Mathematics Commons^™

A Comparative Analysis Of The Origin And Divine Causation Of Death In Ancient Near Eastern Literature And In The Old Testament, Lazarus Castang

Dissertations

The present dissertation attempts a comparative analysis of both the origin of death in the creation accounts and the divine causation of death in the main flood accounts in the ancient Near Eastern (ANE) literature and the Hebrew Old Testament (OT). Both literatures are examined for their implicit or explicit conceptions of the origin and divine causation of death. The origin of death in the ANE literature is located in the Egyptian Osirian myth and the Mesopotamian Enki-Ninmah myth, Enûma Elish, Epic of Gilgamesh, and the Adapa legend. The divine causation of death is studied in the Eridu Genesis, Atra-Hasis …

Metaphors, Metonymies, Modes And Linear Algebra, Persis Samanta Beaven

Open Access Theses & Dissertations

The analysis focused on the presence of different thinking modes, metonymies, and metaphors found on the interview responses to questions related to linear independence, span, and spanning sets of four students taking their first linear algebra course at the college level. The findings provide insight of how first year linear algebra students move from one thinking mode to another and what kind of metonymies and metaphors are used to construct new knowledge. The main purpose of this research was to document and determine the main characteristics that categorize the four students' reasoning.

Rank 2 Distributions Of Monge Equations: Symmetries, Equivalences, Ex-Tensions, Ian M. Anderson, B. Kruglikov

Mathematics and Statistics Faculty Publications

By developing the Tanaka theory for rank 2 distributions, we completely classify classical Monge equations having maximal finite-dimensional symmetry algebras with fixed (albeit arbitrary) pair of its orders. Investigation of the corresponding Tanaka algebras leads to a new Lie-Backlund theorem. We prove that all flat Monge equations are successive integrable extensions of the Hilbert-Cartan equation. Many new examples are provided.

Generalizations Of A Laplacian-Type Equation In The Heisenberg Group And A Class Of Grushin-Type Spaces, Kristen Snyder Childers

USF Tampa Graduate Theses and Dissertations

In [2], Beals, Gaveau and Greiner find the fundamental solution to a 2-Laplace-type equation in a class of sub-Riemannian spaces. This fundamental solution is based on the well-known fundamental solution to the p-Laplace equation in Grushin-type spaces [4] and the Heisenberg group [6]. In this thesis, we look to generalize the work in [2] for a p-Laplace-type equation. After discovering that the "natural" generalization fails, we find two generalizations whose solutions are based on the fundamental solution to the p-Laplace equation.

On Adjoint Entropy Of Abelian Groups, Brendan Goldsmith, Ketao Gong

Articles

The theory of endomorphism rings of algebraic structures allows, in a natural way, a systematic approach based on the notion of entropy borrowed from dynamical systems. In the present work we introduce a \lq dual\rq \ notion based upon the replacement of the finite groups used in the definition of algebraic entropy, by subgroups of finite index. The basic properties of this new entropy are established and a connection to Hopfian groups is investigated.

Holomorphic Liftings From Infinite Dimensional Spaces, Sean Dineen, Milena Venkova

Articles

We obtain a number of positive solutions to a holomorphic lifting problem on a domain in a locally convex space.

Automorphism Groups Of Quandles, Jennifer Macquarrie

USF Tampa Graduate Theses and Dissertations

This thesis arose from a desire to better understand the structures of automorphism groups and inner automorphism groups of quandles. We compute and give the structure of the automorphism groups of all dihedral quandles. In their paper Matrices and Finite Quandles, Ho and Nelson found all quandles (up to isomorphism) of orders 3, 4, and 5 and determined their automorphism groups. Here we find the automorphism groups of all quandles of orders 6 and 7. There are, up to isomoprhism, 73 quandles of order 6 and 289 quandles of order 7.

On Weighted Distributions And Mean Advantage Over Inferiors Functions, Broderick O. Oluyede, Norou Diawara

Mathematical Sciences: Faculty Publications

In this note, some fundamental results including relationship be-tween weighted distribution functions and mean advantage over inferi-ors functions are established. Ordering of reliability and/or distribution functions via mean advantage over inferiors functions and related func-tions for parent and weighted reliability functions are presented. Some applications and examples are given.

