Mathematics Commons^™

Properties Of Skew-Polynomial Rings And Skew-Cyclic Codes, Kathryn Hechtel

Theses and Dissertations--Mathematics

A skew-polynomial ring is a polynomial ring over a field, with one indeterminate x, where one must apply an automorphism to commute coefficients with x. It was first introduced by Ore in 1933 and since the 1980s has been used to study skew-cyclic codes. In this thesis, we present some properties of skew-polynomial rings and some new constructions of skew-cyclic codes. The dimension of a skew-cyclic code depends on the degree of its generating skew polynomial. However, due to the skew-multiplication rule, the degree of a skew polynomial can be smaller than its number of roots and hence tricky to …

Adams Operations On The Burnside Ring From Power Operations, Lewis Dominguez

Theses and Dissertations--Mathematics

Topology furnishes us with many commutative rings associated to finite groups. These include the complex representation ring, the Burnside ring, and the G-equivariant K-theory of a space. Often, these admit additional structure in the form of natural operations on the ring, such as power operations, symmetric powers, and Adams operations. We will discuss two ways of constructing Adams operations. The goal of this work is to understand these in the case of the Burnside ring.

Pairs Of Quadratic Forms Over P-Adic Fields, John Hall

Theses and Dissertations--Mathematics

Given two quadratic forms $Q_1, Q_2$ over a $p$-adic field $K$ in $n$ variables, we consider the pencil $\mathcal{P}_K(Q_1, Q_2)$, which contains all nontrivial $K$-linear combinations of $Q_1$ and $Q_2$. We define $D$ to be the maximal dimension of a subspace in $K^n$ on which $Q_1$ and $Q_2$ both vanish. We define $H$ to be the maximal number of hyperbolic planes that a form in $\mathcal{P}_K(Q_1, Q_2)$ splits off over $K$. We will determine which values for $(D, H)$ are possible for a nonsingular pair of quadratic forms over a $p$-adic field $K$.

Dirichlet Problems In Perforated Domains, Robert Righi

Theses and Dissertations--Mathematics

We establish W^1,p estimates for solutions u_ε to the Laplace equation with Dirichlet boundary conditions in a bounded C¹ domain Ω_{ε, η} perforated by small holes in ℝ^d. The bounding constants will depend explicitly on epsilon and eta, where epsilon is the order of the minimal distance between holes, and eta denotes the ratio between the size of the holes and epsilon. The proof relies on a large-scale L^p estimate for ∇u_ε, whose proof is divided into two main parts. First, we show that solutions of an intermediate problem for a …

Slₖ-Tilings And Paths In ℤᵏ, Zachery T. Peterson

Theses and Dissertations--Mathematics

An SLₖ-frieze is a bi-infinite array of integers where adjacent entries satisfy a certain diamond rule. SL₂-friezes were introduced and studied by Conway and Coxeter. Later, these were generalized to infinite matrix-like structures called tilings as well as higher values of k. A recent paper by Short showed a bijection between bi-infinite paths of reduced rationals in the Farey graph and SL₂-tilings. We extend this result to higher k by constructing a bijection between SLₖ-tilings and certain pairs of bi-infinite strips of vectors in ℤᵏ called paths. The key ingredient in the proof is the relation to Plucker friezes and …

A Multiple-Case Study On The Impact Of An Introductory Real Analysis Course On Undergraduate Students' Understanding Of Function Continuity, Ryan Joseph Rogers

Theses and Dissertations--Mathematics

Undergraduate students' understanding of function continuity has not been explored broadly in previous research. The relevant findings in the literature are predominantly concerned with calculus students' understanding and misconceptions of continuity. Many of these misunderstandings are tied to the relationships which continuity has with limits and differentiability. This multiple-case study explores how, if at all, an introductory real analysis course impacts undergraduate students' understanding of function continuity and its connections to the notions of limits and differentiability. We embed our findings within the theoretical framework of Tall's three worlds of mathematics, namely, the embodied, symbolic, and formal worlds.

