Mathematics Commons^™

Theory And Algorithms For Swept Manifold Intersections, Yuriy Mileyko

Dissertations

Recent developments in such fields as computer aided geometric design, geometric modeling, and computational topology have generated a spate of interest towards geometric objects called swept volumes. Besides their great applicability in various practical areas, the mere geometry and topology of these entities make them a perfect testbed for novel approaches aimed at analyzing and representing geometric objects. The structure of swept volumes reveals that it is also important to focus on a little simpler, although a very similar type of objects - swept manifolds. In particular, effective computability of swept manifold intersections is of major concern.

The main goal …

Electromagnetic And Acoustic Propagation In Strip Lines And Porous Media, Lin Zhou

Dissertations

Wave propagation in two physical structures is described and analyzed in this dissertation. In the first problem, the propagation of a normally incident plane acoustic wave through a three dimensional rigid slab with periodically placed holes is modeled and analyzed. The spacing of the holes A and B, the wavelength λ and the thickness of the slab L are order one parameters compared to the characteristic size D of the holes, which is a small quantity. Scattering matrix techniques are used to derive expressions for the transmission and reflection coefficients of the lowest mode. These expressions depend only on the …

The Control Of Frequency Of A Conditional Oscillator Simultaneously Subjected To Multiple Oscillatory Inputs, Christina L. Ambrosio

Dissertations

A conditional oscillator is one that requires input to oscillate. An example of such is the gastric mill network of the stomatogastric ganglion of the crab Cancer borealis which requires modulatory input from outside the stomatogastric ganglion and fast input from the pyloric network of the animal in order to become active. This dissertation studies how the frequency of the gastric mill network is determined when it is simultaneously subjected to two different rhythmic inputs whose timing may be mismatched. We derive a mathematical model of the gastric mill network and deduce that the difference in timing between the pyloric …

The Lie Symmetries Of A Few Classes Of Harmonic Functions, Willis L. Petersen

Theses and Dissertations

In a differential geometry setting, we can analyze the solutions to systems of differential equations in such a way as to allow us to derive entire classes of solutions from any given solution. This process involves calculating the Lie symmetries of a system of equations and looking at the resulting transformations. In this paper we will give a general background of the theory necessary to develop the ideas of working in the jet space of a given system of equations, applying this theory to harmonic functions in the complex plane. We will consider harmonic functions in general, harmonic functions with …

Hopf Bifurcations And Horseshoes Especially Applied To The Brusselator, Steven R. Jones

Theses and Dissertations

In this paper we explore bifurcations, in particular the Hopf bifurcation. We study this especially in connection with the Brusselator, which is a model of certain chemical reaction-diffusion systems. After a thorough exploration of what a bifurcation is and what classifications there are, we give graphic representations of an occurring Hopf bifurcation in the Brusselator. When an additional forcing term is added, behavior changes dramatically. This includes the introduction of a horseshoe in the time map as well as a strange attractor in the system.

Endomorphism Rings Of Finite Global Dimension, Graham J. Leuschke

Mathematics - All Scholarship

For a commutative local ring R, consider (noncommutative) R-algebras lamda of the form lamda = End R(M) where M is a reflexive R-module with nonzero free direct summand. Such algebras lamda of finite global dimension can be viewed as potential substitutes for, or analogues of, a resolution of singularities of Spec R. For example, Van den Bergh has shown that a three-dimensional Gorenstein normal C-algebra with isolated terminal singularities has a crepant resolution of singularities if and only if it has such an algebra lamda with finite global dimension and which is maximal Cohen–Macaulay over R (a “noncommutative crepant resolution …

General Existence Principles For Nonlocal Boundary Value Problems With Ø-Laplacian And Their Applications, Ravi P. Agarwal, Donal O'Regan, Svatoslav Staněk

Mathematics and System Engineering Faculty Publications

The paper presents general existence principles which can be used for a large class of nonlocal boundary value problems of the form (ø(x′)) ′ = f1(t,x,x′) + f2(t,x,x′)F 1X + f3(t,x,x′)f2x,α(x) = 0, β(x) = 0, where fj satisfy local Carathéodory conditions on some [0,T] × Dj ⊂ ℝ, fj are either regular or have singularities in their phase variables (j = 1,2,3), f i, : C1[0.T] → C0[0,T] (i = 1,2), and α,β : C1[0.T] → ℝ are continuous. The proofs are based on the Leray-Schauder degree theory and use regularization and sequential techniques. Applications of general existence principles …

Orthogonal Curvilinear Coordinates, Lindsey J. Bromenshenkel

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

Graph Theory For The Secondary School Classroom., Dayna Brown Smithers

Electronic Theses and Dissertations

After recognizing the beauty and the utility of Graph Theory in solving a variety of problems, the author decided that it would be a good idea to make the subject available for students earlier in their educational experience. In this thesis, the author developed four units in Graph Theory, namely Vertex Coloring, Minimum Spanning Tree, Domination, and Hamiltonian Paths and Cycles, which are appropriate for high school level.

