A Refinement of some Overrelaxation Algorithms for Solving a System of Linear Equations

In this paper we propose a refinement of some successive overrelaxation methods based on the reverse Gauss–Seidel method for solving a system of linear equations Ax = b by the decomposition A = Tm − Em − Fm, where Tm is a banded matrix of bandwidth 2m + 1. We study the convergence of the methods and give software implementation of algorithms in Mathematica package with numerical examples. ACM Computing Classification System (1998): G.1.3.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Studies on integrating kinematic design method with mechanical systems simulation techniques

Theultimate goal of any research in the mechanism/kinematic/design area may be called predictive design, ie the optimisation of mechanism proportions in the design stage without requiring extensive life and wear testing. This is an ambitious goal and can be realised through development and refinement of numerical (computational) technology in order to facilitate the design analysis and optimisation of complex mechanisms, mechanical components and systems. As a part of the systematic design methodology this thesis concentrates on kinematic synthesis (kinematic design and analysis) methods in the mechanism synthesis process. The main task of kinematic design is to find all possible solutions in the form of structural parameters to accomplish the desired requirements of motion. Main formulations of kinematic design can be broadly divided to exact synthesis and approximate synthesis formulations. The exact synthesis formulation is based in solving n linear or nonlinear equations in n variables and the solutions for the problem areget by adopting closed form classical or modern algebraic solution methods or using numerical solution methods based on the polynomial continuation or homotopy. The approximate synthesis formulations is based on minimising the approximation error by direct optimisation The main drawbacks of exact synthesis formulationare: (ia) limitations of number of design specifications and (iia) failure in handling design constraints- especially inequality constraints. The main drawbacks of approximate synthesis formulations are: (ib) it is difficult to choose a proper initial linkage and (iib) it is hard to find more than one solution. Recentformulations in solving the approximate synthesis problem adopts polynomial continuation providing several solutions, but it can not handle inequality const-raints. Based on the practical design needs the mixed exact-approximate position synthesis with two exact and an unlimited number of approximate positions has also been developed. The solutions space is presented as a ground pivot map but thepole between the exact positions cannot be selected as a ground pivot. In this thesis the exact synthesis problem of planar mechanism is solved by generating all possible solutions for the optimisation process ¿ including solutions in positive dimensional solution sets - within inequality constraints of structural parameters. Through the literature research it is first shown that the algebraic and numerical solution methods ¿ used in the research area of computational kinematics ¿ are capable of solving non-parametric algebraic systems of n equations inn variables and cannot handle the singularities associated with positive-dimensional solution sets. In this thesis the problem of positive-dimensional solutionsets is solved adopting the main principles from mathematical research area of algebraic geometry in solving parametric ( in the mathematical sense that all parameter values are considered ¿ including the degenerate cases ¿ for which the system is solvable ) algebraic systems of n equations and at least n+1 variables.Adopting the developed solution method in solving the dyadic equations in direct polynomial form in two- to three-precision-points it has been algebraically proved and numerically demonstrated that the map of the ground pivots is ambiguousand that the singularities associated with positive-dimensional solution sets can be solved. The positive-dimensional solution sets associated with the poles might contain physically meaningful solutions in the form of optimal defectfree mechanisms. Traditionally the mechanism optimisation of hydraulically driven boommechanisms is done at early state of the design process. This will result in optimal component design rather than optimal system level design. Modern mechanismoptimisation at system level demands integration of kinematic design methods with mechanical system simulation techniques. In this thesis a new kinematic design method for hydraulically driven boom mechanism is developed and integrated in mechanical system simulation techniques. The developed kinematic design method is based on the combinations of two-precision-point formulation and on optimisation ( with mathematical programming techniques or adopting optimisation methods based on probability and statistics ) of substructures using calculated criteria from the system level response of multidegree-of-freedom mechanisms. Eg. by adopting the mixed exact-approximate position synthesis in direct optimisation (using mathematical programming techniques) with two exact positions and an unlimitednumber of approximate positions the drawbacks of (ia)-(iib) has been cancelled.The design principles of the developed method are based on the design-tree -approach of the mechanical systems and the design method ¿ in principle ¿ is capable of capturing the interrelationship between kinematic and dynamic synthesis simultaneously when the developed kinematic design method is integrated with the mechanical system simulation techniques.

The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems

Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented.

Determination of absolute coccolith abundances in deep-sea sediments by spiking with microbeads and spraying - SMS-method (Table 1)

A quick new method is described for the quantification of absolute nannofossil proportions in deep-sea sediments. This method (SMS) is the combination of Spiking a sample with Microbeads and Spraying it on a cover slide. It is suitable for scanning electron microscope (SEM) analyses and for light microscope (LM) analyses. Repeated preparation and counting of the same sample (30 times) revealed a standard deviation of 10.5%. The application of tracer microbeads with different diameters and densities revealed no statistically significant differences between counts. The SMS-method yielded coccolith numbers that are statistically not significantly different from values obtained from the filtration-method. However, coccolith counts obtained by the random settling method are three times higher than the values obtained by the SMS- and the filtration-method.

