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

Development of Zero Water Exchange Shrimp Culture System Integrated With Bioremediation of Detritus and Ammonia- Nitrogen

Aquaculture is one of the fastest growing food sectors in the world. Amongst the various branches of aquaculture, shrimp culture has expanded rapidly across the globe because of its faster growth rate, short culture period, high export value and demand in the International market. Indian shrimp farming has experienced phenomenal development over the decades due to its excellent commercial viability. Farmers have adopted a number of innovative technologies to improve the production and to maximize the returns per unit area. The culture methods adopted can be classified in to extensive, modified extensive and semi intensive based on the management strategies adopted in terms of pond size, stocking density, feeding and environmental control. In all these systems water exchanges through the natural tidal effects, or pump fed either from creek or from estuaries is a common practice. In all the cases, the systems are prone to epizootics due to the pathogen introduction through the incoming water, either brought by vectors, reservoir hosts, infected tissue debris and free pathogens themselves. In this scenario, measures to prevent the introduction of pathogen have become a necessity to protect the crop from the onslaught of diseases as well as to prevent the discharge of waste water in to the culture environment.The present thesis deals with Standardization of bioremediation technology for zero water exchange shrimp culture system

Formation of elliptically polarized beam from h-plane sectoral horns using corrugated flanges

The flange technique, suggested by Reynolds72 is simple technique to improve antenna characteristics. Using flange technique we can trim the antenna characteristic by suitably adjusting the flange parameters75. Later corrugated flanges87 are used for beam shaping. The important parameters of the corrugated flanges are (a) flange angle, (b) flange width, (c) flange position, (d) conductivity of the flange, (e) amplitude excitation of the flange elements, (f) period of corrugation etc. Compared to a compound horn the flange technique offers great convenience in trimming antenna characteristics. Horns are commonly used as a feed in radar and satellite communications. A large number of work had been done to improve the characteristics of horn antennas. It is an established fact that grooved walls on the inner surface of a horn can improve the antenna characteristics44. Corrugated comb surface can be used for the circular polarization98, tilt of polarization99 etc. This suggests the possibility to combine these two phenomena and to obtain a resultant beam. This thesis presents the result of an investigation to study the possibility of controlling different antenna characteristics like polarization, beam shaping, matching etc, using corrugated flange techniques.

Ab initio study of the charge order and Zener polaron formation in half-doped manganites

The character of the electronic ground state of La0.5Ca0.5MnO3 has been addressed with quantum chemical calculations on large embedded clusters. We find a charge ordered state for the crystal structure reported by Radaelli et al. [Phys. Rev. B 55, 3015 (1997)] and Zener polaron formation in the crystal structure with equivalent Mn sites proposed by Daoud-Aladine et al. [Phys. Rev. Lett. 89, 097205 (2002)]. Important O to Mn charge transfer effects are observed for the Zener polaron.

Right to Maintenance Under Criminal Law - A Critical Study

Some study has been made earlier, but no attempt has ever been made to make the study comprehensive and comparative. There exists also no information as to the working of the system. Hence the work is undertaken to provide first hand knowledge of the legal institutions that had handled and now handles annually large masses of deprived and neglected population. An investigation is also necessary to know the legal and social characteristics of the jurisdiction enjoined on the court so that this will help compare the law in the statute with the law and practice. The evaluation of the working system in the changed social atmosphere is also an urgent need of the hour

"Right to Personal Liberty Under the Indian Constitution - With Special Reference to Judicial Process"

The nature and extent of protection secured to personal liberty has been a subject matter of great controversy and debate. The expression "procedure established by law" as a standard of protection for personal liberty has been looked upon as highly unsatisfactory and inadequate. For, unlike the specific attributes of liberty that are separately guaranteed under Art.19, ‘personal liberty‘ as guaranteed by Art.21 does not obligate the .Legislature to comply with the requirements of justice and reasonableness as and when it enchroaches upon that right. Though the concept of ‘personal liberty‘ has received an evolutive and expansive meaning through judicial process, the standard of protection which the judicial process could secure to personal liberty through the interpretation of Art.21 has been far from satisfactory Even after four decades of judicial process in the interpretation of Art.21 the problem of evolving a just and adequate standard of protection for personal liberty in that Article continues to be 21 crucial constitutional issue, craving for a. satisfactory solution. And the present study is a humble attempt to unravel this problem and to Search for a reasonable solution.

