Mathematics Commons^™

Metric And Dominant Metric Dimension Of Weakly Zero-Divisor Graphs, Adnan Hussain

Master of Science in Mathematics

This thesis investigates the metric dimension and dominant metric dimension of weakly zero-divisor graphs associated with commutative rings. The study focuses on determining resolving sets and dominating resolving sets for several classes of Γ(Z𝑛) graphs. These results establish connections between algebraic properties of rings and combinatorial characteristics of their associated graphs.

A Novel Bernstein Operational Matrix Approach For Tempered Fractional Differential Equations: Convergence And Stability Analysis, Jalal Al Hallak, Mohammed Alshbool, Ishak Hashim, Eddie Shahril Ismail, Shaher Momani

All Works

Tempered fractional differential equations (TFDEs) incorporate exponential decay into fractional operators to account for truncated memory and semi-long-range dependence in a variety of applications, including anomalous diffusion, viscoelasticity, transport phenomena, geophysical processes, and financial dynamics. In this work, a tempered fractional Bernstein method (TFBM) was proposed for the numerical solution of TFDEs involving Caputo-type derivatives. The proposed formulation combined a Bernstein polynomial approximation with an analytic representation of the Caputo–tempered fractional derivative through operational matrices. On this basis, two collocation-based variants were developed, namely, a Chebyshev-type method (TFBM-C) and a Legendre-type method (TFBM-L). For the linear setting, a convergence analysis …

Transformer-Based Language Models For Bitcoin Market Prediction And Interpretation, Erich Gozebina

Masters Theses

"In the context of a Master's thesis in applied mathematics, this work investigates compact transformer-based language models as an instrument for Bitcoin-related predictions and decision support. The work connects three topics: the structure of the Bitcoin system and its data, the mathematical and algorithmic foundations of deep autoregressive transformers, and the design of practical training pipelines for financial applications. On this foundation, a reproducible ETL pipeline for Bitcoin data is developed and two forecasting experiments are conducted with the compact language model nanochat. The first experiment approaches the prediction of next-day price movements through autoregressive next-token generation based on structured …

Machine Learning For Predictive Energy And Emissions Modeling Of Vehicles And Power Grids In The United States, S M Tanvir Faysal Alam Chowdhoury

Dissertations

The environmental benefits of electric vehicle (EV) adoption depend on more than replacing internal combustion engine vehicles with electric powertrains. EV adoption reshapes electricity demand, interacts with regional generation mixes, and influences travel behavior and congestion, creating a coupled transportation-energy system in which vehicle and power-plant emissions must be evaluated together. This dissertation develops machine-learning frameworks for predicting energy consumption and emissions from vehicles and power grids under rising EV adoption. The first component forecasts grid emissions from EV charging. Using simulation data from NREL's Cambium database, a Prophet-based time-series framework predicts carbon dioxide, nitrous oxide, and methane emission rates …

Multivariate Quantile Autoregression-Mixed Data Sampling (Mvqar-Midas) Modeling Of Cost Of Living And Supply Chain Dynamics In Canada., Patrick Gbolonyo

Theses and Dissertations (Comprehensive)

In recent years, the rising cost of living as a result of persistent inflationary pressures, disruptions in the global supply chains, and changes in the macroeconomic landscape has become a critical topic of discussion. To address this, we move beyond a mean-based framework and employ a quantile regression approach. This allows the persistence of each series and the transmis- sion of shocks between the Consumer Price Index (CPI) (the total CPI which is a percentage change over the past 12 months), the Interest Rate (IR)(the target for the overnight rate), the New Housing Price Index (NHPI), and high-frequency supply chain …

Strong Q-Analogues For Values Of The Dirichlet Beta Function, Ankush Goswami, Tim Huber

School of Mathematical & Statistical Sciences Faculty Publications

An infinite class of relations between modular forms is constructed that generalizes evaluations of the Dirichlet beta function at odd positive integers. The work is motivated by a base case appearing in Ramanujan’s Notebooks and a parallel construction for the Riemann zeta function. The identities are shown to be strong q-analogues by virtue of their reduction to the classical beta evaluations as 𝑞→1− and explicit evaluations at CM points for |𝑞|< 1. We also determine asymptotic formulas for the Fourier coefficients of the associated modular forms.