A short method with modern doubt. A centenary contribution. In three parts: 1. Jesus His own proof. II. The laws of nature. III. Correspondence with Spinoza.

Mode of access: Internet.

Solid-phase extraction method with high-performance liquid chromatography and electrochemical detection for the quantitative analysis of oxycodone in human plasma

A sensitive and reproducible solid-phase extraction (SPE) method for the quantification of oxycodone in human plasma was developed. Varian Certify SPE cartridges containing both C-8 and benzoic acid functional groups were the most suitable for the extraction of oxycodone and codeine (internal standard), with consistently high (greater than or equal to 80%) and reproducible recoveries. The elution mobile phase consisted of 1.2 ml of butyl chloride-isopropanol (80:20, v/v) containing 2% ammonia. The quantification limit for oxycodone was 5.3 pmol on-column. Within-day and inter-day coefficients of variation were 1.2% and 6.8% respectively for 284 nM oxycodone and 9.5% and 6.2% respectively for 28.4 nM oxycodone using 0.5-ml plasma aliquots. (C) 1998 Elsevier Science BN. All rights reserved.

A double-blind, randomized study comparing pure chromated glycerin with chromated glycerin with 1% lidocaine and epinephrine for sclerotherapy of telangiectasias and reticular veins.

BACKGROUND Chromated glycerin (CG) is an effective, although painful, sclerosing agent for telangiectasias and reticular leg veins treatment. OBJECTIVE To determine pain level and relative efficacy of pure or one-third lidocaine-epinephrine 1% mixed chromated glycerin in a prospective randomized double-blind trial. METHOD Patients presenting with telangiectasias and reticular leg veins on the lateral aspect of the thigh (C(1A) or (S) E(P) A(S) P(N1) ) were randomized to receive pure CG or CG mixed with one-third lidocaine-epinephrine 1% (CGX) treatment. Lower limb photographs were taken before and after treatment and analyzed by blinded expert reviewers for efficacy assessment (visual vein disappearance). Patients' pain and satisfaction were assessed using visual analogue scales. RESULTS Data from 102 of 110 randomized patients could be evaluated. Patient pain scores were significantly higher when pure CG was used than with CGX (p<.001). Patient satisfaction with treatment outcome was similar in the two groups. Objective visual assessment of vessel disappearance revealed no significant difference between the two agents (p=.07). CONCLUSION Addition of lidocaine-epinephrine 1% to CG, in a ratio of one-third, significantly reduces sclerotherapy pain without affecting efficacy when treating telangiectasias and reticular leg veins. The authors have indicated no significant interest with commercial supporters.

Drug susceptibility testing of Mycobacterium tuberculosis by the broth microdilution method with 7H9 broth

In this study, we have evaluated the broth microdilution method (BMM) for susceptibility testing of Mycobacterium tuberculosis. A total of 43 clinical isolates of M. tuberculosis and H37Rv as a control strain were studied. All isolates were tested by the proportion method and the BMM for isoniazid (INH), rifampicin (RIF), streptomycin (STR), and ethambutol (ETM). The proportion method was carried out according to the National Committee for Clinical Laboratory Standards (NCCLS) on Löwenstein-Jensen (LJ) medium. The BMM was carried out using 7H9 broth with 96 well-plates. All strains were tested at 3.2-0.05 µg/ml, 16-0.25 µg/ml, 32-0.5 µg/ml, and 32-0.5 µg/ml concentrations for INH, RIF, STR, and ETM, respectively. When the BMM was compared with the proportion method, sensitivity was 100, 100, 96.9, and 90.2%, while specificity was 100, 85.7, 90.9, and 100% for INH, RIF, STR, and ETM, respectively. The plates were examined 7, 10, 14, and 21 days after incubation. The majority of the result were obtained at 14th days after incubation, while the proportion method result were ended in 21-28 days. According to our results, it may be suggested that the BMM is suitable for early determining of multidrug-resistance-M. tuberculosis strains in developed or developing countries.

An operator formulation of the multiscale finite-volume method with correction function

The multiscale finite-volume (MSFV) method has been derived to efficiently solve large problems with spatially varying coefficients. The fine-scale problem is subdivided into local problems that can be solved separately and are coupled by a global problem. This algorithm, in consequence, shares some characteristics with two-level domain decomposition (DD) methods. However, the MSFV algorithm is different in that it incorporates a flux reconstruction step, which delivers a fine-scale mass conservative flux field without the need for iterating. This is achieved by the use of two overlapping coarse grids. The recently introduced correction function allows for a consistent handling of source terms, which makes the MSFV method a flexible algorithm that is applicable to a wide spectrum of problems. It is demonstrated that the MSFV operator, used to compute an approximate pressure solution, can be equivalently constructed by writing the Schur complement with a tangential approximation of a single-cell overlapping grid and incorporation of appropriate coarse-scale mass-balance equations.

