Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

Application of Lyapunov's Direct Method to the Existence of Integral Manifolds of Impulsive Differential Equations

The present paper investigates the existence of integral manifolds for impulsive differential equations with variable perturbations. By means of piecewise continuous functions which are generalizations of the classical Lyapunov’s functions, sufficient conditions for the existence of integral manifolds of such equations are found.

Periodic nonlinear Fourier transform for fiber-optic communications, Part I:theory and numerical methods

In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.

A Loop-mediated Isothermal Amplification Method for Rapid Direct Detection and Differentiation of Non-pathogenic and Verocytotoxigenic Escherichia coli in Beef and Bovine Faeces

The aim of this study was to develop a multiplex loop-mediated isothermal amplification (LAMP) method capable of detecting Escherichia coli generally and verocytotoxigenic E. coli (VTEC) specifically in beef and bovine faeces. The LAMP assay developed was highly specific (100%) and able to distinguish between E. coli and VTEC based on the amplification of the phoA, and stx1 and/or stx2 genes, respectively. In the absence of an enrichment step, the limit of detection 50% (LOD50) of the LAMP assay was determined to be 2.83, 3.17 and 2.83-3.17 log CFU/g for E. coli with phoA, stx1 and stx2 genes, respectively, when artificially inoculated minced beef and bovine faeces were tested. The LAMP calibration curves generated with pure cultures, and spiked beef and faeces, suggested that the assay had good quantification capability. Validation of the assay, performed using retail beef and bovine faeces samples, demonstrated good correlation between counts obtained by the LAMP assay and by a conventional culture method, but suggested the possibility of false negative LAMP results for 12.5-14.7% of samples tested. The multiplex LAMP assay developed potentially represents a rapid alternative to culture for monitoring E.coli levels in beef or faeces and it would provide additional information on the presence of VTEC. However, some further optimisation is needed to improve detection sensitivity.

Fast And Direct Na And K Determination In Table, Marine, And Low-sodium Salts By X-ray Fluorescence And Chemometrics.

X-ray fluorescence (XRF) is a fast, low-cost, nondestructive, and truly multielement analytical technique. The objectives of this study are to quantify the amount of Na(+) and K(+) in samples of table salt (refined, marine, and light) and to compare three different methodologies of quantification using XRF. A fundamental parameter method revealed difficulties in quantifying accurately lighter elements (Z < 22). A univariate methodology based on peak area calibration is an attractive alternative, even though additional steps of data manipulation might consume some time. Quantifications were performed with good correlations for both Na (r = 0.974) and K (r = 0.992). A partial least-squares (PLS) regression method with five latent variables was very fast. Na(+) quantifications provided calibration errors lower than 16% and a correlation of 0.995. Of great concern was the observation of high Na(+) levels in low-sodium salts. The presented application may be performed in a fast and multielement fashion, in accordance with Green Chemistry specifications.

In vitro evaluation of an alternative method to bond molar tubes

Despite the advances in bonding materials, many clinicians today still prefer to place bands on molar teeth. Molar bonding procedures need improvement to be widely accepted clinically. OBJECTIVE: The purpose of this study was to evaluate the shear bond strength when an additional adhesive layer was applied on the occlusal tooth/tube interface to provide reinforcement to molar tubes. MATERIAL AND METHODS: Sixty third molars were selected and allocated to the 3 groups: group 1 received a conventional direct bond followed by the application of an additional layer of adhesive on the occlusal tooth/tube interface, group 2 received a conventional direct bond, and group 3 received a conventional direct bond and an additional cure time of 10 s. The specimens were debonded in a universal testing machine. The results were analyzed statistically by ANOVA and Tukey's test (α=0.05). RESULTS: Group 1 had a significantly higher (p<0.05) shear bond strength compared to groups 2 and 3. No difference was detected between groups 2 and 3 (p>0.05). CONCLUSIONS: The present in vitro findings indicate that the application of an additional layer of adhesive on the tooth/tube interface increased the shear bond strength of the bonded molar tubes.

Development and validation of a simple and rapid capillary zone electrophoresis method for determination of nnrti nevirapine in pharmaceutical formulations

A simple and fast capillary zone electrophoresis (CZE) method has been developed and validated for quantification of a non-nucleoside reverse transcriptase inhibitor (NNRTI) nevirapine, in pharmaceuticals. The analysis was optimized using 10 mmol L-1 sodium phosphate buffer pH 2.5, +25 kV applied voltage, hydrodynamic injection 0.5 psi for 5 s and direct UV detection at 200 µm. Diazepam (50.0 µg mL-1) was used as internal standard. Under these conditions, nevirapine was analyzed in approximately less than 2.5 min. The analytical curve presented a coefficient of correlation of 0.9994. Limits of detection and quantification were 1.4 µg mL-1 and 4.3 µg mL-1, respectively. Intra- and inter-day precision expressed as relative standard deviations were 1.4% and 1.3%, respectively and the mean recovery was 100.81%. The active pharmaceutical ingredient was subjected to hydrolysis (acid, basic and neutral) and oxidative stress conditions. No interference of degradation products and tablet excipients were observed. This method showed to be rapid, simple, precise, accurate and economical for determination of nevirapine in pharmaceuticals and it is suitable for routine quality control analysis since CE offers benefits in terms of quicker method development and significantly reduced operating costs.

