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Full-Text Articles in Physical Sciences and Mathematics
Geometric Invariants For A Class Of Semi-Fredholm Hilbert Modules., Shibananda Biswas Dr.
Geometric Invariants For A Class Of Semi-Fredholm Hilbert Modules., Shibananda Biswas Dr.
Doctoral Theses
One of the basic problem in the study of a Hilbert module H over the ring of polynomials C[z] := C[z1, . . . , zm] is to find unitary invariants (cf. [15,7]) for H. It is not always possible to find invariants that are complete and yet easy to compute. There are very few instances where a set of complete invariants have been identified. Examples are Hilbert modules over continuous functions (spectral theory of normal operator), contractive modules over the disc algebra (model theory for contractive operator) and Hilbert modules in the class Bn for a bounded domain C …
Studies On Construction And List Decoding Of Codes On Some Towers Of Function Fields., M. Prem Laxman Das Dr.
Studies On Construction And List Decoding Of Codes On Some Towers Of Function Fields., M. Prem Laxman Das Dr.
Doctoral Theses
In everyday life, there arise many situations where two parties, sender and receiver, need to communicate. The channel through which they communicate is assumed to be binary symmetric, that is, it changes 0 to 1 and vice versa with equal probability. At the receiver’s end, the sent message has to be recovered from the corrupted received word using some reasonable mechanism. This real life problem has attracted a lot of research in the past few decades. A solution to this problem is obtained by adding redundancy in a systematic manner to the message to construct a codeword. The collection of …
On Some Generalized Transforms For Signal Decomposition And Reconstruction., Yumnam Singh Dr.
On Some Generalized Transforms For Signal Decomposition And Reconstruction., Yumnam Singh Dr.
Doctoral Theses
In this thesis, we propose two new subband transforms entitled ISITRA and YKSK transforms and their possible applications in image compression and encryption. Both these transforms are developed based on a common model of multiplication known as Bino’s model of multiplication. ISITRA is a convolution based transforms i.e., that both forward and inverse transform of ISITRA is based on convolution as in DWT or 2-channel filter bank. However, it is much more general than the existing DWT or 2-channel filter bank scheme in the sense that it we can get different kinds of filters in addition to the filters specified …
Studies On Finite Linear Cellular Automata., Palash Sarkar Dr.
Studies On Finite Linear Cellular Automata., Palash Sarkar Dr.
Doctoral Theses
Cellular Automata were originally proposed by John von Neumann as formal models of self reproducing organisms. The structure studied was mostly an ane and two dimensional infinite grida, though higher dimensions were also considered. Computation universality and other computation theoretic questions were considered important. See Burks [24] for a collection of essays on important problems on cellular automata during this period. Later physicists and biologists began to study cellular automsta for the purpose of modelling in their respective domains. In the present era, cellalar automata is being atudied from many widely different angles, and the relationship of these structurea to …
Time-Space Harmonic Polynomials For Stochastic Processes., Arindam Sengupta Dr.
Time-Space Harmonic Polynomials For Stochastic Processes., Arindam Sengupta Dr.
Doctoral Theses
The sequence of polynomials of a single variable known as the Hermite polynomialshala) = ), k21, (-1)* ha(z) =has many close links with the Normal distribution. Their association goes very doep, and extends to several connections bet ween the two-variable Hermite polynomialsHll, 2) = the(z/t), . k21.and the prime example of Gaussian processes, that is Brownian motion, as well. Much of this connection stems from what we term the time-space harmonic property of these polynomials for the Brownian motion process. An exact definition of this property follows later. A natural question that arises is, for stochastic processes in general, when …
Some Problems In Joint Spectral Theory., Tirthankar Bhattacharya Dr.
Some Problems In Joint Spectral Theory., Tirthankar Bhattacharya Dr.
Doctoral Theses
No abstract provided.
Study Of Moduli Of Bundles., Indranil Biswas Dr.
Study Of Moduli Of Bundles., Indranil Biswas Dr.
Doctoral Theses
Hitchin (Hi2) realized the importance of studying pairs (E,∅) where E is a vector bundle and ∅ is a homomorphism of E into EOL for a fixed line bundle L. When C is a smooth pro jective algebraic curve this has since been studied quite extensively. One can construct a covering of C in this situation and the given data can be completely recovered by this covering map and a line bundle on the covering curve (see Beauville, Narasimhan and Ramanan (BNR]). When L is the canonical bundle this procedure gives a completely integrable system on the cotangent bundle of …
Combinatorics And Diagonals Of Matrices., K. Balasubramanian Dr.
Combinatorics And Diagonals Of Matrices., K. Balasubramanian Dr.
Doctoral Theses
This theale maindy desie with conbinatoriel aspocte of diayonale of natelees. or enurne, there are aleo eosulte which are nat sunbinatorial in naturos but thase ara neroly by-producta. Chapter-0 gives e very short nary ot the cnntenta of the theete. The raeulte aro ofr tuo kinde. (1) complately rev and (2) old results through rew rethude.Thịa thasle, wholly or pertly, has not baon subnittad to any othor Univerdity or Inatitute for e degree.I exprees hoceby ry doopost sonse of grotitude to br. KA. PARTHASARATHY, Haed of the Doparteant af Mathemties, Indian Inatituta of Tochmlogy, Redras, under uhana bonign guidance thie …
Estimation Of Spectral Variation., Rajendra Bhatia Dr.
Estimation Of Spectral Variation., Rajendra Bhatia Dr.
Doctoral Theses
The study of spectra occupies a central place in the theory of linear operators. One part of this study consists of obtaining a detailed and complete knowledge of the spectrum of a given lincar operator. The other part - perturbation theory - consists of using this knowledge to obtain information about the spectra of nearby operators.Apart from the intrinsic mathematical interest it has, perturbation theory is of great importance in the study of several physical problems. In fact, the theory came into existence with the work of Rayleigh on sound waves and that of Schrodinger on quantum mechanics. Later, their …
Theory Of Estimation In Algebraic And Analytic Exponential Families With Applications To Variance Components Models., Krishnan Unni Dr.
Theory Of Estimation In Algebraic And Analytic Exponential Families With Applications To Variance Components Models., Krishnan Unni Dr.
Doctoral Theses
There are many important statistical problems of the following kind. The family of probability measures O is parametrized by a vector parame ter n varying in a q-dimen- sional domain. P can be represented as an exponential family of probability distributions with k canonical para- me ters where k is greater than q. The canonical parameters do not vary in a domain in R, but are restricted by polyno- mial or analytic equations. They vary on a curved surface defined by the polynomial or analytic equations within the natural parame ter space of the exponential family. The present work is …