Oscillation Of Nonlinear Third-Order Difference Equations With Mixed Neutral Terms, 2021 Missouri University of Science and Technology

#### Oscillation Of Nonlinear Third-Order Difference Equations With Mixed Neutral Terms, Jehad Alzabut, Martin Bohner, Said R. Grace

*Mathematics and Statistics Faculty Research & Creative Works*

In this paper, new oscillation results for nonlinear third-order difference equations with mixed neutral terms are established. Unlike previously used techniques, which often were based on Riccati transformation and involve limsup or liminf conditions for the oscillation, the main results are obtained by means of a new approach, which is based on a comparison technique. Our new results extend, simplify, and improve existing results in the literature. Two examples with specific values of parameters are offered.

Partial Representations For Ternary Matroids, 2021 California State University, San Bernardino

#### Partial Representations For Ternary Matroids, Ebony Perez

*Electronic Theses, Projects, and Dissertations*

In combinatorics, a matroid is a discrete object that generalizes various notions of dependence that arise throughout mathematics. All of the information about some matroids can be encoded (or represented) by a matrix whose entries come from a particular field, while other matroids cannot be represented in this way. However, for any matroid, there exists a matrix, called a partial representation of the matroid, that encodes some of the information about the matroid. In fact, a given matroid usually has many different partial representations, each providing different pieces of information about the matroid. In this thesis, we investigate when a ...

Non-Abelian Finite Simple Groups As Homomorphic Images, 2021 California State University, San Bernardino

#### Non-Abelian Finite Simple Groups As Homomorphic Images, Sandra Bahena

*Electronic Theses, Projects, and Dissertations*

The purpose of exploring infinite groups in this thesis was to discover homomorphic images of non-abelian finite simple groups. These infinite groups are semi-direct products known as progenitors. The permutation progenitors studied were: 2^{*8 }∶ 2^{2} ^{∙} A_{4}, 2^{*10} ∶ D_{20}, 2^{*4} ∶ C_{4}, 2^{*7} ∶ (7 ∶ 6), 3^{*3} ∶ S_{3}, 2^{*15} ∶ ((5 × 3) ∶ 2), and 2^{*20} ∶ A_{5}. When we factored said progenitors by an appropriate number of relations, we produced several original symmetric presentations and constructions of linear groups, other classical groups, and sporadic groups. We have found original symmetric presentations of ...

Matroids Determinable By Two Partial Representations, 2021 California State University - San Bernardino

#### Matroids Determinable By Two Partial Representations, Aurora Calderon Dojaquez

*Electronic Theses, Projects, and Dissertations*

A matroid is a mathematical object that generalizes and connects notions of independence that arise in various branches of mathematics. Some matroids can be represented by a matrix whose entries are from some field; whereas, other matroids cannot be represented in this way. However, every matroid can be partially represented by a matrix over the field GF(2). In fact, for a given matroid, many different partial representations may exist, each providing a different collection of information about the matroid with which they are associated. Such a partial representation of a matroid usually does not uniquely determine the matroid on ...

Applying Deep Learning To The Ice Cream Vendor Problem: An Extension Of The Newsvendor Problem, 2021 East Tennessee State University

#### Applying Deep Learning To The Ice Cream Vendor Problem: An Extension Of The Newsvendor Problem, Gaffar Solihu

*Electronic Theses and Dissertations*

The Newsvendor problem is a classical supply chain problem used to develop strategies for inventory optimization. The goal of the newsvendor problem is to predict the optimal order quantity of a product to meet an uncertain demand in the future, given that the demand distribution itself is known. The Ice Cream Vendor Problem extends the classical newsvendor problem to an uncertain demand with unknown distribution, albeit a distribution that is known to depend on exogenous features. The goal is thus to estimate the order quantity that minimizes the total cost when demand does not follow any known statistical distribution. The ...

Partially Oriented 6-Star Decomposition Of Some Complete Mixed Graphs, 2021 East Tennessee State University

#### Partially Oriented 6-Star Decomposition Of Some Complete Mixed Graphs, Kazeem A. Kosebinu

*Electronic Theses and Dissertations*

Let $M_v$ denotes a complete mixed graph on $v$ vertices, and let $S_6^i$ denotes the partial orientation of the 6-star with twice as many arcs as edges. In this work, we state and prove the necessary and sufficient conditions for the existence of $\lambda$-fold decomposition of a complete mixed graph into $S_6^i$ for $i\in\{1,2,3,4\}$. We used the difference method for our proof in some cases. We also give some general sufficient conditions for the existence of $S_6^i$-decomposition of the complete bipartite mixed graph for $i\in\{1,2,3,4 ...