A sensitive and robust lc-ms/ms method with monolithic column and electrospray ionization for the quantitation of efavirenz in human plasma: application to a bioequivalence study

An LC-MS/MS method has been developed for the determination of efavirenz (EFZ) in human plasma using hydrochlorothiazide as internal standard (I.S.). An ESI negative mode with multiple reaction-monitoring was used monitoring the transitions m/z 313.88→69.24 (EFZ) and 296.02→204.76 (I.S.). Samples were extracted using liquid-liquid extraction. The total run time was 2.0 min. The separation was achieved with HPLC-RP using a monolithic column. The assay was linear in the concentration range of 100 - 5000 ng mL-1. The mean recovery was 83%. Intra- and inter-day precision were < 9.5% and < 8.9%, respectively and accuracy was in the range ± 8.33%. The method was successfully applied to a bioequivalence study.

Partial spectral projected gradient method with active-set strategy for linearly constrained optimization

A method for linearly constrained optimization which modifies and generalizes recent box-constraint optimization algorithms is introduced. The new algorithm is based on a relaxed form of Spectral Projected Gradient iterations. Intercalated with these projected steps, internal iterations restricted to faces of the polytope are performed, which enhance the efficiency of the algorithm. Convergence proofs are given and numerical experiments are included and commented. Software supporting this paper is available through the Tango Project web page: http://www.ime.usp.br/similar to egbirgin/tango/.

Global minimization using an Augmented Lagrangian method with variable lower-level constraints

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the epsilon(k)-global minimization of the Augmented Lagrangian with simple constraints, where epsilon(k) -> epsilon. Global convergence to an epsilon-global minimizer of the original problem is proved. The subproblems are solved using the alpha BB method. Numerical experiments are presented.

Determination of sorbate and benzoate in beverage samples by capillary electrophoresis - Optimization of the method with inspection of ionic mobilities

The aim of this study was to develop a fast capillary electrophoresis method for the determination of benzoate and sorbate ions in commercial beverages. In the method development the pH and constituents of the background electrolyte were selected using the effective mobility versus pH curves. As the high resolution obtained experimentally for sorbate and benzoate in the studies presented in the literature is not in agreement with that expected from the ionic mobility values published, a procedure to determine these values was carried out. The salicylate ion was used as the internal standard. The background electrolyte was composed of 25 mmol L(-1) tris(hydroxymethyl)aminomethane and 12.5 mmol L(-1) 2-hydroxyisobutyric acid, atpH 8.1.Separation was conducted in a fused-silica capillary(32 cm total length and 8.5 cm effective length, 50 mu m I.D.), with short-end injection configuration and direct UV detection at 200 nm for benzoate and salicylate and 254 nm for sorbate ions. The run time was only 28 s. A few figures of merit of the proposed method include: good linearity (R(2) > 0.999), limit of detection of 0.9 and 0.3 mg L(-1) for benzoate and sorbate, respectively, inter-day precision better than 2.7% (n =9) and recovery in the range 97.9-105%. Beverage samples were prepared by simple dilution with deionized water (1:11, v/v). Concentrations in the range of 197-401 mg L(-1) for benzoate and 28-144 mg L(-1) for sorbate were found in soft drinks and tea. (c) 2008 Elsevier B.V. All rights reserved.

A new and improved strategy combining a dispersive-solid phase extraction-based multiclass method with ultra high pressure liquid chromatography for analysis of low molecular weight polyphenols in vegetables

This paper reports on the development and optimization of a modified Quick, Easy, Cheap Effective, Rugged and Safe (QuEChERS) based extraction technique coupled with a clean-up dispersive-solid phase extraction (dSPE) as a new, reliable and powerful strategy to enhance the extraction efficiency of free low molecular-weight polyphenols in selected species of dietary vegetables. The process involves two simple steps. First, the homogenized samples are extracted and partitioned using an organic solvent and salt solution. Then, the supernatant is further extracted and cleaned using a dSPE technique. Final clear extracts of vegetables were concentrated under vacuum to near dryness and taken up into initial mobile phase (0.1% formic acid and 20% methanol). The separation and quantification of free low molecular weight polyphenols from the vegetable extracts was achieved by ultrahigh pressure liquid chromatography (UHPLC) equipped with a phodiode array (PDA) detection system and a Trifunctional High Strength Silica capillary analytical column (HSS T3), specially designed for polar compounds. The performance of the method was assessed by studying the selectivity, linear dynamic range, the limit of detection (LOD) and limit of quantification (LOQ), precision, trueness, and matrix effects. The validation parameters of the method showed satisfactory figures of merit. Good linearity (View the MathML sourceRvalues2>0.954; (+)-catechin in carrot samples) was achieved at the studied concentration range. Reproducibility was better than 3%. Consistent recoveries of polyphenols ranging from 78.4 to 99.9% were observed when all target vegetable samples were spiked at two concentration levels, with relative standard deviations (RSDs, n = 5) lower than 2.9%. The LODs and the LOQs ranged from 0.005 μg mL−1 (trans-resveratrol, carrot) to 0.62 μg mL−1 (syringic acid, garlic) and from 0.016 μg mL−1 (trans-resveratrol, carrot) to 0.87 μg mL−1 ((+)-catechin, carrot) depending on the compound. The method was applied for studying the occurrence of free low molecular weight polyphenols in eight selected dietary vegetables (broccoli, tomato, carrot, garlic, onion, red pepper, green pepper and beetroot), providing a valuable and promising tool for food quality evaluation.