Non‐catalytic,gas‐solid reversible reaction mechanism implementing diffuse interface model

Gas‐solid reactions in chemical and metallurgical industries often involve solid pellets and a gaseous reactant. The progress of chemical reaction is measured by the movement of zones within the pellet and has been explained in terms of diffusion and chemical reaction processes. Earlier models identified a single reaction zone, in addition to product layer and unreacted core. In the present article, two reaction zones are envisaged as a more plausible explanation of the movement of the zones as the reaction proceeds. Earlier models for reversible reactions have assumed that conditions at the interface between the reaction zone and the unreacted core correspond to equilibrium at the prevailing temperature. The gaseous concentrations were assumed to permeate the core at the interfacial values so that no reaction occured in the core. More realistically, the present article envisages an additional zone within which the gaseous concentrations fall from the equilibrium values to zero. It is assumed that in the reaction zone proper, referred to as zone I, having thickness z_I, the concentration profile is sigmoidal. This agrees with the earlier work of Khan and Bowen [1] and Prasannan and Doraswamy. [2] In zone I and the concentration of the reactant gas varies between [A_i] and [A*]. In the zone II, having thickness z₂, concentration varies linearly between [A*] and zero. This model has been applied successfully to the data of the reduction of hematite [3] at different temperatures. The contribution of different forms of resistance, diffusion in product layer, chemical reaction and diffusion in the reactant core, is assessed as function of time (start to the end of reaction). The thickness of the zones remain almost constant as the reaction progresses. In particular, the influences of the product and core diffusion coefficients and chemical equilibrium constant on the extant reaction are evaluated. The dependence of concentration profile and zone thickness on equilibrium constant, K, velocity constant, k, diffusional coefficients D_C and D_P has been investigated thoroughly. The thickness of both zones has been evaluated for leading variables. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 559–570, 1999     

Numerical solutions to initial and boundary value problems for linear fractional partial differential equations

In this article, Haar wavelets have been employed to obtain solutions of boundary value problems for linear fractional partial differential equations. The differential equations are reduced to Sylvester matrix equations. The algorithm is novel in the sense that it effectively incorporates the aperiodic boundary conditions. Several examples with numerical simulations are provided to illustrate the simplicity and effectiveness of the method.     

On <Emphasis Type="Italic">n</Emphasis>-commuting and <Emphasis Type="Italic">n</Emphasis>-skew-commuting maps with generalized derivations in prime and semiprime rings

Let R be a ring with center Z(R), let n be a fixed positive integer, and let I be a nonzero ideal of R. A mapping h: R → R is called n-centralizing (n-commuting) on a subset S of R if [h(x),x ⁿ ] ∈ Z(R) ([h(x),x ⁿ ] = 0 respectively) for all x ∈ S. The following are proved:

Fixed-Point Technique for Implicit Complementarity Problem in Hilbert Lattice

In this paper, we consider and study the implicit complementarity problem in the setting of a Hilbert lattice. It has been shown that this problem can be formulated as a fixed-point problem by using a suitable change of variables. Moreover, this formulation allows us to prove the existence and uniqueness of solutions of the implicit complementarity problem.     

A numerical method for solving boundary value problems for fractional differential equations

A numerical scheme, based on the Haar wavelet operational matrices of integration for solving linear two-point and multi-point boundary value problems for fractional differential equations is presented. The operational matrices are utilized to reduce the fractional differential equation to system of algebraic equations. Numerical examples are provided to demonstrate the accuracy and efficiency and simplicity of the method.     

Synthesis,Photophysical Properties and Application of New Porphyrin Derivatives for Use in Photodynamic Therapy and Cell Imaging

New derivatives of tetrakis(4-carboxyphenyl) porphyrin were designed, synthesized and characterized by IR, proton NMR and mass spectroscopy. The ground and excited state nature of new derivatives were examined using UV-Vis. absorption and fluorescence spectroscopy, fluorescence quantum yield and fluorescence lifetime studies. The singlet oxygen quantum yield of each synthesized derivative of porphyrin was estimated for their further efficacy as potential photosensitizer in biological studies. The significant photophysical data of all synthesized derivatives was supplementary accessed to examine the cell imaging and cytotoxicity against two cancer cell lines viz. MBA-MD-231 and A375. The fluorescence lifetime, fluorescence quantum yield and efficiency of singlet oxygen generation suggests alkyl amine and alkyl hydrazide linked new porphyrin photosensitizers can be useful for PDT agent in cancer treatment.