Mathematics Commons^™

Statistical Characterization Of Fluvial-Deltaic Reservoirs With Archetypes, Laura L. Watkins

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Optimizing the extraction of oil and other hydrocarbon products from existing sites is important. One source of hydrocarbon products is reservoirs found within sedimentary rock formations. Understanding fluid behavior within such formations can be quite useful in optimizing oil production. Fluid behavior within sedimentary formations is influenced by the bedform structure and permeabilities within the formation. Thus, we are concerned with developing a physically and statistically valid method of characterizing sedimentary rock formations. The use of archetypal analysis to generate synthetic bedforms, as well as the use of Kriging to assign permeabilities within a bedform, was explored. With these tools, …

Games To Teach Mathematical Modelling, James A. Powell, Jim S. Cangelosi, Ann M. Harris

Mathematics and Statistics Faculty Publications

We discuss the use of in-class games to create realistic situations for mathematical modelling. Two games are presented which are appropriate for use in post-calculus settings. The first game reproduces predator-prey oscillations and the second game simulates disease propagation in a mixing population. When used creatively these games encourage students to model realistic data and apply mathematical concepts to understanding the data.

Geometric Aspects Of Second-Order Scalar Hyperbolic Partial Differential Equations In The Plane, Martin Jurás

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this dissertation is to address various geometric aspects of second-order scalar hyperbolic partial differential equations in two independent variables and one dependent variable

F(x, y, u, u_x, u_y, u_xx, u_xy, u_yy) = 0

We find a characterization of hyperbolic Darboux integrable equations at level k (1) in terms of the vanishing of the generalized Laplace invariants and provide an invariant characterization of various cases in the Goursat general classification of hyperbolic Darboux integrable equations (1). In particular we give a contact invariant characterization of equations integrable by …

Geršgorin And Beyond•••, Jason Knight Belnap

Undergraduate Honors Capstone Projects

Eigenvalues are useful in various areas of mathematics, such as in testing the critical values of a multi variable function to see if it is a local extrema. One of the more common ways to define eigenvalues is:

Definition (1): Given that A is an n by n matrix, λ is an eigenvalue of A if and only if det(A - λI_n) = 0. Any nonzero vector in Null(A - λI) is called an eigenvector associated with λ.

History Of Fermat's Last Theorem, Amanda Brown

Undergraduate Honors Capstone Projects

Around 1637, Pierre de Fermat made a now-famous mathematical conjecture. However, Fermat's conjecture neither began nor ended with him. Fermat's last theorem, as the conjecture is called, has roots approximately 3600 years old. The proof of the theorem was not realized until 1994, over 350 years after it was proposed by Fermat.

Asymptotic Conservation Laws In Classical Field Theory, Ian M. Anderson, Charles G. Torre

Mathematics and Statistics Faculty Publications

A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the Arnowitt-Deser-Misner energy in general relativity.

Parameter Estimation By Conditional Coding, Taylor Duersch

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Conditional coding is an application of Markov Chain Monte Carlo methods for sampling from conditional distributions. It is applied here to the problem of estimating the parameters of a computer-simulated pattern of fractures in an isomorphic, homotropic material under plane strain. We investigate the theory and procedures of conditional coding and show the viability of the technique by its application.

An Inverse Approach To A Probability Model For Fractured Networks, Stacy G. Vail

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A common problem in science and engineering applications deals with finding information about a system where only limited information is known. One example of this problem is determining the geometry of an aquifer or oil reservoir based on well tests taken at the site. The Conditional Coding Method attacks this type of problem. This method uses the Simulated Annealing Algorithm in conjunction with a probability model which generates possible solutions based on a uniform random number list. The Annealing Algorithm generates a conditional probability distribution on all possible solutions generated by the probability model, conditioned on the observed data set. …

Multiage Classrooms: A New Way To Learn Math, Martha Taylor Dever, Randy Zila, Noel N. Mansano

Teacher Education and Leadership Faculty Publications

No abstract provided.

Symmetries Of The Einstein Equations, Ian M. Anderson, C. Torre

Mathematics and Statistics Faculty Publications

We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions. They consist of constant scalings of the metric, and of the infinitesimal action of generalized spacetime diffeomorphisms. Our results rule out a large class of possible ‘‘observables’’ for the gravitational field, and suggest that the vacuum Einstein equations are not integrable.

Linear Operators That Preserve Qualitative Matrix Structures, Shumin Ye

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We characterized the group of linear operators that preserve sign-nonsingular matrices over M_n(R). Then we extended these results to n show that a linear operator T that strongly preserves L-matrices over M_m,n(R) if and only if T preserves L-matrices and T is also one to one on m,n the set of cells. We also characterized the group of linear operators that strongly preserve L-matrices.

In addition, we characterized the group of linear operators that preserve super L- matrices, the subset of L-matrix. Also we investigated linear …

A Comparison Of Two Linear Nonparametric Regression Techniques, Sylvain Sardy

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis presented a useful tool in regression. Nonparametric linear regression techniques were described in the general context of regression. A comparison of two of these techniques, kernel regression and iterative regression, showed various aspects of nonparametric linear regressors.

