Physical Sciences and Mathematics Commons^™

GröBner Bases With An Application To Tame Functions, Jessica D. Marconi

UNF Graduate Theses and Dissertations

Grobner bases are essential tools in algebraic geometry, used to simplify and solve systems of polynomial equations. These bases revolutionized computational methods in various branches of mathematics after being introduced in 1965 by Bruno Buchberger. This thesis explores the foundational concepts of Grobner bases, including their formation and properties. It also demonstrates their use in solving mathematical problems in algebraic geometry, including the ideal membership problem. As an application, we show how Grobner bases can be used to determine whether a polynomial mapping is tame. This concept is crucial for analyzing the topology near singular points and establishing whether a …

Improveing F-Beta Score In Classifying Shark Data Into Shark Behaviors, Ibrahim M. Ali

CGU Theses & Dissertations

One metric used to measure classification performance in machine learning is F-beta score. The objective in this thesis is to improve the average F-b score computed in classifying shark data into shark behaviors, namely; Resting, Swimming, Feeding, and Non-Directed Motion (NDM). Synthetic Minority Oversampling Technique (SMOTE) and Adaptive Synthetic Sampling (ADASYN) are utilized to balance the data, from which pre-processed Fast Fourier Transform (FFT), Walsh-Hadamard Transform (WHT), and Autocorrelation (AC) features are extracted then classified using Convolutional Neural Network (CNN) and K-Nearest Neighbors (K-NN). All the combinations of the two balancing techniques, the three feature types, and the two machine …

Examining Course Achievement In An Undergraduate Psychology Statistics Course Through The Lens Of Machine Learning Techniques, Sunny Nguyet Le

CGU Theses & Dissertations

The Introductory to Psychology Statistics course stands as a notable challenge for psychology majors, often acting as a gatekeeper course. This study embarks on two primary objectives using machine learning techniques: (1) to identify the determinants of overall course achievement, specifically course grade, and (2) to investigate the influence of statistics anxiety and statistics self-efficacy, when both are present, on overall course grade. Employing a machine-learning approach, both objectives were effectively addressed. The study involved the development of a self-reported questionnaire consisting of perceptions of statistics anxiety and statistics self-efficacy, along with other demographic and academic background variables. Conducted at …

The Independence Polynomial Of A Graph At −1, Phoebe Rose Zielonka

Theses, Dissertations and Culminating Projects

No abstract provided.

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.

Finding Maximal Cap Sizes For Quad Card Decks Using Share Strings, Oliver William Pawelek

Senior Projects Spring 2024

This project introduces the concept of share strings and how they can be used to figure out maximal cap sizes for different decks of the card game EvenQuads. We prove that all caps must map to a share string with respect to a basis and that if no share strings exist for cap size k in a given dimension d, then the maximal cap size of that dimension M (d) must be less than k. We prove the maximal cap sizes up to dimension 7 and show that there are at most 8 possible share strings for 19-caps of dimension …

Results On $K$-Covers In The Game Quads, Daniel Melvin Rose-Levine

Senior Projects Spring 2024

This project explores the $k$-cover conjecture for the game Quads. The conjecture states that for all $k\in\mathbb{N}$, there exists a $k$-cover if and only if $k = 2$ or $k = \frac{2^n-2}{6}$ for some odd $n\in\mathbb{N}$ with $n>1$. We show that if $k$ is one of these values, then there exists a $k$-cover. We discuss partial results in the other direction, i.e., that these are the only values of $k$ for which there exists a $k$-cover.

Symmetry And Structures Of Apn Functions And Sidon Sets, Darrion Thornburgh

Senior Projects Spring 2024

Let $\mathbb{F}_p^n$ be the $n$-dimensional vector space over $\mathbb{F}_p$. The graph $\mathcal{G}_F = \{ (x, F(x)) : x \in \mathbb{F}_p^n \}$ of a vectorial function $F \colon \mathbb{F}_p^n \to \mathbb{F}_p^m$ can have interesting combinatorial properties depending on varying cryptographic conditions on $F$. A vectorial Boolean function $F \colon \mathbb{F}_2^n \to \mathbb{F}_2^n$ is almost perfect nonlinear (APN) if there are at most $2$ solutions to the equation $F(x+a) + F(x) = b$ for all $a,b \in \mathbb{F}_2^n$ where $a \neq 0$. Equivalently, $F$ is APN if and only if $\mathcal{G}_F$ is a Sidon set, that is, a set in $\mathbb{F}_2^n$ where …

