913 resultados para Sobolev-type orthogonal polynomials on the unit ball


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The thesis gives a general introduction about the topic include India, the spatial and temporal variation of the surface meteorological parameters are dealt in detail. The general pattern of the winds over the region in different seasons and the generation and movements of the thermally and dynamically originated local wind systems of Western Ghats region has been studied. The modification of the prevailing winds over region by the Palghat Gap and its effect on the mouth regions pf the gap is analysed in great depth. The thesis gives the information of climatic elements of the mountain region such as energy budgets, rainfall studies, evaporation and condensation and the variation in the heat fluxes over the region. The impact of orography is studied in a different approach. The type of hypothetical study gives more insight into the control of mountain on the distribution of meteorological parameter over the study region and helps to quantify the impact of the mountain in varying the weather climate of region. The detailed study of the hydro-meteorological aspects of the main river basins of the region also should be included to the climatic studies for the total understanding of the weather and climate over the region.

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The thesis report results obtained from a detailed analysis of the fluctuations of the rheological parameters viz. shear and normal stresses, simulated by means of the Stokesian Dynamics method, of a macroscopically homogeneous sheared suspension of neutrally buoyant non-Brownian suspension of identical spheres in the Couette gap between two parallel walls in the limit of vanishingly small Reynolds numbers using the tools of non-linear dynamics and chaos theory for a range of particle concentration and Couette gaps. The thesis used the tools of nonlinear dynamics and chaos theory viz. average mutual information, space-time separation plots, visual recurrence analysis, principal component analysis, false nearest-neighbor technique, correlation integrals, computation of Lyapunov exponents for a range of area fraction of particles and for different Couette gaps. The thesis observed that one stress component can be predicted using another stress component at the same area fraction. This implies a type of synchronization of one stress component with another stress component. This finding suggests us to further analysis of the synchronization of stress components with another stress component at the same or different area fraction of particles. The different model equations of stress components for different area fraction of particles hints at the possible existence a general formula for stress fluctuations with area fraction of particle as a parameter

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The thesis entitled studies on the synthesis and transformations of a few 2(3H)- and 3(2H)- furanones. Furanones represent an interesting class of heterocyclic compounds, which constitute the central ring system of many natural products. The derivatives of furan is divided, depending on their structure 2(3H)-furanones(I), 2(5H)-furanones(II), and 3(2H)-furanones(III). Systems I&II are unsatured gama lactones known as ‘butenolides’. Compounds of this type also known as ‘crotonolactones’ based on the parent crotonic acid. In conclusion a number of 2(3H)-and 3(2H)- furanones were synthesized from dibenzoylalkene precursors and were characterized on the basis of spectral analytical and X-ray data. On direct irradiation 3,3-bis(4-chloropheneyl)-5-aryl-3H-furan -2-ones underwent decarbonylation to yield the corresponding alpha, beta- unsaturated carbonyl compounds and upon sensitized irradiation they underwent dimersation arising through a 2+2 cycloaddition reaction. Our studies on 3(2H)-furanones revealed that these compounds are thermally stable, while they undergo extensive decomposition to intractable mixtures under the influence of light. Similarly, the novel dibenzoylalkenes- type systems containing hetroatomatic rings synthesized by us also underwent extensive decomposition under the influence of heat. Some of the 3(2H)-furanones synthesized by us exhibit remarkable anti-proliferative activity.

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In this thesis, we report our endeavours in the synthesis of a few polycyclic compounds. We were interested in the synthesis of a few bicyclic compounds designed to undergo interesting photochemical transformations including tripletmediated di-π-methane rearrangement and/or competing singlet-mediated electrocyclic reactions. Our target molecules have "inbuilt" structural features which will potentially alter the photochemistry of the substrate under consideration.The present investigation was undertaken to test our hypothesis on selective intramolecular quenching of singlet or triplet excited states of molecules.We adopted Dies-Alder reaction for the synthesis of several of the bicyclic compounds we were interested in. Some of the precursor dienes synthesised by us are capable of undergoing intramolecular cycloaddition reactions as well. So, it was important to delineate the conditions and structural features that will enable a particular molecule to undergo intermolecular and intramolecular Dies-Alder reaction when treated with a suitable dienophile.Though, the main focus of this thesis is on the synthesis of bicyclic and tricyclic systems capable of undergoing di-π-methane rearrangement, in the last chapter of this thesis, we describe our findings on the synthesis of a few dispirocompounds. These systems were encountered as unexpected products in the attempted synthesis of novel dibenzoylalkene-type systems. Consequently, a brief survey on the synthesis and transformations of dibenzoylalkenes is also included as an integral part of this thesis.

