Browsing Mathematics by Title
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FiniteDifference Methods for SecondOrder Wave Equations with Reduced Dispersion Errors
Finite Difference (FD) schemes have been used widely in computing approximations for partial differential equations for wave propagation, as they are simple, flexible and robust. However, even for stable and accurate ... 
FiniteDifference Methods for the Wave Equation with Reduced Dispersion Errors
(20130417)A new methodology was proposed in Finkelstein and Kastner (2007,2008) to derive finitedifference (FD) schemes in the joint timespace domain to reduce dispersion error. The key idea is that the true dispersion relation ... 
Formal group laws and hypergraph colorings
This thesis demonstrates a connection between formal group laws and chromatic symmetric functions of hypergraphs, two seemingly unrelated topics in the theory of symmetric functions. A formal group law is a symmetric ... 
Four Problems in Probability and Optimization
(20140224)This thesis studies bootstrap percolation, a problem in probability, as well as several topics in the application of sums of squares to combinatorial optimization. In the chapter on percolation, we bound the critical ... 
A Geometric Perspective on FirstPassage Competition
(20130417)We study the macroscopic geometry of firstpassage competition on the integer lattice <bold>Z</bold><super>d</super>, with a particular interest in describing the behavior when one species initially occupies the exterior ... 
Geometry and Optimization of Relative Arbitrage
This thesis is devoted to the mathematics of volatility harvesting, the idea that extra portfolio growth may be created by systematic rebalancing. First developed by E. R. Fernholz in the late 90s and the early 2000s, ... 
Graded group schemes
We define graded group schemes and graded group varieties and develop their theory. We give a generalization of the result that connected graded bialgebras are graded Hopf algebra. Our result is given for a broader class ... 
Grothendieck Duality on Diagrams of Schemes
The Du Bois complex and Du Bois singularities, which extend results of Hodge theory to singular complex varieties, can be defined in terms of a cubical hyperresolution. In this dissertation I further develop the language ... 
The Grothendieck Groups of Module Categories over Coherent Algebras
Let <italic>k</italic> be a field and <italic>B</italic> either a finitely generated free <italic>k</italic>algebra, or a regular <italic>k</italic>algebra of global dimension two with at least three generators, generated ... 
Heat Kernel Estimates for Markov Processes Associated with TimeDependent Dirichlet Forms
In this paper, timeinhomogeneous stablelike processes are investigated. We establish the relation between the transition operators and timedependent parabolic equations, as well as upper heat kernel estimates. 
Hopf algebras of finite GelfandKirillov dimension
(20131114)We study Hopf algebras of finite GelfandKirillov dimension. By analyzing the free pointed Hopf algebra F(t), we show the existence of certain Hopf subalgebras of pointed Hopf domains H whose GKdimension are finite and ... 
Hybrid inverse problems
(20131114)Inverse problems arise in different disciplines including exploration geophysics, medical imaging and nondestructive evaluation. In some settings, a single modality displays either high contrast or high resolution but not ... 
Hybrid Inverse Problems Arising from AcoustoElectric Coupling
(20131114)We study hybrid imaging techniques that aim to overcome the illposedness of the Electric Impedance Tomography using the acoustoelectric coupling. For the isotropic case, we consider the problem of reconstructing the ... 
Interacting particle systems with partial annihilation through membranes
This thesis studies the <italic>hydrodynamic limit</italic> and the <italic>fluctuation limit</italic> for a class of interacting particle systems in domains. These systems are introduced to model the transport of positive ... 
Inverse BoundaryValue Problems on an Infinite Slab
In this work, we study the stability aspect of two inverse boundaryvalue problems (IBVPs) on an infinite slab with partial data. The uniqueness aspects of these IBVPs were considered and studied by Li and Uhlmann for the ... 
Inverse Problems for Linear and Nonlinear Elliptic Equations
An inverse problem is a mathematical framework that is used to obtain information about a physical object or system from observed measurements. A typical inverse problem is to recover the coefficients of a partial differential ... 
Inverse Problems for Scalar Elliptic Equations and Systems
In this thesis, we discuss inverse boundary value problems for scalar equations and for systems. First we introduce the famous Calder\'on problem and its recent developments. We focus on deriving the stability estimate of ... 
An Inverse Source Problem in Radiative Transfer
(20130225)We consider the inverse source problem for the radiative transfer equation, under various assumptions on the scattering and absorption parameters, as well as on the accessible data. In such a setup, we measure the outgoing ... 
Inverse transport with angularly averaged measurements
(2008)The inverse problem in radiative transfer is considered. The measurement setup involves controlling incoming radiation at the boundary of a convex domain in Rn and measuring the outgoing radiation in an attempt to ... 
Isolated Curves for Hyperelliptic Curve Cryptography
(20130225)We introduce the notion of isolated genus two curves. There is no known efficient algorithm to explicitly construct isogenies between two genus two curves with large conductor gap. Thus there is no known way of transporting ...