Mathematics Commons^™

Asymptotic Quantization For A Condensation System Associated With A Discrete Distribution, Shankar Parajulee

Theses and Dissertations

Let P := (1/3)P ○ S1–1 + (1/3)P ○ S2–1 + (1/3)v be a condensation measure on R, where S1(x) = (1/5)x, S2(x) = (1/5)x + 4/5 for all x ∈ R , and v is a discrete distribution on R with the support of v equals C := {(2/5), (3/5)}. For such a measure P we determine the optimal sets of n–means and the nth quantization errors for all n ≥ 2. In addition, we show that the quantization dimension of the condensation measure P exists and equals …

Exploring Flag Matroids And Duality, Zachary Garcia

Electronic Theses, Projects, and Dissertations

Matroids capture an abstraction of independence in mathematics, and in doing so, connect discrete mathematical structures that arise in a variety of contexts. A matroid can be defined in several cryptomorphic ways depending on which perspective of a matroid is most applicable to the given context. Among the many important concepts in matroid theory, the concept of matroid duality provides a powerful tool when addressing difficult problems. The usefulness of matroid duality stems from the fact that the dual of a matroid is itself a matroid. In this thesis, we explore a matroid-like object called a flag matroid. In particular, …

Symmetric Presentations And Double Coset Enumeration, Charles Seager

Electronic Theses, Projects, and Dissertations

In this project, we demonstrate our discovery of original symmetric presentations and constructions of important groups, including nonabelian simple groups, and groups that have these as factor groups. The target nonabelian simple groups include alternating, linear, and sporadic groups. We give isomorphism types for each finite homomorphic image that has been found. We present original symmetric presentations of $M_{12}$, $M_{21}:(2 \times 2)$, $L_{3}(4):2^2$, $2:^{\cdot}L_{3}(4):2$, $S(4,3)$, and $S_{7}$ as homomorphism images of the progenitors $2^{*20}$ $:$ $A_{5}$, $2^{*10}$ $:$ $PGL(2,9)$, $2^{*10}$ $:$ $Aut(A_{6})$, $2^{*10}$ $:$ $A_{6}$, $2^{*10}$ $:$ $A_{5}$, and $2^{*24}$ $:$ $S_{5}$, respectively. We also construct $M_{12}$, $M_{21}:(2 \times 2)$, …

Larval Food Limitation In A Speyeria Butterfly (Nymphalidae): How Many Butterflies Can Be Supported?, Ryan I. Hill, Cassidi E. Rush, John Mayberry

College of the Pacific Faculty Articles

For herbivorous insects the importance of larval food plants is obvious, yet the role of host abundance and density in conservation are relatively understudied. Populations of Speyeria butterflies across North America have declined and Speyeria adiaste is an imperiled species endemic to the southern California Coast Ranges. In this paper, we study the link between the food plant Viola purpurea quercetorum and abundance of its herbivore Speyeria adiaste clemencei to better understand the butterfly’s decline and aid in restoration of this and other Speyeria species. To assess the degree to which the larval food plant limits adult abundance of S. …

Multi-Resolution Analysis Using Wavelet Basis Conditioned On Homogenization, Abibat Adebisi Lasisi

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This dissertation considers an approximation strategy using a wavelet reconstruction scheme for solving elliptic problems. The foci of the work are on (1) the approximate solution of differential equations using multiresolution analysis based on wavelet transforms and (2) the homogenization process for solving one and two-dimensional problems, to understand the solutions of second order elliptic problems. We employed homogenization to compute the average formula for permeability in a porous medium. The structure of the associated multiresolution analysis allows for the reconstruction of the approximate solution of the primary variable in the elliptic equation. Using a one-dimensional wavelet reconstruction algorithm proposed …

Generalized Line Graphs, Mohra Abdullah Z. Alqahtani

Dissertations

With every nonempty graph, there are associated many graphs. One of the best known and most studied of these is the line graph L (G) of a graph G, whose vertices are the edges of G and where two vertices of L (G) are adjacent if the corresponding edges of G are adjacent. This concept was implicitly introduced by Whitney in 1932. Over the years, characterizations of graphs that are line graphs have been given, as well as graphs whose line graphs have some specified property. For example, Beineke characterized graphs that are line graphs by forbidding certain graphs …

