Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes

In this article, we discuss and analyze new conforming virtual element methods (VEMs) for the approximation of semilinear parabolic problems on convex polygonal meshes in two spatial dimension. The spatial discretization is based on polynomial and suitable nonpolynomial functions, and a Euler backward scheme is employed for time discretization. The discrete formulation of both the proposed schemes—semidiscrete and fully discrete (with time discretization) is discussed in detail, and the unique solvability of the resulted schemes is discussed. A priori error estimates for the proposed schemes (semidiscrete and fully discrete) in H¹‐ and L²‐norms are derived under the assumption that the source term f is Lipschitz continuous. Some numerical experiments are conducted to illustrate the performance of the proposed scheme and to confirm the theoretical convergence rates.     

Electrical characterization of PVA-based nanocomposite electrolyte nanofibre mats doped with a multiwalled carbon nanotube

An attempt has been made to prepare and characterise ammonium thiocyanate (NH₄SCN) salt and a multiwall carbon nanotube (MWNT)-doped polyvinyl alcohol-based nanofibre mats using an electrospinning process. The X-ray diffraction result shows an improvement in the amorphous nature of composite electrolyte fibre mats with increasing concentrations of the MWNT filler. The DSC behaviour of these nanofibre mat exhibits better thermal response upon dispersal of the filler. Composite electrolyte nanofibre mat doped with 6 wt% MWNT shows optimum conductivity, viz., 5.8?×?10^?4 Scm^?1. The temperature dependence of the bulk electrical conductivity displays a combination of Arrhenius and Vogel–Tammam–Fulcher nature. Dielectric loss studies have also been used to understand the conduction process in the system. Jonscher power law seems to be obeyed during ac conductivity measurements of the fibre mats.     

A Stress Stability Behavior and Development of an LC Assay Method for Anastrozole

This present work narrates the stress stability behavior and development of a liquid chromatographic method for the quantitative determination of anastrozole. Anastrozole is appropriately used when using substantial amounts of aromatizing steroids, or when one is prone to gynecomastia and using moderate amounts of such steroids. A chromatographic separation was achieved on a Hichrom RPB18 (250 × 4.6 mm, 5 μ) column using water and mixture of acetonitrile and methanol (1:1 ratio) as mobile phase. Forced degradation studies were performed on bulk samples of anastrozole using acid, base, hydrogen peroxide, heat and UV light. Degradation of the drug substance was observed in base hydrolysis. Degradation product formed under base hydrolysis was found to be Imp-C. The sample solution and mobile phase were found to be stable up to 48 h. The developed method was validated with respect to linearity, accuracy, precision, robustness and forced degradation studies prove the stability indicating power of the method.     

Mn site substitution of La0.67Ca0.33MnO3 with closed shell ions: Effect on magnetic transition temperature

Mn site is substituted with closed shell ions (Al, Ga, Ti, Zr and a certain combination of Zr and Al) and also with Fe and Ru ions carrying the magnetic moment (S=5/2 and 2 respectively) at a fixed concentration of 5 at %. Substitution did not change either the crystal symmetry or the oxygen stoichiometry. All substituents were found to suppress both the metal-insulator and ferromagnetic transition temperatures (T _p(ρ) and T _C, respectively) to varied extents. Two main contributions identified for the suppression are the lattice disorder arising due to difference in the ionic radii between the substituent (r _M) and the Mn³⁺ ion (r _Mn ³⁺) and in the case of the substituents carrying a magnetic moment, the type of magnetic coupling between the substituent and that of the neighboring Mn ion.     

Structural studies on fullerenes

Amongst the other physical properties, the structure of fullerene solids, and the structural transformations with temperature, pressure and doping have all evoked considerable interest and during the last two years tremendous progress has been made in this area. This paper provides a brief review of the studies on the structural properties of pristine and doped fullerenes. The results of our own investigations are also presented.     

A novel access to highly functionalised β-lactams by regio- and stereoselective 1,3-dipolar cycloaddition reaction

A highly regio- and stereoselective synthesis of novel spiro pyrrolidines/pyrrolizidines containing β-lactam and oxazolone moieties under two different conditions is achieved using [3+2] cycloaddition methodology in moderate to good yield.     

A new dendrimer scaffold for preparing dimers or tetramers of biologically active molecules

Synthesis of a new scaffold derived from iminodipropionic acid for the preparation of peptide dimers and tetramers is described.     

Rate constants for reactions of iodine atoms in solution

Laser flash photolysis (at 248 or 308 nm) or aryl iodides in water or water/methanol solutions produces iodine atoms and phenyl radicals. Iodine atoms react rapidly with added I^? to form I₂^? but do not react rapidly with O₂ (k ? 10⁷ L mol^?1 s^?1). Iodine atoms oxidize phenols to phenoxyl radicals, with rate constants that vary from 1.6 × 10⁷ L mol^?1 s^?1 for phenol to about 6 × 10⁹ L mol^?1 s^?1 for 4-methoxyphenol and hydroquinone. Ascorbate and a Vitamin E analogue are also oxidized very rapidly. N-Methylindole is oxidized by I atoms to its radical cation with a diffusion-controlled rate constant, 1.9 × 10¹⁰ L mol^?1 s^?1. Iodine atoms also oxidize sulfite and ferrocyanide ions rapidly but do not add to double bonds. The phenyl radicals, produced along with the I atoms, react with O₂ to give phenylperoxyl radicals, which react with phenols much more slowly than I atoms. © 1995 John Wiley & Sons, Inc.