Finite size effects on the electrical properties of sol–gel synthesized CoFe2O4 powders: deviation from Maxwell–Wagner theory and evidence of surface polarization effects

Fine particles of cobalt ferrite were synthesized by the sol–gel method. Subsequent heat treatment at different temperatures yielded cobalt ferrites having different grain sizes. X-ray diffraction studies were carried out to elucidate the structure of all the samples. Dielectric permittivity and ac conductivity of all the samples were evaluated as a function of frequency, temperature and grain size. The variation of permittivity and ac conductivity with frequency reveals that the dispersion is due to Maxwell–Wagner type interfacial polarization in general, with a noted variation from the expected behaviour for the cold synthesized samples. High permittivity and conductivity for small grains were explained on the basis of the correlated barrier-hopping model

Some problems of discrete function theory

An attempt is made by the researcher to establish a theory of discrete functions in the complex plane. Classical analysis q-basic theory, monodiffric theory, preholomorphic theory and q-analytic theory have been utilised to develop concepts like differentiation, integration and special functions.

Some Generalizations of Fuzzy Metrizability

The main purpose of the study is to extent concept of the class of spaces called ‘generalized metric spaces’ to fuzzy context and investigates its properties. Any class of spaces defined by a property possessed by all metric spaces could technically be called as a class of ‘generalized metric spaces’. But the term is meant for classes, which are ‘close’ to metrizable spaces in some under certain kinds of mappings. The theory of generalized metric spaces is closely related to ‘metrization theory���. The class of spaces likes Morita’s M- spaces, Borges’s w-spaces, Arhangelskii’s p-spaces, Okuyama’s  spaces have major roles in the theory of generalized metric spaces. The thesis introduces fuzzy metrizable spaces, fuzzy submetrizable spaces and proves some characterizations of fuzzy submetrizable spaces, and also the fuzzy generalized metric spaces like fuzzy w-spaces, fuzzy Moore spaces, fuzzy M-spaces, fuzzy k-spaces, fuzzy -spaces study of their properties, prove some equivalent conditions for fuzzy p-spaces. The concept of a network is one of the most useful tools in the theory of generalized metric spaces. The -spaces is a class of generalized metric spaces having a network.

Concomitants of Order Statistics from Morgenstern Family

The study deals with the distribution theory and applications of concomitants from the Morgenstern family of bivariate distributions.The Morgenstern system of distributions include all cumulative distributions of the form FX,Y(X,Y)=FX(X) FY(Y)[1+α(1-FX(X))(1-FY(Y))], -1≤α≤1.The system provides a very general expression of a bivariate distributions from which members can be derived by substituting expressions of any desired set of marginal distributions.It is a brief description of the basic distribution theory and a quick review of the existing literature.The Morgenstern family considered in the present study provides a very general expression of a bivariate distribution from which several members can be derived by substituting expressions of any desired set of marginal distributions.Order statistics play a very important role in statistical theory and practice and accordingly a remarkably large body of literature has been devoted to its study.It helps to develop special methods of statistical inference,which are valid with respect to a broad class of distributions.The present study deals with the general distribution theory of Mk, [r: m] and Mk, [r: m] from the Morgenstern family of distributions and discuss some applications in inference, estimation of the parameter of the marginal variable Y in the Morgestern type uniform distributions.

Inherent Powers of the High Court under Section 482 of the Code of Criminal Procedure 1973

This thesis is shows the result of the research work on the inherent Powers of the High Court in criminal jurisdiction. The criminal justice system in India recognizes inherent powers only of the High Court. The Theory and Philosophy of inherent powers are concerned the Distinction between civil and Criminal laws are of very little consequence. In formulating the research programme the confusion created by the concept of inherent powers and its application by High Court form the central point. How fully the concept is understood, how correctly the power is used, and how far it has enhanced the rationale of the administration of criminal justice, what is its importance and what are the solutions for the inherent power to earn a permanent status in the province of criminal jurisprudence are the themes of this study. The precipitation of new dimensions is the yardstick to acknowledge the inherent powers of the High Court and Supreme Court. It is of instant value in criminal justice system. This study concludes innovativeness provided by the inherent powers has helped the justice administration draw inspiration from the Constitution. A jurisprudence of inherent powers has developed with the weilding of inherent powers of the Supreme Court and the High Court. It is to unravel mystery of jurisprudence caused by the operation of the concept of inherent powers this research work gives emphasis. Its significance is all the more relevant when the power is exercised in the administration of criminal justice. Application or non application of inherent powers in a given case would tell upon the maturity and perfection of the standard of justice

Salting Coefficients of Fluorobenzoic Acids

The Setschenow parameter and thermodynamic parameters of transfer of 2-, 3- and 4-fluorobenzoic acid from water to salt solution are reported. The data have been rationalized by considering the structure breaking effects of the ions of the salts, the localized hydrolysis model and the internal pressure theory.