“Right to Privacy and Freedom of Press - Conflicts and Challenges”

India is a signatory to the United Nations Declaration of Human Rights 1948 and the International Covenant on Civil and Political 1966, the two major International instruments, building the foundations of the major democracies and the constitutions of the world. Both these instruments give an independent and upper position to right to privacy compared to right to freedom of speech and expression. The freedom of press finds its place under this right to freedom of speech and expression. Both these rights are the two opposite faces of the same coin. Therefore, without the right of privacy finding an equal place in Indian law compared to right to freedom of speech and expression, the working of democracy would be severely handicapped and violations against citizens rights will be on the rise It was this problem in law and need to bring a balance between these two conflicting rights that induced me to undertake this venture. This heavy burden to bring in a mechanism to balance these two rights culminated in me to undertake this thesis titled “Right to Privacy and Freedom of Press – Conflicts and Challenges

Photometric and fundamental plane studies of galaxies

Determining the morphological parameters that describe galaxies has always been a challenging task. The studies on the correlations between different photometric as well as spectroscopic parameters of the galaxies help in understanding their structure, properties of the stars and gas which constitute the galaxy, the various physical and chemical processes which determine the properties, and galaxy formation and evolution. In the last few decades, the advent of Charge Coupled Devices (CCDs) and near infrared arrays ha\·e provided quick and reliable digitized data acquisition, in the optical and near infrared bands. This has provided an avalanche of data, which can be processed using sophisticated image analysis techniques to obtain information about the morphology of galaxies. The photometric analysis performed in this thesis involve the extraction of structural parameters of early type gala.xies imaged in the near infrared K (2.2ttm) band, obtaining correlations between these, parameters and using them to constrain the large scale properties of galaxi,~s.

Planar UWB Antenna with Modified Slotted Ground Plane

A compact coplanar waveguide-fed (CPW) monopole antenna for ultra-wideband wireless communication is presented. The proposed antenna comprises of a CPW-fed beveled rectangular patch with a modified slotted ground. The overall size of the antenna is 30 mm 27 mm 1.6 mm. The lower edge of the band is attained by properly decoupling the resonant frequencies due to the extended ground plane and the beveled rectangular patch of the antenna. The upper edge of the radiating band is enhanced by beveling the ground plane corners near the feed point. Experimental results show that the designed antenna operates in the 2.7–12 GHz band, for S11 10 dB with a gain of 2.7–5 dBi. Both the frequency domain and time domain characteristics of the antenna are investigated using antenna transfer function. It is observed that the antenna exhibits identical radiation patterns and reasonable transient characteristics over the entire operating band

Design Of Compact Microstrip Antennas Using A Modified Ground Plane

A method for simultaneously enhancing the bandwidth and reducing the size of microstrip antennas (MSAs) using a modified ground plane (GP) has been proposed with design formulas. A combshaped truncated GP is used for this purpose. This method provides an overall compactness up to 85% for proximity-coupled MSAs in the frequency range of 900 MHz–5.5 GHz with an improvement inbandwidth up to seven times when compared with the conventional ones

Design and Analysis of Zero Cogging Brushless DC Motor for Spacecraft Applications

This paper presents the optimal design of a sur- face mounted permanent magnet Brushless DC mo- tor (PMBLDC) meant for spacecraft applications. The spacecraft applications requires the choice of a torques motor with high torque density, minimum cogging torque, better positional stability and high torque to inertia ratio. Performance of two types of machine con¯gurations viz Slotted PMBLDC and Slotless PMBLDC with halbach array are compared with the help of analytical and FE methods. It is found that unlike a Slotted PMBLDC motor, the Slotless type with halbach array develops zero cogging torque without reduction in the developed torque. Moreover, the machine being coreless provides high torque to inertia ratio and zero magnetic stiction

