ETD at Indian Institute of Science
(1.920 recursos)
Repository of Theses and Dissertations of Indian Institute of Science, Bangalore, India. The repository has been developed to capture, disseminate and preserve research theses of Indian Institute of Science.
Mathematics (math)
Mostrando recursos 1 - 20 de 29
1.
An Algorithmic Approach To Crystallographic Coxeter Groups - Malik, Amita
Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. It turns out that the finite Coxeter groups are precisely the finite Euclidean reflection groups. Coxeter studied these groups and classified all finite ones in 1935, however they were known as reflection groups until J. Tits coined the term Coxeter groups for them in the sixties.
Finite crystallographic Coxeter groups, also known as finite Weyl groups, play a prominent role in many branches of mathematics like combinatorics, Lie theory, number theory, and geometry. The computational aspects of these groups are...
3.
Irreducible Representations Of The Symmetric Group And The General Linear Group - Verma, Abhinav
Representation theory is the study of abstract algebraic structures by representing their elements as linear transformations or matrices. It provides a bridge between the abstract symbolic mathematics and its explicit applications in nearly every branch of mathematics. Combinatorial representation theory aims to use combinatorial objects to model representations, thus answering questions in this field combinatorially. Combinatorial objects are used to help describe, count and generate representations. This has led to a rich symbiotic relationship where combinatorics has helped answer algebraic questions and algebraic techniques have helped answer combinatorial questions.
In this thesis we discuss the representation theory of the symmetric...
16.
Some Descriptions Of The Envelopes Of Holomorphy Of Domains in Cn - Gupta, Purvi
It is well known that there exist domains Ω in Cn,n ≥ 2, such that all holomorphic functions in Ω continue analytically beyond the boundary. We wish to study this remarkable phenomenon. The first chapter seeks to motivate this theme by offering some well-known extension results on domains in Cn having many symmetries. One important result, in this regard, is Hartogs’ theorem on the extension of functions holomorphic in a certain neighbourhood of (D x {0} U (∂D x D), D being the open unit disc in C. To understand the nature of analytic continuation in greater detail, in Chapter...
17.
Bounded Analytic Functions On The Unit Disc - Rupam, Rishika
In this thesis, we have dealt primarily with two function algebras. The first one is the space of all holomorphic functions on the unit disc D in the complex plane which are continuous up to the boundary, denoted by A(D). The second one is H1(D), the space of all bounded analytic functions on D. We study results that characterize their maximal ideals. We start with necessary definitions and recall some useful results. In particular, the factorization of Hp functions in terms of Blaschke products, inner and outer functions is stated. Using this factorization, we provide an exposition of a beautiful...
18.
Some Aspects Of The First Passage Time Problem In Neuroscience - Bhupatiraju, Sandeep
In the stochastic modeling of neurons, the first passage time problem arises as a natural object of study when considering the inter spike interval distribution. In this report, we study some aspects of this problem as it arises in the context of neuroscience. In the first chapter we describe the basic neurophysiology required to model the neuron. In the second, we study the Poisson model, Stein’s model, and some diffusion models, calculating or indicating methods to compute the density of the first passage time random variable or its moments. In the third and fourth chapters, we study the Fokker-Planck equation,...
19.
Hand-Movement Prediction Using LFP Data - Muralidharan, Prasanna
The last decade has seen a surge in the development of Brain-Machine Interfaces (BMI) as assistive neural devices for paralysis patients. Current BMI research typically involves a subject performing movements by controlling a robotic prosthesis. The neural signal that we consider for analysis is the Local Field Potential (LFP). The LFP is a low frequency neural signal recorded from intra-cortical electrodes, and has been recognized as one containing movement information. This thesis investigates hand-movement prediction using LFP data as input. In Chapter 1, we give an overview of Brain Machine Interfaces. In Chapter 2, we review the necessary concepts in...
20.
Exploring Polynomial Convexity Of Certain Classes Of Sets - Gorai, Sushil
Let K be a compact subset of Cn . The polynomially convex hull of K is defined as The compact set K is said to be polynomially convex if = K. A closed subset is said to be locally polynomially convex at if there exists a closed ball centred at z such that is polynomially convex. The aim of this thesis is to derive easily checkable conditions to detect polynomial convexity in certain classes of sets in
This thesis begins with the basic question: Let S1 and S2 be two smooth, totally real surfaces in C2 that contain the...
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