Some inhomogeneous magnetized viscous-fluid cosmological models with varyingΛ

Some cylindrically symmetric inhomogeneous viscous-fluid cosmological models with electromagnetic field are obtained. To get a solution a supplementary condition between metric potentials is used. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density. Without assuming anyad hoc law, we obtain a cosmological constant as a decreasing function of time. The behaviour of the electromagnetic field tensor together with some physical aspects of the model are also discussed.     

Analysis of finite capacity discrete-time <Emphasis Type="Italic">GI</Emphasis>/<Emphasis Type="Italic">Geo</Emphasis>/1 queueing system with multiple vacations

This paper investigates a discrete-time single-server finite-buffer queueing system with multiple vacations in which arrivals occur according to a discrete-time renewal process. Service and vacation times are mutually independent and geometrically distributed. We obtain steady-state system length distributions at prearrival, arbitrary and outside observer's observation epochs under the late arrival system with delayed access and early arrival system. The analysis of actual waiting-time for both the systems has also been carried out. The model has potential application in high-speed computer network, digital communication systems and other related areas.     

Direct and inverse estimates for a new family of linear positive operators

In the present paper we introduce a new family of linear positive operators and study some direct and inverse results in simultaneous approximation.     

An efficient palladium catalyzed synthesis of 2-arylbenzothiazoles

A novel and convergent palladium catalyzed synthesis of 2-arylbenzothiazoles has been investigated. The key step in the synthesis is a Suzuki biaryl coupling of 2-bromobenzothiazole with aryl boronic acids to provide a variety of 2-arylbenzothiazole derivatives in good yield. The synthetic utility of this methodology is demonstrated by the synthesis of 2-(4-aminophenyl)-6-methoxybenzothiazole, a PET probe precursor for the in vivo imaging of Alzheimer's disease.     

Wavelength-scanning Talbot effect and its application for arbitrary three-dimensional step-height measurement

We demonstrate the phenomenon of Talbot self-image plane shift by tuning the wavelength of the broadband light source. A superluminescent diode (SLD) is used as a broad-band light source and an acousto-optic tunable filter (AOTF) as wavelength-scanning device. A periodic grating is illuminated by the wavelength tuned light of SLD using AOTF and Talbot self-image plane is shifted continuously in the longitudinal direction without mechanically moving the grating. The wavelength-scanning Talbot effect is then implemented for the measurement of arbitrary step-height of discontinuous objects with extended range. The main advantages of the proposed system are non-mechanical scanning, high stability because of it’s common-path geometry and compactness. Since the measurement of the phase is not required the system is free from phase ambiguity problem and therefore, the range of measurement is large as compare to interferometric techniques.     

Modified Householder iterative method free from second derivatives for nonlinear equations

In this paper, we suggest and analyze a new two-step predictor–corrector type iterative method free from second derivatives for solving nonlinear equations of the type f(x)=0. This new method includes the two-step Newton method as a special case. We prove that the new iterative method is of fourth-order. Several examples are given to illustrate the efficiency of this new method and its comparison with other iterative methods. This method can be considered as a significant improvement of the Newton method and its variant forms.     

A rapid and sensitive extractive spectrophotometric determination of copper(II) in pharmaceutical and environmental samples using benzildithiosemicarbazone.

Benzildithiosemicarbazone (BDTSC) is proposed as a sensitive and selective analytical reagent for the extractive spectrophotometric determination of copper(II). BDTSC reacts with copper(II) in the pH range 1.0-7.0 to form a yellowish complex. Beer's law is obeyed in the concentration range 0.5-0.4 microg cm(-3). The yellowish Cu(II)-BDTSC complex in chloroform shows a maximum absorbance at 380 nm, with molar absorptivity and Sandell's sensitivity values of 1.63 x 10(4) dm3 mol(-1) cm(-1) and 0.00389 microg cm(-2), respectively. A repetition of the method is checked by finding the relative standard deviation (RSD) (n = 10), which is 0.6%. The composition of the Cu(II)-BDTSC complex is established as 1:1 by slope analysis, molar ratio and Asmus' methods. An excellent linearity with a correlation coefficient value of 0.98 is obtained for the Cu(II)-BDTSC complex. The instability constant of the complex calculated from Edmond and Birnbaum's method is 7.70 x 10(-4) and that of Asmus' method is 7.66 x 10(-4), at room temperature. The method is successfully employed for the determination copper(II) in pharmaceutical and environmental samples. The reliability of the method is assured by analyzing the standard alloys (BCS 5g, 10g, 19e, 78, 32a, 207 and 179) and by inter-comparison of experimental values, using an atomic absorption spectrometer.     

On the dispersion of a solute in oscillating flow of a non-Newtonian fluid in a channel

The paper presents an exact analysis of the dispersion of an immiscible solute in a non-Newtonian fluid (known as an incompressible second-order fluid which shows viscoelastic behaviour) flowing slowly in a parallel plate channel in the presence of a periodic pressure gradient. Using a generalized dispersion model which is valid for all times after the solute injection, the diffusion coefficients K _i (τ)(i=1,2,3,…) are obtained as functions of time τ in the case when the initial solute distribution is in the form of a slug of finite extent. The analysis leads to the novel result that K ₂(τ) (which is a measure of the longitudinal dispersion coefficient of the solute) has a steady part S in addition to a fluctuating part D ₂(τ) due to the pulsatility of the flow. It is found that S decreases with increase in the viscoelastic parameter M for given values of the amplitude λ and frequency ω of the pressure pulsation. On the other hand, it is found that at a fixed instant τ, the amplitude of D ₂(τ) increases with increase in M for given values of λ and ω. Further it is shown that at a given instant τ, the amplitude of D ₂(τ) decreases with increase in ω for given λ and M and the profile for D ₂(τ) becomes progressively flatter with increase in ω. Finally the axial distribution of the average concentration θ _m of the solute over the channel cross-section is determined at different instants after the solute injection for several values of M, λ and ω. The present study is likely to have important bearing on the problem of dispersion of tracers in blood flow through arteries.     

Diastereoselective formation of 2-aryl-3-arenesulfonyl 4-ethyl-1,3-oxazolidines: An X-ray crystallographic and H NMR study

N-Arylsulfonamides of (R)- and (S)-2-amino-1-butanol, on condensation with aromatic aldehydes produced diastereomerically pure 2-aryl-3-arenesulfonyl 4-ethyl-1,3-oxazolidines. The absolute configurations of one enantiomeric pair have been determined from two fully refined X-ray structures, supplemented by nmr data.