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

Method for cadmium and lead longitudinal profiles determination in hair by solid sampling graphite furnace atomic absorption spectrometry

This paper describes methods for the direct determination of Cd and Pb in hair segments (c.a. 5 mm similar to 80 mu g) by solid sampling graphite furnace atomic absorption spectrometry, becoming possible longitudinal profiles in a single strand of hair. To distinguish endogenous and exogenous content. strands of hair were washed by using two different procedures: IAEA protocol (acetone + water + acetone) and the combination of IAEA protocol with HCl washing (acetone + water + acetone + 0.1 mol l(-1) HCl). The concentration of Cd and Pb increased from the root Until the tip of hair washed according to IAEA protocol. However, when the strand of hair was washed using the combination of IAEA protocol and 0.1 mol l(-1) HCl, Cd concentrations decreased in all segments, and Pb concentrations decreased drastically near to the root (5 to 12 mm) and was systematically higher ill the end. The proposed method showed to be useful to assess the temporal variation to Cd and Pb exposure and call be Used for toxicological and environmental investigations. The limits of detection were 2.8 ng g(-1) for Cd and 40 ng g(-1) for Pb. The characteristic masses based oil integrated absorbance were 2.4 pg for Cd and 22 pg for Pb.

Consolidation of elastic-plastic saturated porous media by the boundary element method

This paper presents a domain boundary element formulation for inelastic saturated porous media with rate-independent behavior for the solid skeleton. The formulation is then applied to elastic-plastic behavior for the solid. Biot`s consolidation theory, extended to include irreversible phenomena is considered and the direct boundary element technique is used for the numerical solution after time discretization by the implicit Euler backward algorithm. The associated nonlinear algebraic problem is solved by the Newton-Raphson procedure whereby the loading/unloading conditions are fully taken into account and the consistent tangent operator defined. Only domain nodes (nodes defined inside the domain) are used to represent all domain values and the corresponding integrals are computed by using an accurate sub-elementation scheme. The developments are illustrated through the Drucker-Prager elastic-plastic model for the solid skeleton and various examples are analyzed with the proposed algorithms. (c) 2008 Elsevier B.V. All rights reserved.

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Methods of Fourier optics in digital holographic microscopy

In this paper, processing methods of Fourier optics implemented in a digital holographic microscopy system are presented. The proposed methodology is based on the possibility of the digital holography in carrying out the whole reconstruction of the recorded wave front and consequently, the determination of the phase and intensity distribution in any arbitrary plane located between the object and the recording plane. In this way, in digital holographic microscopy the field produced by the objective lens can be reconstructed along its propagation, allowing the reconstruction of the back focal plane of the lens, so that the complex amplitudes of the Fraunhofer diffraction, or equivalently the Fourier transform, of the light distribution across the object can be known. The manipulation of Fourier transform plane makes possible the design of digital methods of optical processing and image analysis. The proposed method has a great practical utility and represents a powerful tool in image analysis and data processing. The theoretical aspects of the method are presented, and its validity has been demonstrated using computer generated holograms and images simulations of microscopic objects. (c) 2007 Elsevier B.V. All rights reserved.

Direct Detection of Mycobacterium bovis in Bovine Lymph Nodes by PCR

P>Thirty-five lymph node samples were taken from animals with macroscopic lesions consistent with Mycobacterium bovis infection. The animals were identified by postmortem examination in an abattoir in the northwestern region of state of Parana, Brazil. Twenty-two of the animals had previously been found to be tuberculin skin test positive. Tissue samples were decontaminated by Petroff`s method and processed for acid-fast bacilli staining, culture in Stonebrink and Lowenstein-Jensen media and DNA extraction. Lymph node DNA samples were amplified by PCR in the absence and presence (inhibitor controls) of DNA extracted from M. bovis culture. Mycobacterium bovis was identified in 14 (42.4%) lymph node samples by both PCR and by culture. The frequency of PCR-positive results (54.5%) was similar to that of culture-positive results (51.5%, P > 0.05). The percentage of PCR-positive lymph nodes increased from 39.4% (13/33) to 54.5% (18/33) when samples that were initially PCR-negative were reanalysed using 2.5 mu l DNA (two samples) and 1 : 2 diluted DNA (three samples). PCR sensitivity was affected by inhibitors and by the amount of DNA in the clinical samples. Our results indicate that direct detection of M. bovis in lymph nodes by PCR may be a fast and useful tool for bovine tuberculosis epidemic management in the region.

Development and validation of a method for quantitative determination of econazole nitrate in cream formulation by capillary zone electrophoresis

A simple, fast, inexpensive and reliable capillary zone electrophoresis (CZE) method for the determination of econazole nitrate in cream formulations has been developed and validated. Optimum conditions comprised a pH 2.5 phosphate buffer at 20 mmol L(-1) concentration, +30 kV applied voltage in a 31.5 cm x 50 mu m I.D. capillary. Direct UV detection at 200 nm led to an adequate sensitivity without interference from sample excipients. A single extraction step of the cream sample in hydrochloric acid was performed prior to injection. Imidazole (100 mu g mL(-1)) was used as internal standard. Econazole nitrate migrates in approximately 1.2 min. The analytical curve presented a coefficient of correlation of 0.9995. Detection and quantitation limits were 1.85 and 5.62 mu g mL(-1), respectively. Excellent accuracy and precision were obtained. Recoveries varied from 98.1 to 102.5% and intra- and inter-day precisions, calculated as relative standard deviation (RSD), were better than 2.0%. The proposed CZE method presented advantageous performance characteristics and it can be considered suitable for the quality control of econazole nitrate cream formulations. (c) 2008 Elsevier B.V. All rights reserved.