Can't We Just Use Computers? Initial Efforts On Technology-Enhanced Learning Of Operations Research In A Philippine University, Lester Hao, Jeric C. Briones, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Operations Research (OR) is a required course in any applied math program in the Philippines. It involves complex and computation-heavy algorithms to guide and improve decision-making in organizations and relevant contexts. Despite the advent of software that have automated the computations or the implementation of algorithms, the teaching and learning of OR may still be rife with procedures being performed manually by hand. In this paper, we report on our initial progress on a research project that aims to revise the OR syllabi in one Philippine university, by integrating more technological tools in the teaching and learning of OR for …

Utility In Time Description In Priority Best-Worst Discrete Choice Models: An Empirical Evaluation Using Flynn's Data, Sasanka Adikari, Norou Diawara

Mathematics & Statistics Faculty Publications

Discrete choice models (DCMs) are applied in many fields and in the statistical modelling of consumer behavior. This paper focuses on a form of choice experiment, best-worst scaling in discrete choice experiments (DCEs), and the transition probability of a choice of a consumer over time. The analysis was conducted by using simulated data (choice pairs) based on data from Flynn's (2007) 'Quality of Life Experiment'. Most of the traditional approaches assume the choice alternatives are mutually exclusive over time, which is a questionable assumption. We introduced a new copula-based model (CO-CUB) for the transition probability, which can handle the dependent …

Testing Informativeness Of Covariate-Induced Group Sizes In Clustered Data, Hasika K. Wickrama Senevirathne, Sandipan Duttta

Mathematics & Statistics Faculty Publications

Clustered data are a special type of correlated data where units within a cluster are correlated while units between different clusters are independent. The number of units in a cluster can be associated with that cluster’s outcome. This is called the informative cluster size (ICS), which is known to impact clustered data inference. However, when comparing the outcomes from multiple groups of units in clustered data, investigating ICS may not be enough. This is because the number of units belonging to a particular group in a cluster can be associated with the outcome from that group in that cluster, leading …

A Copula Discretization Of Time Series-Type Model For Examining Climate Data, Dimuthu Fernando, Olivia Atutey, Norou Diawara

Mathematics & Statistics Faculty Publications

The study presents a comparative analysis of climate data under two scenarios: a Gaussian copula marginal regression model for count time series data and a copula-based bivariate count time series model. These models, built after comprehensive simulations, offer adaptable autocorrelation structures considering the daily average temperature and humidity data observed at a regional airport in Mobile, AL.

Hyperparameter Estimation For Sparse Bayesian Learning Models, Feng Yu, Lixin Shen, Guohui Song

Mathematics & Statistics Faculty Publications

Sparse Bayesian learning (SBL) models are extensively used in signal processing and machine learning for promoting sparsity through hierarchical priors. The hyperparameters in SBL models are crucial for the model’s performance, but they are often difficult to estimate due to the nonconvexity and the high-dimensionality of the associated objective function. This paper presents a comprehensive framework for hyperparameter estimation in SBL models, encompassing well-known algorithms such as the expectation-maximization, MacKay, and convex bounding algorithms. These algorithms are cohesively interpreted within an alternating minimization and linearization (AML) paradigm, distinguished by their unique linearized surrogate functions. Additionally, a novel algorithm within the …

Implementasi Geometric Brownian Motion Dalam Memprediksi Harga Minyak Mentah Pada Masa Pandemi Covid-19, Feby Seru, Christian Dwi Suhendra, Agung Dwi Saputra

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Minyak mentah atau crude oil memiliki peranan yang vital dalam pertumbuhan ekonomi suatu negara, karena minyak mentah merupakan sumber energi penggerak perekonomian. Untuk menjaga kestabilan perekonomian, maka harga minyak mentah pada periode mendatang perlu diantisipasi dengan cara melakukan prediksi terhadap harga komoditas minyak mentah dunia. Salah satu model yang dapat digunakan untuk memprediksi harga minyak mentah dalam jangka waktu pendek adalah Geometric Brownian Motion (GBM). Tujuan dari penelitian ini adalah mengimplementasikan model GBM dalam memprediksi harga minyak mentah di masa pandemi Covid-19, serta mengukur keakuratan model tersebut. Pada penelitian ini, prediksi harga minyak menggunakan model GBM dilakukan dengan 50, 100, …

Analisa Kestabilan Bebas Kecanduan Pada Penyebaran Penggunaan Media Sosial Berdasarkan Model Searqs, Ratna Widayati, Intrada Reviladi