Salting Coefficients of 2-, 3-, and 4-Methylbenzoic Acids

The Setschenow parameter and thermodynamic parameters of transfer of 2-, 3-, and 4-methylbenzoic acids from water to salt solutions have been reported. The data have been rationalized by considering the structure breaking effects of the ions of the salts, the localized hydrolysis model, and the internal pressure theory.

Signatures of Higher Functions of Brain Dynamics in Electroencephalogram: A Nonlinear Analysis

The brain with its highly complex structure made up of simple units,imterconnected information pathways and specialized functions has always been an object of mystery and sceintific fascination for physiologists,neuroscientists and lately to mathematicians and physicists. The stream of biophysicists are engaged in building the bridge between the biological and physical sciences guided by a conviction that natural scenarios that appear extraordinarily complex may be tackled by application of principles from the realm of physical sciences. In a similar vein, this report aims to describe how nerve cells execute transmission of signals ,how these are put together and how out of this integration higher functions emerge and get reflected in the electrical signals that are produced in the brain.Viewing the E E G Signal through the looking glass of nonlinear theory, the dynamics of the underlying complex system-the brain ,is inferred and significant implications of the findings are explored.

Thermodynamics of Transfer of Aminobenzoic Acids from Water to Aqueous Salt Solutions

The Setschenow parameter and thermodynamic parameters of transfer of 2- and 4-aminobenzoic acids from water to salt solutions have been reported. The results are discussed in terms of the structure- breaking effects of the ions of the salts, the localized hydrolysis model, and the internal pressure theory.

Judicial Creativity in Constitutional Interpretation

The focus of study in this thesis is on the necessity and extent of judicial creativity in interpreting provisions in certain crucial areas in the Constitution of India. Judicial innovation was essential to adapt the constitutional provisions to modern changed context. Creativity of the Court has been mainly in the creation and introduction of certain new concepts not found in any specific provision of the Constitution which, but were essential for its meaningful interpretation.Independence of the judiciary, basic structure and certain elements of social justice cherished as ideal by the makers of the Constitution are some such concepts infused into the Constitution by the judiciary. The second aspect of creativity lies in the attempt of the Court to construe provisions in the Constitution with a view to upholding and maintaining the concepts so infused into the Constitution. Introduction of those concepts into the Constitution was necessary and is justified. all important features of the Constitution like democratic form of government, federal structure, judicial review, independence of judiciary and rule of law were thus included in the doctrine to prevent their alteration by amendments.As a result of such a construction, the nature of those directive principles itself has changed. They ceased to be mere directives for state action but became mandate for it. If left to legislative or executive will for their implementation, the directives would have remained enforceable as ordinary right.To conclude, notwithstanding the errors committed by the Supreme Court in construing the provisions in the above areas, they stand testimony to its creative and innovative response in interpreting the Constitution. If this trend is continued, it will be possible to achieve through the judicial process, maintenance of independence of the judiciary, avoidance of destruction of the Constitution through the process of amendment and realisation of social justice envisaged in the directive principles. It can be hoped that the Court would maintain its energetic and vibrant mind and rise up to the occasions and extend the same to other areas in future.

Studies in the geometry of the discrete plane

This thesis is an attempt to initiate the development of a discrete geometry of the discrete plane H = {(qmxo,qnyo); m,n e Z - the set of integers}, where q s (0,1) is fixed and (xO,yO) is a fixed point in the first quadrant of the complex plane, xo,y0 ¢ 0. The discrete plane was first considered by Harman in 1972, to evolve a discrete analytic function theory for geometric difference functions. We shall mention briefly, through various sections, the principle of discretization, an outline of discrete a alytic function theory, the concept of geometry of space and also summary of work done in this thesis

