Uniqueness Of Solutions Implies Existence And Uniqueness Of Solutions Of Boundary Value Problems For Third Order Differential Equations, 2010 University of Dayton

#### Uniqueness Of Solutions Implies Existence And Uniqueness Of Solutions Of Boundary Value Problems For Third Order Differential Equations, Veronica Respress

*Undergraduate Mathematics Day: Proceedings and Other Materials*

In this paper we are concerned with uniqueness implies uniqueness and uniqueness implies existence questions for solutions of a class of boundary value problems for the third order ordinary differential equation (ODE). First we show uniqueness of solutions of a class of two-point problems implies the uniqueness of solutions of an associated class of three-point problems. Then we establish uniqueness of solutions of the class of two-point problems implies the existence of solutions of the class of two point problems and the associated class of three-point problems.

Just Sit Back And Let The Girth Model Make Money For You, 2010 University of Dayton

#### Just Sit Back And Let The Girth Model Make Money For You, Ellham Negahdary

*Undergraduate Mathematics Day: Proceedings and Other Materials*

The Girth Model will use the 10-period exponential moving average (EMA) and the 20-period EMA as their proxy for market trend. The Girth Model is a trend following model incorporating volatility, momentum and velocity. We will use girth as an early close indication to both long and short positions. Typically, early exit due to decreasing girth results in a more favorable profit position than that taken if the trader simply waited for an exit on the EMA cross to the downside.

The Marshall Differential Analyzer: A Visual Interpretation Of Mathematics, 2010 University of Dayton

#### The Marshall Differential Analyzer: A Visual Interpretation Of Mathematics, Bonita A. Lawrence, Richard P. Merritt, Devon A. Tivener

*Undergraduate Mathematics Day: Proceedings and Other Materials*

Mechanical integration is an idea dating back to the late 1800's discovered by James Thomson, brother of Lord Kelvin. This idea was then expanded to build a calculating machine, called a differential analyzer, by Vannevar Bush (M.I.T) in 1929. The Marshall University Differential Analyzer Team has followed in the footsteps of Dr. Bush and a gentleman named Dr. Arthur Porter, who was the first to build a differential analyzer in England when he was a student of Dr. Douglas Hartree. He built his machine of Meccano components, the British version of Erector Set. In the early days ...

Distance Functions And Attribute Weighting In A K-Nearest Neighbors Classifier, 2010 University of Dayton

#### Distance Functions And Attribute Weighting In A K-Nearest Neighbors Classifier, Alyssa C. Frazee, Matthew A. Hathcock, Samantha C. Bates Prins

*Undergraduate Mathematics Day: Proceedings and Other Materials*

To assess environmental health of a stream, field, or other ecological object, characteristics of that object should be compared to a set of reference objects known to be healthy. Using streams as objects, we propose a k-nearest neighbors algorithm (Bates Prins and Smith, 2006) to find the appropriate set of reference streams to use as a comparison set for any given test stream. Previously, investigations of the k-nearest neighbors algorithm have utilized a variety of distance functions, the best of which has been the Interpolated Value Difference Metric (IVDM), proposed by Wilson and Martinez (1997). We propose two alternatives to ...

Initial-Value Technique For Singularly Perturbed Two Point Boundary Value Problems Via Cubic Spline, 2010 University of Central Florida

#### Initial-Value Technique For Singularly Perturbed Two Point Boundary Value Problems Via Cubic Spline, Luis G. Negron

*Electronic Theses and Dissertations, 2004-2019*

A recent method for solving singular perturbation problems is examined. It is designed for the applied mathematician or engineer who needs a convenient, useful tool that requires little preparation and can be readily implemented using little more than an industry-standard software package for spreadsheets. In this paper, we shall examine singularly perturbed two point boundary value problems with the boundary layer at one end point. An initial-value technique is used for its solution by replacing the problem with an asymptotically equivalent first order problem, which is, in turn, solved as an initial value problem by using cubic splines. Numerical examples ...

A Generalization Of Bernoulli's Inequality, 2010 Department of Mathematics and Statistics, Florida International University

#### A Generalization Of Bernoulli's Inequality, Laura De Carli, Steve M. Hudson

*Department of Mathematics and Statistics*

No abstract provided.

