Applied Mathematics Commons^™

Effect Of Variable Dose Rate On Biologically Effective Dose, Vadim Y. Kuperman, Gregory S. Spradlin

Publications

Purpose: to investigate the effect of variable dose rate on biologically effective dose ( BED ).

Materials and methods: by using the linear-quadratic (LQ) model with bi-exponential repair, we analytically determine the time-dependent dose rate R ~ which minimizes the effective protraction factor ( eff G ) and BEDunder the condition of fixed fraction time and dose per fraction.  Because normal tissue complication probability ( NTCP) monotonically decreases with decreasingBED , the dose rate R ~ also minimizes NTCP.

Results: the dependences of Geff, BED, and NTCP on fraction time were determined for different radiobiological parameters and two different …

Stochastic Dea With A Perfect Object And Its Application To Analysis Of Environmental Efficiency, Alexander Vaninsky

Publications and Research

The paper introduces stochastic DEA with a Perfect Object (SDEA PO). The Perfect Object (PO) is a virtual Decision Making Unit (DMU) that has the smallest inputs and greatest outputs. Including the PO in a collection of actual objects yields an explicit formula of the efficiency index. Given the distributions of DEA inputs and outputs, this formula allows us to derive the probability distribution of the efficiency score, to find its mathematical expectation, and to deliver common (group–related) and partial (object-related) efficiency components. We apply this approach to a prospective analysis of environmental efficiency of the major national and regional …

Schematics Of A Water Balloon Launcher Design And Reproducible Water-Balloon-Filling Procedures Used For A Middle School Summer Science Camp, Mike A. Christiansen, Boyd F. Edwards, David D. Sam

USU Uintah Basin Faculty Publications

We recently held a Science Summer Camp for middle school students, designed to infuse young people with increased excitement for STEM (Science, Technology, Engineering, and Math) subjects. Our efforts, which received nationally-syndicated news coverage, included the invention of a versatile water balloon launcher.

This document contains:

(1) detailed construction schematics and user operation guidelines for our balloon launcher;

(2) data and instructions for reproducibly filling water balloons to specific volumes and weights, within used by students during the summer camp.

A Mathematical Model And Numerical Method For Thermoelectric Dna Sequencing, Liwei Shi

Doctoral Dissertations

DNA sequencing is the process of determining the precise order of nucleotide bases, adenine, guanine, cytosine, and thymine within a DNA molecule. It includes any method or technology that is used to determine the order of the four bases in a strand of DNA. The advent of rapid DNA sequencing methods has greatly accelerated biological and medical research and discovery. Thermoelectric DNA sequencing is a novel method to sequence DNA by measuring the heat that is released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a growing DNA strand. The thermoelectric device for this project is composed of four parts: …

Exploration Of Aqueous Interfaces And Their Effect On Ion Behavior, Oneka T. Cummings

Doctoral Dissertations

An in-depth understanding of a wide range of physical, chemical, atmospheric and biological processes can only be achieved after the structure and dynamics of interfaces and the interfacial behavior of aqueous species, such as ions, are thoroughly studied and understood. This dissertation describes computational studies conducted to gain a more comprehensive understanding of such interfaces and the behavior of ions in the bulk and interfacial regions of the (1) air/water interface, and (2) alkane/water interfaces.

At the air/water interface the effect of counterion (sodium cations) charge and the influence of ion pairing on anion (chloride) propensity for the air/water interface …

Generalized Finite-Difference Time-Domain Schemes For Solving Nonlinear Schrödinger Equations, Frederick Ira Moxley Iii

Doctoral Dissertations

The nonlinear Schrödinger equation (NLSE) is one of the most widely applicable equations in physical science, and characterizes nonlinear dispersive waves, optics, water waves, and the dynamics of molecules. The NLSE satisfies many mathematical conservation laws. Moreover, due to the nonlinearity, the NLSE often requires a numerical solution, which also satisfies the conservation laws. Some of the more popular numerical methods for solving the NLSE include the finite difference, finite element, and spectral methods such as the pseudospectral, split-step with Fourier transform, and integrating factor coupled with a Fourier transform. With regard to the finite difference and finite element methods, …

Substance Abuse Via Legally Prescribed Drugs: The Case Of Vicodin In The United States, Wendy K. Caldwell, Benjamin Freedman, Luke Settles, Michael M. Thomas, Anarina Murillo, Erika Camacho, Stephen Wirkus