Effect of Concentration of DYE on the Storage Life of Plane Wave Gratings on Photopolymer Film

Holographic grating with good storage life in poly(vinyl alcohol) based photopolymer film, prepared by gravity settling method, with reduced concentration of the dye was found to give good diffraction efficiency without crosslinking. The material was found to show good diffraction efficiency and sensitivity (75% diffraction efficiency at exposure energy of 80 mJ/cm2). The shelf life of the photopolymer solution could be improved by storage at a temperature 4 C in refrigerator

Synthesis, Characterization and Applications of Modified TiO2 Systems

This thesis is divided in to 9 chapters and deals with the modification of TiO2 for various applications include photocatalysis, thermal reaction, photovoltaics and non-linear optics. Chapter 1 involves a brief introduction of the topic of study. An introduction to the applications of modified titania systems in various fields are discussed concisely. Scope and objectives of the present work are also discussed in this chapter. Chapter 2 explains the strategy adopted for the synthesis of metal, nonmetal co-doped TiO2 systems. Hydrothermal technique was employed for the preparation of the co-doped TiO2 system, where Ti[OCH(CH3)2]4, urea and metal nitrates were used as the sources for TiO2, N and metals respectively. In all the co-doped systems, urea to Ti[OCH(CH3)2]4 was taken in a 1:1 molar ratio and varied the concentration of metals. Five different co-doped catalytic systems and for each catalysts, three versions were prepared by varying the concentration of metals. A brief explanation of physico-chemical techniques used for the characterization of the material was also presented in this chapter. This includes X-ray Diffraction (XRD), Raman Spectroscopy, FTIR analysis, Thermo Gravimetric Analysis, Energy Dispersive X-ray Analysis (EDX), Scanning Electron Microscopy(SEM), UV-Visible Diffuse Reflectance Spectroscopy (UV-Vis DRS), Transmission Electron Microscopy (TEM), BET Surface Area Measurements and X-ray Photoelectron Spectroscopy (XPS). Chapter 3 contains the results and discussion of characterization techniques used for analyzing the prepared systems. Characterization is an inevitable part of materials research. Determination of physico-chemical properties of the prepared materials using suitable characterization techniques is very crucial to find its exact field of application. It is clear from the XRD pattern that photocatalytically active anatase phase dominates in the calcined samples with peaks at 2θ values around 25.4°, 38°, 48.1°, 55.2° and 62.7° corresponding to (101), (004), (200), (211) and (204) crystal planes (JCPDS 21-1272) respectively. But in the case of Pr-N-Ti sample, a new peak was observed at 2θ = 30.8° corresponding to the (121) plane of the polymorph brookite. There are no visible peaks corresponding to dopants, which may be due to their low concentration or it is an indication of the better dispersion of impurities in the TiO2. Crystallite size of the sample was calculated from Scherrer equation byusing full width at half maximum (FWHM) of the (101) peak of the anatase phase. Crystallite size of all the co-doped TiO2 was found to be lower than that of bare TiO2 which indicates that the doping of metal ions having higher ionic radius into the lattice of TiO2 causes some lattice distortion which suppress the growth of TiO2 nanoparticles. The structural identity of the prepared system obtained from XRD pattern is further confirmed by Raman spectra measurements. Anatase has six Raman active modes. Band gap of the co-doped system was calculated using Kubelka-Munk equation and that was found to be lower than pure TiO2. Stability of the prepared systems was understood from thermo gravimetric analysis. FT-IR was performed to understand the functional groups as well as to study the surface changes occurred during modification. EDX was used to determine the impurities present in the system. The EDX spectra of all the co-doped samples show signals directly related to the dopants. Spectra of all the co-doped systems contain O and Ti as the main components with low concentrations of doped elements. Morphologies of the prepared systems were obtained from SEM and TEM analysis. Average particle size of the systems was drawn from histogram data. Electronic structures of the samples were identified perfectly from XPS measurements. Chapter 4 describes the photocatalytic degradation of herbicides Atrazine and Metolachlor using metal, non-metal co-doped titania systems. The percentage of degradation was analyzed by HPLC technique. Parameters such as effect of different catalysts, effect of time, effect of catalysts amount and reusability studies were discussed. Chapter 5 deals with the photo-oxidation of some anthracene derivatives by co-doped catalytic systems. These anthracene derivatives come underthe category of polycyclic aromatic hydrocarbons (PAH). Due to the presence of stable benzene rings, most of the PAH show strong inhibition towards biological degradation and the common methods employed