Applied Mathematics Commons^™

Green's Functions Of Discrete Fractional Calculus Boundary Value Problems And An Application Of Discrete Fractional Calculus To A Pharmacokinetic Model, Sutthirut Charoenphon

Masters Theses & Specialist Projects

Fractional calculus has been used as a research tool in the fields of pharmacology, biology, chemistry, and other areas [3]. The main purpose of this thesis is to calculate Green's functions of fractional difference equations, and to model problems in pharmacokinetics. We claim that the discrete fractional calculus yields the best prediction performance compared to the continuous fractional calculus in the application of a one-compartmental model of drug concentration. In Chapter 1, the Gamma function and its properties are discussed to establish a theoretical basis. Additionally, the basics of discrete fractional calculus are discussed using particular examples for further calculations. …

Analysis Of A Partial Differential Equation Model Of Surface Electromigration, Selahittin Cinar

Masters Theses & Specialist Projects

A Partial Differential Equation (PDE) based model combining surface electromigration and wetting is developed for the analysis of the morphological instability of mono-crystalline metal films in a high temperature environment typical to operational conditions of microelectronic interconnects. The atomic mobility and surface energy of such films are anisotropic, and the model accounts for these material properties. The goal of modeling is to describe and understand the time-evolution of the shape of film surface. I will present the formulation of a nonlinear parabolic PDE problem for the height function h(x,t) of the film in the horizontal …

Spectrum Of The Kerzman-Stein Operator For A Family Of Smooth Regions In The Plane, Michael Bolt

University Faculty Publications and Creative Works

The Kerzman-Stein operator is the skew-hermitian part of the Cauchy operator defined with respect to an unweighted hermitian inner product on the boundary. For bounded regions with smooth boundary, the Kerzman-Stein operator is compact on the Hilbert space of square integrable functions. Here we give an explicit computation of its Hilbert-Schmidt norm for a family of simply connected regions. We also give an explicit computation of the Cauchy operator acting on an orthonormal basis, and we give estimates for the norms of the Kerzman-Stein and Cauchy operators on these regions. The regions are the first regions that display no apparent …

Analysis Of The Suitability Of The Trauma Center Location Configuration In The State Of Arkansas, Katy Accurso

Industrial Engineering Undergraduate Honors Theses

With the Arkansas trauma system framework having been so recently enacted, analysis of the suitability of the trauma center location configuration has yet to be explored. A variety of optimization models were created that placed an emphasis on different objectives. These results were then used to evaluate the effectiveness of Arkansas current system in relation to the optimal system generated by the mathematical models. Initial results indicated the areas that are not covered by the current trauma system. In addition, further research revealed the optimal number of trauma centers that could service the same population currently being served. Assessing the …

The Intelligent Driver Model: Analysis And Application To Adaptive Cruise Control, Rachel Malinauskas

All Theses

There are a large number of models that can be used to describe traffic flow. Although some were initially theoretically derived, there are many that were constructed with utility alone in mind. The Intelligent Driver Model (IDM) is a microscopic model that can be used to examine traffic behavior on an individual level with emphasis on the relation to an ahead vehicle. One application for this model is that it is easily molded to performing the operations for an Adaptive Cruise Control (ACC) system. Although it is clear that the IDM holds a number of convenient properties, like easily interpreted …

Improved Mixed-Integer Models Of A Two-Dimensional Cutting Stock Problem, William Lassiter

All Theses

This paper is concerned with a family of two-dimensional cutting stock problems that seeks to cut rectangular regions from a finite collection of sheets in such a manner that the minimum number of sheets is used. A fixed number of rectangles are to be cut, with each rectangle having a known length and width. All sheets are rectangular, and have the same dimension. We review two known mixed-integer mathematical formulations, and then provide new representations that both economize on the number of discrete variables and tighten the continuous relaxations. A key consideration that arises repeatedly in all models is the …

High Frequency Data: Modeling Durations Via The Acd And Log Acd Models, Lilian Cheung