Measuring Inter-Rater Agreement Among Pathologists In Cancer Screening Studies, Krystle S. Oates

Electronic Dissertations and Theses

Although cervical cancer is one of the most preventable forms of cancer in the United States, it still remains the leading cause of cancer mortality in El Salvador. This is attributed to poor cancer screening in El Salvador. The Pap smear test is the traditional screening method that pathologists use for the direction of cervical cancer in women, but the Thin Prep test is said to be an improvement to the Prep smear test. In this project, we will use the data from pathologists in the United States and El Salvador who analyzed the slides of 471 Salvadoran women who …

Abelson’S Paradox And The Michelson-Morley Experiment, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

No abstract provided.

Teaching Random Assignment: Do You Believe It Works?, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

Textbook authors admonish students to check on the comparability of two randomly assigned groups by conducting statistical tests on pretest means to determine if randomization worked. A Monte Carlo study was conducted on a sample of n = 2 per group, where each participant’s personality profile was represented by 7,500 randomly selected and assigned scores. Independent samples t tests were conducted and the results demonstrated that random assignment was successful in equating the two groups on 7,467 variables. The students’ focus is redirected from the ability of random assignment to create comparable groups to the testing of the claims of …

Fréchet Subdifferential Calculus And Optimality Conditions In Nondifferentiable Programming, Boris S. Mordukhovich, Nguyen Mau Nam, N. D. Yen

Mathematics Research Reports

We develop various (exact) calculus rules for Frechet lower and upper subgradients of extended-realvalued functions in general Banach spaces. Then we apply this calculus to derive new necessary optimality conditions for some remarkable classes of problems in constrained optimization including minimization problems for difference-type functions under geometric and operator constraints as well as subdifferential optimality conditions for the so-called weak sharp minima.

Bayesian Wavelet Estimation Of Long Memory Parameter, Leming Qu

Mathematics Faculty Publications and Presentations

A Bayesian wavelet estimation method for estimating parameters of a stationary I(d) process is represented as an useful alternative to the existing frequentist wavelet estimation methods. The effectiveness of the proposed method is demonstrated through Monte Carlo simulations. The sampling from the posterior distribution is through the Markov Chain Monte Carlo (MCMC) easily implemented in the WinBUGS software package.

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

A Stochastic Calculus For Systems With Memory, Feng Yan, Salah-Eldin A. Mohammed

Articles and Preprints

For a given stochastic process X, its segment X_t at time t represents the "slice" of each path of X over a fixed time-interval [t-r, t], where r is the length of the "memory" of the process. Segment processes are important in the study of stochastic systems with memory (stochastic functional differential equations, SFDEs). The main objective of this paper is to study non-linear transforms of segment processes. Towards this end, we construct a stochastic integral with respect to the Brownian segment process. The difficulty in this construction is the fact that the …

Introduction (2005), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2005

Fifteenth Conference of the Association of Christians in the Mathematical Sciences

Analysis Of Economic Models Through Calculus Of Variations, Raman Arora

Masters Theses & Specialist Projects

This thesis is a combination of two science fields: Mathematics and Economics. Mathematics is often used to formulate a clear and concise solution to economic problems. In my observation calculus of variation has often been used in various macroeconomic problems. This mathematical method deals with maximizing or minimizing of various objective functions given a set of constraints. This topic brings out one of the best ways to show the relationship between mathematics and economics. My thesis consists of three parts: The first chapter contains a review of the calculus of variations. Basic definitions and important conditions have been stated. The …

Determining The Effects Of Psychosocial Interventions On Quality Of Life For Cancer Patients: Analysis Of Pilot Data And Recommendations For Full Experimental Design And Statistical Analysis, Sarah Julia Thomas

Renée Crown University Honors Thesis Projects - All

The Hematology and Oncology Specialists Foundation plans to carry out a scientific study to assess the effects of several of its psychosocial interventions, or “wellness programs,” on the quality of life (QoL) experienced by cancer patients. Pilot data showed that participation in a meditation program significantly reduced the symptoms of stress experienced by the patients (t = 2.70, p = 0.011), and that participation in psychological counseling significantly reduced the anxiety and depression levels of the patients (t = 5.33, p = 0.002; t = 8.70, p < 0.001, respectively).

