
Ethamakula, Bharath Kumar
Algebraic geometric codes were first introduced by V.D.Goppa . They were well recognized and developed by Tsfasman, Vladut and Zink because they have parameters better than GilbertVarshmov bound and thus giving rise to Tsfasman VladutZink bound. While the codes given by Ihara, Tsfasman, Vladut and Zink have complicated construction, Garcia and Stichtenoth on the other hand gave an explicit construction of codes attaining TsfasmanVlasutZink bound using the terminology of function fields. In coding theory one of the challenging problem is to find a sequence of cyclic codes that are asymptotically good. While this has not been achieved, Stichtenoth generalized cyclic...

Ramkrishnan, Gayatri
Significant advancements in genome sequencing techniques and other highthroughput initiatives have resulted in the availability of complete sequences of genomes of a large number of organisms, which provide an opportunity to study detailed biological information encoded therein. Identification of functional roles of proteins can aid in comprehension of various cellular activities in an organism, which is traditionally achieved using techniques pertaining to the field of molecular biology, protein chemistry and macromolecular crystallography. The established experimental methods for protein structure and function determination, although accurate and resourceful, are laborious and time consuming. Computational analyses of sequences of gene products and exploration...

Chowdhury, Sudipto
The primary goal of this thesis is to study finite element based a priori and a posteriori error estimates of optimal control problems of various kinds governed by linear elliptic PDEs (partial differential equations) of second and fourth orders. This thesis studies interior and boundary control (Neumann and Dirichlet) problems.
The initial chapter is introductory in nature. Some preliminary and fundamental results of finite element methods and optimal control problems which play key roles for the subsequent analysis are reviewed in this chapter. This is followed by a brief literature survey of the finite element based numerical analysis of PDE...

Adhikari, Kartick

Chandel, Vikramjeet Singh
The Pick–Nevanlinna interpolation problem, in its fullest generality, is as follows:
Given domains D1, D2 in complex Euclidean spaces, and a set f¹ zi; wiº : 1 i N g D1 D2, where zi are distinct and N 2 š+, N 2, find necessary and sufficient conditions for the existence of a holomorphic map F : D1 ! D2 such that F¹ziº = wi, 1 i N.
When such a map F exists, we say that F is an interpolant of the data. Of course, this problem is intractable at the above level of generality. However, two special cases of...

Aiyappan, S
In this thesis, we study homogenization of optimal control problems in various oscillatory domains. Specifically, we consider four types of domains given in Figure 1 below.
Figure 1: Oscillating Domains
The thesis is organized into six chapters. Chapter 1 provides an introduction to our work and the rest of the thesis. The main contributions of the thesis are contained in Chapters 25. Chapter 6 presents the conclusions of the thesis and possible further directions. A brief description of our work (Chapters 25) follows:
Chapter 2: Asymptotic behaviour of a fourth order boundary optimal control problem with Dirichlet boundary data posed...

Hazra, Somnath
A bounded operator T on a complex separable Hilbert space is said to be homogeneous if '(T ) is unitarily equivalent to T for all ' in M•ob, where M•ob is the M•obius group. A complete description of all homogeneous weighted shifts was obtained by Bagchi and Misra. The first examples of irreducible bilateral homogeneous 2shifts were given by Koranyi. We describe all irreducible homogeneous 2shifts up to unitary equivalence completing the list of homogeneous 2shifts of Koranyi.
After completing the list of all irreducible homogeneous 2shifts, we show that every homogeneous operator whose associated representation is a direct sum...

Basak, Biplab
A simplicial cell complex K is the face poset of a regular CW complex W such that the boundary complex of each cell is isomorphic to the boundary complex of a simplex of same dimension. If a topological space X is homeomorphic to W then we say that K is a pseudotriangulation of X.
For d 1, a (d + 1)colored graph is a graph = (V; E) with a proper edge coloring
: E ! f0; : : : ; dg. Such a graph is called contracted if (V; E n 1(i)) is connected for each color
A contracted graph...

Senthil Raani, K S
One of the basic questions in harmonic analysis is to study the decay properties of the Fourier transform of measures or distributions supported on thin sets in Rn. When the support is a smooth enough manifold, an almost complete picture is available. One of the early results in this direction is the following: Let f in Cc∞(dσ), where dσ is the surface measure on the sphere Sn1 Rn.Then the modulus of the Fourier transform of fdσ is bounded above by (1+x)(n1)/2. Also fdσ in Lp(Rn) for all p > 2n/(n1) . This result can be extended to compactly supported measure...

Pal, Ratna
Thesis Abstract
In the first part of the thesis, we study some dynamical properties of skew products of H´enon maps of C2 that are fibered over a compact metric space M . The problem reduces to understanding the dynamical behavior of the composition of a pseudorandom sequence of H´enon mappings. In analogy with the dynamics of the iterates of a single H´enon map, it is possible to construct fibered Green functions that satisfy suitable invariance properties and the corresponding stable and unstable currents. Further, it is shown that the successive pullbacks of a suitable current by the skew H´enon maps converge...