Properties of Anisotropic Superconductors in SR Model

The present thesis deals with the theoretical investigations on the effect of anisotropy on various properties of magnetically doped superconductors described by fihiba — Rusinov model.Chapter 1 is introductory. It contains a brief account of the current status of theory of superconductivity. In’ chapter 2 we give the formulation of the problem. Chapter 2.1 gives the BCS theory. The effect of magnetic impurities in superconductors as described by A8 theory is given in chapter 2.2A and that described by SR model is discussed in chapter 2.28. Chapter 2.2c deals with Kondo effect. In chapter 2.3 the anisotropy problem is reviewed. Our calculations, results and discussions are given in chapter 3. Chapter 3.1 deals with Josephson tunnel effect. In chapter 3.2 the thermodynamic critical field H62 is described. Chtpter 3.3 deals with the density of states. The ultrasonic attenuation coefficient and ufitlear spin relaxation are given in chapter 3.4 and 3.5 respectively. In chapter 3.6 we give the upper critical field calculations and chapter 3.7 deals with the response function. The Kondo effect is given in chapter 3.8. In chapter 4 we give the sumary of our results

Design, Development and Realization of Quadratic Volterra Filters for Selected Applications

The basic concepts of digital signal processing are taught to the students in engineering and science. The focus of the course is on linear, time invariant systems. The question as to what happens when the system is governed by a quadratic or cubic equation remains unanswered in the vast majority of literature on signal processing. Light has been shed on this problem when John V Mathews and Giovanni L Sicuranza published the book Polynomial Signal Processing. This book opened up an unseen vista of polynomial systems for signal and image processing. The book presented the theory and implementations of both adaptive and non-adaptive FIR and IIR quadratic systems which offer improved performance than conventional linear systems. The theory of quadratic systems presents a pristine and virgin area of research that offers computationally intensive work. Once the area of research is selected, the next issue is the choice of the software tool to carry out the work. Conventional languages like C and C++ are easily eliminated as they are not interpreted and lack good quality plotting libraries. MATLAB is proved to be very slow and so do SCILAB and Octave. The search for a language for scientific computing that was as fast as C, but with a good quality plotting library, ended up in Python, a distant relative of LISP. It proved to be ideal for scientific computing. An account of the use of Python, its scientific computing package scipy and the plotting library pylab is given in the appendix Initially, work is focused on designing predictors that exploit the polynomial nonlinearities inherent in speech generation mechanisms. Soon, the work got diverted into medical image processing which offered more potential to exploit by the use of quadratic methods. The major focus in this area is on quadratic edge detection methods for retinal images and fingerprints as well as de-noising raw MRI signals

Studies on collective excitations of quasi-two-dimensional Bose-Einstein condensate

Theory Division Department of Physics

Studies on Bio-Geochemistry, Bio-Optical Properties and Satellite Validation of Coastal Waters of South Eastern Arabian Sea

In situ methods used for water quality assessment have both physical and time constraints. Just a limited number of sampling points can be performed due to this, making it difficult to capture the range and variability of coastal processes and constituents. In addition, the mixing between fresh and oceanic water creates complex physical, chemical and biological environment that are difficult to understand, causing the existing measurement methodologies to have significant logistical, technical, and economic challenges and constraints. Remote sensing of ocean colour makes it possible to acquire information on the distribution of chlorophyll and other constituents over large areas of the oceans in short periods. There are many potential applications of ocean colour data. Satellite-derived products are a key data source to study the distribution pattern of organisms and nutrients (Guillaud et al. 2008) and fishery research (Pillai and Nair 2010; Solanki et al. 2001. Also, the study of spatial and temporal variability of phytoplankton blooms, red tide identification or harmful algal blooms monitoring (Sarangi et al. 2001; Sarangi et al. 2004; Sarangi et al. 2005; Bhagirathan et al., 2014), river plume or upwelling assessments (Doxaran et al. 2002; Sravanthi et al. 2013), global productivity analyses (Platt et al. 1988; Sathyendranath et al. 1995; IOCCG2006) and oil spill detection (Maianti et al. 2014). For remote sensing to be accurate in the complex coastal waters, it has to be validated with the in situ measured values. In this thesis an attempt to study, measure and validate the complex waters with the help of satellite data has been done. Monitoring of coastal ecosystem health of Arabian Sea in a synoptic way requires an intense, extensive and continuous monitoring of the water quality indicators. Phytoplankton determined from chl-a concentration, is considered as an indicator of the state of the coastal ecosystems. Currently, satellite sensors provide the most effective means for frequent, synoptic, water-quality observations over large areas and represent a potential tool to effectively assess chl-a concentration over coastal and oceanic waters; however, algorithms designed to estimate chl-a at global scales have been shown to be less accurate in Case 2 waters, due to the presence of water constituents other than phytoplankton which do not co-vary with the phytoplankton. The constituents of Arabian Sea coastal waters are region-specific because of the inherent variability of these optically-active substances affected by factors such as riverine input (e.g. suspended matter type and grain size, CDOM) and phytoplankton composition associated with seasonal changes.