Faculty Articles

Vicodin is the most commonly prescribed pain reliever in the United States. Research indicates that there are two million people who are currently abusing Vicodin, and the majority of those who abuse Vicodin were initially exposed to it via prescription. Our goal is to determine the most effective strategies for reducing the overall population of Vicodin abusers. More specifically, we focus on whether prevention methods aimed at educating doctors and patients on the potential for drug abuse or treatment methods implemented after a person abuses Vicodin will have a greater overall impact. We consider one linear and two non-linear compartmental …

Optimal Control Modeling And Simulation, With Application To Cholera Dynamics, Chairat Modnak

Mathematics & Statistics Theses & Dissertations

The theory of optimal control, a modern extension of the calculus of variations. has found many applications in a wide range of scientific fields, particularly in epidemiology with respect to disease prevention and intervention. In this dissertation. we conduct optimal control modeling, simulation and analysis to cholera dynamics. Cholera is a severe intestinal infectious disease that remains a serious public health threat in developing countries. Transmission of cholera involves complex interactions between the human host, the pathogen, and the environment. The worldwide cholera outbreaks and their increasing severity, frequency and duration in recent years underscore the gap between the complex …

Multi-Objective Preliminary Design Optimization Of Planing Craft Using Differential Evolution And Artificial Networks, Robert Eugene Weidman

Mechanical & Aerospace Engineering Theses & Dissertations

The differential evolution (DE) algorithm is an evolutionary algorithm that has been utilized as a metaheuristic optimizer in the last few years. A recently developed multi-objective version of DE is utilized in this research in order to optimize the preliminary design of planing craft. The craft performance is evaluated using the planing hull preliminary design software PHAST. The optimization problem objectives are the craft acquisition cost and the overall measure of effectiveness; the latter comprises various performance aspects: ride quality, transportability, payload, and mobility. Static stability and operating constraints are also considered. Each of the aforementioned four measures of effectiveness …

Linear Programming Algorithm With Mixed Real-Integer Variables In Matlab Environments, Gelareh Bakhtyar

Civil & Environmental Engineering Theses & Dissertations

Efficient numerical procedures for solving general Linear Programming (LP) problems with mixed real-integer variables are developed in this work. The proposed algorithms employ the revised dual simplex with Branch and Bound (B&B) algorithms, with special procedures for limited search of subsequent branches. Computational time can be significantly reduced by incorporating the updated inverse formulas into the developed procedures. Both generic LP problems and deterministic pavement maintenance and rehabilitation (M&R) problems are used in this study to vaiidate the developed procedures. Medium to large-scale examples ( 11 pavement M&R) presented in this work have demonstrated that the developed numerical procedures consistently …

Topics In Electromagnetic, Acoustic, And Potential Scattering Theory, Umaporn Nuntaplook

Mathematics & Statistics Theses & Dissertations

With recent renewed interest in the classical topics of both acoustic and electromagnetic aspects for nano-technology, transformation optics, fiber optics, metamaterials with negative refractive indices, cloaking and invisibility, the topic of time-independent scattering theory in quantum mechanics is becoming a useful field to re-examine in the above contexts. One of the key areas of electromagnetic theory scattering of plane electromagnetic waves — is based on the properties of the refractive indices in the various media. It transpires that the refractive index of a medium and the potential in quantum scattering theory are intimately related. In many cases, understanding such scattering …

Bimodules Over Cartan Masas In Von Neumann Algebras, Norming Algebras, And Mercer's Theorem, Jan Cameron, David R. Pitts, Vrej Zarikian

Department of Mathematics: Faculty Publications

In a 1991 paper, R. Mercer asserted that a Cartan bimod- ule isomorphism between Cartan bimodule algebras A1 and A2 extends uniquely to a normal -isomorphism of the von Neumann algebras gener- ated by A1 and A2 (Corollary 4.3 of Mercer, 1991). Mercer's argument relied upon the Spectral Theorem for Bimodules of Muhly, Saito and Solel, 1988 (Theorem 2.5, there). Unfortunately, the arguments in the literature supporting their Theorem 2.5 contain gaps, and hence Mercer's proof is incomplete.