Algorithms Related To Triangle Groups, 2021 Louisiana State University and Agricultural and Mechanical College

#### Algorithms Related To Triangle Groups, Bao The Pham

*LSU Doctoral Dissertations*

Given a finite index subgroup of $\PSL_2(\Z)$, one can talk about the different properties of this subgroup. These properties have been studied extensively in an attempt to classify these subgroups. Tim Hsu created an algorithm to determine whether a subgroup is a congruence subgroup by using permutations \cite{hsu}. Lang, Lim, and Tan also created an algorithm to determine if a subgroup is a congruence subgroup by using Farey Symbols \cite{llt}. Sebbar classified torsion-free congruence subgroups of genus 0 \cite{sebbar}. Pauli and Cummins computed and tabulated all congruence subgroups of genus less than 24 \cite{ps}. However ...

Holomorphic Functions, Relativistic Sum, Blaschke Products And Superoscillations, 2021 Chapman University

#### Holomorphic Functions, Relativistic Sum, Blaschke Products And Superoscillations, Daniel Alpay, Fabrizio Colombo, Stefano Pinton, Irene Sabadini

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

Superoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. The notion of superoscillation is a particular case of that one of supershift. In the recent years, superoscillating functions, that appear for example in weak values in quantum mechanics, have become an interesting and independent field of research in complex analysis and in the theory of infinite order differential operators. The aim of this paper is to study some infinite order differential operators acting on entire functions which naturally arise in the study of superoscillating functions. Such operators are of particular interest because they are associated ...

Irreducibility And Galois Groups Of Random Polynomials, 2021 Stanford University

#### Irreducibility And Galois Groups Of Random Polynomials, Hanson Hao, Eli Navarro, Henri Stern

*Rose-Hulman Undergraduate Mathematics Journal*

In 2015, I. Rivin introduced an effective method to bound the number of irreducible integral polynomials with fixed degree d and height at most N. In this paper, we give a brief summary of this result and discuss the precision of Rivin's arguments for special classes of polynomials. We also give elementary proofs of classic results on Galois groups of cubic trinomials.

Lebesgue Measure Preserving Thompson Monoid And Its Properties Of Decomposition And Generators, 2021 Stanford University

#### Lebesgue Measure Preserving Thompson Monoid And Its Properties Of Decomposition And Generators, William Li

*Rose-Hulman Undergraduate Mathematics Journal*

This paper defines the Lebesgue measure preserving Thompson monoid, denoted by **G**, which is modeled on the Thompson group **F** except that the elements of **G** preserve the Lebesgue measure and can be non-invertible. The paper shows that any element of the monoid **G** is the composition of a finite number of basic elements of the monoid **G** and the generators of the Thompson group **F**. However, unlike the Thompson group **F**, the monoid **G** is not finitely generated. The paper then defines equivalence classes of the monoid **G**, use them to construct a monoid **H** that is finitely generated ...

Repeat Length Of Patterns On Weaving Products, 2021 Rose-Hulman Institute of Technology

#### Repeat Length Of Patterns On Weaving Products, Zhuochen Liu

*Rose-Hulman Undergraduate Mathematics Journal*

On weaving products such as fabrics and silk, people use interlacing strands to create artistic patterns. Repeated patterns form aesthetically pleasing products. This research is a mathematical modeling of weaving products in the real world by using cellular automata. The research is conducted by observing the evolution of the model to better understand products in the real world. Specifically, this research focuses on the repeat length of a weaving pattern given the rule of generating it and the configuration of the starting row. Previous studies have shown the range of the repeat length in specific situations. This paper will generalize ...

Disjointness Of Linear Fractional Actions On Serre Trees, 2021 Brown University

#### Disjointness Of Linear Fractional Actions On Serre Trees, Henry W. Talbott

*Rose-Hulman Undergraduate Mathematics Journal*

Serre showed that, for a discrete valuation field, the group of linear fractional transformations acts on an infinite regular tree with vertex degree determined by the residue degree of the field. Since the p-adics and the polynomials over the finite field of order p act on isomorphic trees, we may ask whether pairs of actions from these two groups are ever conjugate as tree automorphisms. We analyze permutations induced on finite vertex sets, and show a permutation classification result for actions by these linear fractional transformation groups. We prove that actions by specific subgroups of these groups are conjugate only ...

New Results On Subtractive Magic Graphs, 2021 Centre College

#### New Results On Subtractive Magic Graphs, Matthew J. Ko, Jason Pinto, Aaron Davis

*Rose-Hulman Undergraduate Mathematics Journal*

For any edge *xy* in a directed graph, the subtractive edge-weight is the sum of the label of *xy* and the label of *y* minus the label of *x*. Similarly, for any vertex *z* in a directed graph, the subtractive vertex-weight of *z* is the sum of the label of *z* and all edges directed into *z* and all the labels of edges that are directed away from *z*. A subtractive magic graph has every subtractive edge and vertex weight equal to some constant *k*. In this paper, we will discuss variations of subtractive magic labelings on directed graphs.