Haridas, Pranav
In the ﬁrst part of this thesis, we prove two density theorems for quadrature domains in Cn ,n≥2. It is shown that quadrature domains are dense in the class of all product domains of the form D×Ωwhere D⊂Cn−1 is a smoothly bounded pseudoconvex domain satisfying Bell’s Condition R and Ω⊂Cis a smoothly bounded domain. It is also shown that quadrature domains are dense in the class of all smoothly bounded complete Hartogs domains in C2.
In the second part of this thesis, we study the behaviour of the critical points of the Green’s function when a sequence of domains Dk⊂Rn...

Mukherjee, Sumanta
Cytotoxic Tlymphocytes (CTLs) are important components of the adaptive immune system and function by scanning the intracellular environment so as to detect and destroy infected cells. CTL responses play a major role in controlling virusinfected cells such as in HIV or influenza and cells infected with intracellular bacteria such as in tuberculosis. To do so they require the antigens to be presented to them, which is fulfilled by the major histocompatibility complex (MHC), commonly known as human leukocyte antigen or HLA molecules in humans. Recognition of antigenic peptides to Class1 HLA molecules is a prerequisite for triggering CTL immune responses....

Bagchi, Sayan
In this thesis we deal with two problems in harmonic analysis. In the ﬁrst problem we discuss weighted norm inequalities for Weyl multipliers satisfying Mauceri’s condition. As an application, we prove certain multiplier theorems on the Heisenberg group and also show in the context of a theorem of Weis on operator valued Fourier multipliers that the Rboundedness of the derivative of the multiplier is not necessary for the boundedness of the multiplier transform. In the second problem we deal with a variation of a theorem of Mauceri concerning the Lp boundedness of operators Mwhich are known to be bounded on...

Gupta, Rajeev
The validity of the vonNeumann inequality for commuting $n$  tuples of $3\times 3$ matrices remains open for $n\geq 3$. We give a partial answer to this question, which is used to obtain a necessary condition for the CarathéodoryFejérinterpolation problem on the polydisc$\D^n. $ in the special case of $n=2$ (which follows from Ando's theorem as well), this necessary condition is made explicit.
We discuss an alternative approach to the CarathéodoryFejérinterpolation problem, in the special case of $n=2$, adapting a theorem of Korányi and Pukánzsky. As a consequence, a class of polynomials are isolated for which a complete solution to...

Mehrotra, Prachi
Proteins are essential for the growth, survival and maintenance of the cell. Understanding the functional roles of proteins helps to decipher the working of macromolecular assemblies and cellular machinery of living organisms. A thorough investigation of the link between sequence, structure and function of proteins, helps in building a comprehensive understanding of the complex biological systems. Proteins have been observed to be composed of single and multiple domains. Analysis of proteins encoded in diverse genomes shows the ubiquitous nature of multidomain proteins. Though the majority of eukaryotic proteins are multidomain in nature, 3D structures of only a small proportion of...

Maitra, Sayantan
This thesis is broadly divided in two parts. In the first part we give a survey of various distances between metric spaces, namely the uniform distance, Lipschitz distance, Hausdor distance and the Gramoz Hausdor distance. Here we talk about only the most basic of their properties and give a few illustrative examples. As we wish to study collections of metric measure spaces, which are triples (X; d; m) consisting of a complete separable metric space (X; d) and a Boral probability measure m on X, there are discussions about some distances between them. Among the three that we discuss, the...

Srivastava, Shweta
Problems governed by partial differential equations (PDEs) in deformable domains, t Rd; d = 2; 3; are of fundamental importance in science and engineering. They are of particular relevance in the design of many engineering systems e.g., aircrafts and bridges as well as to the analysis of several biological phenomena e.g., blood ow in arteries. However, developing numerical scheme for such problems is still very challenging even when the deformation of the boundary of domain is prescribed a priori. Possibility of excessive mesh distortion is one of the major challenge when solving such problems with numerical methods using boundary tted...

Garg, Naveen Kumar
The class of hyperbolic conservation laws model the phenomena of nonlinear wave propagation, including the presence and propagation of discontinuities and expansion waves. Such nonlinear systems can generate discontinuities in the solution even for smooth initial conditions. Presence of discontinuities results in break down of a solution in the classical sense and to show existence, weak formulation of a problem is required. Moreover, closed form solutions are di cult to obtain and in some cases such solutions are even unavailable. Thus, numerical algorithms play an important role in solving such systems. There are several discretization techniques to solve hyperbolic systems...

Ghosh, Soma
Mycobacterium tuberculosis (M.tb), the causative agent of tuberculosis (TB), has remained the largest killer among infectious diseases for over a century. The increasing emergence of drug resistant varieties such as the multidrug resistant (MDR) and extremely drug resistant (XDR) strains are only increasing the global burden of the disease. Available statistics indicate that nearly onethird of the world’s population is infected, where the bacteria remains in the latent state but can reactivate into an actively growing stage to cause disease when the individual is immunocompromised. It is thus immensely important to rethink newer strategies for containing and combating the spread...

Bhattacharya, Atreyee
We discuss two topics in this talk. First we study compact Ricciflat four dimensional manifolds without boundary and obtain point wise restrictions on curvature( not involving global quantities such as volume and diameter) which force the metric to be flat. We obtain the same conclusion for compact Ricciflat K¨ahler surfaces with similar but weaker restrictions on holomorphic sectional curvature.
Next we study the reaction ODE associated to the evolution of the Riemann curvature operator along the Ricci flow. We analyze the behavior of this ODE near algebraic curvature operators of certain special type that includes the Riemann curvature operators of various(locally)...