On real matrices with positive definite symmetric component

Inequalities concerning real square matrices A with positive definite symmetric component A+A^*are derived from certain inertia relations which hold for any complex (not necessarily real) square matrices A with positive definite

A+A^*     

An analysis of overlapping Schwarz method for a weakly coupled system of singularly perturbed convection-diffusion equations

In this article, we have developed an overlapping Schwarz method for a weakly coupled system of convection-diffusion equations. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region, we use the central finite difference scheme on a uniform mesh, whereas on the nonlayer region, we use the mid-point difference scheme on a uniform mesh. It is shown that the numerical approximations converge in the maximum norm to the exact solution. We have proved that, when appropriate subdomains are used, the method produces almost second-order convergence. Furthermore, it is shown that two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantage of this method used with the proposed scheme is that it reduces iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.     

Biosynthesis and characterization of Dillenia indica-mediated silver nanoparticles and their biological activity

Dillenia indica L. is a traditional medicinal plant well known for its ability to cure various human diseases. In the current study, silver nanoparticles have been synthesized by simple and eco-friendly method using Dillenia indica extract. The green synthesized nanoparticles were characterized by Fourier transform infrared (FTIR), UV–visible spectroscopy, Atomic force microscopy (AFM), High-resolution transmission electron microscopy (HR-TEM), Zeta Potential and Size Distribution. UV–visible and FTIR spectra, AFM, HR-TEM and Zeta Potential readings and size distribution conformed that the synthesized silver particles were in the size of nano. The green synthesized silver nanoparticles were subjected for antibacterial activity against Gram-positive bacteria Enterococcus faecalis and Gram-negative bacteria Escherichia coli by agar well diffusion method. The synthesized AgNPs exhibited significant inhibition of 27 and 16 mm against the test bacteria at 0.25 mg/ml. Further the antibacterial activity was confirmed by live and dead cell assay by fluorescence microscopy and morphological changes of bacteria were studied by Scanning electron microscope (SEM). The study recommends that the synthesized silver nanoparticles using Dillenia indica extract have potential application in inhibition of bacteria owing to their potent antibacterial activity.     

Polymer network as a template for control of photoconductivity of a liquid crystal semiconductor

We report a novel method of confining a photoconducting liquid crystalline material using a polymer templating approach. The attractive feature of this approach is that the magnitude of the photocurrent of the photoconducting material does not diminish, i.e. it is unaltered by the polymer matrix. The results are compared with another method of encapsulation that was recently reported and wherein the photoconductivity decreases upon having the photoconducting material in the polymer matrix. The difference in the behaviour between the two methods is explained using a nanophase segregation model. The method described is particularly suitable for creating patterned photoconductors.     

An unusual reductive cyclization

Li-NH₃ reduction of 1α-Ethynyl-1β-hydroxy-6-oxo-8a-methyl-1,2,3,4,6,7,8,8a octahydronaphthalene 5 furnishes, in addition to reported products, the tricyclic compound $\text{8}$.     

On finite groups whose every proper normal subgroup is a union of a given number of conjugacy classes

Let G be a finite group andA be a normal subgroup ofG. We denote by ncc(A) the number ofG-conjugacy classes ofA andA is calledn-decomposable, if ncc(A)= n. SetK _G = {ncc(A)|A ⊲ G}. LetX be a non-empty subset of positive integers. A groupG is calledX-decomposable, ifK _G =X. Ashrafi and his co-authors [1-5] have characterized theX-decomposable non-perfect finite groups forX = {1, n} andn ≤ 10. In this paper, we continue this problem and investigate the structure ofX-decomposable non-perfect finite groups, forX = {1, 2, 3}. We prove that such a group is isomorphic to Z₆, D₈, Q₈, S₄, SmallGroup(20, 3), SmallGroup(24, 3), where SmallGroup(m, n) denotes the mth group of ordern in the small group library of GAP [11].     

Runge-Kutta methods for quadratic ordinary differential equations

Many systems of ordinary differential equations are quadratic: the derivative can be expressed as a quadratic function of the dependent variable. We demonstrate that this feature can be exploited in the numerical solution by Runge-Kutta methods, since the quadratic structure serves to decrease the number of order conditions. We discuss issues related to construction design and implementation and present a number of new methods of Runge-Kutta and Runge-Kutta-Nyström type that display superior behaviour when applied to quadratic ordinary differential equations.     

Conductometric determination of carbon in uranium carbide and its solution in nitric acid

A simple but accurate method has been developed for the determination of carbon in uranium carbide powders/pellets as well as in solutions of uranyl nitrates. The methodology involves quantitative conversion of carbon present in the sample to carbon dioxide that is subsequently absorbed in a dilute solution of barium hydroxide. The conductivity shift of the barium hydroxide solution is monitored on-line continuously using a laboratory-built PC-based conductivity measurement system that has been developed in-house based on the direct conversion of conductance to the digital pulse frequency. A new gas absorption cell has been designed to ensure quantitative absorption during the residence time of the gas in the cell. The method is sensitive, accurate and precise to 1-3% at 600-1000 mug of carbon in samples of uranium carbide.