Italian Domination On Ladders And Related Products, Bradley Gardner

Electronic Theses and Dissertations

An Italian dominating function on a graph $G = (V,E)$ is a function such that $f : V \to \{0,1,2\}$, and for each vertex $v \in V$ for which $f(v) = 0$, we have $\sum_{u\in N(v)}f(u) \geq 2$. The weight of an Italian dominating function is $f(V) = \sum_{v\in V(G)}f(v)$. The minimum weight of all such functions on a graph $G$ is called the Italian domination number of $G$. In this thesis, we will consider Italian domination in various types of products of a graph $G$ with the complete graph $K_2$. We will find the value of the Italian domination …

Finite Simple Graphs And Their Associated Graph Lattices, James B. Hart, Brian Frazier

Theory & Applications of Graphs

In his 2005 dissertation, Antoine Vella explored combinatorical aspects of finite graphs utilizing a topological space whose open sets are intimately tied to the structure of the graph. In this paper, we go a step further and examine some aspects of the open set lattices induced by these topological spaces. In particular, we will characterize all lattices that constitute the opens for finite simple graphs endowed with this topology, explore the structure of these lattices, and show that these lattices contain information necessary to reconstruct the graph and its complement in several ways.

Group Theory And Particles, Elizabeth V. Hawkins

Honors College Theses

We begin by a brief overview of the notion of groups and Lie groups. We then explain what group representations are and give their main properties. Finally, we show how group representation form a natural framework to understand the Standard Model of physics.

Markov Chains And Generalized Wavelet Multiresolutions, Myung-Sin Song, Palle Jorgensen

SIUE Faculty Research, Scholarship, and Creative Activity

We develop some new results for a general class of transfer operators, as they are used in a construction of multi-resolutions. We then proceed to give explicit and concrete applications. We further discuss the need for such a constructive harmonic analysis/dynamical systems approach to fractals.

Distance And Intersection Number In The Curve Complex Of A Closed Surface, Nancy C. Wrinkle

Faculty Research and Creative Activities Symposium

No abstract provided.

Linear Analysis Of Tumor Morphology During Growth Using Bending Energy, Emma A. Turian

Faculty Research and Creative Activities Symposium

No abstract provided.

Punctuated Cognitive Psychological Interventions On Student's Disposition To Learn And The Effects On Mathematical Achievement, Matthew D. Graham

Faculty Research and Creative Activities Symposium

No abstract provided.

Singular And Ill-Conditioned Linear Systems, Zhonggang Zeng

Faculty Research and Creative Activities Symposium

No abstract provided.

Vacuum Polarization For Varying Quantum Scalar Field Parameters In Schwarzschild–Anti–De Sitter Spacetime, Cormac Breen, Peter Taylor

Articles

Equipped with new powerful and efficient methods for computing quantum expectation values in static-spherically symmetric spacetimes in arbitrary dimensions, we perform an in-depth investigation of how the quantum vacuum polarization varies with the parameters in the theory. In particular, we compute and compare the vacuum polarization for a quantum scalar field in the Schwarzschild–anti–de Sitter black hole spacetime for a range of values of the field mass and field coupling constant as well as the black hole mass and number of spacetime dimensions. In addition, a new approximation for the vacuum polarization in asymptotically anti–de Sitter black hole spacetimes is …

Predicting Cost Of Care In Total Hip Replacement, Cecily Corrine Froemke, Martin Zwick

Complex Systems Faculty Publications and Presentations

Legislative reforms aimed at slowing growth of US healthcare costs are focused on achieving greater value per dollar. To increase value healthcare providers must not only provide high quality care, but deliver this care at a sustainable cost. Predicting risks that may lead to poor outcomes and higher costs enable providers to augment decision making for optimizing patient care and inform the risk stratification necessary in emerging reimbursement models. Healthcare delivery systems are looking at their high volume service lines and identifying variation in cost and outcomes in order to determine the patient factors that are driving this variation and …

Not So Many Non-Disjoint Translations, Andrzej Roslanowski, Vyacheslav V. Rykov

Mathematics Faculty Publications

We show that, consistently, there is a Borel set which has uncountably many pairwise very non-disjoint translations, but does not allow a perfect set of such translations.

