Dissertations & Theses: Recent submissions
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Comparative Analysis Of Various Continuoustime Deterministic Models Of Tumorimmune Interactions
Cancer is historically a leading cause of death in the United States. In 2013,cancer was the second leading cause of death with 584,881 deaths \cite{CDC}.Having solely been responsible for 22.5\% of all deaths in 2013 ... 
Numerical Methods For Spontaneous And Evoked Glutamate Release
As synapses are responsible for the majority of neuron communications in the brain, the events of evoked and spontaneous synaptic vesicle release/fusion are key features of all synaptic current. These release events typically ... 
Advancements And Applications Of Nonstandard Finite Difference Methods
A class of dynamically consistent numerical methods are analyzed for general ndimensional productivedestructive systems (PDS). Using this analysis, a methodology for constructing positive and elementary stable nonstandard ... 
On Solving Finitely Reflected Backward Stochastic Differential Equations
Classical theory gives a closed form representation of the density p(t,x), a solution to a linear parabolic PDE, via the FeynmanKac Formula of the underlying diffusion process. In the nonlinear PDE case there is no closed ... 
On Minverse Loops And Quasigroups Of Order N With A Long Inverse Cycle.
In 2002, A.D Keedwell and V.A Sherbacov introduced the concept of finite minverse quasigroups with long inverse cycles. Keedwell and Sherbacov observed that finite minverse loops and quasigroups with a long inverse cycle ... 
A Modeling Study In The Regulation Of Stress On Neuronal Plasticity
How stress can affect human cognitive functions has been a very popular topic for researchers from different fields including physiology, psychology, biology, neuroscience, and applied mathematics. Hypothalamic−pituitary−adrenal ... 
Some Multivariate Process Capability Indices
Process capability indices (PCIs) play an important role in the field of Statistical Process Control. Prior to the last 25 years, PCIs had been formulated to assess the quality of a single product characteristic. Product ... 
The Influence Of Dynamic Visualization On Undergraduate Calculus Learning
The urgent need in the United States to produce an additional one million graduates in the areas of science, technology, engineering and mathematics and previous research into why students choose to abandon their quest to ... 
Property D Cyclic Neofields
In 1948 L. J. Paige introduced the notion of a neofield (N,\oplus,\cdot) as a set N with two binary operations, generally referred to as addition (\oplus) and multiplication (\cdot) such that (N,\oplus) is a loop with ... 
Nilpotent Lie Algebras And Nilmanifolds Constructed From Graphs
The interaction between graph theory and differential geometry has been studied previously, but S. Dani and M. Mainkar brought a new approach to this study by associating a twostep nilpotent Lie algebra (and thereby a ... 
Weight Modules Of Orthosymplectic Lie Superalgebras
A longstanding problem in representation theory is the classification of all simple weight modules of the classical Lie superalgebras. This problem was reduced to the classification of simple bounded highest weight ... 
Numerical LES For MVG Controlled Supersonic Ramp Flow
An implicitly implemented large eddy simulation by using the fifth order bandwidthoptimized WENO scheme is applied to make comprehensive studies on ramp flows with microramp vortex generators (MVG) at Mach 2.5 and Re=5760. ... 
Properties Of The Pinched Tensor Product
For complexes of modules we study a new construction, called the pinched tensor product, which was introduced by Lars Winther Christensen and David A. Jorgensen to study Tate homology. We explore properties of the pinched ... 
Haplotypebased Statistical Inference For Casecontrol Genetic Association Studies With Complex Sampling
(Mathematics, 20140917)With the advances in human genome research, it is now believed that the risks of many complex diseases are triggered by the interplay of genetic susceptibilities and environmental exposures. The populationbased casecontrol ... 
A Method For Exact Solutions To Integrable Evolution Equations In 2+1 Dimensions
(Mathematics, 20140917)A systematic method is developed to obtain solution formulas for certain explicit solutions to integrable nonlinear partial differential equations in two spatial variables and one time variable. The method utilizes an ... 
Representation Theory Of Totally Reflexive Modules Over Nongorenstein Rings
(Mathematics, 20140917)In the late 1960's Auslander and Bridger published Stable Module Theory, in whichthe idea of totally reflexive modules first appeared. These modules have been studiedby many. However, a bulk of the information known about ... 
Estimation Of Variance In Bivariate Normal Distribution After Preliminary Test Of Homogeneity
(Mathematics, 20140917)A preliminary test estimator of variance in the bivariate normal distribution is proposed after PitmanMorgan test of homogeneity of two variances. We propose one estimator of variance after preliminary test of two tails ... 
Applications Of Cubical Arrays In The Study Of Finite Semifields
(Mathematics, 20140917)It is well known that any finite semifield, S, can be viewed as an ndimensional vector space over a finite field or prime order, Fp, and that the multiplication in S defines and can be defined by an n x n x n cubical ... 
A Generalized Approach To Darboux Transformations For Differential Equations
(Mathematics, 20140714)A Darboux transformation is a mathematical procedure to produce a solution to a differential equation when the solution to a related differential equation is known. The basic idea behind a Darboux transformation is to ... 
DNS Study For The Origin Of The Chaos In Late Boundary Layer Transition Over A Flat Plate
(Mathematics, 20140312)This dissertation is devoted to the investigation of the origin and mechanism of chaos ( asymmetric or disorganized flow) in late boundary layer transition over a flat plate without pressure gradient. This kind of flow not ...