New algorithm for optimal parameter estimation with linear constraints

This paper presents a new algorithm for optimal parameter estimation problems with linear constraints. The algorithm developed is based on least absolute-value approximations. The problem is solved first using a least-error-square technique, where we add to the cost function the equality constraints via Lagrange multipliers, to obtain a good estimate for the residuals of the measurements, having gained this information, we choose a number of measurements with the smallest residuals. This number equals the number of parameters to be estimated minus the number of constraints. Using these measurements together with the constraints, we obtain a number of observations equal to the number of parameters to be estimated. By using this technique, we show that there is no need to either iterate or use linear programming to obtain the estimation.This work was supported by the Natural Sciences and Engineering Research Council of Canada, Grant A4146.     

A search-and-track algorithm for controlling the number of guided modes of planar optical waveguides with arbitrary refractive index profiles

A search-and-track algorithm is proposed for controlling the number of guided modes of planar optical waveguides with arbitrary refractive index profiles. The algorithm starts with an initial guess point in the parameter space that supports a specific number of guided modes. Then, it searches for, and tracks, the boundaries of this space or another space supporting different number of modes. It does so by monitoring the sign of a unified cutoff dispersion function. The algorithm is applied to both symmetric and asymmetric silicon-based parabolic-index waveguides. It shows that unlike asymmetric waveguides, the single-mode condition of symmetric waveguides is controlled by TM-, as opposed to TE-, polarization. This abnormal polarization control is strongest for high index contrast waveguides of sub-micrometer core sizes. The results are verified by full-vectorial beam propagation method.     

Electrochemical study of zolpidem at glassy carbon electrode and its determination in a tablet dosage form by differential pulse voltammetry

The oxidative behaviour of, a hypnotic drug, zolpidem was studied at glassy carbon electrode in Britton-Robinson buffer over the pH range 2.0-11.0 using cyclic, linear sweep and differential pulse voltammetry. Oxidation of the drug was effected in a single irreversible, diffusion-controlled step. Using differential pulse voltammetry (DPV), the drug yielded a well-defined voltammetric response in Britton-Robinson buffer, pH 8.0 at +0.889 V (vs. Ag/AgCl) on glassy carbon electrode. This process could be used to determine zolpidem concentrations in the range 5.0 x 10(-7) M to 1.0 x 10(-5) M with a detection limit of 2.0 x 10(-7) M. The method was applied, without any interference from the excipients, to the determination of the drug in a tablet dosage form.     

Kinetic study of the complex reaction between copper(II) and 2-(2′-hydroxy-3′-methoxyphenyl)benzothiazole

2-(2′-Hydroxy-3′-methoxyphenyl)benzothiazole reacts with copper(II) in an ethanol/water mixture to form an O,S chelate which exhibits the remarkable property of changing the chelation site above a pH of ca. 5.0, to the O,N site. The detailed kinetics of this reaction in an ethanol/water mixture (3:1) at a temperature of 25 °C was investigated using a stopped-flow spectrophotometric technique employing a wavelength of 400 nm. The initial complex, Cu(O,S), is formed via a fast, reversible second-order complex formation step whereupon the formation of the Cu (O,N) follows first order kinetics. The Cu(O,N) complex is, however, unstable towards internal electron exchange and after the reaction is complete, a black polymeric material very slowly precipitates out of solution. Rate and equilibrium constants for the postulated reactions are presented and discussed.     

Conformational stability, r 0 structural parameters, barriers to internal rotation, ab initio calculations, and vibrational assignment for 2,2-difluoroethanol

The infrared spectra (4,000–30 cm^?1) of the gas and solid and the Raman spectrum of liquid 2,2-difluoroethanol as well as variable temperature infrared spectra of krypton/xenon solutions have been recorded. From all these data, two (Gg and Tg) out of the five possible stable conformers have been confidently identified. The order of the stabilities has been predicted to be Gg > Tg > Gt > Gg′ > Tt by utilizing ab initio MP2 (full) and DFT (B3LYP method) calculations, where the first indicator (capital letter) is in reference to rotation around the C–C bond (G = gauche or T = trans) and the second one (small letter) refers to the orientation of the hydroxyl group. The percentage of the minor conformer Tg, at ambient temperature, is estimated to be (16 ± 3%). The optimized geometries, fundamental frequencies, infrared intensities, Raman activities, and depolarization values as well as centrifugal distortion constants have been obtained from ab initio and density functional theory calculations by utilizing a variety of basis sets as well as those with diffuse functions. By utilizing the previously reported microwave rotational constants for two isotopomers of the Gg conformer combined with ab initio MP2(full)/6-311+G(d,p) predicted structural values, adjusted r ₀ parameters have been obtained. The determined heavy atom distances (Å) for the Gg conformer are: C₁–C₂ = 1.510(3), C₂–F₄ = 1.371(3), C₂–F₅ = 1.362(3), C₁–O₃ = 1.412(3) Å and angles ∠O₃C₁C₂ = 111.0(5), ∠F₄C₂C₁ = 108.8(5), ∠F₅C₂C₁ = 109.8(5), τF₄C₂C₁O₃ = 63.5(5), τF₅C₂C₁O₃ = 179.1(5)°. Barriers of internal rotation have been obtained and vibrational assignments for the Gg and Tg conformers are given. The five predicted centrifugal distortion constants compared to the experimental values are in reasonable agreement except for ?_K, which appears to be in error. The results are discussed and the structural parameters compared to the corresponding ones for 2-fluoroethanol and 2,2,2-trifluoroethanol where those for the latter molecule have been redetermined. The currently determined heavy atom parameters are quite different from the earlier assumed values, which led to poor values of the six adjusted parameters.     