for their removal. According to environmental protection agency, most of the PAH are highly toxic in nature. TiO2 photochemistry has been extensively investigated as a method for the catalytic conversion of such organic compounds, highlighting the potential of thereof in the green chemistry. There are actually two methods for the removal of pollutants from the ecosystem. Complete mineralization is the one way to remove pollutants. Conversion of toxic compounds to another compound having toxicity less than the initial starting compound is the second way. Here in this chapter, we are concentrating on the second aspect. The catalysts used were Gd(1wt%)-N-Ti, Pd(1wt%)-N-Ti and Ag(1wt%)-N-Ti. Here we were very successfully converted all the PAH to anthraquinone, a compound having diverse applications in industrial as well as medical fields. Substitution of 10th position of desired PAH by phenyl ring reduces the feasibility of photo reaction and produced 9-hydroxy 9-phenyl anthrone (9H9PA) as an intermediate species. The products were separated and purified by column chromatography using 70:30 hexane/DCM mixtures as the mobile phase and the resultant products were characterized thoroughly by 1H NMR, IR spectroscopy and GCMS analysis. Chapter 6 elucidates the heterogeneous Suzuki coupling reaction by Cu/Pd bimetallic supported on TiO2. Sol-Gel followed by impregnation method was adopted for the synthesis of Cu/Pd-TiO2. The prepared system was characterized by XRD, TG-DTG, SEM, EDX, BET Surface area and XPS. The product was separated and purified by column chromatography using hexane as the mobile phase. Maximum isolated yield of biphenyl of around72% was obtained in DMF using Cu(2wt%)-Pd(4wt%)-Ti as the catalyst. In this reaction, effective solvent, base and catalyst were found to be DMF, K2CO3 and Cu(2wt%)-Pd(4wt%)-Ti respectively. Chapter 7 gives an idea about the photovoltaic (PV) applications of TiO2 based thin films. Due to energy crisis, the whole world is looking for a new sustainable energy source. Harnessing solar energy is one of the most promising ways to tackle this issue. The present dominant photovoltaic (PV) technologies are based on inorganic materials. But the high material, low power conversion efficiency and manufacturing cost limits its popularization. A lot of research has been conducted towards the development of low-cost PV technologies, of which organic photovoltaic (OPV) devices are one of the promising. Here two TiO2 thin films having different thickness were prepared by spin coating technique. The prepared films were characterized by XRD, AFM and conductivity measurements. The thickness of the films was measured by Stylus Profiler. This chapter mainly concentrated on the fabrication of an inverted hetero junction solar cell using conducting polymer MEH-PPV as photo active layer. Here TiO2 was used as the electron transport layer. Thin films of MEH-PPV were also prepared using spin coating technique. Two fullerene derivatives such as PCBM and ICBA were introduced into the device in order to improve the power conversion efficiency. Effective charge transfer between the conducting polymer and ICBA were understood from fluorescence quenching studies. The fabricated Inverted hetero junction exhibited maximum power conversion efficiency of 0.22% with ICBA as the acceptor molecule. Chapter 8 narrates the third order order nonlinear optical properties of bare and noble metal modified TiO2 thin films. Thin films were fabricatedby spray pyrolysis technique. Sol-Gel derived Ti[OCH(CH3)2]4 in CH3CH2OH/CH3COOH was used as the precursor for TiO2. The precursors used for Au, Ag and Pd were the aqueous solutions of HAuCl4, AgNO3 and Pd(NO3)2 respectively. The prepared films were characterized by XRD, SEM and EDX. The nonlinear optical properties of the prepared materials were investigated by Z-Scan technique comprising of Nd-YAG laser (532 nm,7 ns and10 Hz). The non-linear coefficients were obtained by fitting the experimental Z-Scan plot with the theoretical plots. Nonlinear absorption is a phenomenon defined as a nonlinear change (increase or decrease) in absorption with increasing of intensity. This can be mainly divided into two types: saturable absorption (SA) and reverse saturable absorption (RSA). Depending on the pump intensity and on the absorption cross- section at the excitation wavelength, most molecules show non- linear absorption. With increasing intensity, if the excited states show saturation owing to their long lifetimes, the transmission will show SA characteristics. Here absorption decreases with increase of intensity. If, however, the excited state has strong absorption compared with that of the ground state, the transmission will show RSA characteristics. Here in our work most of the materials show SA behavior and some materials exhibited RSA behavior. Both these properties purely depend on the nature of the materials and alignment of energy states within them. Both these SA and RSA have got immense applications in electronic devices. The important results obtained from various studies are presented in chapter 9.

