Kinetics of reactions of N1-phenylbiguanidine with CeIV and [MnO4]− in aqueous sulphuric acid media

Summary In the title reaction each mole of N¹-phenylbiguanidine, R–HNC(=X)NHC(=NH)NH₂ (R=Ph, X=NH), consumes 4 moles of Ce^IV and produces guanylurea (R=H, X=O), 1,4-benzoquinone and ammonia. On the other hand, the reaction of N¹-phenylbiguanidine (pbg) with [MnO₄]^– proceeds with variable stoicheiometry which depends on reaction conditions. In the case of [MnO₄]^– no benzoquinone is detected among the reaction products; instead, carbon dioxide, guanylurea, and ammonia were identified. Pbg itself in acid solution slowly hydrolyses to aniline which rapidly reacts with Ce^IV and [MnO₄]^–. The kinetics for the reactions of pbg with the oxidants is consistent with the rate law –d[oxidant]/dt=k[pbg].The k values and the corresponding activation enthalpies and entropies for the reaction of bpg with Ce^IV, [MnO₄]^–, and Cr^VI lie within a narrow range. These results are interpreted in terms of rate-determining hydrolysis of pbg in all the three cases.     

Gromov-Witten invariants and quantum cohomology

This article is an elaboration of a talk given at an international conference on Operator Theory, Quantum Probability, and Noncommutative Geometry held during December 20–23, 2004, at the Indian Statistical Institute, Kolkata. The lecture was meant for a general audience, and also prospective research students, the idea of the quantum cohomology based on the Gromov-Witten invariants. Of course there are many important aspects that are not discussed here. Dedicated to Professor K B Sinha on the occasion of his 60th birthday     

Finite volume element method for the incompressible miscible displacement problems in porous media

We present the finite volume element method (FVEM) for incompressible miscible displacement problems in porous media. Optimal error estimates in L^∞(L²) are derived for velocity and concentration. Numerical experiments are also presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Novel synthesis of isoxazolo[5,4-b]quinolines

Isoxazolo[5,4-b]quinolines have been prepared by reacting 3-acyl or aroyl-2-chloro-6-alkoxy or 6,7-dialkoxyquinolines with hydroxylamine. The method is of general applicability for obtaining this class of compounds and involves the use of easily available starting materials.     

Surfactant-assisted synthesis and characterization of stable silver bromide nanoparticles in aqueous media

Colloidal dispersions of silver bromide (AgBr) in aqueous surfactant medium have been prepared using a surfactant-assisted synthesis approach with hexadecyltrimethylammonium bromide (CTAB). The surfactant acts both as source of bromide ion as well as the stabilizing agent. Upon progressive addition of silver nitrate to aqueous CTAB solution, stable AgBr dispersions were obtained. Formation of surfactant cation (CTA(+)) stabilized AgBr was confirmed by way of XRD, FTIR and NMR studies. Thermal behavior of the isolated nanoparticles was investigated by differential scanning calorimetry (DSC) and thermal gravimetric analysis (TGA), where the occurrence of phase transition in the surfactant-stabilized nanoparticles was observed. Kinetics of the particle growth was investigated by dynamic light scattering measurements, which predicted the formation of surfactant bilayered structures associated with the nanoparticles of AgBr. Band gap of the nanoparticles was determined by suitably analyzing the UV-visible spectral data, which concluded that the particles behaved like insulators. Morphology of the particles, studied by TEM measurements, was found to be spherical. Finally, enthalpy of formation of surfactant-stabilized AgBr, determined calorimetrically, was found to be dependent on the concentration of the precursors.     

Mixed finite element methods for a fourth order reaction diffusion equation

Mixed finite element methods are applied to a fourth order reaction diffusion equation with different types of boundary conditions. Some a priori bounds are established with the help of Lyapunov functional. The semidiscrete schemes are derived using C⁰‐piecewise linear finite elements in spatial direction and error estimates are obtained. The semidiscrete problem is then discretized in the temporal direction using backward Euler method and the wellposedness of the completely discrete scheme is discussed. Finally, a priori error estimates are established. While deriving a priori error estimates, Gronwall's lemma is applied and the constants involved in the error bounds do not depend exponentially on $\frac{1}{\gamma}$, where γ is a parameter appeared in the fourth order derivative. © 2011Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012     

Discontinuous Galerkin finite volume element methods for second‐order linear elliptic problems

In this article, a one parameter family of discontinuous Galerkin finite volume element methods for approximating the solution of a class of second‐order linear elliptic problems is discussed. Optimal error estimates in L² and broken H¹‐ norms are derived. Numerical results confirm the theoretical order of convergences. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Optical soliton perturbation for time fractional resonant nonlinear Schrödinger equation with competing weakly nonlocal and full nonlinearity

In this article, we retrieve optical soliton solutions of the perturbed time fractional resonant nonlinear Schrödinger equation having competing weakly nonlocal and full nonlinearity. We study the equation for two different forms of nonlinearity, namely Kerr law and anti-cubic law. The F-expansion method along with fractional complex transformation is used to obtain the optical solitons. Moreover, the existence of these solitons are guaranteed with the constraint relations between the model coefficients and the traveling wave frequency coefficient.