Browsing Mathematics by Title
Now showing items 120 of 45

[20120323] Acousticwave nonlinearity in stimulated Brillouin scattering
Stimulated Brillouin scattering is investigated here under conditions characterized by high optical pump intensity. Calculations are carried out at 1.3 and 3.8 /jm with pump intensities equal to approximately three times ... 
[20120322] Algorithmic dimensionality reduction for molecular structure analysis
Dimensionality reduction approaches have been used to exploit the redundancy in a Cartesian coordinate representation of molecular motion by producing lowdimensional representations of molecular motion. This has been used ... 
[20100909] Analysis of nonlinear Black Scholes models
The Black Scholes equation is a fundamental model for derivative pricing. Modifying its assumptions will lead to more realistic but mathematically more complicated models. This dissertation consists of analytical and ... 
[20110702] Analysis of the organization and dynamics of proteins in cell membranes
Cells communicate with the outside world through membrane receptors that recognize one of many possible stimuli (hormones, antibodies, peptides) in the extracellular environment and translate this information to intracellular ... 
[20120322] The Approximate Functional Formula for the Theta Function and Diophantine Gauss Sums
By introducing the discrete curvature of the polygonal line, and by exploiting the similarity of segments of the line, for small w, to Cornu spirals (Cspirals), we prove the precise renormalization formula. This formula, ... 
[20120705] Arithmetic jet spaces and modular forms
In this thesis, we would look into the theory of arithmetic jet spaces and its application in modular forms. The arithmetic jet spaces can be thought of as an analogue of jet spaces in differential algebra. In the case of ... 
[20120323] Caustics and virtual cathodes in electron beams
A simplified model is discussed that captures the basic physics of the phenomenon of oscillatory virtual cathodes in electron beams. A monoenergetic nonrelativistic onedimensional electron beam is injected through a ... 
[20100909] Commutators and dyadic paraproducts on weighted Lebesgue spaces
We prove that the operator norm on weighted Lebesgue space L^2(w) of the commutators of the Hilbert, Riesz and Beurling transforms with a BMO function b depends quadratically on the A2 characteristic of the weight, as ... 
[20131125] Computing a logarithm of a unitary matrix with general spectrum [dataset]
\begin{abstract} We analyze an algorithm for computing a skewHermitian logarithm of a unitary matrix, and also skewHermitian approximate logarithms for nearly unitary matrices. This algorithm is very easy to implement ... 
[20100910] Contact homology of toric contact manifolds of Reeb type
We use contact homology to distinguish contact structures on various manifolds. We are primarily interested in contact manifolds which admit an action of Reeb type of a compact Lie group. In such situations it is well ... 
[20120322] Delayinduced destabilization of entrainment of nerve impulses on ephaptically coupled nerve fibers
We study the effect of delay on the synchronization of two nerve impulses traveling along two ephaptically coupled, unmyelinated nerve fibers. The system is modeled as a pair of delaycoupled FitzhughNagumo equations. A ... 
[20090709] Development of scoring rubrics and preservice teachers’ ability to validate mathematical proofs
The basic aim of this exploratory research study was to determine if a specific instructional strategy, that of developing scoring rubrics within a collaborative classroom setting, could be used to improve preservice ... 
[20120322] Dynamical properties of forced shear layers in an annular geometry
Results of numerical simulations of a forced shear flow in an annular geometry are presented. The particular geometry used in this work reduces the effects of centrifugal and Coriolis forces. However, there are still a ... 
[20120323] Effects of thermal spread on the space charge limit of an electron beam
An asymptotic analysis is carried out to calculate the effects of a small thermal spread in the injection energy of an electron beam on its space charge limit. It is found that the space charge limit is lowered proportionally ... 
[20120322] AN EFFICIENT SPECTRAL METHOD FOR ORDINARY DIFFERENTIAL EQUATIONS WITH RATIONAL FUNCTION COEFFICIENTS
We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, ... 
[20131202] Estimating norms of commutators
\begin{abstract} We find estimates on the norm of a commutator of the form $[f(x),y]$ in terms of the norm of $[x,y]$, assuming that $x$ and $y$ are bounded linear operators on Hilbert space, with $x$ normal and with ... 
[20131202] Estimating norms of commutators [dataset]
\begin{abstract} We find estimates on the norm of a commutator of the form $[f(x),y]$ in terms of the norm of $[x,y]$, assuming that $x$ and $y$ are bounded linear operators on Hilbert space, with $x$ normal and with ... 
[20120320] The FALCLoop web server for protein loop modeling
The FALCLoop web server provides an online interface for protein loop modeling by employing an ab initio loop modeling method called FALC (fragment assembly and analytical loop closure). The server may be used to construct ... 
[20090827] High performance damper optimization using computer simulation and design of experiments
Design of experiments has become an increasingly popular tool used by racing teams in professional motorsports. A race car has literally hundreds of adjustable parameters associated with it. Specialized racing engineers ... 
[20120322] Invertibility of current density from nearfield electromagnetic data
The problem of determining a current density confined to a volume from measurements of the magnetic and electric fields it produces exterior to that volume is known to have nonunique solutions. Despite the nonuniqueness ...