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Relative Symplectic Caps, Fibered Knots And 4-Genus
(2014-04-07)
The 4-genus of a knot in S3 is an important measure of complexity, related to the unknotting number. A fundamental result used to study the 4-genus and related invariants of homology classes is the Thom conjecture, proved ...
Vector Bundles Over Hypersurfaces Of Projective Varieties
(2014-06-02)
In this thesis we study some questions related to vector bundles over hypersurfaces. More precisely, for hypersurfaces of dimension ≥ 2, we study the extension problem of vector bundles. We find some cohomological conditions ...
Curvature Calculations Of The Operators In Cowen-Douglas Class
(2014-03-03)
In a foundational paper “Operators Possesing an Open Set of Eigenvalues” written several decades ago, Cowen and Douglas showed that an operator T on a Hilbert space ‘H possessing an open set Ω C of eigenvalues determines ...
Development Of NMR Methods For Metabolomics And Protein Resonance Assignments
(2017-05-25)
Nuclear Magnetic Resonance (NMR) spectroscopy is a quantitative, non-invasive and non-destructive technique useful in biological studies. By manipulating the magnetization of nuclei with non-zero spin, NMR gives insights ...
Toward Computationally Efficient Models for Near-infrared and Photoacoustic Tomographic Imaging
(2017-11-28)
Near Infrared (NIR) and Photoacoustic (PA) Imaging are promising imaging modalities that provides functional information of the soft biological tissues in-vivo, with applica-tions in breast and brain tissue imaging. These ...
On The Structure of Proper Holomorphic Mappings
(2017-09-28)
The aim of this dissertation is to give explicit descriptions of the set of proper holomorphic mappings between two complex manifolds with reasonable restrictions on the domain and target spaces. Without any restrictions, ...
Some Problems in Multivariable Operator Theory
(2017-12-10)
In this thesis we have investigated two different types of problems in multivariable operator theory. The first one deals with the defect sequence for contractive tuples and maximal con-tractive tuples. These condone deals ...
An Introduction to Minimal Surfaces
(2017-12-10)
In the first chapter of this report, our aim is to introduce harmonic maps between Riemann surfaces using the Energy integral of a map. Once we have the desired prerequisites, we move on to show how to continuously deform ...
Goldman Bracket : Center, Geometric Intersection Number & Length Equivalent Curves
(2017-11-30)
Goldman [Gol86] introduced a Lie algebra structure on the free vector space generated by the free homotopy classes of oriented closed curves in any orientable surface F . This Lie bracket is known as the Goldman bracket ...
Grothendieck Inequality
(2016-06-20)
Grothendieck published an extraordinary paper entitled ”Resume de la theorie metrique des pro¬duits tensoriels topologiques” in 1953. The main result of this paper is the inequality which is commonly known as Grothendieck ...