Optimal Quantization On Spherical Surfaces: Continuous And Discrete Models—A Beginner-Friendly Expository Study, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

This expository paper provides a unified and pedagogical introduction to optimal quantization for probability measures supported on spherical curves and discrete subsets ofthe sphere, emphasizing both continuous and discrete settings. We first present a detailedgeometric and analytical foundation for intrinsic quantization on the unit sphere, includingdefinitions of great and small circles, spherical triangles, geodesic distance, Slerp interpolation,the Fréchet mean, spherical Voronoi regions, centroid conditions, and quantizationdimensions. Building upon this framework, we develop explicit continuous and discretequantization models on spherical curves, namely great circles, small circles, and greatcircular arcs—supported by rigorous derivations and pedagogical exposition. For uniformcontinuous distributions, we compute optimal …

Exploring Caring Pedagogy Through Self-Study: A Mathematics Educator’S Journey, Kien H. Lim

Departmental Papers (Math)

This self-study examines my efforts to cultivate a positive learning environment in a capstone mathematics course for preservice middle school teachers. Motivated by earlier negative course evaluations and guided by heart-centered pedagogy, I explored how my beliefs, emotions, and instructional practices evolved as I sought to integrate kindness, foster mathematical thinking, and support students’ well-being. Drawing on dialogue transcripts, reflective journals, and reconstructed tutoring notes, I analyzed tensions between content coverage and relational pedagogy, as well as between deficit- and strength-based perspectives of students. Through critical dialogue and reflective inquiry, I gained deeper insight into my identity as a caring …

Creating A Positive Learning Environment In A Math Course For Preservice Teachers, Kien H. Lim, Hilda Y. Sotelo

Departmental Papers (Math)

This study examines how a mathematics instructor cultivated a positive learning environment in a synchronous online course for 23 preservice teachers. Guided by self-determination theory, growth mindset, and mathematical caring, the course integrated high-cognitive-demand tasks, collaborative problem solving, flexible policies, and motivational supports. Data sources included reflection logs (Likert-scale items and open-ended responses) and a focus group; the instructor’s reflexive self-study informed result interpretation. Wilcoxon signed-rank tests indicated significant gains in students’ sense of inclusion and trust, though some instructor- related ratings declined late in the semester. Qualitative findings emphasized students’ appreciation for flexibility, encouragement, and growth-oriented feedback. Despite time …

The Classical Limit In Geometric Quantization By Group Extension, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Physical systems as a rule are associated with a symmetry group. The group approach to geometric quantization makes use of this to introduce a quantization by means of group extension. This procedure is discussed and applied to a physical system whose group law has its origin with the Galilean group. The main intention is to investigate the classical limit and its relationship under this approach to geometric quantization. The classical quantization conditions are obtained based on a deeper foundation.

Computational Insights Into Orthotropic Fracture: Crack-Tip Fields In Strain-Limiting Materials Under Non-Uniform Loads, Saugata Ghosh, Dambaru Bhatta, S. M. Mallikarjunaiah

School of Mathematical & Statistical Sciences Faculty Publications

A finite element framework is presented for analyzing crack-tip phenomena in transversely isotropic, strain-limiting elastic materials. Mechanical response is characterized by an algebraically nonlinear constitutive model, relating stress to linearized strain. Non-physical strain singularities at the crack apex are mitigated, ensuring bounded strain magnitudes. This methodology significantly advances boundary value problem (BVP) formulation, especially for first-order approximate theories. For a transversely isotropic elastic solid with a crack, the governing equilibrium equation, derived from linear momentum balance and the nonlinear constitutive model, is reduced to a second-order, vector-valued, quasi-linear elliptic BVP. This BVP is solved using a robust numerical scheme combining …

Odd Colorings Of Graphs With Maximum Degree And Surface Conditions, Matthew Kyle

Graduate Studies Theses and Dissertations 2026

A proper vertex coloring of a graph is said to be odd if, for each vertex, there is a color that is present an odd number of times in its neighborhood. Introduced as a softening of other coloring problems, this problem has recently seen much research interest. It has been conjectured that all planar graphs are odd-5-colorable. Further research has suggested bounds for odd coloring numbers of graphs with different maximum degree conditions, different girths, and on different surfaces; we progress results in all of these areas. We improve an upper bound for odd coloring numbers of graphs of maximum …