The full scale study has a 6×2 factorial design with six treatments (non-participation, …

Hand-Held Calculators And Mathematics Achievement: What The 1996 National Assessment Of Educational Progress Eighth-Grade Mathematics Exam Scores Tell Us, Kenneth L. Wareham

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this study was to analyze the 1996 National Assessment of Educational Progress data to identify the relationship between calculator use and student performance on the National Assessment of Educational Progress Mathematics Assessment. This general purpose includes several sub issues. In addition to being interested in the overall relationship between use and National Assessment of Educational Progress achievement (including the effort to control for spurious factors), this study examined the contextual factors that moderate the impact of calculator use. Similarly, it analyzed the relationship between calculator use and student performance on calculator-allowed and calculator-restricted items, as well as …

Wavelet Factorization Via A Homogenization Analogy For Solutions Of Linear Systems, Andrea Van Sickle

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

A system of linear equations can be solved using a factorization method that produces a wavelet structure and is akin to a homogenization process used in determining the solution of differential equations. The method is dependant on the particular structure of Hadamard matrices and their implementation in a similarity transform. This paper details the development of such a method for systems of size 2n x 2n, including establishing the theoretical underpinnings necessary to define an orthogonal transform. Also, we present the development of an algorithm to implement the method for a simple 2 x 2 system, which will then be …

Dynamical Systems And The Logistic And Tent Maps, Kathleen Larkin Spires

Honors Capstones

No abstract provided.

On The Nature Of Connectivity Types, Miao Xu

Honors Capstones

No abstract provided.

Ramanujan And The Regular Continued Fraction Expansion Of Real Numbers, James Mclaughlin, Nancy Wyshinski

Mathematics Faculty Publications

In some recent papers, the authors considered regular continued fractions of the form [a0; a, · · · , a | {z } m , a2 , · · · , a2 | {z } m , a3 , · · · , a3 | {z } m , · · · ], where a0 ≥ 0, a ≥ 2 and m ≥ 1 are integers. The limits of such continued fractions, for general a and in the cases m = 1 and m = 2, were given as ratios of certain infinite series. However, these formulae can be derived …

Special Classification Models For Lichens In The Pacific Northwest, Janeen Ardito

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

A common problem in ecological studies is that of determining where to look for rare species. This paper shows how statistical models, such as classification trees, may be used to assist in the design of probability-based surveys for rare species using information on more abundant species that are associated with the rare species. This model assisted approach to survey design involves first building models for the more abundant species. The models are then used to determine stratifications for the rare species that are associated with the more abundant species. The goal of this approach is to increase the number of …

Wavelet Analysis Of Magnetometer Data, Inga Maslova

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The wavelet analysis of the ground-based magnetograms' records is performed in this project. We explore the records from low, medium and high latitude stations during a calm period and a stormy one. Different methods for detecting and estimating the tail index of heavy-tailed distributions are compared. A detailed analysis of the properties of the distributions of the discrete wavelet transform coefficients of magnetometer data is presented. Conclusions on the tail index estimation techniques and the distribution of the discrete wavelet transform coefficients are made.

The Convergence Of Difference Boxes, Antonio Behn, Christopher Kribs-Zaleta, Vadim Ponomarenko

Mathematics Faculty Research

We consider an elementary mathematical puzzle known as a "difference box" in terms of a discrete map from R4 to R4 or, canonically, from a subset of the first quadrant of R2 into itself. We find the map's unique canonical fixed point and answer the general question of how many iterations a given "difference box" takes to reach zero.

Simulation Study Of Estimation And Inference In Factor Analysis: Normal And Non-Normal Noise Distributions, Ping Zhang

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Objective: To study the estimation and inference m factor analyses when the data have normal or non-normal noise distributions.

Methods: Population data were created in package R with a specified number of factors, factor structure and observable variables with known loadings. Then, repeated simple random samples (SRS's) were taken from the population, independently. The maximum likelihood method with varimax rotation was used to perform factor analysis and inference on each sampled dataset. Factor loadings were estimated to determine if the estimation of the loadings was (approximately) unbiased and/or efficient for each specified population and chi-square x2-statistics were obtained to test …

Using Wavelets As A Computational And Theoretical Tool For Homogenization, Laura Lee Watkins

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Since the cost of petroleum fluctuates widely, it is advisable to optimize extraction of oil and other hydrocarbon products form existing oil reserves. Because of the costs involved in recovering oil from a reservoir, predicting reservoir performance can be a useful tool for determining whether continued extraction might be profitable. This can be done using computer simulations of the physical processes involved such as pressure/head, fluid velocities, and so forth. Fluid flow within a reservoir occurs at a very small scale relative to the size of the reservoir. This size difference makes performing simulations at the physically appropriate scale unfeasible. …

Estimation, Testing, And Monitoring Of Generalized Autoregressive Conditionally Heteroskedastic Time Series, Aonan Zhang

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We study in this dissertation Generalized Autoregressive Conditionally Heteroskedastic (GARCH) time series. The research focuses on squared GARCH sequences. Our main results are as follows:

1. We compare three methods of constructing confidence intervals for sample autocorrelations of squared returns modeled by models from the GARCH family. We compare the residual bootstrap, block bootstrap and subsampling methods. The residual bootstrap based on the standard GARCH(l,1) model is seen to perform best. Confidence intervals for cross-correlations of a bivariate GARCH model are also studied.

2. We study a test to discriminate between long memory and volatility changes in financial returns data. …