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Magnetism and magnetic materials have been an ever-attractive subject area for engineers and scientists alike because of its versatility in finding applications in useful devices. They find applications in a host of devices ranging from rudimentary devices like loud speakers to sophisticated gadgets like waveguides and Magnetic Random Access Memories (MRAM).The one and only material in the realm of magnetism that has been at the centre stage of applications is ferrites and in that spinel ferrites received the lions share as far as practical applications are concerned.It has been the endeavour of scientists and engineers to remove obsolescence and improve upon the existing so as to save energy and integrate in to various other systems. This has been the hallmark of material scientists and this has led to new materials and new technologies.In the field of ferrites too there has been considerable interest to devise new materials based on iron oxides and other compounds. This means synthesising ultra fine particles and tuning its properties to device new materials. There are various preparation techniques ranging from top- down to bottom-up approaches. This includes synthesising at molecular level, self assembling,gas based condensation. Iow temperature eo-precipitation, solgel process and high energy ball milling. Among these methods sol-gel process allows good control of the properties of ceramic materials. The advantage of this method includes processing at low temperature. mixing at the molecular level and fabrication of novel materials for various devices.Composites are materials. which combine the good qualities of one or more components. They can be prepared in situ or by mechanical means by the incorporation of fine particles in appropriate matrixes. The size of the magnetic powders as well as the nature of matrix affect the processability and other physical properties of the final product. These plastic/rubber magnets can in turn be useful for various applications in different devices. In applications involving ferrites at high frequencies, it is essential that the material possesses an appropriate dielectric permittivity and suitable magnetic permeability. This can be achieved by synthesizing rubber ferrite composites (RFC's). RFCs are very useful materials for microwave absorptions. Hence the synthesis of ferrites in the nanoregirne.investigations on their size effects on the structural, magnetic, and electrical properties and the incorporation of these ferrites into polymer matrixes assume significance.In the present study, nano particles of NiFe204, Li(!5Fe2S04 and Col-e-O, are prepared by sol gel method. By appropriate heat treatments, particles of different grain sizes are obtained. The structural, magnetic and electrical measurements are evaluated as a function of grain size and temperature. NiFel04 prepared in the ultrafine regime are then incorporated in nitrile rubber matrix. The incorporation was carried out according to a specific recipe and for various loadings of magnetic fillers. The cure characteristics, magnetic properties, electrical properties and mechanical properties of these elastomer blends are carried out. The electrical permittivity of all the rubber samples in the X - band are also conducted.

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The constructional activities in the coastal belt of our country often demand deep foundations because of the poor engineering properties and the related problems arising from weak soil at shallow depths.The soil profile in coastal area often consists of very loose sandy soils extending to a depth of 3 to 4 m from the ground level underlain by clayey soils of medium consistency.The very low shearing resistance of the foundation bed causes local as well as punching shear failure.Hence structures built on these soils may suffer from excessive settlements.This type of soil profile is very common in coastal areas of Kerala,especially in Cochin. Further,the high water table and limited depth of the top sandy layer in these areas restrict the depth of foundation thereby further reducing the safe bearing capacity.