Unified Analysis Of Kernel-Based Interior-Point Methods For P *(Κ)-Lcp, Goran Lesaja, C. Roos

Mathematical Sciences: Faculty Publications

We present an interior-point method for the P∗(κ)-linear complementarity problem (LCP) that is based on barrier functions which are defined by a large class of univariate functions called eligible kernel functions. This class is fairly general and includes the classical logarithmic function and the self-regular functions, as well as many non-self-regular functions as special cases. We provide a unified analysis of the method and give a general scheme on how to calculate the iteration bounds for the entire class. We also calculate the iteration bounds of both long-step and short-step versions of the method for several …

Core Compactness And Diagonality In Spaces Of Open Sets, Francis Jordan, Frédéric D. Mynard

Mathematical Sciences: Faculty Publications

We investigate when the space OX of open subsets of a topological space X endowed with the Scott topology is core compact. Such conditions turn out to be related to infraconsonance of X, which in turn is characterized in terms of coincidence of the Scott topology of OX × OX with the product of the Scott topologies of OX at (X,X). On the other hand, we characterize diagonality of OX endowed with the Scott convergence and show that this space can be diagonal without being pretopological. New examples are provided to clarify the relationship between pretopologicity, topologicity and diagonality of …

Modeling, Analysis, And Simulation Of Discrete-Continuum Models Of Step-Flow Epitaxy: Bunching Instabilities And Continuum Limits, Nicholas O. Kirby

University of Kentucky Doctoral Dissertations

Vicinal surfaces consist of terraces separated by atomic steps. In the step-flow regime, deposited atoms (adatoms) diffuse on terraces, eventually reaching steps where they attach to the crystal, thereby causing the steps to move. There are two main objectives of this work. First, we analyze rigorously the differences in qualitative behavior between vicinal surfaces consisting of infinitely many steps and nanowires whose top surface consists of a small number of steps bounded by a reflecting wall. Second, we derive the continuum model that describes the macroscopic behavior of vicinal surfaces from detailed microscopic models of step dynamics.

We use the …

Holomorphic Motions And Extremal Annuli, Zhe Wang

Dissertations, Theses, and Capstone Projects

Holomorphic motions, soon after they were introduced, became an important subject in complex analysis. It is now an important tool in the study of complex dynamical systems and in the study of Teichmuller theory. This thesis serves on two purposes: an expository of the past developments and a discovery of new theories.

First, I give an expository account of Slodkowski's theorem based on the proof given by Chirka. Then I present a result about infinitesimal holomorphic motions. I prove the |ε log ε| modulus of continuity for any infinitesimal holomorphic motion. This proof is a very well application of Schwarz's …

Convergence Of Eigenvalues For Elliptic Systems On Domains With Thin Tubes And The Green Function For The Mixed Problem, Justin L. Taylor

University of Kentucky Doctoral Dissertations

I consider Dirichlet eigenvalues for an elliptic system in a region that consists of two domains joined by a thin tube. Under quite general conditions, I am able to give a rate on the convergence of the eigenvalues as the tube shrinks away. I make no assumption on the smoothness of the coefficients and only mild assumptions on the boundary of the domain.

Also, I consider the Green function associated with the mixed problem on a Lipschitz domain with a general decomposition of the boundary. I show that the Green function is Hölder continuous, which shows how a solution to …

Topological And Combinatorial Properties Of Neighborhood And Chessboard Complexes, Matthew Zeckner

University of Kentucky Doctoral Dissertations

This dissertation examines the topological properties of simplicial complexes that arise from two distinct combinatorial objects. In 2003, A. Björner and M. de Longueville proved that the neighborhood complex of the stable Kneser graph SG_n,k is homotopy equivalent to a k-sphere. Further, for n = 2 they showed that the neighborhood complex deformation retracts to a subcomplex isomorphic to the associahedron. They went on to ask whether or not, for all n and k, the neighborhood complex of SG_n,k contains as a deformation retract the boundary complex of a simplicial polytope. Part one of this dissertation …

Question 1: Lhc Magnets; Question 2: Lhc Projectile Energy, Larry Weinstein

Physics Faculty Publications

What is the strength of the magnetic field used to keep the protons in the Large Hadron Collider (LHC) moving in a circle?

What is the kinetic energy of one lead ion in the Large Hadron Collider (LHC)? How does that compare to the kinetic energy of a ping-pong (table tennis) ball?

Characterizations Of Exponential Distribution Via Conditional Expectations Of Record Values, George Yanev

School of Mathematical & Statistical Sciences Faculty Publications

We prove that the exponential distribution is the only one which satisfies a regression identity. This identity involves conditional expectation of the sample mean of record values given two record values outside of the sample.

