A numerical solution of a two-dimensional IHCP

In this paper, we will first study the existence and uniqueness of the solution of a two-dimensional inverse heat conduction problem (IHCP) which is severely ill-posed, i.e., the solution does not depend continuously on the data. We propose a stable numerical approach based on the finite-difference method and the least-squares scheme to solve this problem in the presence of noisy data. We prove the convergence of the numerical solution, then to regularize the resultant ill-conditioned linear system of equations, we apply the Tikhonov regularization 0th, 1st and 2nd method to obtain the stable numerical approximation to the solution. The stability and accuracy of the scheme presented is evaluated by comparison with the Singular Value Decomposition (SVD) method.     

Stability-Indicating LC Method for Assay of Cholecalciferol

This paper discusses the development of a stability-indicating reversed-phase LC method for analysis of cholecalciferol as the bulk drug and in formulations. The mobile phase was acetonitrile–methanol–water 50:50:2 (v/v). The calibration plot for the drug was linear in the range 0.4–10 μg mL⁻¹. The method was accurate and precise with limits of detection and quantitation of 64 and 215 ng, respectively. Mean recovery was 100.71%. The method was used for analysis of cholecalciferol in pharmaceutical formulations in the presence of its degradation products and commonly used excipients.

     

Colorimetric Procedure for the Microdetermination of the Antibilharzial Drug Praziquantel and its Applications to Pharmaceutical Formulations

 A procedure for the colorimetric assay of praziquantel has been developed. The method is based on the formation of charge-transfer complexes with p-chloranil (I), dichloronitrophenol (II), 2,3-dichloro-5,6 dicyano-p-benzoquinone (III), 7,7,8,8-tetracyanoquinodimethane (IV) and tetracyanoethylene (V) as π-acceptors to give highly coloured species. The coloured products are measured spectrophotometrically at 550, 425, 460, 844 and 393 nm for I, II, III, IV and V, respectively. Optimization of the different reaction conditions is described. The colour system obeyed Beer’s law in non-aqueous media in the concentration range 2.0–48 μg ml⁻¹. It was stable for at least 4.0 h. The detection limit was found to be 0.6 μg ml⁻¹. Applications of the procedure to the analysis of various pharmaceutical samples gave reproducible and accurate results. Further, the validity of the procedure was confirmed by applying the standard addition technique. The total average recovery was 100.2%. Received June 10, 2000. Revision December 23, 2000.     

Mechanical response of proton beam irradiated nitinol

The present investigation deals with the study of mechanical behavior of proton beam irradiated nitinol at room temperature. The specimens in austenitic phase were irradiated over periods of 15, 30, 45 and 60 min at room temperature using 2 MeV proton beam obtained from Pelletron accelerator. The stress-strain curves of both unirradiated and irradiated specimens were obtained using a universal testing machine at room temperature. The results of the experiment show that an intermediate rhombohedral (R) phase has been introduced between austenite and martensite phase, which resulted in the suppression of direct transformation from austenite to martensite (A-M). Stresses required to start R-phase (σ_RS) and martensitic phase (σ_MS) were observed to decrease with increase in exposure time. The hardness tests of samples before and after irradiation were also carried out using Vickers hardness tester. The comparison reveals that the hardness is higher in irradiated specimens than that of the unirradiated one. The increase in hardness is quite sharp in specimens irradiated for 15 min, which then increases linearly as the exposure time is increased up to 60 min. The generation of R-phase, variations in the transformation stresses σ_RS and σ_MS and increase in hardness of irradiated nitinol may be attributed to lattice disorder and associated changes in crystal structure induced by proton beam irradiation.     

Von Neumann Regularity and Quadratic Conorms in JB^＊-triples and C^＊-algebras

We revise the notion of von Neumann regularity in JB^＊-triples by finding a new characterisation in terms of the range of the quadratic operator Q（a）. We introduce the quadratic conorm of an element a in a JB^＊-triple as the minimum reduced modulus of the mapping Q（a）. It is shown that the quadratic conorm of a coincides with the infimum of the squares of the points in the triple spectrum of a. It is established that a contractive bijection between JBW^＊-triples is a triple isomorphism if, and only if, it preserves quadratic conorms. The continuity of the quadratic conorm and the generalized inverse are discussed. Some applications to C^＊-algebras and von Neumann algebras are also studied.     

Effects of a small length scale on vibrations of an embedded double-walled carbon nanotube

Extensive continuum analyses are carried out to estimate the influence of matrix stiffness, a small length scale, and intertubular radial displacements on free vibrations of an individual double-walled carbon nanotybe. The analyses are based on both local and classical Euler–Bernoulli and Timoshenko elasticity theories with concentricity and nonconcentricity assumptions. The effect of a small length scale is incorporated in the formulations. New intertubular resonant frequencies are calculated based on these theories. Detailed results are demonstrated for the resonant frequencies as functions of matrix stiffness and the small length scale. The results indicate that the internal radial displacement and the stiffness of the surrounding matrix can greatly affect the resonant frequencies, especially at higher frequencies, and thus the latter does not keep the otherwise concentric structure at ultrahigh frequencies. More over, at high frequencies and small aspect ratios, the effect of the small length scale be comes more significant.     

Spatial-dependent probe transmission based high-precision two-dimensional atomic localization

Herein, we propose a scheme for the realization of two-dimensional atomic localization in aλ-type three-level atomic medium such that the atom interacts with the two orthogonal standing-wave fields and a probe field. Because of the spatially dependent atom-field interaction, the information about the position of the atom can be obtained by monitoring the probe transmission spectra of the weak probe field for the first time. A single and double sharp localized peaks are observed in the one-wavelength domain. We have theoretically archived high-resolution and high-precision atomic localization within a region smaller thanλ/25×λ/25. The results may have potential applications in the field of nano-lithography and advance laser cooling technology.     

Efficient two-dimensional atom localization in a five-level conductive chiral atomic medium via birefringence beam absorption spectrum

We have theoretically investigated two-dimensional atom localization using the absorption spectra of birefringence beams of light in a single wavelength domain.The atom localization is controlled and modified through tunneling effect in a conductive chiral atomic medium with absorption spectra of birefringent beams.The significant localization peaks are investigated in the left and right circularly polarized beam.Single and double localized peaks are observed in different quadrants with minimum uncertainty and significant probability.The localized probability is modified by controlling birefringence and tunneling conditions.These results may be useful for the capability of optical microscopy and atom imaging.     

Green and mild laccase-catalyzed aerobic oxidative coupling of benzenediol derivatives with various sodium benzenesulfinates

The oxidative coupling reaction between hydroquinone or catechols and various sodium benzenesulfinates was investigated using the laccase from Trametes versicolor, in the presence of O₂ in a phosphate buffer solution at room temperature to afford sulfonyl benzenediols in 75–95% yield.