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In this thesis, the concept of reversed lack of memory property and its generalizations is studied.We we generalize this property which involves operations different than the ”addition”. In particular an associative, binary operator ” * ” is considered. The univariate reversed lack of memory property is generalized using the binary operator and a class of probability distributions which include Type 3 extreme value, power function, reflected Weibull and negative Pareto distributions are characterized (Asha and Rejeesh (2009)). We also define the almost reversed lack of memory property and considered the distributions with reversed periodic hazard rate under the binary operation. Further, we give a bivariate extension of the generalized reversed lack of memory property and characterize a class of bivariate distributions which include the characterized extension (CE) model of Roy (2002a) apart from the bivariate reflected Weibull and power function distributions. We proved the equality of local proportionality of the reversed hazard rate and generalized reversed lack of memory property. Study of uncertainty is a subject of interest common to reliability, survival analysis, actuary, economics, business and many other fields. However, in many realistic situations, uncertainty is not necessarily related to the future but can also refer to the past. Recently, Di Crescenzo and Longobardi (2009) introduced a new measure of information called dynamic cumulative entropy. Dynamic cumulative entropy is suitable to measure information when uncertainty is related to the past, a dual concept of the cumulative residual entropy which relates to uncertainty of the future lifetime of a system. We redefine this measure in the whole real line and study its properties. We also discuss the implications of generalized reversed lack of memory property on dynamic cumulative entropy and past entropy.In this study, we extend the idea of reversed lack of memory property to the discrete set up. Here we investigate the discrete class of distributions characterized by the discrete reversed lack of memory property. The concept is extended to the bivariate case and bivariate distributions characterized by this property are also presented. The implication of this property on discrete reversed hazard rate, mean past life, and discrete past entropy are also investigated.

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Nanosized ZnFe2O4 particles containing traces of a-Fe2O3 by intent were produced by low temperature chemical coprecipitation methods. These particles were subjected to high-energy ball milling. These were then characterised using X-ray diffraction, magnetisation and dielectric studies. The effect of milling on zinc ferrite particles have been studied with a view to ascertaining the anomalous behaviour of these materials in the nanoregime. X-ray diffraction and magnetisation studies carried out show that these particles are associated with strains and it is the surface effects that contribute to the magnetisation. Hematite percentage, probably due to decomposition of zinc ferrite, increases with milling. Dielectric behaviour of these particles is due to interfacial polarisation as proposed by Koops. Also the defects caused by the milling produce traps in the surface layer contributes to dielectric permittivity via spin polarised electron tunnelling between grains. The ionic mechanism is enhanced in dielectrics with the rise in temperature which results in the increase of dielectric permittivity with temperature.

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The present study helped to understand the trend in rainfall patterns at smaller spatial scales and the large regional differences in the variability of rainfall. The effect of land use and orography on the diurnal variability is also understood. But a better understanding on the long term variation in rainfall is possible by using a longer dataset,which may provide insight into the rainfall variation over country during the past century. The basic mechanism behind the interannual rainfall variability would be possible with numerical studies using coupled Ocean-Atmosphere models. The regional difference in the active-break conditions points to the significance of regional studies than considering India as a single unit. The underlying dynamics of diurnal variability need to be studied by making use of a high resolution model as the present study could not simulate the local onshore circulation. Also the land use modification in this study, selected a region, which is surrounded by crop land. This implies the high possibility for the conversion of the remaining region to agricultural land. Therefore the study is useful than considering idealized conditions, but the adverse effect of irrigated crop is more than non-irrigated crop. Therefore, such studies would help to understand the climate changes occurred in the recent period. The large accumulation of rainfall between 300-600 m height of western Ghats has been found but the reason behind this need to be studied, which is possible by utilizing datasets that would better represent the orography and landuse over the region in high resolution model. Similarly a detailed analysis is needed to clearly identify the causative relations of the predictors identified with the predictant and the physical reasons behind them. New approaches that include nonlinear relationships and dynamical variables from model simulations can be included in the existing statistical models to improve the skill of the models. Also the statistical models for the forecasts of monsoon have to be continually updated.

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The thesis entitled ‘Studies on the Solvent Dependence in the Reaction of a Few (Anthracen-9-yl)methylamines and Sulfanes with Reactive Acetylenes’ is divided into six chapters. ln Chapter l a general survey of electron transfer reactions, Diels-Alder reactions and Michael-type additions is presented. A detailed discussion on the synthesis of several (anthracen-9-yl)methylamines is presented in Chapter 2. In Chapter 3, results of preliminary photophysical studies on a few (anthracen-9yl) methylamines are compiled. A detailed discussion on extensive examination of dependence in the reaction of (anthracen-9-yl)methylamines with reactive acetylenes is presented Chapter 4. Details on the synthesis and reaction of a few (anthracen-9-yl)methylsulfanes with DMAD are described in Chapter 5.