The cases …

Advanced Mathematical Graph-Based Machine Learning And Deep Learning Models For Drug Design, Farjana Tasnim Mukta

Theses and Dissertations--Mathematics

Drug discovery is a highly complicated and time-consuming process. One of the main challenges in drug development is predicting whether a drug-like molecule will interact with a specific target protein. This prediction accelerates target validation and drug development. Recent research in biomolecular sciences has shown significant interest in algebraic graph-based models for representing molecular complexes and predicting drug-target binding affinity. In this thesis, we present algebraic graph-based molecular representations to create data-driven scoring functions (SF) using extended atom types to capture wide-range interactions between targets and drug candidates. Our model employs multiscale weighted colored subgraphs for the protein-ligand complex, colored …

Neural Correlates Of Audiovisual Narrative Speech Perception In Children And Adults On The Autism Spectrum: A Functional Magnetic Resonance Imaging Study, Lars A. Ross, Sophie Molholm, John S. Butler, Victor A. Del Bene, Tufikameni Brima, John J. Foxe

Articles

Autistic individuals show substantially reduced benefit from observing visual articulations during audiovisual speech perception, a multisensory integration deficit that is particularly relevant to social communication. This has mostly been studied using simple syllabic or word-level stimuli and it remains unclear how altered lower-level multisensory integration translates to the processing of more complex natural multisensory stimulus environments in autism. Here, functional neuroimaging was used to examine neural correlates of audiovisual gain (AV-gain) in 41 autistic individuals to those of 41 age-matched non-autistic controls when presented with a complex audiovisual narrative. Participants were presented with continuous narration of a story in auditory-alone, …

Multiple Imputation For Robust Cluster Analysis To Address Missingness In Medical Data, Arnold Harder, Gayla R. Olbricht, Godwin Ekuma, Daniel B. Hier, Tayo Obafemi-Ajayi

Mathematics and Statistics Faculty Research & Creative Works

Cluster Analysis Has Been Applied To A Wide Range Of Problems As An Exploratory Tool To Enhance Knowledge Discovery. Clustering Aids Disease Subtyping, I.e. Identifying Homogeneous Patient Subgroups, In Medical Data. Missing Data Is A Common Problem In Medical Research And Could Bias Clustering Results If Not Properly Handled. Yet, Multiple Imputation Has Been Under-Utilized To Address Missingness, When Clustering Medical Data. Its Limited Integration In Clustering Of Medical Data, Despite The Known Advantages And Benefits Of Multiple Imputation, Could Be Attributed To Many Factors. This Includes Methodological Complexity, Difficulties In Pooling Results To Obtain A Consensus Clustering, Uncertainty Regarding …

Centers Of N-Degree Poncelet Circles, Georgia Corbett

Honors Theses

Given a circle inscribed in a polygon inscribed in the unit circle, if one connects all the vertices with line segments we get a family of circles called a package of Poncelet circles, due to its connection to a theorem of Poncelet. We are interested in where the centers of the Poncelet circles can be. Specifically, we have shown that if one of the circles in the Poncelet package is centered at 0, then all of the circles must be centered at 0 as well. This was proven by Spitkovsky and Wegert in 2021 using elliptic integrals but we …

Applications And Analysis Of Nlp Deep Learning Models For Antibiotic's Side Effects Classifications, An Ly

CGU Theses & Dissertations

I introduce a novel recursive modification to the classical Goemans-Williamson MaxCut algorithm, offering improved performance in vectorized data clustering tasks. Focusing on the clustering of medical publications, I suggest to employ recursive iterations in conjunction with a dimension relaxation method to enhance density of clustering results. Furthermore, I propose a new vectorization technique for articles, leveraging conditional probabilities for more effective clustering. I believe that these methods will provide advantages in both computational efficiency and clustering accuracy. I will analyze the effectiveness of recursive iterations and higher-dimensional generalizations of the GWA in the hopes of achieving more accurate dissimilarity-based clustering. …