In this paper, we use the outline in Pitts, 2008, Remark 2.17, to give a proof of Mercer's Theorem under the additional …

Modelling Locally Changing Variance Structured Time Series Data By Using Breakpoints Bootstrap Filtering, Rajan Lamichhane

Mathematics & Statistics Theses & Dissertations

Stochastic processes have applications in many areas such as oceanography and engineering. Special classes of such processes deal with time series of sparse data. Studies in such cases focus in the analysis, construction and prediction in parametric models. Here, we assume several non-linear time series with additive noise components, and the model fitting is proposed in two stages. The first stage identifies the density using all the clusters information, without specifying any prior knowledge of the underlying distribution function of the time series. The effect of covariates is controlled by fitting the linear regression model with serially correlated errors. In …

Current Barriers To Successful Implementation Of Fist Principles, Brandon Keller, Joseph R. Wirthlin

Faculty Publications

The Fast, Inexpensive, Simple, and Tiny (FIST) framework proposes a broad set of organizational values, but provides limited guidance on practical implementation. Implementing FIST principles requires clarifying the definitions of “fast,” “inexpensive,” and “simple,” recognizing where FIST does and does not apply. Additionally, a subset of the FIST heuristics was expanded upon to increase their usefulness for practitioners. The primary research findings are that FIST principles are less conducive for highly complex or novel systems, immature technologies, future needs, acquisitions in early development phases, or when performance is the foremost value. FIST principles were also found to be constrained by …

Problems And Prospects Of Hydraulic Modelling For Environmental Flows Assessment Studies In East Africa, Preksedis Ndomba

Tanzania Journal of Engineering and Technology (TJET)

The objective of this paper is to document the problems and prospects of hydraulic modelling for Environmental Flows Assessment (EFA) studies based on selected case studies. Most of studies in East Africa use Holistic methodologies. An ideal data set for defining river hydraulics for most of these methods would be six data points of stage measurements over a good distribution of discharges, the stage of zero discharge and some flood-related data. Besides, in East African region EFA studies suffer from data scarcity (i.e., poorly gauged sites) and limited expertise and funding. The hydraulics studies conducted by the authors entailed desktop …

Open Source Kiswahili Spell Checker (Sw-Tz), Hashim Twaakyondo

Tanzania Journal of Engineering and Technology (TJET)

Different English software products are localized into many native languages spoken around the world, the most popular software products localized so far are word processing software and web browsers. The effort has begun to localize these software products in Kiswahili language which is widely spoken in Tanzania, East and Central Africa. Kiswahili is an official language of Tanzania, and is a national language in Uganda and Kenya. To make these software products useful to Kiswahili speaking community particularly in Tanzania a new Kiswahili spell checker has been developed and, it uses most of the Kiswahili words spoken in Tanzania and …

2d Autocad Geometric Data Extraction And Post Processing For Numerical Control, Tito Mwinuka

Tanzania Journal of Engineering and Technology (TJET)

In this paper, a method of extracting 2D geometric data from AutoCAD drawing and post processing for Numerical Control (NC) is presented. Geometric data already available in the Drawing Interchange Files (DXF) can be utilized to accurately and economically prepare part programs for controlling NC/CNC machine tools. AutoCAD, being general purpose software, stores its geometric data in a form that cannot be directly applied for automatic generation of Numerical Control (NC) codes. The way around the discrepancy between the structure of a drawing database (DXF files) and the information requirement for part programming is addressed in this work. NC programming …

On The Impulse Control Of Jump Diffusions, Erhan Bayraktar, Thomas Emmerling, José-Luis Menaldi

Mathematics Faculty Research Publications

Regularity of the impulse control problem for a nondegenerate n-dimensional jump diffusion with infinite activity and finite variation jumps was recently examined in [M. H. A. Davis, X. Guo, and G. Wu, SIAM J. Control Optim., 48 (2010), pp. 5276–5293]. Here we extend the analysis to include infinite activity and infinite variation jumps. More specifically, we show that the value function u of the impulse control problem satisfies u ∈ W_loc^2,p(Rⁿ).

Insights On The Neyman - Pearson Lemma: Alternative Critical Regions, And Their Power., David E. Wetzell

ACMS Conference Proceedings 2013

The Neyman-Pearson Lemma is a powerful fundamental lemma in the area of hypothesis testing in Statistics. It gives the best test when testing simple vs. simple hypotheses. In this talk we would like to investigate testing a population mean H0 μ = μ0 vs. H1 μ = μ1 > μ0. As a result of the N-P Lemma, the best test is of the form, “Reject H0 if x>c” , where c is chosen so that the Type I error probability is a. Let n be small. What are some alternative decision rules of size a, what …

Service-Learning Panel, Dave Klanderman, Josh Wilkerson, Maria Zack

ACMS Conference Proceedings 2013

Many of us have wanted to incorporate service experiences in courses, or are being asked by our institutions to do so. Service-learning is a way of looking at service as being a partner with and leading to learning for our students. But in math, there are not a lot of resources to use! Our panelists will present classroom-tested ideas from several different levels of course, and we will end with a short time for more brainstorming among all participants.