Riordan Arrays Associated With Laurent Series And Generalized Sheffer-Type Groups, Tian-Xiao He

Scholarship

A relationship between a pair of Laurent series and Riordan arrays is formulated. In addition, a type of generalized Sheffer groups is defined using Riordan arrays with respect to power series with non-zero coefficients. The isomorphism between a generalized Sheffer group and the group of the Riordan arrays associated with Laurent series is established. Furthermore, Appell, associated, Bell, and hitting-time subgroups of the groups are defined and discussed. A relationship between the generalized Sheffer groups with respect to different power series is presented. The equivalence of the defined Riordan array pairs and generalized Stirling number pairs is given. A type …

Robustness Analysis Of Slow Learning In Iterative Learning Control Systems, John R. Singler, Douglas A. Bristow

Mechanical and Aerospace Engineering Faculty Research & Creative Works

This paper examines robust stability and robust transient growth in Iterative Learning Control (ILC). It is well known that small perturbations in system dynamics can result in very large transient growth of some ILC systems. Even larger perturbations can result in instability. One ad hoc technique commonly employed to improve robustness is to slow the learning rate by reducing the learning filter gain or lowpass filtering the error signal. Here, pseudospectra analysis is used to analyze the robustness of ILC algorithms with slow learning. It is found that robustness bounds can be increased and transient growth decreased with decreasing learning …

Spreadsheets Across The Curriculum, 3: Finding A List Of Mathematical Skills For Quantitative Literacy Empirically, H L. Vacher, Emily Lardner

Numeracy

What mathematical topics do educators committed to teaching mathematics in context choose for their students when given the opportunity to develop an educational resource explicitly to teach mathematics in context? This paper examines the choices made for the 55 modules by 40 authors in the General Collection of the Spreadsheets Across the Curriculum (SSAC) library. About half of the modules were made by authors from natural science, and about 60% of the other modules were by authors from mathematics. The modules are tagged with terms of a search vocabulary developed for the browse page of the collection. The four terms …

Long Path Lemma Concerning Connectivity And Independence Number, Shinya Fujita, Alexander Halperin, Colton Magnant

Mathematical Sciences: Faculty Publications

We show that, in a k-connected graph G of order n with α(G)=α, between any pair of vertices, there exists a path P joining them with

|P|≥min{n,(k−1)(n−k)/α +k}.

This implies that, for any edge e∈E(G), there is a cycle containing e of length at least

min{n,(k−1)(n−k)/α +k}.

Moreover, we generalize our result as follows: for any choice S of s≤k vertices in G, there exists a tree T whose set of leaves is S with

|T|≥min{n,(k−s+1)(n−k)/α +k}.

Independence Number And Disjoint Theta Graphs, Shinya Fujita, Colton Magnant

Mathematical Sciences: Faculty Publications

The goal of this paper is to find vertex disjoint even cycles in graphs. For this purpose, define a θ-graph to be a pair of vertices u,v with three internally disjoint paths joining u to v. Given an independence number α and a fixed integer k, the results contained in this paper provide sharp bounds on the order f(k,α) of a graph with independence number α(G)≤α which contains no k disjoint θ-graphs. Since every θ-graph contains an even cycle, these results provide k disjoint even cycles in graphs of order at least f(k,α)+1. We also discuss the relationship between this …

Meander Graphs And Frobenius Seaweed Lie Algebras, Colton Magnant, Vincent E. Coll, Anthony Giaquinto

Mathematical Sciences: Faculty Publications

The index of a seaweed Lie algebra can be computed from its associated meander graph. We examine this graph in several ways with a goal of determining families of Frobenius (index zero) seaweed algebras. Our analysis gives two new families of Frobenius seaweed algebras as well as elementary proofs of known families of such Lie algebras.

On An Identity Of Gessel And Stanton And The New Little Göllnitz Identities, Carla D. Savage, Andrew Sills

Mathematical Sciences: Faculty Publications

We show that an identity of Gessel and Stanton [I. Gessel, D. Stanton, Applications of q-Lagrange inversion to basic hypergeometric series, Trans. Amer. Math. Soc. 277 (1983) 197, Eq. (7.24)] can be viewed as a symmetric version of a recent analytic variation of the little Göllnitz identities. This is significant, since the Göllnitz–Gordon identities are considered the usual symmetric counterpart to little Göllnitz theorems. Is it possible, then, that the Gessel–Stanton identity is part of an infinite family of identities like those of Göllnitz–Gordon?