Honors Scholar Theses

This thesis proposes a method of finding initial parameter estimates in the Log ACD₁ model for use in recursive estimation. The recursive estimating equations method is applied to the Log ACD₁ model to find recursive estimates for the unknown parameters in the model. A literature review is provided on the ACD and Log ACD models, and on the theory of estimating equations. Monte Carlo simulations indicate that the proposed method of finding initial parameter estimates is viable. The parameter estimation process is demonstrated by fitting an ACD model and a Log ACD model to a set of IBM …

A Radial Basis Function Partition Of Unity Method For Transport On The Sphere, Kevin Aiton

Boise State University Theses and Dissertations

The transport phenomena dominates geophysical fluid motions on all scales making the numerical solution of the transport problem fundamentally important for the overall accuracy of any fluid solver. In this thesis, we describe a new high-order, computationally efficient method for numerically solving the transport equation on the sphere. This method combines radial basis functions (RBFs) and a partition of unity method (PUM). The method is mesh-free, allowing near optimal discretization of the surface of the sphere, and is free of any coordinate singularities. The basic idea of the method is to start with a set of nodes that are quasi-uniformly …

A Numerical Model For Nonadiabatic Transitions In Molecules, Devanshu Agrawal

Undergraduate Honors Theses

In molecules, electronic state transitions can occur via quantum coupling of the states. If the coupling is due to the kinetic energy of the molecular nuclei, then electronic transitions are best represented in the adiabatic frame. If the coupling is instead facilitated through the potential energy of the nuclei, then electronic transitions are better represented in the diabatic frame. In our study, we modeled these latter transitions, called ``nonadiabatic transitions.'' For one nuclear degree of freedom, we modeled the de-excitation of a diatomic molecule. For two nuclear degrees of freedom, we modeled the de-excitation of an ethane-like molecule undergoing cis-trans …

Are Highly Dispersed Variables More Extreme? The Case Of Distributions With Compact Support, Benedict E. Adjogah

Electronic Theses and Dissertations

We consider discrete and continuous symmetric random variables X taking values in [0; 1], and thus having expected value 1/2. The main thrust of this investigation is to study the correlation between the variance, Var(X) of X and the value of the expected maximum E(Mn) = E(X1,...,Xn) of n independent and identically distributed random variables X1,X2,...,Xn, each distributed as X. Many special cases are studied, some leading to very interesting alternating sums, and some progress is made towards a general theory.

Physiologically-Based Pharmacokinetic Model For Ertapenem, Whitney Forbes

Electronic Theses and Dissertations

Ertapenem is a carbapenem used to treat a wide range of bacterial infections. What sets ertapenem apart from other carbapenems is its longer half-life which implies it need only be administered once daily. We developed a physiologically-based pharmacokinetic model for the distribution of ertapenem within the body. In the model, parameters such as human body weight and height, age, organ volumes, blood flow rates, and partition coefficients of particular tissues are used to examine the absorption, distribution, metabolism, and excretion of ertapenem. The total and free blood concentrations found were then compared to experimental data. We then examined the sensitivity …

An Applied Functional And Numerical Analysis Of A 3-D Fluid-Structure Interactive Pde, Thomas J. Clark

Department of Mathematics: Dissertations, Theses, and Student Research

We will present qualitative and numerical results on a partial differential equation (PDE) system which models a certain fluid-structure dynamics. In Chapter \ref{ChWellposedness}, the wellposedness of this PDE model is established by means of constructing for it a nonstandard semigroup generator representation; this representation is essentially accomplished by an appropriate elimination of the pressure. This coupled PDE model involves the Stokes system which evolves on a three dimensional domain $\mathcal{O}$ being coupled to a fourth order plate equation, possibly with rotational inertia parameter $\rho >0$, which evolves on a flat portion $\Omega$ of the boundary of $\mathcal{O}$. The coupling on …

The Szego Kernel Of Certain Polynomial Models, And Heat Kernel Estimates For Schrodinger Operators With Reverse Holder Potentials, Michael Tinker

Graduate Theses and Dissertations

We present two different results on operator kernels, each in the context of its relationship to a class of CR manifolds M={z,w1,...wn) element of Cn⁺¹ : Im wifi(Re z)} where n d 2 and (phi)i( x) is subharmonic for i = 1,...,n. Such models have proven useful for studying canonical operators such as the Szegö projection on weakly pseudoconvex domains of finite type in C², and may play a similar role in work on higher codimension CR manifolds in C³. Our study in Part II concerns the Szegö kernel on M for which the (empty set)i are subharmonic nonharmonic polynomials. …