Polymer Length Distributions For Catalytic Polymerization Within Mesoporous Materials: Non-Markovian Behavior Associated With Partial Extrusion, 2010 Ames Laboratory

#### Polymer Length Distributions For Catalytic Polymerization Within Mesoporous Materials: Non-Markovian Behavior Associated With Partial Extrusion, Da-Jiang Liu, Hung-Ting Chen, Victor S.-Y. Lin, James W. Evans

*Physics and Astronomy Publications*

We analyze a model for polymerization at catalytic sites distributed within parallel linear pores of a mesoporous material. Polymerization occurs primarily by reaction of monomers diffusing into the pores with the ends of polymers near the pore openings. Monomers and polymers undergo single-file diffusion within the pores. Model behavior, including the polymer length distribution, is determined by kinetic Monte Carlo simulation of a suitable atomistic-level lattice model. While the polymers remain within the pore, their length distribution during growth can be described qualitatively by a Markovian rate equation treatment. However, once they become partially extruded, the distribution is shown to ...

Curve Interpolation And Coding Theory, 2010 Gettysburg College

#### Curve Interpolation And Coding Theory, Darren B. Glass

*Math Faculty Publications*

Whether it is downloading files from the Internet, having conversations between cell phones, or sending information from a laptop to a printer, we often want to transmit data in situations where we need to worry about interference from other signals that may cause errors in the transmission. The branch of mathematics known as coding theory is dedicated to finding ways to tell when these are errors in transmission and, when possible, how to correct those errors. The goal of coding theory is to build as much redundancy as possible into a message without greatly increasing its length. [excerpt]

Use Of Cognitive Constructs In Linear Algebra, 2010 University of Texas at El Paso

#### Use Of Cognitive Constructs In Linear Algebra, Azucena Zamora

*Open Access Theses & Dissertations*

Thesis analyzed the presence of two cognitive entities-- modes of thinking and metonymies and metaphors- in the reasoning of three students enrolled in a first year matrix algebra course at a southwest university via the responses given to a set of eight questions asked during one-on-one interviews. The findings of our analysis shed light on the cognitive constructs that students employ to form their understanding of linear algebra concepts. Furthermore, our findings provide clues about the ways in which students move from one mode of thinking to another in the context of varying levels of exposure to graphical, algebraic, and ...

Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, 2010 Wright State University - Main Campus

#### Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, Joaquin Riviera, Yi Li

*Mathematics and Statistics Faculty Publications*

In this paper we discuss the existence of traveling wave solutions for a nonlocal reaction-diffusion model of Influenza A proposed in Lin et. al. (2003). The proof for the existence of the traveling wave takes advantage of the different time scales between the evolution of the disease and the progress of the disease in the population. Under this framework we are able to use the techniques from geometric singular perturbation theory to prove the existence of the traveling wave.

The Norm Of A Truncated Toeplitz Operator, 2010 University of Richmond

#### The Norm Of A Truncated Toeplitz Operator, William T. Ross, Stephan Ramon Garcia

*Math and Computer Science Faculty Publications*

We prove several lower bounds for the norm of a truncated Toeplitz operator and obtain a curious relationship between the *H ^{2} *and

*H*norms of functions in model spaces.

^{∞}Multigrid In A Weighted Space Arising From Axisymmetric Electromagnetics, 2010 Portland State University

#### Multigrid In A Weighted Space Arising From Axisymmetric Electromagnetics, Dylan M. Copeland, Jay Gopalakrishnan, Minah Oh

*Mathematics and Statistics Faculty Publications and Presentations*

Consider the space of two-dimensional vector functions whose components and curl are square integrable with respect to the degenerate weight given by the radial variable. This space arises naturally when modeling electromagnetic problems under axial symmetry and performing a dimension reduction via cylindrical coordinates. We prove that if the original three-dimensional domain is convex then the multigrid Vcycle applied to the inner product in this space converges, provided certain modern smoothers are used. For the convergence analysis, we first prove several intermediate results, e.g., the approximation properties of a commuting projector in weighted norms, and a superconvergence estimate for ...

A Mathematical Analysis Of Multiple-Target Selex, 2010 Iowa State University

#### A Mathematical Analysis Of Multiple-Target Selex, Yeon-Jung Seo

*Graduate Theses and Dissertations*

This thesis develops a mathematical model of the biological procedure SELEX (Systematic Evolution of Ligands by EXponential Enrichment). The procedure is an *in vitro* method for identifying nucleic acid (NA) molecules that have an ability to bind tightly and specifically to target species of interest, such as small organic molecules, peptides or proteins.

We explore two main algorithms: multiple target (positive) SELEX and alternate SELEX. The schemes are considered as *discrete time dynamical systems*, and the limiting (steady-state) behaviors of the processes are characterized by the initial parameters of each system: concentration of total targets, concentration of a pool of ...

