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.

Vacuum-ultraviolet photochemically initiated modification of polystyrene surfaces: morphological changes and mechanistic investigations

Vacuum-ultraviolet (VUV) irradiation (kexc: 172 ± 12 nm) of polystyrene films in the presence of oxygen produced not only oxidatively functionalized surfaces, but generated also morphological changes. Whereas OH- and C=O-functionalized surfaces might be used for e.g. secondary functionalization, enhanced aggregation or printing, processes leading to morphological changes open new possibilities of microstructurization. Series of experiments made under different experimental conditions brought evidence of two different reaction pathways: introduction of OH- and C=O-groups at the polystyrene pathways is mainly due to the reaction of reactive oxygen species (hydroxyl radicals, atomic oxygen, ozone) produced in the gas phase between the VUV-radiation source and the substrate. However, oxidative fragmentation leading to morphological changes, oxidation products of low molecular weight and eventually to mineralization of the organic substrate is initiated by electronic excitation of the polymer leading to C–C-bond homolysis and to a complex oxidation manifold after trapping of the C-centred radicals by molecular oxygen. The pathways of oxidative functionalization or fragmentation could be differentiated by FTIR-ATR analysis of irradiated polystyrene surfaces before and after washing with acetonitrile and microscopic fluorescence analysis of the surfaces secondarily functionalized with the N,N,N-tridodecyl-triaza-triangulenium (TATA) cation. Ozonization of the polystyrene leads to oxidative functionalization of the polymer surface but cannot initiate the fragmentation of the polymer backbone. Oxidative fragmentation is initiated by electronic excitation of the polymer (contact-mode AFM analysis), and evidence of the generation of intermediate C-centred radicals is given e.g. by experiments in the absence of oxygen leading to cross-linking (solubility effects, optical microscopy, friction-mode AFM) and disproportionation (fluorescence).

Elastic Constants And Structural Parameters Of Selected Polycrystalline Ceramics By Ultrasonic Technique

The present work is an attempt to probe the elastic properties in some dielectric ceramics, by using ultrasonic pulse echo overlap technique. The base Ba6-xSm8+2xTi18O54 and Ca5Nb2TiO12 are very important dielectrics ceramics used for microwave communication as well as for substrate materials. Ultrasonic is one of the most widely used and powerful techniques to measure elastic properties of solids. The ultrasonic technique is nondestructive in nature and the measurements are relatively straightforward to perform. One unique advantantage of the ultrasonic technique is that both static and dynamic properties can be measured simultaneously. The velocity and attenuation coefficients of the ultrasonic waves propagating through a medium are related to the microscopic structure of the material and they provide valuable information about the structural changes in the system. Among the various ultrasonic techniques, the pulse echo overlap method is the most accurate and precise one. In the present case the decreased elastic properties of Cas-XMg,Nb2TiO12 and Cas-,ZnNb2TiO12 ceramics can be attributed to their mixture phases beyond x = 1. Moreover, the abrupt change in elastic properties observed for x >1 can also be correlated to the structural transformation of the materials from their phase pure form to mixture phases for higher extent of substitution of the concerned material . Ca4(ANb2Ti)012 (A = Mg, Zn) is the strongest compound with the maximum values for elastic properties . This could be due to the possible substitution of Mg/Zn ions with lesser radius [25] than Ca2+ in perovskite B-site of Ca(Cali4Nb2i4Tili4) O3 material to contribute more ordering and symmetry to the system [20]. All other compositions (x > 1) contain mixed-phases and for such mixed-phase samples, the mechanical properties are difficult to explain.

Surface Properties and Catalytic Activity of Manganese Ferrospinels

In recent years considerable advances have been achieved in the study of the surface structure and mechanism of action of environmentally benign heterogeneous catalysts. The study entitled as surface properties and catalytic activity of manganese ferrospinels. In the present study we have prepared manganese ferrospinels of general formula Mn(1-x)BxFe2O4 via low temperature controlled co-precipation method. The study employed low temperature co-precipitation method for the preparation ofMn(1-x)BxFe2O4 specimens, where B is a metal cation such as Cr,Co, Ni,Cu and Zn. The catalytic activities of the systems were investigated for liquid-phase benzoylation of aromatic compounds and phenol hydroxylation and for vapour-phase reactions such as aniline alkylation, phenol methylation and ODH of ethylbenzene. The different series of manganese ferrites are proved to be excellent catalysts for various industrially important reactions such as Friedel-crafts benzoylation of aromatic compounds, methylation of aniline and phenol, hydroxylation of phenol and oxidative dehydrogenation of ethylbenzene. Due to the tightening of the environmental regulations, production of diphenols from phenol hydroxylation and reduction of phenolic pollutants in waste waters using these catalysts can be a promising approach because it demands only simple techniques and produce little environmental pollution.

