Digital Commons Network^™

How An Instructor's Noticing For Equity Can Foster Students' Sense Of Belonging And Mathematical Confidence, Sthefania Espinosa

Theses and Dissertations

There are many aspects a teacher can notice inside the mathematics classroom, and the more a teacher notices, the more difficult it is to teach. In this study, I particularly focus on noticing for equity, which describes the role of the teacher in attending to students’ mathematical thinking through an equity lens that can allow the instructor to notice the aspects of classroom mathematical activity that can make students feel less or more empowered in their mathematical practices (van Es et al., 2017). There exists few research about how students perceive their instructor’s effort to promote equity and …

The Construction Of Khovanov Homology, Shiaohan Liu

Master's Theses

Knot theory is a rich topic in topology that studies the how circles can be embedded in Euclidean 3-space. One of the main questions in knot theory is how to distinguish between different types of knots efficiently. One way to approach this problem is to study knot invariants, which are properties of knots that do not change under a standard set of deformations. We give a brief overview of basic knot theory, and examine a specific knot invariant known as Khovanov homology. Khovanov homology is a homological invariant that refines the Jones polynomial, another knot invariant that assigns a Laurent …

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …

Zero-Knowledge Reductions And Confidential Arithmetic, Marvin Jones

All Dissertations

The changes in computing paradigms to shift computations to third parties have resulted in the necessity of these computations to be provable. Zero-knowledge arguments are probabilistic arguments that are used to to verify computations without secret data being leaked to the verifying party.

In this dissertation, we study zero-knowledge arguments with specific focus on reductions. Our main contributions are:

1. Provide a thorough survey in a variety of zero-knowledge techniques and protocols.
2. Prove various results of reductions that can be used to study interactive protocols in terms of subroutines. Additionally, we identify an issue in the analogous definition of zero-knowledge for …

Turing Patterns In A P-Adic Fitzhugh-Nagumo System On The Unit Ball, L. F. Chacón-Cortés, C. A. Garcia-Bibiano, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

We introduce discrete and p-adic continuous versions of the FitzHugh-Nagumo system on the one-dimensional p-adic unit ball. We provide criteria for the existence of Turing patterns. We present extensive simulations of some of these systems. The simulations show that the Turing patterns are traveling waves in the p-adic unit ball.

Measuring The Lengths Of Sperm Whales Of The Northern Gulf Of Mexico By Wavelet Analysis Of Their Usual Clicks, George Drouant

LSU New Orleans Theses and Dissertations

Abstract

Acoustic recordings of underwater sounds produced by marine mammals present an attractive alternative to costly and logistically complex ship based visual surveys for collecting population data for various species.

The first reported use of underwater acoustic recordings in the long-term monitoring of sperm whale populations was by Ackleh et al. (Ackleh et al., 2012). The paper describes counting sperm whale clicks at different locations to track population changes over time.

Analysis of sperm whale clicks offers additional insight into sperm whale populations. The echo location clicks (usual clicks) of sperm whales can be used to give an estimate of …

Lie Algebras And Lie Groups, Nhi Nguyen

Algebra Seminar

No abstract provided.

Lie Algebras And Lie Groups, Nhi Nguyen

Mathematics Colloquium Series

No abstract provided.

The Heisenberg Lie Algebra And Its Role In The Quantum Mechanical Harmonic Oscillator, Angelina Georg

Algebra Seminar

No abstract provided.

Irreducible Representations Of Sl(2,C), Della Medovoy

Algebra Seminar

No abstract provided.

Irreducible Representations Of Sl(2,C), Della Medovoy

Mathematics Colloquium Series

No abstract provided.

The Heisenberg Lie Algebra And Its Role In The Quantum Mechanical Harmonic Oscillator, Angelina Georg

Mathematics Colloquium Series

No abstract provided.

The Factors Affecting Fashion Trends Have Changing Over The Years By Different Age Groups & The Evolution Of Media., Omnahqiran Dazz

Honors Theses

Introduction:

Fashion trends undergo continuous evolution, influenced by factors such as age groups and the ever-changing landscape of media. This research delves into the intricate relationship between these elements. Initially driven by a passion for fashion, the project expanded to explore the profound impact of social media evolution over the past 15-20 years.

Objectives: Investigate changing fashion trends across age groups.

Examine the evolution of media.

Analyze the factors affecting current-day fashion trends.

Explore the influence of social media on fashion choices.

