On Szegö’s Type Theorems

This study is to look the effect of change in the ordering of the Fourier system on Szegö’s classical observations of asymptotic distribution of eigenvalues of finite Toeplitz forms.This is done by checking proofs and Szegö’s properties in the new set up.The Fourier system is unconditional [19], any arbitrary ordering of the Fourier system forms a basis for the Hilbert space L2 [-Π, Π].Here study about the classical Szegö’s theorem.Szegö’s type theorem for operators in L2(R+) and check its validity for certain multiplication operators.Since the trigonometric basis is not available in L2(R+) or in L2(R) .This study discussed about the classes of orderings of Haar System in L2 (R+) and in L2(R) in which Szegö’s Type TheoreT Am is valid for certain multiplication operators.It is divided into two sections. In the first section there is an ordering to Haar system in L2(R+) and prove that with respect to this ordering, Szegö’s Type theorem holds for general class of multiplication operators Tƒ with multiplier ƒ ε L2(R+), subject to some conditions on ƒ.Finally in second section more general classes of ordering of Haar system in L2(R+) and in L2(R) are identified in such a way that for certain classes of multiplication operators the asymptotic distribution of eigenvalues exists.

Selective N-monomethylation of aniline over Zn1-xNixFe2O4 (x=0, 0.2, 0.5, 0.8 and 1) type systems

The reaction of aniline with methanol was carried out over Zn1-xNixFe2O4 (x= 0, 0.2, 0.5, 0.8 and 1) type systems in a fixed-bed down-flow reactor. It was observed that systems possessing low ``x'' values are highly selective and active for mono N-alkylation of aniline leading to N-methyl aniline. Selectivity for N-methyl aniline over ZnFe2O4 was more than 99% under the optimized reaction conditions. Even at methanol to aniline molar ratio of 2, the yield of N-methyl aniline was nearly 55.5%, whereas its yield exceeded 67% at the molar ratio of 7. The Lewis acid sites of the catalysts are mainly responsible for the good catalytic performance. Cation distribution in the spinel lattice influences their acido-basic properties, and hence, these factors have been considered as helpful to evaluate the activity and stability of the systems.

Selective N-monomethylation of aniline using Zn1-x CoxFe2O4( x=0, 0.2, 0.5, 0.8 and 1.0)type systems

A series of ferrites having the general formula Zn1-xCoxFe2O4 (x=0, 0.2, 0.5, 0.8 and 1.0)were prepared by soft chemical route. The materials were characterized by adopting various physico-chemical methods. The reaction of aniline with methanol was studied in a fixed-bed reactor system as a potential source for the production of various methyl anilines. It was observed that systems possessing low ‘ x’ values are highly selective and active for N-monoalkylation of aniline leading to N-methylaniline. Reaction parameters were properly varied to optimize the reaction conditions for obtaining N-methylaniline selectively and in better yield. Among the systems Zn0.8Co0.2Fe2O4 is remarkable due to its very high activity and excellent stability. Under the optimized conditions N-methylaniline selectivity exceeded 98%. Even at a methanol to aniline molar ratio of 2, the yield of N-methylaniline was nearly 50%, whereas its yield exceeded 71% at the molar ratio of 5. ZnFe2O4, though executed better conversion than Zn0.8Co0.2Fe2O4 in the initial period of the run, deactivates quickly as the reaction proceeds. The Lewis acidity of the catalysts is mainly responsible for the good performance. Cation distribution in the spinel lattice influences their acido-basic properties and, hence, these factors have been considered as helpful parameters to evaluate the activity of the systems.

Electrochemical studies on Metal phthalocyanines

The primary aim of these investigations was to probe the elecnuchemical and material science aspects of some selected metal phthalocyanines(MPcs).Metal phthalocyanines are characterised by a unique planar molecular structure. As a single class of compounds they have been the subject of ever increasing number of physicochemical and technological investigations. During the last two decades the literature on these compounds was flooded by an outpour of original publications and patents. Almost every branch of materials science has benefited by their application-swface coating, printing, electrophotography, photoelectrochemistry, electronics and medicine to name a few.The present study was confined to the electrical and electrochemical properties of cobalt, nickel, zinc. iron and copper phthalocyanines. The use of soluble Pes as corrosion inhibitor for aluminium was also investigated.In the introductory section of the thesis, the work done so far on MPcs is reviewed. In this review emphasis is given to their general methods of synthesis and the physicochemical properties.In phthalocyanine chemistry one of the formidable tasks is the isolation of singular species. In the second chapter the methods of synthesis and purification are presented with necessary experimental details.The studies on plasma modified films of CoPe, FePc, ZnPc. NiPc and CuPc are also presented.Modification of electron transfer process by such films for reversible redox systems is taken as the criterion to establish enhanced electrocatalytic activity.Metal phthalocyanines are p- type semiconductors and the conductivity is enhanced by doping with iodine. The effect of doping on the activation energy of the conduction process is evaluated by measuring the temperature dependent variation of conductivity. Effect of thennal treatment on iodine doped CoPc is investigated by DSC,magnetic susceptibility, IR, ESR and electronic spectra. The elecnucatalytic activity of such doped materials was probed by cyclic voltammetry.The electron transfer mediation characteristics of MPc films depend on the film thickness. The influence of reducing the effective thickness of the MPc film by dispersing it into a conductive polymeric matrix was investigated. Tetrasulphonated cobalt phthalocyanine (CoTSP) was electrostatically immobilised into polyaniline and poly(o-toluidine) under varied conditions.The studies on corrosion inhibition of aluminium by CoTSP and CuTSP and By virtue of their anionic character they are soluble in water and are strongly adsorbed on aluminium. Hence they can act as corrosion inhibitors. CoTSP is also known to catalyze the reduction of dioxygen.This reaction can accelerate the anodic dissolution of metal as a complementary reaction. The influence of these conflicting properties of CoTSP on the corrosion of aluminium was studied and compared with those of CuTSP.In the course of these investigations a number of gadgets like cell for measuring the electrical conductivity of solids under non-isothermal conditions, low power rf oscillator and a rotating disc electrode were fabricated.

Studies on the digestive enzymes of the Indian white prawn Penaeus indicus H. Milne Edwards

The efficiency of a diet not only depends on its nutrient composition and nutrient balance but also on the effective utilization by the animal. In the utilization of dietary nutrients, the digestive enzymes play the crucial role of catalysing the hydrolytic reactions, splitting the macromolecules into simple absorbable molecules. The activity of these biocatalysts is regulated by alterations in pH, temperature, substrate type and concentrations, and also by the presence of activators and inhibitors. Thus any shift from the optimum conditions necessary for these enzymes may affect their activity, thereby correspondingly modify the digestibility of the nutrients supplied to the animals. Thus, investigations on the important digestive enzymes and their preferential conditions of activity are essential, so that the results obtained could be used in rationally adjusting the quality and quantity of feed supplied to the different stages of prawns In India, directed research on nutritional physiology and biochemical approaches to digestion in commercially important prawns is taken up_ only recently, and the field is still in an infant stage. In view of its emerging importance it is identified as an area of priority and the present investigation has been carried out on the Indian white prawn Penaeus indicus