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.

Preparation, Characterisation And Microwave Dielectric Properties Of Anbn-1o3n (N=5,6,8) Type Perovskite Compounds

The present study on the preparation , characterization and microwave dielectric properties of AnBn-1O3n (N=5,6,8) type perovskite compounds. The explored ceramics show dielectric constant between 11 and 54,quality factor in the range 2400 to 88900 GHz and Tf in the range -73 to +231ppm/0C.Most of the investigated cation deficient hexagonal perovskites show intermediate dielectric constant with high quality factors. This study gives a general introduction about material, scientific and technological aspects of DRs.Three important ,€r ,Q and Tf, used for the DR characterization are described. The relationship of the above parameters with the fundamental material characteristics is discussed. Different modes are excited when a DR is excited with suitable microwave spectrum of frequencies .A description of analytical determination of frequencies and construction of mode charts used for sample design and mode identification are also discussed. In this study several ceramics are developed for DR purposes, very little attention has been paid to grow the single crystals. It might be due to the fact that the difficulties and time involved in the growth of single crystals, big enough to function as microwave resonators make them expensive .However single crystals of these materials may have very high Q values. It is also possible that a better understanding of the dielectric properties in relation to the structure can be arrived using single crystals. Hence one of the future directions of dielectric resonator research should be to grow good quality single crystals of the above materials.

Studies on some nonlinear schrodinger type equations describing pulse propagation through optical fibers

The discovery of the soliton is considered to be one of the most significant events of the twentieth century. The term soliton refers to special kinds of waves that can propagate undistorted over long distances and remain unaffected even after collision with each other. Solitons have been studied extensively in many fields of physics. In the context of optical fibers, solitons are not only of fundamental interest but also have potential applications in the field of optical fiber communications. This thesis is devoted to the theoretical study of soliton pulse propagation through single mode optical fibers.

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.

Development of p-type transparent semiconducting oxides for thin film transistor applications

Semiconductor physics has developed significantly in the field of re- search and industry in the past few decades due to it’s numerous practical applications. One of the relevant fields of current interest in material science is the fundamental aspects and applications of semi- conducting transparent thin films. Transparent conductors show the properties of transparency and conductivity simultaneously. As far as the band structure is concerned, the combination of the these two properties in the same material is contradictory. Generally a trans- parent material is an insulator having completely filled valence and empty conduction bands. Metallic conductivity come out when the Fermi level lies within a band with a large density of states to provide high carrier concentration. Effective transparent conductors must nec- essarily represent a compromise between a better transmission within the visible spectral range and a controlled but useful electrical con- ductivity [1–6]. Generally oxides like In2O3, SnO2, ZnO, CdO etc, show such a combination. These materials without any doping are insulators with optical band gap of about 3 eV. To become a trans- parent conductor, these materials must be degenerately doped to lift the Fermi level up into the conduction band. Degenerate doping pro- vides high mobility of extra carriers and low optical absorption. The increase in conductivity involves an increase in either carrier concen- tration or mobility. Increase in carrier concentration will enhance the absorption in the visible region while increase in mobility has no re- verse effect on optical properties. Therefore the focus of research for new transparent conducting oxide (TCO) materials is on developing materials with higher carrier mobilities.