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Penelitian ini membahas mengenai model penyebaran penggunaan media sosial dan analisa kestabilan di sekitar titik ekuilibrium serta simulasi numeriknya dengan mengasumsikan populasi individu dibagi menjadi 5 kelas yaitu individu yang rentan terhadap kecanduan media sosial, individu yang menggunakan media sosial tetapi belum timbul kecanduan, individu kecanduan/adiktif media sosial, individu sembuh dari kecanduan media dan individu yang berhenti menggunakan media sosial. Model matematika yang digunakan adalah SEARQS dengan asumsi tidak ada kematian karena kecanduan media sosial. Selain itu, individu yang telah berhenti dari kecanduan media sosial, dapat kembali menjadi individu rentan. Permasalahan yang timbul dari penyebaran penggunaan media sosial yang berlebihan …

Analisis Sentimen Terhadap Kalimat Finansial Pada Fiqa Dan The Financial Phrasebank, Maximilianus Noel Brilianto, Yuliana Susanti, Etik Zukhronah

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Analisis sentimen atau bisa disebut juga opinion mining merupakan salah satu tugas utama dari Natural Language Processing (NLP) yang merupakan studi komputasi yang mempelajari tentang pendapat seseorang terhadap suatu topik bahasan atau entitas. Analisis dilakukan dengan algoritma machine learning (pembelajaran mesin) Naïve Bayes, Decision Tree, dan K-Nearest Neighbor dengan membagi sentimen ke dalam dua kategori sentimen yaitu sentimen positif dan sentimen negatif. Data analisis diambil dari Financial Opinion Mining and Question Answering (FiQA) dan The Financial PhraseBank yang terdiri dari 4.840 kalimat yang dipilih dari berbagai berita keuangan dan dianotasi oleh 16 annotator berbeda yang berpengalaman dalam domain finansial. Penelitian …

Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage

CODEE Journal

Many examples of 2x2 nonlinear systems in a first-course in ODE or a mathematical modeling class come from physics or biology. We present an example that comes from the business or management sciences, namely, the Bass diffusion model. We believe that students will appreciate this model because it does not require a lot of background material and it is used to analyze sales data and serve as a guide in pricing decisions for a single product. In this project, we create a 2x2 ODE system that is inspired by the Bass diffusion model; we call the resulting system the Bass …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

How To Intercept A High-Speed Rocket With A Pair Of Compasses And A Straightedge?, Yagub N. Aliyev

CODEE Journal

In this paper a nonlinear differential equation arising from an elementary geometry problem is discussed. This geometry problem was inspired by one of the proofs of the first remarkable limit discussed in a typical first semester undergraduate Calculus course. It is known that the involved differential equation can be reduced to Abel’s differential equation of the first kind. In this paper the problem was solved using an approximate geometric method which constructs a piecewise linear solution approximation for the curve. The compass tool of GeoGebra was extensively used for these constructions. At the end of the paper, some generalizations are …

Difference Of Facial Achromatic Numbers Between Two Triangular Embeddings Of A Graph, Kengo Enami, Yumiko Ohno

Theory and Applications of Graphs

A facial $3$-complete $k$-coloring of a triangulation $G$ on a surface is a vertex $k$-coloring such that every triple of $k$-colors appears on the boundary of some face of $G$. The facial $3$-achromatic number $\psi_3(G)$ of $G$ is the maximum integer $k$ such that $G$ has a facial $3$-complete $k$-coloring. This notion is an expansion of the complete coloring, that is, a proper vertex coloring of a graph such that every pair of colors appears on the ends of some edge.

For two triangulations $G$ and $G'$ on a surface, $\psi_3(G)$ may not be equal to $\psi_3(G')$ even if $G$ …

The Ricci Curvature On Simplicial Complexes, Taiki Yamada

Theory and Applications of Graphs

We define the Ricci curvature on simplicial complexes modifying the definition of the Ricci curvature on graphs, and prove upper and lower bounds of the Ricci curvature. These properties are generalizations of previous studies. Moreover, we obtain an estimate of the eigenvalues of the Laplacian on simplicial complexes by the Ricci curvature.

Social Justice Mathematics: Classroom Practices That Give Students Rigor While Building Agency, Emily Marquise

Masters Theses

The purpose of this study is to examine the impact of a social justice approach to mathematics instruction. While many students have math aversion, students in low socioeconomic communities exhibit this to a higher degree putting them at a disadvantage as they progress through their educational career. More than 3.4 million K-12 students in the United States come from families that earn less than the median income yet achieve scores in the top percentile (Wyner et al., 2007). This raises the question of why so many students in low-socioeconomic settings are not given rigorous content that will keep them competitive …

Building Community, Competency, And Creativity In Calculus 2: Summary Of A Pilot Year Of Project Implementation, Jennifer Beichman, Candice R. Price

Feminist Pedagogy

In light of the COVID-19 pandemic, instructional modes at our institution moved to fully online and remote, then fully online but on campus, and back to in-person learning in fall 2021. To combat perceived issues in student engagement, we piloted using group projects in place of exams at the natural content break points in Calculus 2.