A Maple Package For The Variational Calculus, Cinnamon Hillyard

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The HELMHOLTZ package, written in Maple V, is a collection of commands to support research in the variational calculus. These commands include the standard operators on differential forms, Euler-Lagrange operators, homotopy operators, Lie bracket, Lie derivatives, and the prolongation of a vector field. We give a brief introduction to the variational calculus. We describe each of the commands in the HELMHOLTZ package completely along with numerous examples of each. Applications of the package include verification of symmetry groups for differential equations, solving the inverse problem of the calculus of variations, computing generalized symmetries, and finding variational integrating factors. A complete …

Inverse Problem In Porous Medium Using Homogenization, Helen Alkes

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The problem under consideration is that of obtaining a representation of the permeability of a porous medium which is heterogeneous and anisotropic from limited information. To solve this inverse problem we propose the use of two different pieces that work together. A simulated annealing algorithm is presented and coupled with an homogenization technique; together these solve the problem which was posed. Further, numerical simulation results are presented illustrating the use of the simulated annealing algorithm as well as a coupling with the homoginization technique. This study illustrates that the performance of the annealing algorithm is enhanced with usage of homogenization.

Disconjugacy And Oscillation Theory Of Linear Differential And Difference Equations, Yuhua Xu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This dissertation is both a literature survey and a presentation of new and independent results.

The survey gives an overview of disconjugacy and oscillation theory for linear differential and difference equations with an emphasis on comparing the theory of difference equations to the theory of differential equations. Second order scalar equations, higher order scalar equations, matrix equations (systems) and Hamiltonian systems are discussed. A chapter on three-term recurrences of systems is also included. Both similarities and differences between differential and difference equations are described.

The new and independent results are for Hamiltonian systems of difference equations. Those results include the …

Hopf Bifurcation In A Parabolic Free Boundary Problem, Yoon-Mee Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We deal with a free boundary problem for a nonlinear parabolic equation, which includes a parameter in the free boundary condition. This type of system has been used in models of ecological systems, in chemical reactor theory and other kinds of propagation phenomena involving reactions and diffusion.

The main purpose of this dissertation is to show the global existence, uniqueness of solutions and that a Hopf bifurcation occurs at a critical value of the parameter r. The existence and uniqueness of the solution for this problem are shown by finding an equivalent regular free boundary problem to which existence …

Introduction To The Variational Bicomplex, Ian M. Anderson

Mathematics and Statistics Faculty Publications

The variational bicomplex was first introduced in the mid 1970's as a means of studying the inverse problem of the calculus of variations. This is the problem of characterizing those differential equations which are the Euler-Lagrange equations for a classical, unconstrained variational problem. Since then, the variational bicomplex has emerged as an effective means for studying other formal, differential-geometric aspects of the calculus of variations. Moreover, it has been shown that the basic variational bicomplex constructed to solve the inverse problem can be modified in various ways and that the cohomology groups associated with these modified bicomplexes are relevant to …

Linear Operators Strongly Preserving Polynomial Equations Over Antinegative Semirings, Sang-Gu Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We characterized the group of linear operators that strongly preserve r-potent matrices over the binary Boolean semiring, nonbinary Boolean semirings, and zero-divisor free antinegative semirings. We extended these results to show that linear operators that strongly preserve r-potent matrices are equivalent to those linear operators that strongly preserve the matrix polynomial equation p(X) = X. where p(X) = X^r₁ + X^r₂ + ... + X^r_t and r₁>r₂>...>r_t≥2.

In addition, we characterized the group of linear operators that strongly preserve r-cyclic matrices over the same semirings. We …

Numerical Simulation Of Saturated Flow With Fractal Analysis Of The Hydraulic Conductivity Distribution, Joan Leilani Oana

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

The purpose of this report is to investigate the behavior of a nonreactive contaminant in a perfectly stratified aquifer under uniform, steady-state flow. The design and the implementation of a solute transport model which characterizes the heterogeneities of the aquifer properties in a stochastic framework is reviewed. The model closely examines the advection and dispersion of the plume. The advection is the process by which the plume is transported in the aquifer by the bulk average motion of the groundwater whereas the dispersion refers to the spreading of the plume about its mean displacement position. The relationship between the fractally …

Mathematical Programming Applications In Agroforestry Planning, Laurence H. Reeves

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Agroforestry as a sustainable production system has been recognized as a land use system with the potential to slow encroachment of agriculture onto forested lands in developing countries. However, the acceptance of nontraditional agroforestry systems has been hampered in some areas due to the risk-averse nature of rural agriculturalists. By explicitly recognizing risk in agroforestry planning, a wider acceptance of agroforestry is possible. This thesis consists of a collection of three papers that explore the potential of modern stock portfolio theory to reduce financial risk in agroforestry planning.

