar tau(+)tau(-) and as -0.026 less than or equal to Deltaa less than or equal to 0.027 and -0.23 less than or equal to b less than or equal to 0.23 in the case of the reaction e(+)e(-) --> v (v) over barb (b) over bar. It is emphasized that the contribution of the fusion Subprocess WW --> H in the channel involving an electron neutrino is of particular importance, since this contribution enhances the sensitivity of data to the parameters being analyzed. (C) 2004 MAIK Nauka/Inierperiodica.