Browsing School of Mathematics Theses and Dissertations by Title
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Mahler's conjecture in convex geometry: a summary and further numerical analysis
(Georgia Institute of Technology, 20100809)In this thesis we study Mahler's conjecture in convex geometry, give a short summary about its history, gather and explain different approaches that have been used to attack the conjecture, deduce formulas to calculate the ... 
Markov chains at the interface of combinatorics, computing, and statistical physics
(Georgia Institute of Technology, 20120322)The fields of statistical physics, discrete probability, combinatorics, and theoretical computer science have converged around efforts to understand random structures and algorithms. Recent activity in the interface of ... 
Matching structure and Pfaffian orientations of graphs
(Georgia Institute of Technology, 20050720)The first result of this thesis is a generation theorem for bricks. A brick is a 3connected graph such that the graph obtained from it by deleting any two distinct vertices has a perfect matching. The importance of ... 
Mathematical approaches to digital color image denoising
(Georgia Institute of Technology, 20090914)Many mathematical models have been designed to remove noise from images. Most of them focus on grey value images with additive artificial noise. Only very few specifically target natural color photos taken by a digital ... 
A mathematical investigation of the occurrence of vortices in flow past irregular surfaces
(Georgia Institute of Technology, 195912) 
Mathematical Modeling of Fines Migration snd Clogging in Porous Media
(Georgia Institute of Technology, 20070802)Mathematical Modeling of Fines Migration and Clogging in Porous Media Guido Kampel 87 Pages Directed by Dr. Guillermo H. Goldsztein A porous medium is a material that contains regions filled with fluid embedded ... 
Mathematical models of physical phenomena
(Georgia Institute of Technology, 196308) 
A mathematical study of mimicry and opportunism
(Georgia Institute of Technology, 198908) 
The Mathematical Theory of Thin Film Evolution
(Georgia Institute of Technology, 20070703)We try to explain the mathematical theory of thin liquid film evolution. We start with introducing physical processes in which thin film evolution plays an important role. Derivation of the classical thin film equation ... 
The maximum clique problem  on finding an upper bound with application to protein structure alignment
(Georgia Institute of Technology, 200308) 
Maximum Codes with the Identifiable Parent Property
(Georgia Institute of Technology, 20061120)We study codes that have identifiable parent property. Such codes are called IPP codes. Research on IPP codes is motivated by design of schemes that protect against piracy of digital products. Construction and decoding ... 
Method of evolving junctions: a new approach to path planning and optimal control
(Georgia Institute of Technology, 20140407)This thesis proposes a novel and efficient method (Method of Evolving Junctions) for solving optimal control problems with path constraints, and whose optimal paths are separable. A path is separable if it is the concatenation ... 
Minimal Surfaces in threesphere with special spherical symmetry
(Georgia Institute of Technology, 20040714)We introduce the notion of special spherical symmetry and classify the complete regular minimal surfaces in the three sphere having this symmetry. We also show that the Clifford torus is the unique embedded minimal ... 
Minimization problems involving polyconvex integrands
(Georgia Institute of Technology, 20150602)This thesis is mainly concerned with problems in the areas of the Calculus of Variations and Partial Differential Equations (PDEs). The properties of the functional to minimize with respect to the given topology play an ... 
Minimum principle of the temperature in compressible NavierStokes equations with application to the existence theory
(Georgia Institute of Technology, 20140508)This thesis is on the NavierStokes equations which model the motion of compressible viscous fluid. A minimum principle on the temperate variable is established. Under the thermoinsulated boundary conditions and some ... 
Minorminimal nonprojective planar graphs with an internal 3separation
(Georgia Institute of Technology, 20121113)The property that a graph has an embedding in the projective plane is closed under taking minors. Thus by the well known Graph Minor theorem of Robertson and Seymour, there exists a finite list of minorminimal graphs, ... 
Model and analysis of the geometric characteristics of primary carpet backing
(Georgia Institute of Technology, 20031201) 
Models of intracavity of frequency doubled lasers
(Georgia Institute of Technology, 199005) 
Modulation spaces, BMO and the Zak transform, and minimizing IPH functions over the unit simplex
(Georgia Institute of Technology, 20100707)This thesis consists of two parts. In the first chapter, we give some results on modulation spaces. First the relationship between the classical spaces and the modulation spaces is established. It is proved that certain ... 
Multifold sums and products over R, and combinatorial problems on sumsets
(Georgia Institute of Technology, 20150722)We prove a new bound on a version of the sumproduct problem studied by Chang. By introducing several combinatorial tools, this expands upon a method of Croot and Hart which used the TarryEscott problem to build distinct ...