Limit Distributions Of Products Of Independent And Identically Distributed Random 2 × 2 Stochastic Matrices: A Treatment With The Reciprocal Of The Golden Ratio, Santanu Chakraborty

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Consider a sequence (Xn)n≥1 of i.i.d. 2×2 stochastic matrices with each Xn distributed as μ. This μ is described as follows. Let (Cn,Dn)T denote the first column of Xn and for a given real r with 012 is very challenging. Considering the extreme nontriviality of this case, we stick to a very special such r, namely, r=√5−12 (the reciprocal of the golden ratio), briefly mention the challenges in this nontrivial case, and completely identify λ for a very special situation.

An Empirical Study Of Machine Learning Techniques For Accurate Stock Price Forecasting, Daniel Paliulis, Hari Patchigolla

Honors Scholar Theses

This paper presents a comprehensive approach to predicting future stock prices of companies using machine learning and time series analysis. The research problem is centered around addressing the complexity and emotion-driven nature of stock investment decisions. To create an objective determinant in stock decisions, we propose a machine learning model utilizing time series data from major companies, including Amazon, Apple, Google, Nvidia, Meta, Tesla, Salesforce, Intel, and Microsoft. We explore the use of Long Short-Term Memory (LSTM) neural networks, to capture the temporal dynamics of stock prices. These models are designed to process sequential data, maintaining short term and long …

Toughness Of Recursively Partitionable Graphs, Calum Buchanan, Brandon Du Preez, K. E. Perry, Puck Rombach

Theory and Applications of Graphs

A simple graph G = (V,E) on n vertices is said to be recursively partitionable (RP) if G ≃ K1, or if G is connected and satisfies the following recursive property: for every integer partition a₁, a₂, . . . , a_k of n, there is a partition {A₁,A₂, . . . ,A_k} of V such that each |A_i| = a_i, and each induced subgraph G[A_i] is RP (1 ≤ i ≤ k). We show that if S is a …

Investigating Bremsstrahlung Radiation In Tungsten Targets: A Geant4 Simulation Study, Sindor Ashurov, Satimboy Palvanov, Abror Tuymuradov, Dilmurod Tuymurodov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Bremsstrahlung radiation, a pivotal phenomenon in high-energy physics, presents numerous applications and implications in both theoretical studies and practical scenarios. This article explores the Bremsstrahlung radiation of electrons in tungsten (W) targets of varying widths subjected to different energy beams using GEANT4 simulations. By systematically altering the target widths and electron beam energies, we assess the corresponding effects on radiation yield and spectrum. The findings contribute to a deeper understanding of Bremsstrahlung processes in high-$Z$ materials and offer valuable insights for applications ranging from radiation therapy to materials analysis.

Holomorphic Motion Of Julia Sets Of Polynomial-Like Maps, And Continuity Of Compact Sets And Their Green Functions, Bazarbaev Sardor, Sobir Boymurodov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we study holomorphic motion of Julia sets of polynomial-like maps. In particular, we prove that in the stable family of polynomial-like maps if all the continuos functions move continuously by parameter then the Julia sets move holomorphically. Moreover, we also study the relation between continuity of regular compact sets and their Green functions.

Translation-Invariant Gibbs Measures For Potts Model With Competing Interactions With A Countable Set Of Spin Values On Cayley Tree, Zarinabonu Mustafoyeva

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the present paper we consider of an infinite system of functional equations for the Potts model with competing interactions and countable spin values Φ = {0, 1, ..., } on a Cayley tree of order k. We study translation-invariant Gibbs measures that gives the description of the solutions of some infinite system of equations. For any k ≥ 1 and any fixed probability measure ν we show that the set of translation-invariant splitting Gibbs measures contains one and two points for odd k and even k, respectively, independently on parameters of the Potts model with a countable …

An Analogue Of Hartogs Lemma For Separately Harmonic Functions With Variable Radius Of Harmonicity, Sevdiyor Imomkulov, Sultanbay Abdikadirov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this note we prove that if a function u(x,y) is separately harmonic in a domain D × V_r = D × {y∈ℝ²:|y|<r,  r>1} ⊂ ℝⁿ × ℝ² and for each fixed point x⁰ ∈ D the function u(x⁰,y) of variable y continues harmonically into the great circle {y∈ℝ²:|y|<R(x⁰),  R(x⁰)>r}, then it continues harmonically into a domain {(x …