Berglund–Hübsch Transpose Rule And Sasakian Geometry, Ralph R. Gomez

Mathematics & Statistics Faculty Works

We apply the Berglund–Hübsch transpose rule from BHK mirror symmetry to show that to an n−1-dimensional Calabi–Yau orbifold in weighted projective space defined by an invertible polynomial, we can associate four (possibly) distinct Sasaki manifolds of dimension 2n+1 which are n−1-connected and admit a metric of positive Ricci curvature. We apply this theorem to show that for a given K3 orbifold, there exist four seven-dimensional Sasakian manifolds of positive Ricci curvature, two of which are actually Sasaki–Einstein.

The Computational Search For Unidentified Central Configurations Of The Newtonian N-Body Problem, Hannah G. Havel

CURE Proceedings

The N-body problem is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It is vital in celestial mechanics, such as planning collision-free satellite orbit trajectories. When beginning to understand the N-body problem, we can start by looking at equal masses of these particles or celestial bodies. As particles move, their position and velocity change, both energy and angular momentum are conserved. Sets of constant energy and angular momentum, known as integral manifolds, are higher-dimensional figures that represent constraints of movement to a system. Integral manifolds are described …

Adaptive Neh With Constrained Nearest Neighbor Subtours For The Electric Vehicle Routing Problem With Time Windows, Andrew Struthers

All Master's Theses

The development of electric vehicles is currently considered one of the most innovative areas in manufacturing. Largely driven by the desire to reduce greenhouse emissions, electric vehicles are seen as a viable alternative to internal combustion engine cars. Starting from consumer cars, a dedicated effort is being made to translate this into commercial vehicles for freight and delivery. This research introduces a novel adaptive Nawaz, Enscore, Ham (NEH) algorithm with constrained nearest neighbor subtour (NEH-NN). This algorithm is tested on the standard benchmark problems in literature and used as a seed solution for the Genetic Algorithm (GA). The performance and …

Echolocation On Manifolds, Kerong Wang

Honors Theses

We consider the question asked by Wyman and Xi [WX23]: ``Can you hear your location on a manifold?” In other words, can you locate a unique point x on a manifold, up to symmetry, if you know the Laplacian eigenvalues and eigenfunctions of the manifold? In [WX23], Wyman and Xi showed that echolocation holds on one- and two-dimensional rectangles with Dirichlet boundary conditions using the pointwise Weyl counting function. They also showed echolocation holds on ellipsoids using Gaussian curvature.

In this thesis, we provide full details for Wyman and Xi's proof for one- and two-dimensional rectangles and we show that …

A Generalization Of The Graham-Pollak Tree Theorem To Even-Order Steiner Distance, Joshua Cooper, Gabrielle Tauscheck

Faculty Publications

Graham and Pollak showed in 1971 that the determinant of a tree’s distance matrix depends only on its number of vertices, and, in particular, it is always nonzero. The Steiner distance of a collection of k vertices in a graph is the fewest number of edges in any connected subgraph containing those vertices; for k = 2, this reduces to the ordinary definition of graphical distance. Here we show that the hyperdeterminant of the kth order Steiner distance hypermatrix is always nonzero if k is even, extending their result beyond k = 2. Previously, the authors showed that the k-Steiner …

Constacyclic Codes Of Length With Three Prime Factors And Primitive Idempotents, Supakarn Rakphon

Chulalongkorn University Theses and Dissertations (Chula ETD)

Let Fq be a finite field of order q and t be a prime such that q t − 1 = l v1 1 l v2 2 l v3 3 c where l1, l2, l3 are distinct odd primes with gcd(l1l2l3, q(q−1)) = 1 and c is a positive integer with gcd(l1l2l3, c) = 1. In this thesis, we find all irreducible divisors of x l m1 1 l m2 2 l m3 3 −a over Fq and all generator polynomials for constructing a-constacyclic codes of length l m1 1 l m2 2 l m3 3 . In addition, we …