Directed Graphs Of The Finite Tropical Semiring, 2021 Dordt University

#### Directed Graphs Of The Finite Tropical Semiring, Caden G. Zonnefeld

*Rose-Hulman Undergraduate Mathematics Journal*

The focus of this paper lies at the intersection of the fields of tropical algebra and graph theory. In particular the interaction between tropical semirings and directed graphs is investigated. Originally studied by Lipvoski, the directed graph of a ring is useful in identifying properties within the algebraic structure of a ring. This work builds off research completed by Beyer and Fields, Hausken and Skinner, and Ang and Shulte in constructing directed graphs from rings. However, we will investigate the relationship (x, y)→(min(x, y), x+y) as defined by the operations of tropical algebra and applied to tropical ...

The Degeneration Of The Hilbert Metric On Ideal Pants And Its Application To Entropy, 2021 University of Michigan, Ann Arbor

#### The Degeneration Of The Hilbert Metric On Ideal Pants And Its Application To Entropy, Marianne Debrito, Andrew Nguyen, Marisa O'Gara

*Rose-Hulman Undergraduate Mathematics Journal*

Entropy is a single value that captures the complexity of a group action on a metric space. We are interested in the entropies of a family of ideal pants groups $\Gamma_T$, represented by projective reflection matrices depending on a real parameter $T > 0$. These groups act on convex sets $\Omega_{\Gamma_T}$ which form a metric space with the Hilbert metric. It is known that entropy of $\Gamma_T$ takes values in the interval $\left(\frac{1}{2},1\right]$; however, it has not been proven whether $\frac{1}{2}$ is the sharp lower bound. Using Python programming, we generate approximations of ...

An Introduction To Fractal Analysis, 2021 Reed College

#### An Introduction To Fractal Analysis, Lucas Yong

*Rose-Hulman Undergraduate Mathematics Journal*

Classical analysis is not able to treat functions whose domain is fractal. We present an introduction to analysis on a particular class of fractals known as post-critically finite (PCF) self-similar sets that is suitable for the undergraduate reader. We develop discrete approximations of PCF self-similar sets, and construct discrete Dirichlet forms and corresponding discrete Laplacians that both preserve self-similarity and are compatible with a notion of harmonic functions that is analogous to a classical setting. By taking the limit of these discrete Laplacians, we construct continuous Laplacians on PCF self-similar sets. With respect to this continuous Laplacian, we also construct ...

Irrational Philosophy? Kronecker's Constructive Philosophy And Finding The Real Roots Of A Polynomial, 2021 University of Missouri - Kansas City

#### Irrational Philosophy? Kronecker's Constructive Philosophy And Finding The Real Roots Of A Polynomial, Richard B. Schneider

*Rose-Hulman Undergraduate Mathematics Journal*

The prominent mathematician Leopold Kronecker (1823 – 1891) is often relegated to footnotes and mainly remembered for his strict philosophical position on the foundation of mathematics. He held that only the natural numbers are intuitive, thus the only basis for all mathematical objects. In fact, Kronecker developed a complete school of thought on mathematical foundations and wrote many significant algebraic works, but his enigmatic writing style led to his historical marginalization. In 1887, Kronecker published an extended version of his paper, “On the Concept of Number,” translated into English in 2010 for the first time by Edward T. Dean, who confirms ...

Infinite Peirce Distribution In The Algebra Of Compact Operators And Description Of Its Local Au-Tomorphisms, 2021 Andizhan State University

#### Infinite Peirce Distribution In The Algebra Of Compact Operators And Description Of Its Local Au-Tomorphisms, Farhodjon N. Arzikulov, Rejabboy Qo’Shaqov

*Scientific Bulletin. Physical and Mathematical Research*

In the present paper the infinite Peirce decomposition of the algebra 𝐾(𝐻) of com-pact operators on an infinite dimensional separable Gilbert space 𝐻 is constructed, using the norm of the algebra 𝐾(𝐻) and a maximal family of mutually or-thogonal minimal projections, i.e., self-adjoint,idempotent elements. The infinite Peirce decompo-sition on the norm of a 𝐶∗-algebra is also con-structed in 2012 by the first author. But, it turns, the condition, applied then, is not sufficient for the infi-nite Peirce decomposition on the norm constructed in 2012 to be an algebra. Therefore, in the present paper, the infinite ...

The French Connection: Borda, Condorcet And The Mathematics Of Voting Theory, 2021 Colorado State University-Pueblo

#### The French Connection: Borda, Condorcet And The Mathematics Of Voting Theory, Janet Heine Barnett

*General Education and Liberal Studies*

No abstract provided.

Effects Of Virtual Math Mentorships On Elementary Student Math Scores, 2021 Liberty University

#### Effects Of Virtual Math Mentorships On Elementary Student Math Scores, Tammy T. May

*Doctoral Dissertations and Projects*

The purpose of this quantitative, quasi-experimental study was to examine the relationship between college students’ virtual math mentorships and instruction on third grade students’ math academic success. College students in teacher preparation programs investigated deficiencies in third grade students’ competency of math concepts as specified by state standards, and they designed lessons to address these challenges through weekly virtual meetings. Third grade teachers wanted to provide additional math supports for their struggling students, and this partnership between the college students and the third graders was the foundation of this study at four Title 1 rural elementary schools. This research is ...