Incidence Functions, 2010 University of Texas at El Paso

#### Incidence Functions, Yiyu Liao

*Open Access Theses & Dissertations*

In the mid 1960's, the incidence algebra was introduced in the seminal paper of Gian-Carlo Rota. He addressed the importance of the Mobius function in combinatorics. In particular, the incidence algebra of a locally finite poset plays an essentially unifying role in the theory of the Mobius function. One of the significant generalizations is the incidence algebra of a Mobius category introduced by Pierre Leroux. With the help from Mobius category, it was exciting to be able to extend the combinatorial results more broadly than just on posets. Before attempting to study this generalization of the Mobius function, we ...

Augmented Measurement System Assessment, 2010 University of San Francisco

#### Augmented Measurement System Assessment, Nathaniel Stevens, R Browne, S H. Steiner, R J. Mackay

*Mathematics*

The standard plan for the assessment of the variation due to a measurement system involves a number of operators repeatedly measuring a number of parts in a balanced design. In this article, we consider the performance of two types of (unbalanced) assessment plans. In each type, we use a standard plan augmented with a second component. In type A augmentation, each operator measures a different set of parts once each. In type B augmentation, each operator measures the same set of parts once each. The goal of the paper is to identify good augmented plans for estimating the gauge repeatability ...

Positive Solutions For A System Of Singular Second Order Nonlocal Boundary Value Problems, 2010 National University of Sciences and Technology, Rawalpindi, Pakistan

#### Positive Solutions For A System Of Singular Second Order Nonlocal Boundary Value Problems, Naseer Ahmad Asif, Paul W. Eloe, Rahmat Ali Khan

*Mathematics Faculty Publications*

Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type (see PDF for details) are obtained. The nonlinearities (see PDF) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. … An example is provided to illustrate the results.

U-Singularity And T-Topos Theoretic Entropy, 2010 California Polytechnic State University - San Luis Obispo

#### U-Singularity And T-Topos Theoretic Entropy, Goro C. Kato

*Mathematics*

We will give descriptions of *u*-singularities as we introduce the notion of *t*-topos theoretic entropies. The unifying methodology for a *u*-singularity is the universal mapping property of an inverse or direct limit. The qualitative, conceptual, and structural analyses of u-singularities are given in terms of inverse and direct limits of micro decompositions of a presheaf and coverings of an object in t-site in the theory of temporal topos.

Urcohomologies And Cohomologies Of N -Complexes, 2010 Okayama University

#### Urcohomologies And Cohomologies Of N -Complexes, Naoya Hiramatsu, Goro Kato

*Mathematics*

For a general sequence of objects and morphisms, we construct two N-complexes. Then we can define cohomologies (i, k)-type of the N-complexes not only on a diagonal region but also in the triangular region. We obtain an invariant defined on a general sequence of objects and morphisms. For a short exact sequence of N-complexes, we get the associated long exact sequence generalizing the classical long exact sequence. Lastly, several properties of the vanishing cohomologies of N-complexes are given.

Using Correlation Coefficients To Estimate Slopes In Multiple Linear Regression, 2010 University of Montana, Missoula

#### Using Correlation Coefficients To Estimate Slopes In Multiple Linear Regression, Rudy Gideon

*Mathematical Sciences Faculty Publications*

This short note takes correlation coefficients as the starting point to obtain inferential results in linear regression. Under certain conditions, the population correlation coefficient and the sampling correlation coefficient can be related via a Taylor series expansion to allow inference on the coefficients in simple and multiple regression. This general method includes nonparametric correlation coefficients and so gives a universal way to develop regression methods. This work is part of a correlation estimation system that uses correlation coefficients to perform estimation in many settings, for example, time series, nonlinear and generalized linear models, and individual distributions.

Methods Of Competing Risks Analysis Of End-Stage Renal Disease And Mortality Among People With Diabetes, 2010 University of Saskatchewan College of Medicine

#### Methods Of Competing Risks Analysis Of End-Stage Renal Disease And Mortality Among People With Diabetes, Hyun J. Lim, Xu Zhang, Roland Dyck, Nathaniel Osgood

*Mathematics and Statistics Faculty Publications*

Background: When a patient experiences an event other than the one of interest in the study, usually the probability of experiencing the event of interest is altered. By contrast, disease-free survival time analysis by standard methods, such as the Kaplan-Meier method and the standard Cox model, does not distinguish different causes in the presence of competing risks. Alternative approaches use the cumulative incidence estimator by the Cox models on cause-specific and on subdistribution hazards models. We applied cause-specific and subdistribution hazards models to a diabetes dataset with two competing risks (end-stage renal disease (ESRD) or death without ESRD) to measure ...