Contrastive Learning, With Application To Forensic Identification Of Source, Cole Ryan Patten

Electronic Theses and Dissertations

Forensic identification of source problems often fall under the category of verification problems, where recent advances in deep learning have been made by contrastive learning methods. Many forensic identification of source problems deal with a scarcity of data, an issue addressed by few-shot learning. In this work, we make specific what makes a neural network a contrastive network. We then consider the use of contrastive neural networks for few-shot learning classification problems and compare them to other statistical and deep learning methods. Our findings indicate similar performance between models trained by contrastive loss and models trained by cross-entropy loss. We …

Optimal Network Analysis Through Vertex Order Coloring Of Intuitionistic Fuzzy Graph Operations, A. Meenakshi, S. Dhanushiya, Hong Qin, Maniyandy Elangovan

Data Science Faculty Publications

Intuitionistic fuzzy graphs IFGs are a powerful tool for modeling uncertainty and complex relationships. They offer versatile frameworks for addressing real-world challenges. In this research, we have introduced intuitionistic fuzzy vertex order coloring IFVOC and analyzed the alpha-strong (alpha str), beta-strong (beta str), and gamma-strong (gamma str) vertices through their degree. We explored important theorems based on the types of strong vertices, broadening the scope of our study. We analyzed multiple IFG products to determine the most optimal network based on some important metrics, including the weight and total number of alpha str vertices, the chromatic number, and the weight …

Partial Collisions Of Unmater-Matter, Unmatter-Antimatter, And Unmatter1-Unmatter2 To Generate High Energy, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we present the possibility of partial collisions between unmatter with matter, and unmatter with antimatter, and two or more different types of unmatters colliding between themselves to create high energy. In general, the collisions between unmatter with matter, or with antimatter, or with other type of unmatter, because being partial, they release less energy than the matter-unmatter collision which is a total collision. But the unmatter may be easier to produce in laboratory than antimatter.

Combined Plithogenic Hypersoft Sets In Decision Making On Supplier Selection With Different Mcdm Approaches., Sikkanan Sudha, Ravi Priya, Nivetha Martin, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Decision making methods integrated with Plithogenic sets are highly feasible and resilient in designing optimal solutions. This research work identifies the research gaps of limited applications of combined plithogenic hypersoft sets (CPHSS) and hence proposes a supplier selection decision problem with an integrated approach combining CPHSS with MCDM methods. A generalized form of Plithogenic accuracy function is used in determining the plithogenic accuracy matrix to which the prominent ranking methods of TOPSIS, ELECTRE, VIKOR and MAIRCA are applied. The proposed hybrid decision approach is illustrated using supplier selection decision problem as a case study. The ranking results are compared with …

Introduction To Upside-Down Logic: Its Deep Relation To Neutrosophic Logic And Applications, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In the study of uncertainty, concepts such as fuzzy sets [113], fuzzy graphs [79], and neutrosophic sets [88] have been extensively investigated. This paper focuses on a novel logical framework known as Upside-Down Logic, which systematically transforms truths into falsehoods and vice versa by altering contexts, meanings, or perspectives. The concept was first introduced by F. Smarandache in [99]. To contribute to the growing interest in this area, this paper presents a mathematical definition of Upside-Down Logic, supported by illustrative examples, including applications related to the Japanese language. Additionally, it introduces and explores Contextual Upside-Down Logic, an advanced extension that …

Remark On Falaco Soliton As A Tunneling Mechanism In A Navier-Stokes Universe, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper is a follow up to our previous article [1] suggesting that it is possible to find tunneling time solutions for Schrodinger equation considering quasicrystalline as interstellar matter, by virtue of quasicrystalline potential. The paper also discusses the mapping of these equations to Riccati equations, a class of nonlinear differential equations. This mapping can provide insights into the behavior of the Navier-Stokes equations and may lead to new methods for solving them. The Navier-Stokes equations, a set of nonlinear partial differential equations, are fundamental in fluid mechanics. They describe the motion of viscous fluids. In three dimensions, these equations …