Toward this end, we derive partners and generalizations of the Gessel–Stanton identity. We show that …

Hybrid Proofs Of The Q-Binomial Theorem And Other Identities, Dennis Eichhorn, James Mclaughlin, Andrew Sills

Mathematical Sciences: Faculty Publications

We give "hybrid" proofs of the q-binomial theorem and other identities. The proofs are "hybrid" in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the Identity Theorem) to prove the full version.

We prove three somewhat unusual summation formulae, and use these to give hybrid proofs of a number of identities due to Ramanujan.

Finally, we use these new summation formulae to give new partition interpretations of the Rogers-Ramanujan identities and the Rogers-Selberg identities.

Providing Preservice Teachers With Worthwhile Field-Based Experiences In Mathematics, Glenn Nelson

Faculty Work

Providing preservice teachers with worthwhile field-based experiences is recognized as an important component in their development as good teachers. Because mathematics instruction in general has moved from a teacher-directed, procedurally-focused process to a more student-centered, conceptually-oriented approach, preservice mathematics education classes – especially methods courses - should reflect this shift as well. Field-based opportunities can be instances for preservice teachers to personally experience such a shift to real-world relevance.

From Isotropic To Anisotropic Side Chain Representations: Comparison Of Three Models For Residue Contact Estimation, Weitao Sun, Jing He

Computer Science Faculty Publications

The criterion to determine residue contact is a fundamental problem in deriving knowledge-based mean-force potential energy calculations for protein structures. A frequently used criterion is to require the side chain center-to-center distance or the C-alpha-to-C-alpha atom distance to be within a pre-determined cutoff distance. However, the spatially anisotropic nature of the side chain determines that it is challenging to identify the contact pairs. This study compares three side chain contact models: the Atom Distance criteria (ADC) model, the Isotropic Sphere Side chain (ISS) model and the Anisotropic Ellipsoid Side chain (AES) model using 424 high resolution protein structures in the …

An Ethnographic Study Of In-Service And Pre-Service Teacher Collaboration In The Development And Execution Of Mathematics Lessons, Jessica Munns

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

While much is known about effective strategies for teaching mathematics, less is understood about how to lead new teachers to employ research-based practices in their work. To address this issue we followed a Methods of Teaching Secondary and Middle School Mathematics course at Utah State University where collaboration between inservice and pre-service teachers was emphasized. This report documents examples of the implementation of research-based teaching practices by collaborative groups during the course. The structure of collaboration followed a lesson study model involving research and planning, execution and observation, and reflection and revision of lessons. Preservice and in-service teachers met twice …

Extremal Problems For Independent Set Enumeration, Jonathan Cutler, A. J. Radcliffe

Department of Mathematics: Faculty Publications

The study of the number of independent sets in a graph has a rich history. Recently, Kahn proved that disjoint unions of Kr,r’s have the maximum number of independent sets amongst r-regular bipartite graphs. Zhao extended this to all r-regular graphs. If we instead restrict the class of graphs to those on a fixed number of vertices and edges, then the Kruskal-Katona theorem implies that the graph with the maximum number of independent sets is the lex graph, where edges form an initial segment of the lexicographic ordering. In this paper, we study three related questions. Firstly, we …

An Entropy Proof Of The Kahn-Lovasz Theorem, Jonathan Cutler, A. J. Radcliffe

Department of Mathematics: Faculty Publications

Bregman [2], gave a best possible upper bound for the number of perfect matchings in a balanced bipartite graph in terms of its degree sequence. Recently Kahn and Lovasz [8] extended Bregman’s theorem to general graphs. In this paper, we use entropy methods to give a new proof of the Kahn-Lovasz theorem. Our methods build on Radhakrishnan’s [9] use of entropy to prove Bregman’s theorem.

Short-Term Facilitation May Stabilize Parametric Working Memory Trace, Vladimir Itskov, David Hansel, Misha Tsodyks

Department of Mathematics: Faculty Publications

Networks with continuous set of attractors are considered to be a paradigmatic model for parametric working memory (WM), but require fine tuning of connections and are thus structurally unstable. Here we analyzed the network with ring attractor, where connections are not perfectly tuned and the activity state therefore drifts in the absence of the stabilizing stimulus. We derive an analytical expression for the drift dynamics and conclude that the network cannot function as WM for a period of several seconds, a typical delay time in monkey memory experiments. We propose that short-term synaptic facilitation in recurrent connections significantly improves the …