An Introduction To Psychological Statistics, Garett C. Foster, David Lane, David Scott, Mikki Hebl, Rudy Guerra, Dan Osherson, Heidi Zimmer

Open Educational Resources Collection

This work has been superseded by Introduction to Statistics in the Psychological Sciences available from https://irl.umsl.edu/oer/25/.

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We are constantly bombarded by information, and finding a way to filter that information in an objective way is crucial to surviving this onslaught with your sanity intact. This is what statistics, and logic we use in it, enables us to do. Through the lens of statistics, we learn to find the signal hidden in the noise when it is there and to know when an apparent trend or pattern is really just randomness. The study of statistics involves math and relies …

The Compensation For Few Clusters In Clustered Randomized Trials With Binary Outcomes, Lily Stalter

Mathematics & Statistics ETDs

Cluster randomized trials are increasingly popular in epidemiological and medical research. When analyzing the data from such studies it is imperative that the hierarchical structure of the data be taken into account. Multilevel logistic regression is used to analyze clustered data with binary outcomes. Previous literature shows that a greater number of clusters is more important than a large number of subjects per cluster. This paper investigates if it is possible to compensate for the increased bias found for parameter estimates when the number of clusters is decreased. A simulation study was conducted where the absolute percent relative bias for …

Teaching Differential Equations Without Computer Graphics Solutions Is A Crime, Beverly H. West

CODEE Journal

In the early 1980s computer graphics revolutionized the teaching of ordinary differential equations (ODEs). Yet the movement to teach and learn the qualitative methods that interactive graphics affords seems to have lost momentum. There still exist college courses, even at big universities, being taught without the immense power that computer graphics has brought to differential equations. The vast majority of ODEs that arise in mathematical models are nonlinear, and linearization only approximates solutions sufficiently near an equilibrium. Introductory courses need to include nonlinear DEs. Graphs of phase plane trajectories and time series solutions allow one to see and analyze the …

Experiences Using Inquiry-Oriented Instruction In Differential Equations, Keith Nabb

CODEE Journal

Student-centered instruction can be a challenging endeavor for teachers and students. This article reports on the use of the Inquiry-Oriented Differential Equations (IO-DE) curriculum (Rasmussen, 2002) in an undergraduate differential equations course. Examples of student work are shared with specific reference to research in mathematics education.

A Complete Characterization Of Near Outer-Planar Graphs, Tanya Allen Lueder Genannt Luehr

Doctoral Dissertations

A graph is outer-planar (OP) if it has a plane embedding in which all of the vertices lie on the boundary of the outer face. A graph is near outer-planar (NOP) if it is edgeless or has an edge whose deletion results in an outer-planar graph. An edge of a non outer-planar graph whose removal results in an outer-planar graph is a vulnerable edge. This dissertation focuses on near outer-planar (NOP) graphs. We describe the class of all such graphs in terms of a finite list of excluded graphs, in a manner similar to the well-known Kuratowski Theorem for planar …

How Hilbert’S Attempt To Unify Gravitation And Electromagnetism Failed Completely, And A Plausible Resolution, Victor Christianto, Florentin Smarandache, Robert N. Boyd

Branch Mathematics and Statistics Faculty and Staff Publications

In the present paper, these authors argue on actual reasons why Hilbert’s axiomatic program to unify gravitation theory and electromagnetism failed completely. An outline of plausible resolution of this problem is given here, based on: a) Gödel’s incompleteness theorem, b) Newton’s aether stream model. And in another paper we will present our calculation of receding Moon from Earth based on such a matter creation hypothesis. More experiments and observations are called to verify this new hypothesis, albeit it is inspired from Newton’s theory himself.

Catalytic Deoxygenation Of Model And Realistic Feeds To Fuel-Like Hydrocarbons Over Supported Nickel-Copper Catalysts, Deyshon Ward, Kazi Javed

Posters-at-the-Capitol

The goal was to make a renewable fuel by using catalysts to remove oxygen molecules from fats. This is a current issue that society faces today because nonrenewable fossil fuels hurt the environment more than they help it. There are two components that make up a heterogeneous catalyst, a support and a reduced metal active phase. The active metal phases Nickel, Palladium, Platinum have been studied in the past on an alumina and carbon supports. We were investigating other supports using Nickel as the active phase component to determine the effect the support has on the catalyst removing oxygen of …