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The thesis entitled Studies on the Dynamics of Cochin Estuary. This thesis is addressed to an investigation on the tidal, seasonal and spatial variations of the hydrographic parameters, circulation and mixing processes of the Cochin estuary. The present programme of study is aimed at obtaining a comprehensive picture of the tidal characteristics, hydrography, circulation and mixing present in this estuarine system during different seasons. The studies have been carried out through field collection of data on salinity, temperature and water currents to get a picture of their spatial and temporal variations. The hydrographic data have been analysed in relation to tide, rainfall and river discharges. From the findings it is seen that at the Cochin inlet, the estuarine features vary annually. During July and August, the estuary is characterised as almost saltwedge type; during June, September, October, December and January it shows appreciabie stratification, and during the rest of the months the estuary shows almost well mixed nature. Seasonal variations are well reflected in water temperature in the Cochin estuary, where the temperature reaches its maximum during the dry pre monsoon period with very weak thermal gradients indicating strong vertical mixing

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There is no baseline data available at present on the nature of various diseases that occur in a orchid population, under cultivation, in any commercial orchid farm maintained by small scale entrepreneurs who invest considerable amount of money, effort and time. The available data on type of disease symptoms, causative agent, , nature of pathogens, as to bacteria or ftmgi or any other biological agents, and their source, appropriate and effective control measures could not be devised, for large scale implementation and effective management, although arbitrary methods are being practiced by very few farms. Further influence of seasonal variations and environmental factors on disease outbreak is also not scientifically documented and statistically verified as to their authenticity. In this context, the primary objective of the present study was to create a data bank on the following aspects 1. Occurrence of different disease symptoms in Dendrobium hybrid over a period of one year covering all seasons 2. Variations in the environmental parameters at the orchid farms 3. Variations in the characteristics of water used for irrigation in the selected orchid farm 4. Microbial population associated with the various disease symptoms 5. Isolation and identification of bacteria isolated from diseased plants 6. Statistical treatment of the quantitative data and evolving statistical model

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It is important that long superconducting tape must have desired strain tolerance (less reduction of Jc with applied strains) and stress tolerance (less reduction of JC in applied stresses) for its use as coils and magnets. Ag addition to the BPSCCO system has many advantages with its physical and chemical inertness to the system, reduces the processing temperature, and promotes the grain growth, grain alignment and connectivity. All these not only enhance the critical current density of the tapes but also improve the mechanical properties. But the published results show very much scattering on the type of Ag additive to be selected, method of addition and its optimum percentage. Also there are some negative reports in this regard. The present work has been undertaken to study the effect of silver addition in different forms (Ag powder, Ag2O, AgNO3) on the superconducting and mechanical properties of (Bi,Pb)-2223/Ag tapes and to find out a suitable form of Ag additive and its optimum percentage to have better superconducting and mechanical properties. Also it is the aim of the present work is to optimise the process parameters needed to prepare (Bi,Pb)-2223/Ag multifilamentary tapes of length ~ 12 m in solenoid and pancake coil forms with good critical current density and homogeneity of J C along the length of the tapes.

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In the present work different new approaches for the synthesis of Vitamin A are investigated. In these synthetic schemes, all the twenty carbon atoms of the target molecule are derived either fully from components isolated from common essential oils or partially from commercially available materials. By retrosynthetic analysis, Vitamin A molecule can be disconnected into a cyclic and a linear unit. Different methods for the synthesis of the linear and the cyclic components are described. The monoterpenes, geraniol and citral, major constituents of palmarosa and lemongrass oils, have the required basic carbon framework for consideration as starting materials for the synthesis of Vitamin A. The potential of these easily available naturally occurring compounds as promising starting materials for Vitamin A synthesis is demonstrated. Organoselenium and organosulfur mediated functional group transformations for the synthesis of the functionalised conjugated C10 linear components (ie., the dimethyloctatriene derivatives) are reported. The classical approaches as well as the attempted preparation of cyclic C10 and C13 units employed in the present study as intermediates for Vitamin A synthesis are described. The utility of commercially available materials namely 2-acetylbutyrolactone and levulinic acid in -the preparation of C5 intermediates for Vitamin A synthesis is demonstrated.