Microwave dielectric properties of MO -La2O3-TiO2 (M = Ca, Sr, Ba) ceramics

Single-phase polycrystalline ceramics in the MO-La2O3-Ti02 (M = Ca, Sr, Ba) system, such as cation-deficient hexagonal perovskites CaLa4Ti4O15, SrLa4Ti4O15, BaLa4Ti4O15, and Ca2La4Ti5O18 and the orthorhombic phases CaLa4Ti5O17 and CaLa8Ti9O31, were prepared through the solid-state ceramic route. The phases and structure of the ceramics were analyzed through x-ray diffraction and scanning electron microscopy. The microwave dielectric properties of the ceramics were studied using a network analyzer. The investigated ceramics show high Er in the range 42 to 54, high quality factors with Q x f in the range 16,222 to 50,215 GHz, and low Tf in the range -25 to +6 ppm3/°C. These high dielectric constant materials with high Q x f up to 50,215 GHz are suitable for applications where narrow bandwidth and extremely low insertion loss is necessary, especially at frequencies around 1.9 GHz

Acidity and catalytic activity of rare earth modified Al/Zr pillared clays

The pillared montmorillonite has been prepared by exchanging Na+ in the interlayer of montmorillonite with Al hydroxy cation followed by calcination. Pillared clays are also prepared after exchanging Na' ions with Ce, La, Sm-ions and then pillarcd with aluminium oxides, The surface characterisation of the prepared catalysts has been done using XRD and surface area measurements. To probe the acidic property of the system, temperature programmed desorption (TPD) of NH, has been done. Toluene alkylation by benzyl chloride has been carried out for the evaluation of catalytic activity. The most active system is found to be mixed Al/Zr pillarcd montrnorillonite.

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.

Selective alkylation of aniline to N-methyl aniline using chromium manganese ferrospinels

Various compositions of chromium manganese ferrospinels were tested as catalysts for the vapour phase alkylation of aniline with methanol. The samples were prepared by room temperature co-precipitation technique and characterized by various physico-chemical methods. The acidity–basicity determination revealed that the samples possess greater amount of basic sites than acidic sites. All the ferrite samples proved to be selective and active for N-monoalkylation of aniline leading to N-methyl aniline; Cr0.6Mn0.4Fe2O4, Cr0.8Mn0.2Fe2O4 and CrFe2O4 exhibited cent percent selectivity for N-methyl aniline. Neither C-alkylated products nor any other side products were detected for all catalyst samples. The catalytic activity of the samples studied in this reaction is related to their acid–base properties and also on the cation distribution. Under the optimized reaction conditions all the systems showed constant activity for a long duration.

Lewis acidity of rare earth exchanged zeolites

The Lewis acidity of yttrium and dysprosium exchanged zeolite Y and ZSM-5 has been determined by titration method using Hammett indicators. The acidity of the Y form increases with increase in concentration of the rare earth cation in the Y zeolite. It is independent of the amount of the rare earth ion for ZSM-5. The data have been correlated with the activity of these zeolites for the esterification of butanol using acetic acid.

Catalysis By Ferrites And Cobaltites For The Alkylation And Oxidation Of Organic Compounds

Catalysis is a very important process from an industrial point of view since the production of most industrially important chemicals involves catalysis.Solid acid catalysts are appealing since the nature of acid sites is known and their chemical behavior in acid catalyzed reactions can be rationalized by means of existing theories and models. Mixed oxides crystallizing in spinel structure are of special interest because the spinel lattice imparts extra stability to the catalyst under various reaction conditions so that theses systems have sustained activities for longer periods. The thesis entitled" Catalysis By Ferrites And Cobaltites For The Alkylation And Oxidation Of Organic Compounds " presents the preparation ,characterization ,and activity studies of the prepared spinels were modified by incorporating other ions and by changing the stoichiometry.The prepared spinels exhibiting better catalytic activity towards the studied reactions with good product selectivity.Acid-base properties and cation distribution of the spinels were found to control the catalytic activity.