General Sampling Schemes For The Bergman Spaces, Newton Foster

Graduate Theses and Dissertations

A characterization of sampling sequences for the Bergman spaces was originally provided by Seip and later expanded upon by Schuster. We consider a generalized notion of sampling using the infimum norm of the quotient space. Adapting some old techniques, we provide a characterization of general sampling sequences in terms of the lower uniform density.

Closed-Range Composition Operators On Weighted Bergman Spaces And Applications, Shanda Renee Fulmer

Graduate Theses and Dissertations

We will discuss necessary and sufficient conditions for a Composition Operator to be closed range on the weighted Bergman spaces. The function phi is an analytic self map of the unit disk and our results extend those previously intended for the classical Bergman space. We will also give applications.

Generating Combinatorial Objects- A New Perspective, Alexander Chizoma Nwala

Computer Science Theses & Dissertations

Combinatorics is the science of "possibilities." This definition, while not formal is a fair statement because all too often, in order to gain insight into the solution of many counting problems, we explore the possibilities. In some cases we seek to know how many options, while in other cases we seek to enumerate or list the options. Irrespective of the scenario, combinatorics plays a vital role today. In many instances such as exploring the options for choosing a new password for a combination lock, we employ combinatorics. In considering the possible license plate permutations for a state, or to see …

Spatial Scheduling Algorithms For Production Planning Problems, Sudharshana Srinivasan

Theses and Dissertations

Spatial resource allocation is an important consideration in shipbuilding and large-scale manufacturing industries. Spatial scheduling problems (SSP) involve the non-overlapping arrangement of jobs within a limited physical workspace such that some scheduling objective is optimized. Since jobs are heavy and occupy large areas, they cannot be moved once set up, requiring that the same contiguous units of space be assigned throughout the duration of their processing time. This adds an additional level of complexity to the general scheduling problem, due to which solving large instances of the problem becomes computationally intractable. The aim of this study is to gain a …

Experimental Evidence For Heterogeneous Expectations In A Simple New Keynesian Framework, Atticus David Holm Graven

Business and Economics Honors Papers

This paper is a two-dimensional analysis of agent behavior in a standard New Keynesian (NK) Macroeconomic model. On the dimension of pure mathematics, we analyze the parameters of the NK model and of possible prediction rules. On the other dimension we continue a practice of empirical study of heterogeneous expectations with an experiment. The experiment will ask participants to make predictions of future output and inflation. Their responses will create a data-set upon which analysis will be performed to illuminate and corroborate current theories of economic decision making. The literature has shown that most agents' forecasting rules can be modeled …

Combinatorial And Algebraic Coding Techniques For Flash Memory Storage, Kathryn A. Haymaker

Department of Mathematics: Dissertations, Theses, and Student Research

Error-correcting codes are used to achieve reliable and efficient transmission when storing or sending information across a noisy channel. This thesis investigates a mathematical approach to coding techniques for storage devices such as flash memory storage, although many of the resulting codes and coding schemes can be applied in other contexts. The main contributions of this work include the design of efficient codes and decoding algorithms using discrete structures such as graphs and finite geometries, and developing a variety of strategies for adapting codes to a multi-level setting.

Information storage devices are prone to errors over time, and the frequency …

A Comparison Of Clustering And Missing Data Methods For Health Sciences, Ran Zhao, Deanna Needell, Christopher Johansen, Jerry L. Grenard

CMC Faculty Publications and Research

In this paper, we compare and analyze clustering methods with missing data in health behavior research. In particular, we propose and analyze the use of compressive sensing's matrix completion along with spectral clustering to cluster health related data. The empirical tests and real data results show that these methods can outperform standard methods like LPA and FIML, in terms of lower misclassification rates in clustering and better matrix completion performance in missing data problems. According to our examination, a possible explanation of these improvements is that spectral clustering takes advantage of high data dimension and compressive sensing methods utilize the …