Resolving The Paradoxism With The Logic Of “Not” In Javanese Puppetry: A Re-Reading Of Wrekodoro And Dewaruci’S Mytology, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

There are a large number of text collections in Indonesia, related to wayang theme, cf Zoetmulder (1971). And the text collections do not consist only of wayang purwa but also variations of this theme, including wayang wahyu etc. In the mean time, a Japanese scholar Shoshichi Nagatomo proposed the concept of "Asian Logic" which differs from Western logic. In Western thought, things are often seen as black or white, good or bad. However, Asian logic embraces certain degree of ambiguity. Here, "good" characters can exhibit flaws, and "bad" characters can possess redeeming qualities; especially among Javanese people preference is given …

Associated A Nexus With A Treesoft Sets And Vice Versa, Akbar Rezae, Karim Ghadimi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We recall the definitions of a nexus and a TreeSoft Set, and investigate the relation between them. We associated a nexus with a TreeSoft Set induced by a tree graph and vice versa.

Row-Column Designs: A Novel Approach For Analyzing Imprecise And Uncertain Observations, Abdulrahman Alaita, Muhammad Aslam, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Classical row-column designs cannot be applied when the underlying data set contains some imprecise, uncertain, or undetermined observations. In this paper, we discuss row-column design under a neutrosophic statistical framework. A significant contribution of our study is to propose a novel approach to analyzing row-column designs using neutrosophic data. This approach involves calculating the neutrosophic analysis of variance (NANOVA) table for the proposed design and using it to derive the FN -test in an uncertain environment. Two numerical examples have been used to assess the proposed design’s performance. Results from the study indicated that a row column design under …

Extremal Graphs For Widom–Rowlinson Colorings In K-Chromatic Graphs, John Engbers, Aysel Erey

Mathematical and Statistical Science Faculty Research and Publications

The Widom–Rowlinson graph, H_WR , is the fully looped path on three vertices. Let hom(G,H_WR) be the number of graph homomorphisms from G to H_WR or, equivalently, the number of H_WR-colorings of G. We investigate extremal graphs for hom(G,H_WR) for G in the family of k-chromatic graphs subject to various connectivity requirements. In particular, we determine the graphs G maximizing hom(G,H_WR) in the families of n-vertex k-chromatic graphs, n-vertex connected k-chromatic graphs, n-vertex k-chromatic graphs with c components, n …

Use Of Hydroxychloroquine In Multidrug Protocols For Sars-Cov-2, Eleftherios Gkioulekas, Peter A. Mccullough

School of Mathematical & Statistical Sciences Faculty Publications

We review the available evidence supporting the use of hydroxychloroquine-based multidrug protocols in the treatment of COVID-19, in response to a recently published editorial in the Tasman Medical Journal.

Multicolor Bipartite Ramsey Number Of Double Stars, Gregory M. Decamillis

Honors Undergraduate Theses

The core idea of Ramsey theory is that complete disorder is impossible. Given a large structure, no matter how complex it is, we can always find a smaller substructure that has some sort of order. For positive integers $n, m$, the double star $S(n,m)$ is the graph consisting of the disjoint union of two stars $K_{1,n}$ and $K_{1,m}$ together with an edge joining their centers. The $k$-color bipartite Ramsey number of $ S(n,m)$, denoted by $r_{bip}(S(n,m);k)$, is the smallest integer $N$ such that, in any $k$-coloring of the edges of the complete bipartite graph $K_{N,N}$, there is a monochromatic copy …

Id Numbers Of Lobster Graphs, Mark Anthony C. Tolentino, Luis Silvestre Jr, Richwell T. Chan Sim, Amir Jann Erikson Diga, Althea Julia R. Loyola

Mathematics Faculty Publications

No abstract provided.