An Efficient Synthesis of <Emphasis Type="Italic">O</Emphasis>-Methyl Protected Emodin Aldehyde and Emodin Nitrile

Summary. An efficient synthesis of tri-O-methylemodin aldehyde was achieved via bromination of tri-O-methylemodin utilizing N-bromosuccinimide yielding the monobromo and dibromo derivatives. Sommelet reaction of the monobromomethyl derivative as well as hydrolysis of the dibromomethyl analog with aqueous silver nitrate afforded the protected aldehyde in good yield. Accordingly, both bromo derivatives can be used even when they are obtained as a mixture of the bromination reaction, which could not be controlled easily to yield the bromo products selectively. From the aldehyde the tri-O-methylemodin nitrile was prepared in a one-pot reaction using hydroxylamine-O-sulfonic acid.Received February 18, 2003; accepted March 3, 2003 Published online June 2, 2003     

A Convenient Regiospecific Synthesis of New Conjugated Tetrazole Derivatives via the Reaction of Dienones with the Tetrachlorosilane-Sodium Azide Reagent and their NMR Structural Assignment

Summary. Several new 1-aryl-, aralkyl-, and heteroaryl-5-(4-phenylbuta-1,3-dienyl)tetrazole derivatives and annulated tetrazole derivatives were efficiently and regiospecifically prepared in nearly quantitative yield via a facile one step reaction of dienones with a combination of tetrachlorosilane and sodium azide in acetonitrile under mild conditions. A complete structure assignment of three representative examples of the tetrazoles was achieved by advanced 2D NMR measurements including COSY, TOCSY, HSQC, HMBC, NOESY, and ROESY experiments.Received March 17, 2003; accepted March 18, 2003 Published online July 28, 2003     

Poly(vinyl alcohol)-Graft-Poly(ethylene glycol)-Supported Hydroxyproline Catalysis of Stereoselective Aldol Reactions

Summary: The good swelling and high loading of poly(vinyl alcohol)-graft-poly(ethylene glycol) (PVA-g-PEG) resins proved to be effective for performing supported proline-catalyzed aldol reactions stereoselectively in a wide range of polar non-protic, protic and non-polar solvents as well as in neat substrate. The catalysts could be recovered by filtration and recycled, without significant loss of activity. The use of poly(vinyl alcohol)-graft-poly(ethylene glycol) matrix improved the solubility of the proline-derived catalysts and expanded the scope of permissible solvents for performing selective aldol chemistry.     

Gradient HPLC-DAD stability indicating determination of miconazole nitrate and lidocaine hydrochloride in their combined oral gel dosage form

The pharmaceutical combination of miconazole nitrate (MZ) and lidocaine hydrochloride (LD) is used in the curative and prophylactic therapy of the oral and gastro-intestinal infections caused by Candida albicans. To the best of our knowledge, no attempts have yet been made to assay this combination by any analytical method. A simple and selective high-performance liquid chromatography-diode array detection (HPLC-DAD) stability-indicating method was developed for the simultaneous determination of MZ and LD in their combined formulation. Effective chromatographic separation was achieved using a Zorbax SB-C8 column with gradient elution of the mobile phase composed of 0.05 M phosphoric acid and acetonitrile. The gradient elution started with 25% (by volume) acetonitrile, ramped up linearly to 65% in 6 min, then kept constant until the end of the run. The mobile phase was pumped at a flow rate of 1 mL/min. The multiple wavelength detector was set at 215 nm and analytes were quantified by measuring their peak areas. The retention times for LD and MZ were approximately 4.1 and 8.4 min, respectively. The reliability and analytical performance of the proposed HPLC procedure were statistically validated with respect to linearity, ranges, precision, accuracy, selectivity, robustness, detection and quantification limits. Calibration curves were linear in the ranges of 5-100 μg/ml for both drugs with correlation coefficients > 0.999. Both drugs were subjected to stress conditions of hydrolysis, oxidation, photolysis and thermal degradation. The proposed method proved to be stability-indicating by the resolution of the two analytes from the related substance and potential impurity (2,6-dimethylaniline) and from the forced-degradation products. The validated HPLC method was applied to the analysis of MZ and LD in the combined oral gel preparation, in which the two analytes were successfully quantified and resolved from the pharmaceutical additives. The proposed method made use of DAD as a tool for peak identity and purity confirmation.