This study provides invaluable insights for fashion designers, brands, and retailers, aiding in the development of effective market …

Jumping Frogs On Cyclic Graphs, Jake Mitchell

Honors College Theses

From the traditional game of Solitaire to modern video games like Candy Crush and Five Nights at Freddy’s, single-player games have captivated audiences for gener- ations. We investigate a lesser-known single-player game, the Jumping Frogs problem, on various classes of simple graphs, a graph with no multiple edges or looped ver- tices. We determine whether frogs can be stacked together on one vertex of a given graph. In a graph with k vertices and one frog on each vertex, the frogs must make legal jumps to form a stack of k frogs. The problem is known to be solvable on …

1324-Avoiding (0,1)-Matrices, Megan Bennett

Mathematics Colloquium Series

A 1324-avoiding (0,1)-matrix is an 𝑚×𝑛 matrix that does not contain the 1324-pattern. Our goal is to find the maximum number of 1’s that an 𝑚 × 𝑛 1324-avoiding (0,1)-matrix can contain. We build upon Brualdi and Cao’s recent work, where they characterized the 𝑚 × 𝑛 1234-avoiding matrices with the maximum number of 1’s. They found that these matrices can contain up to 3(𝑚 + 𝑛 − 3) 1’s. We originally conjectured that 1324-avoiding matrices must contain at most the same number of 1’s, as is the case with the six patterns formed by permutations of {1,2,3}. However, we …

The Negative Stigma Surrounding Mathematics, Marissa A. Greisen

PSU McNair Scholars Online Journal

There is a negative stigma that surrounds mathematics in our education system. It is important to bring notice to this for the benefit of future students. There is a lot of research claiming that math is looked down on, but they do not answer why, or what we can do to fix it. Why is there a greater negative stigma around math and not other subjects? What roles to teachers, parents, and peers play in this stigma? In this article, I created a survey for people to answer questions regarding their opinion on math, who they believe typically does well …

Exploring Non-Orientable Topology: Deriving The Poincaré Conjecture And Possibility Of Experimental Vindication With Liquid Crystal, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This review investigates the potential of non-orientable topology as a fundamental framework for understanding the Poincaré conjecture and its implications across various scientific disciplines. Integrating insights from Dokuchaev (2020), Rapoport, Christianto, Chandra, Smarandache (under review), and other pioneering works, this article explores the theoretical foundations linking non-orientable spaces to resolving the Poincaré conjecture and its broader implications in theoretical physics, geology, cosmology, and biology.

On Determining The Equation Of A Salkowski Curve Satisfying Tau/Kappa=1/S, Yun Myung Oh, Devin Garcia-Roblero

Faculty Publications

In this paper, we determine the equation of a Salkowski curve whose ratio of torsion to curvature is given by 1/s, where s is the arc length of the curve. The Frenet-Serret equations provide the third-order vector differential equation for the unit tangent vector T(s) and the general (series) solution was obtained. In the end, the series solution is entirely determined by the given initial conditions.

Eigenvalue Algorithm For Hausdorff Dimension On Complex Kleinian Groups, Jacob Linden, Xuqing Wu

Rose-Hulman Undergraduate Mathematics Journal

In this manuscript, we present computational results approximating the Hausdorff dimension for the limit sets of complex Kleinian groups. We apply McMullen's eigenvalue algorithm \cite{mcmullen} in symmetric and non-symmetric examples of complex Kleinian groups, arising in both real and complex hyperbolic space. Numerical results are compared with asymptotic estimates in each case. Python code used to obtain all results and figures can be found at \url{https://github.com/WXML-HausDim/WXML-project}, all of which took only minutes to run on a personal computer.

Population Growth Models: Relationship Between Sustainable Fishing And Making A Profit, James Sandefur

CODEE Journal

In this paper, we develop differential equations that model the sustainable harvesting of species having different characteristics. Specifically, we assume the species satisfies one of two different types of density dependence. From these equations, we consider maximizing sustainable harvests. We then introduce a cost function for fishing and study how maximizing profit affects the harvesting strategy. We finally introduce the concept of open access which helps explain the collapse of many fish stocks.

The equations studied involve relatively simple rational and exponential functions. We analyze the differential equations using phase-line analysis as well as graphing approximate solutions using Euler's method, …

Combinatorially Orthogonal Paths, Sean A. Bailey, David E. Brown, Leroy Beaseley

Communications on Number Theory and Combinatorial Theory

Vectors x=(x₁,x₂,...,x_n)^T and y=(y₁,y₂,...,y_n)^T are combinatorially orthogonal if |{i:x_iy_i≠0}|≠1. An undirected graph G=(V,E) is a combinatorially orthogonal graph if there exists f:V→ℝⁿ such that for any u,v∈V, uv∉E iff f(u) and f(v) are combinatorially orthogonal. We will show that every graph has a combinatorially orthogonal representation. We will show …

Differentiating By Prime Numbers, Jack Jeffries

Department of Mathematics: Faculty Publications

It is likely a fair assumption that you, the reader, are not only familiar with but even quite adept at differentiating by x. What about differentiating by 13? That certainly didn’t come up in my calculus class! From a calculus perspective, this is ridiculous: are we supposed to take a limit as 13 changes? One notion of differentiating by 13, or any other prime number, is the notion of p-derivation discovered independently by Joyal [Joy85] and Buium [Bui96]. p-derivations have been put to use in a range of applications in algebra, number theory, and arithmetic geometry. Despite the wide range …

Forest Generating Functions Of Directed Graphs, Ewan Joaquin Kummel

Dissertations and Theses

A spanning forest polynomial is a multivariate generating function whose variables are indexed over both the vertex and edge sets of a given directed graph. In this thesis, we establish a general framework to study spanning forest polynomials, associating them with a generalized Laplacian matrix and studying its properties. We introduce a novel proof of the famous matrix-tree theorem and show how this extends to a parametric generalization of the all-minors matrix-forest theorem. As an application, we derive explicit formulas for the recently introduced class of directed threshold graphs.

