Double stage estimation of population variance

Summary Consider a normal population with mean μ and variance σ². We are interested in the estimation of population variance with the help of guess value σ ₀ ² and a sample of observations. In this paper, a double stage shrinkage estimator based on the shrinkage estimatorks ₁ ² +(1-k)σ ₀ ² ifs ₁ ² ∈R and the usual estimator ifs ₁ ² ∋R, whereR is some specified region, have been proposed. The expressions for bias and mean squared error have been obtained. Comparison with the usual estimators ² have been made. It was found that though the largest gain is obtained fork=0, we can use with 0≦k≦1/2 even when σ² is very close to σ ₀ ²     

Site-selective C–H nitration of N-aryl-7-azaindoles under palladium(II) catalysis

The site-selective C–H nitration reaction of 7-azaindoles with t-butyl nitrite under palladium catalysis is described. This protocol provides an efficient method for the construction of ortho-nitrated N-aryl-7-azaindoles with excellent site-selectivity and functional group compatibility. The formed 7-azaindole derivatives can be readily transformed into 7-azaindoles containing an aniline functional group under palladium-catalyzed hydrogenation conditions.     

Highly Selective and Sensitive Graphene Based Electrochemical Sensor for Quantification of Receptor Agonist Rizatriptan

A highly selective and sensitive electrochemical sensor has been developed by modification of a glassy carbon electrode (GCE) with graphene (GRP) for quantification of Rizatriptan. The significant increase of the peak current and the improvement of the oxidation peak potential indicate that the electrochemical sensor facilitates the electron transfer of Rizatriptan. The oxidation peak current was proportional to the Rizatriptan concentration in the range from 100 to 600 µg/mL with detection (LOD) and quantification limit (LOQ) of 36.52 and 121.73 µg/mL, respectively. The developed method was successfully employed for quantification of Rizatriptan in pharmaceutical formulations. The sensor shows great promise for simple, sensitive and quantitative detection of Rizatriptan.     

Siloxane polymers containing azo moieties synthesized by click chemistry for photo responsive and liquid crystalline applications

Three new types of siloxane‐based photoactive liquid crystalline polymers containing azo side groups were synthesized through the click chemistry route. The polymers having molecular weight range of 14,000–34,000 g mol^?1 were soluble in most of the polar solvents like chloroform, tetrahydrofuran, dimethylformamide, dimethyl sulfoxide, and dichloromethane. The photoresponsive trans–cis photoisomerization under UV radiation and cis–trans relaxation process in dark for the polymers were studied. The isomerization rate constants were found to be 0.01–0.04 sec^?1 and 1.16*10^?4–4.67*10^?4 sec^?1, respectively. It has been noted that the polymers showed high intensity absorption for n‐π* in chloroform. Both trans and cis forms of azide monomers having azo moiety exhibited molar extinction coefficient ( ? _max) in the range of 22,000–33,000 L mol^?1 cm^?1. The thermotropic behavior of the polymers was studied by polarizing optical microscope (POM) and differential scanning calorimetry (DSC) experiments. Polymer P1 showed liquid crystalline textures of nematic droplets, whereas P2 showed smectic focal conic texture and nematic droplets. Polymer P1 was also studied for photomechanical bending on exposure to UV radiation. The polymers showed initial degradation temperature in the range of 210–275°C. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

SH-waves in viscoelastic heterogeneous layer over half-space with self-weight

The effect of gravity, heterogeneity and internal friction on propagation of SH-waves (horizontally polarised shear waves) in viscoelastic layer over a half-space has been studied. Using the method of separation of variables, dispersion equation has been obtained and used to recover the damped velocity of SH-waves. Both the real and imaginary parts of dispersion equation are in well agreement with the classical Love wave equation. It has been observed that heterogeneity of the medium affects the velocity profile of SH-wave significantly. Some other peculiarities have been observed and discussed in our study.     

Interpreting nucleation as a network formation process

In this paper we interpret nucleation as a network formation process. Inspired by this interpretation we propose a social network model which produces networks with communities.