Faktorisierung in Schief-Polynomringen

In der Arbeit werden zunächst die wesentlichsten Fakten über Schiefpolynome wiederholt, der Fokus liegt dabei auf Shift- und q-Shift-Operatoren in Charakteristik Null. Alle für die Arithmetik mit diesen Objekten notwendigen Konzepte und Algorithmen finden sich im ersten Kapitel. Einige der zur Bestimmung von Lösungen notwendigen Daten können aus dem Newtonpolygon, einer den Operatoren zugeordneten geometrischen Figur, abgelesen werden. Die Herleitung dieser Zusammenhänge ist das Thema des zweiten Kapitels der Arbeit, wobei dies insbesondere im q-Shift-Fall in dieser Form neu ist. Das dritte Kapitel beschäftigt sich mit der Bestimmung polynomieller und rationaler Lösungen dieser Operatoren, dabei folgt es im Wesentlichen der Darstellung von Mark van Hoeij. Der für die Faktorisierung von (q-)Shift Operatoren interessanteste Fall sind die sogenannten (q-)hypergeometrischen Lösungen, die direkt zu Rechtsfaktoren erster Ordnung korrespondieren. Im vierten Kapitel wird der van Hoeij-Algorithmus vom Shift- auf den q-Shift-Fall übertragen. Außerdem wird eine deutliche Verbesserung des q-Petkovsek-Algorithmus mit Hilfe der Daten des Newtonpolygons hergeleitet. Das fünfte Kapitel widmet sich der Berechnung allgemeiner Faktoren, wozu zunächst der adjungierte Operator eingeführt wird, der die Berechnung von Linksfaktoren erlaubt. Dann wird ein Algorithmus zur Berechnung von Rechtsfaktoren beliebiger Ordnung dargestellt. Für die praktische Benutzung ist dies allerdings für höhere Ordnungen unpraktikabel. Bei fast allen vorgestellten Algorithmen tritt das Lösen linearer Gleichungssysteme über rationalen Funktionenkörpern als Zwischenschritt auf. Dies ist in den meisten Computeralgebrasystemen nicht befriedigend gelöst. Aus diesem Grund wird im letzten Kapitel ein auf Evaluation und Interpolation basierender Algorithmus zur Lösung dieses Problems vorgestellt, der in allen getesteten Systemen den Standard-Algorithmen deutlich überlegen ist. Alle Algorithmen der Arbeit sind in einem MuPAD-Package implementiert, das der Arbeit beiliegt und eine komfortable Handhabung der auftretenden Objekte erlaubt. Mit diesem Paket können in MuPAD nun viele Probleme gelöst werden, für die es vorher keine Funktionen gab.