Impact of zinc substitution on the structural and magnetic properties of chemically derived nanosized manganese zinc mixed ferrites

Mn1-xZnxFe2O4 nanoparticles (x=0-1) were synthesized by wet chemical co-precipitation techniques. X-ray diffraction, transmission electron microscopy and high-resolution transmission electron microscopy were effectively utilized to investigate the different structural parameters. The elemental analysis was conducted using energy-dispersive spectrum and inductively coupled plasma analysis. The magnetic properties such as magnetization and coercivity were measured using vibrating sample magnetometer. The observed magnetization values of the nanoparticles were found to be lower compared to the bulk counterpart. The magnetization showed a gradual decrease with zinc substitution except for a small increase from x=0.2 to 0.3. The Curie temperature was found to be enhanced in the case of ferrites in the nanoregime. The variation in lattice constant, reduced magnetization values, variation of magnetization with zinc substitution, the presence of a net magnetic moment for the zinc ferrite and the enhancement in Curie temperature in Mn1-xZnxFe2O4 all provide evidence to the existence of a metastable cation distribution together with possible surface effects at the nanoregime.

Studies on Production of Bacterial Xylanases

Xylanases with hydrolytic activity on xylan, one of the hemicellulosic materials present in plant cell walls, have been identified long back and the applicability of this enzyme is constantly growing. All these applications especially the pulp and paper industries require novel enzymes. There has been lot of documentation on microbial xylanases, however, none meeting all the required characteristics. The characters being sought are: higher production, higher pH and temperature optima, good stabilities under these conditions and finally the low associated cellulase and protease production. The present study analyses various facets of xylanase biotechnology giving emphasis on bacterial xylanases. Fungal xylanases are having problems like low pH values for both enzyme activity and growth. Moreover, the associated production of cellulases at significant levels make fungal xylanases less suitable for application in paper and pulp industries.Bacillus SSP-34 selected from 200 isolates was clearly having xylan catabolizing nature distinct from earlier reports. The stabilities at higher temperatures and pH values along with the optimum conditions for pH and temperature is rendering Bacillus SSP-34 xylanase more suitable than many of the previous reports for application in pulp and paper industries.Bacillus SSP-34 is an alkalophilic thertmotolerant bacteria which under optimal cultural conditions as mentioned earlier, can produce 2.5 times more xylanase than the basal medium.The 0.5% xylan concentration in the medium was found to the best carbon source resulting in 366 IU/ml of xylanase activity. This induction was subjected to catabolite repression by glucose. Xylose was a good inducer for xylanase production. The combination of yeast extract and peptone selected from several nitrogen sources resulted in the highest enzyme production (379+-0.2 IU/ml) at the optimum final concentration of 0.5%. All the cultural and nutritional parameters were compiled and comparative study showed that the modified medium resulted in xylanase activity of 506 IU/ml, 5 folds higher than the basal medium.The novel combination of purification techniques like ultrafiltraton, ammonium sulphate fractionation, DEAE Sepharose anion exchange chromatography, CM Sephadex cation exchange chromatography and Gel permeation chromatography resulted in the purified xylanase having a specific activity of 1723 U/mg protein with 33.3% yield. The enzyme was having a molecular weight of 20-22 kDa. The Km of the purified xylanase was 6.5 mg of oat spelts xylan per ml and Vmax 1233 µ mol/min/mg protein.Bacillus SSP-34 xylanase resulted in the ISO brightness increase from 41.1% to 48.5%. The hydrolytic nature of the xylanase was in the endo-form.Thus the organism Bacillus SSP-34 was having interesting biotechnological and physiological aspects. The SSP-34 xylanase having desired characters seems to be suited for application in paper and pulp industries.

Vacancy-assisted domain-growth in asymmetric binary alloys: A Monte Carlo Study

A Monte Carlo simulation study of the vacancy-assisted domain growth in asymmetric binary alloys is presented. The system is modeled using a three-state ABV Hamiltonian which includes an asymmetry term. Our simulated system is a stoichiometric two-dimensional binary alloy with a single vacancy which evolves according to the vacancy-atom exchange mechanism. We obtain that, compared to the symmetric case, the ordering process slows down dramatically. Concerning the asymptotic behavior it is algebraic and characterized by the Allen-Cahn growth exponent x51/2. The late stages of the evolution are preceded by a transient regime strongly affected by both the temperature and the degree of asymmetry of the alloy. The results are discussed and compared to those obtained for the symmetric case.