The first paper presents a theoretical framework that incorporates modern stock portfolio …

Applied Chaotic Dynamics: An Introduction, James Frankenfield

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

These lecture notes served as the basis for a two credit graduate level seminar offered through the USU physics department during the fall quarter of 1989. It was oriented towards graduate students in physics and engineering and assumed no mathematical background beyond introductory differential equations. All problems were attempted by the students and discussed as a group. The seminar appears to have been successful in that the students enjoyed it and learned a lot.

Maximal Rank-One Spaces Of Matrices Over Chain Semirings, Daniel Joseph Scully

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Vectors and matrices over the Boolean (0,1) semiring have been studied extensively along with their applications to graph theory. The Boolean (0,1) semiring has been generalized to a class of semirings called chain semirings. This class includes the fuzzy interval. Vectors and matrices over chain semirings are examined. Rank-1 sets of vectors are defined and characterized. These rank-1 sets of vectors are then used to construct spaces of matrices (rank-1 spaces) with the property that all nonzero matrices in the space have semiring rank equal to 1. Finally, three classes of maximal (relative to containment) rank-1 spaces are identified.

Least-Change Secant Updates Of Non-Square Matrices, Samih Kassem Bourji

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In many problems involving the solution of a system of nonlinear equations, it is necessary to keep an approximation to the Jacobian matrix which is updated at each iteration. Computational experience indicates that the best updates are those that minimize some reasonable measure of the change to the current Jacobian approximation subject to the new approximation obeying a secant condition and perhaps some other approximation properties such as symmetry.

All of the updates obtained thus far deal with updating an approximation to an nxn Jacobian matrix. In this thesis we consider extending most of the popular updates to the non-square …

On The Generalizations Of Gershgorin's Theorem, Sang-Gu Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper deals with generalization fo Gershgorin's theorem. This theorem is investigated and generalized in terms of contour integrals, directed graphs, convex analysis, and clock matrices.

These results are shown to apply to some specified matrices such as stable and stochastic matrices and some examples will show the relationship of eigenvalue inclusion regions among them.

Role And Responsibilities Of State Cooperative Extension Services For Wildlife Damage Control, James L. Byford

Wildlife Damage Management Conference

The Cooperative Extension Service was established by the Smith-Lever Act in 1914. It was designed to improve the lives of people, through education in: agriculture, natural resources, home economics and community development. Its audiences include both adult and youth. 4-H is the primary youth audience. The Cooperative Extension Service is an "extension" of the Land employees include university faculty (specialists) and professional agents in every county, in every state in the country. Extension's primary mission is to conduct an educational program, using research-based information. Research results are condensed into a form that the average person can understand. The role of …

Brownian Motion Applied To Partial Differential Equations, Steven M. Mckay

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This work is a study of the relationship between Brownian motion and elementary, linear partial differential equations. In the text, I have shown that Brownian motion is a Markov process, and that Brownian motion itself, and certain Stochastic processes involving Brownian motion are also martingales. In particular, Dynkin's formula for Brownian motion was shown. Using Dynkin's formula and Brownian motion, I then constructed solutions for the classical Dirichlet problem and the heat equation, given by Δu=0 and u_t= 1/2Δu+g, respectively. I have shown that the bounded solution is unique if Brownian motion will always exit the domain of …

The Reconstruction Conjecture In Graph Theory, Susan M. Loveland

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this paper we show that specific classes of graphs are reconstructible; we explore the relationship between the reconstruction and edge-reconstruction conjectures; we prove that several classes of graphs are actually Harary to the reconstructible; and we give counterexamples reconstruction and edge-reconstruction conjectures for infinite graphs.

Comparison Of Bootstrap And Jacknife Statistical Procedures, Amanuel Gobena

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

This report compares the bootstrapping to jacknifing statistical procedures in terms in bias, confidence interval and estimation of median. Related literature have been reviewed. A bootstrap allows a researcher to get an approximation to the distribution of possibly complicated statistical summaries. It is based on random sampling with replacement from experimental units. Jacknife has also been in operation prior to bootstrapping statistical procedure. The jacknife divides the data into subgroups and obtains partial estimates of these subgroups by omitting one subgroup at a time. When both of these statistical resampling procedures are compared the bootstrap has less bias, more accurate …

Monte Carlo Simulation Of The Game Of Twenty-One, Douglas E. Loer

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

The purpose of this paper is to demonstrate the application of computer simulation to the game of Twenty-One to predict a player's expected return from the game. Twenty-One has traditionally been one of the most popular casino games and has attracted much effort to accurately estimate the house's true advantage. Probability theory has been tried, but the thousands of different combinations of cards possible in all hands throughout the entire pack make it practically impossible to apply probability theory without overlooking some possibilities. For this reason, Twenty-One is a perfect candidate for simulation. By blocking several simulations, normal theory can …

Multiple Shooting, Monique St-Maurice

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

The purpose of this report was to study the Multiple Shooting method, a numerical method to solve boundary value ordinary differential equation. A FORTRAN program was written to solve the specific problem.

y'' = -y, y(0) = 0, y(π/2) = 1

on a microcomputer, using the microsoft FORTRAN compiler and the 8087 coprocessor.