We prove that multivariate forest polynomials are, in general, irreducible and …

Legendre Pairs Of Lengths ℓ ≡ 0 (Mod 5), Ilias S. Kotsireas, Christopher Koutschan, Dursun A. Bulutoglu, David M. Arquette, Jonathan S. Turner, Kenneth J. Ryan

Faculty Publications

By assuming a type of balance for length ℓ = 87 and nontrivial subgroups of multiplier groups of Legendre pairs (LPs) for length ℓ = 85 , we find LPs of these lengths. We then study the power spectral density (PSD) values of m compressions of LPs of length 5 m . We also formulate a conjecture for LPs of lengths ℓ ≡ 0 (mod 5) and demonstrate how it can be used to decrease the search space and storage requirements for finding such LPs. The newly found LPs decrease the number of integers in the range ≤ 200 for …

An Extensive Note On Characteristic Properties And Possible Implications Of Some Operators Designated By Various Type Derivatives, Ömer Faruk Kulali, Hüseyi̇n Irmak

Turkish Journal of Mathematics

In this extensive note, various differential-type operators in certain domains of the complex plane will be first introduced, a number of their comprehensive characteristic properties will be next pointed out and an extensive theorem dealing with some argument properties for several multivalent(ly) analytic functions will be also presented. In addition, numerous implications and suggestions, which can be obtained with the help of general result, will be determined.

Fibonomial Matrix And Its Domain In The Spaces $\Ell_P$ And $\Ell_{\Infty}$, Muhammet Ci̇hat Dağli, Taja Yaying

Turkish Journal of Mathematics

In this paper, we introduce the fibonomial sequence spaces $b_{p}^{r,s,F}$ and $b_{\infty}^{r,s,F},$ and show that these are BK-spaces. Also, we prove that these new spaces are linearly isomorphic to $\ell_{p}$ and $\ell_{\infty}.$ Moreover, we determine the $\alpha$-, $\beta$-, $\gamma$-duals for these new spaces and characterize some matrix classes. The final section is devoted to the investigation of some geometric properties of the newly defined space $b_{p}^{r,s,F}.$

Best Proximity For Proximal Operators On $B$-Metric Spaces, Ariana Pitea, Monica Stanciu

Turkish Journal of Mathematics

The paper presents existence results of $(\phi,\varphi)$ best proximity points for operators that fulfill implicit type inequalities. Classes of mappings endowed with continuity, monotone or monotone-type properties, and which additionally satisfy some adequate inequalities are studied from this point of view. Applications of our results are given with regard to fixed point theory.

Multiplication Of Closed Balls In $\Mathbb{C}^N$, Patrícia Damas Beites, Alejandro Piñera Nicolás, José Da Silva Lourenço Vitória

Turkish Journal of Mathematics

Motivated by circular complex interval arithmetic, some operations on closed balls in $\mathbb{C}^n$ are considered. Essentially, the properties of possible multiplications for closed balls in $\mathbb{C}^n$, related either to the Hadamard product of vectors or to the $2$-fold vector cross product when $n \in \{3, 7\}$, are studied. In addition, certain equations involving the defined multiplications are solved.

On Polynomially Partial-$A$-Isometric Operators, Mohamed Amine Aouichaoui, Dijana Mosic

Turkish Journal of Mathematics

This paper presents a generalization of the concepts of partial-$A$-isometry and left polynomially partial isometry. Our investigation is inspired by previous work in the field [5, 30, 31]. By extending the definition of partial-$A$-isometry, we provide new insights into the properties and applications of these mathematical objects. In particular, we define the notion of left $p$-partial-$A$-isometry as a broader class of operators, including partial-$A$-isometry and left polynomially partial isometry. Some basic properties of a left $p$-partial-$A$-isometry are proven, as well as its relation with $A$-isometry. Several decompositions of a left $p$-partial-$A$-isometry are developed. We consider spectral properties and matrix representation …

Various Types Of Continuity And Their Interpretations In Ideal Topological Spaces, Anika Njamcul, Aleksandar Pavlovi?

Turkish Journal of Mathematics

In this paper we work on preserving various types of continuity in ideal topological spaces. The accent will be on $\theta$-continuity and weak continuity. We will give their translations in ideal topological spaces. As a consequence of those results, we will prove that every $\theta$-continuous function is continuous if topologies are generated by $\theta$-open sets and we will give an example of a weakly continuous function which is not $\tau_\theta$-continuous. This will complete the diagram of relations between continuous, $\tau_\theta$-continuous, $\theta$-continuous, weakly continuous, and faintly continuous functions.