Translation Theorems For The Fourier-Feynman Transform On The Product Function Space C2 A,B, [0,T], Seung Jun Chang, Jae Gil Choi, David Skoug

Department of Mathematics: Faculty Publications

In this article, we establish the Cameron{Martin translation theo- rems for the analytic Fourier{Feynman transform of functionals on the product function space C2 a;b[0; T]. The function space Ca;b[0; T] is induced by the gener- alized Brownian motion process associated with continuous functions a(t) and b(t) on the time interval [0; T]. The process used here is nonstationary in time and is subject to a drift a(t). To study our translation theorem, we introduce a Fresnel-type class Fa;b A1;A2 of functionals on C2 a;b[0; T], which is a generaliza- tion of the Kallianpur and Bromley{Fresnel class FA1;A2 . We then …

Developmental Parameters Of A Southern Mountain Pine Beetle (Coleoptera: Curculionidae) Population Reveal Potential Source Of Latitudinal Differences In Generation Time, Anne E. Mcmanis, James A. Powell, Barbara J. Bentz

Mathematics and Statistics Faculty Publications

Mountain pine beetle (Dendroctonus ponderosae, Hopkins) is a major disturbance agent in pine ecosystems of western North America. Adaptation to local climates has resulted in primarily univoltine generation time across a thermally diverse latitudinal gradient. We hypothesized that voltinism patterns have been shaped by selection for slower developmental rates in southern populations inhabiting warmer climates. To investigate traits responsible for latitudinal differences we measured lifestage-specific development of southern mountain pine beetle eggs, larvae and pupae across a range of temperatures. Developmental rate curves were fit using maximum posterior likelihood estimation with a Bayesian prior to improve fit stability. …

Lump Solutions And Riemann-Hilbert Approach To Soliton Equations, Sumayah A. Batwa

USF Tampa Graduate Theses and Dissertations

In the first part of this dissertation we introduce two matrix iso-spectral problems, a Kaup-Newell type and a generalization of the Dirac spectral problem, associated with the three-dimensional real Lie algebras sl(2;R) and so(3;R), respectively. Through zero curvature equations, we furnish two soliton hierarchies. Hamiltonian structures for the resulting hierarchies are formulated by adopting

the trace identity. In addition, we prove that each of the soliton hierarchies has a bi-Hamiltonian structure which leads to the integrability in the Liouville sense. The motivation of the first part is to construct soliton hierarchies with infinitely many commuting symmetries and conservation laws.

The …

Why Early Galaxies Were Pickle-Shaped: A Geometric Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The vast majority of currently observed geometric shapes of celestial bodies can be explained by a simple symmetry idea: the initial distribution of matter is invariant with respect to shifts, rotations, and scaling, but this distribution is unstable, so we have spontaneous symmetry breaking. According to statistical physics, among all possible transitions, the most probable are the ones that retain the largest number of symmetries. This explains the currently observed shapes and -- on the qualitative level -- their relative frequency. According to this idea, the most probable first transition is into a planar (pancake) shape, then into …

Bhutan Landscape Anomaly: Possible Effect On Himalayan Economy (In View Of Optimal Description Of Elevation Profiles), Thach N. Nguyen, Laxman Bokati, Aaron A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

Economies of countries located in seismic zones are strongly effected by this seismicity. If we underestimate the seismic activity, then a reasonably routine earthquake can severely damage the existing structures and thus, lead to huge economic losses. On the other hand, if we overestimate the seismic activity, we waste a lot of resources on unnecessarily fortifying all the buildings -- and this too harms the economies. From this viewpoint, it is desirable to have estimations of regional seismic activities which are as accurate as possible. Current predictions are mostly based on the standard geophysical understanding of earthquakes as being largely …

Towards Optimal Implementation Of Decentralized Currencies: How To Best Select Probabilities In An Ethereum-Type Proof-Of-Stake Protocol, Thach N. Nguyen, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

Nowadays, most financial transactions are based on a centralized system, when all the transaction records are stored in a central location. This centralization makes the financial system vulnerable to cyber-attacks. A natural way to make the financial system more robust and less vulnerable is to switch to decentralized currencies. Such a transition will also make financial system more transparent. Historically first currency of this type -- bitcoin -- use a large amount of electric energy to mine new coins and is, thus, not scalable to the level of financial system as a whole. A more realistic and less energy-consuming scheme …