Gain-Delay Decoupling In Human Stimulus Frequency Otoacoustic Emissions Reveals Constraints On Cochlear Nonlinear Amplification, Yoshita Sharma, Arturo Moleti, Renata Sisto, Teresa Botti, Hansapani Rodrigo, Sri Mishra

School of Mathematical & Statistical Sciences Faculty Publications

Purpose: The nonlinear cochlear amplifier, driven by outer hair cells, underlies the remarkable sensitivity and frequency selectivity of the mammalian auditory system. Stimulus frequency otoacoustic emissions (SFOAEs) provide a noninvasive window into these active cochlear processes, yet the relationship between emission gain and delay across stimulus levels remains incompletely understood. This study examined the level dependence of SFOAEs in normal-hearing human listeners to characterize cochlear nonlinear response properties. We tested how emission gain and delay vary with stimulus level and estimated the frequency of the apical–basal transition associated with the breakdown of the approximate local scaling symmetry.

Methods: SFOAEs were …

(R2151) Error Estimates Of Barycentric Lagrange Interpolation, Alvira Yawar, Swarnima Bahadur

Applications and Applied Mathematics: An International Journal (AAM)

Barycentric interpolation, which comes from Lagrange interpolation, is a useful method in numerical analysis. In this research paper, we explain how the barycentric interpolation formula is derived and discuss its features. We compare its stability and performance with the traditional Lagrange formula. First, we show how to get the barycentric formula from the Lagrange polynomial and present it as a rational function. We also provide an estimate of the error. Then, we use numerical examples to show that the barycentric formula is more stable and works better, especially when the degree of interpolation is high. Our results show that the …

Optimal Control Of Stochastic Systems: A Numerical Study Of The Stochastic Linear Quadratic Regulator Framework, Gülşen Orucova Büyüköz, Yaprak Güldoğan Dericioğlu, Tuğçem Partal

Mathematical Modelling and Numerical Simulation with Applications

Optimal control of stochastic linear systems is fundamental in control theory, with applications in robotics, finance, and engineering. The Stochastic Linear Quadratic Regulator (SLQR) derives optimal feedback laws via the Riccati equation but requires numerical discretization of the resulting stochastic dynamics. Despite extensive studies on numerical methods for stochastic differential equations, their performance within the SLQR framework remains insufficiently explored. This study compares two predictor–corrector schemes of different orders: the Order 1.0 Predictor-Corrector (PC) method and the Order 2.0 Weak PC method. A one-dimensional linear quadratic problem with a closed-form solution enables precise error evaluation against the analytical trajectory. Convergence …

Exploring The Metric Dimension Of The Graph Representing A Four-Ring Polycyclic Aromatic Hydrocarbon: Interstellar 1-Cyanopyrene, Andrei Matthew V. Robino, Sebastian Alex C. Traviña, Karl Benedict P. Narag, Mark Anthony B. Casao, Helix Raven C. Llanes, Azriel C. Alejo, Jonel C. Celamor

Sinaya: A Philippine Journal for Senior High School Teachers and Students

A graph's metric dimension is a parameter that denotes the minimum possible number of vertices in a subset that gives each vertex in the graph a unique representation. Despite extensive research on the metric dimension of polycyclic aromatic hydrocarbons (PAHs), there is currently no focused analysis on the metric basis and metric dimension of 1-cyanopyrene. In chemistry, graphs can be used to depict molecular structures. In this study, graph theory, specifically the concept of metric dimensions, is applied to the molecular structure of 1-cyanopyrene, which was detected in space for the first time in 2024. 1-cyanopyrene is a molecule made …

Integration Of Islamic Values In Mathematics Learning, Ai Mulya, Surya Faradiba

Jurnal Pendidikan Sains

This study aims to identify the integration of Islamic values in mathematics learning and its contribution to student character development. The method used is a systematic literature study by reviewing relevant accredited scientific articles. The results of the study indicate that the integration of Islamic values is carried out through the preparation of Islamic-context-based mathematics problems, linking concepts to verses of the Qur'an and hadith, the application of ethnomathematics with Islamic cultural nuances, and the introduction of Islamic economic concepts. The dominant values that emerge include honesty, responsibility, discipline, justice, and piety. These findings indicate that the integration of Islamic …

Locally Integral Involutive Po-Semigroups, José Gil-Férez, Peter Jipsen, Melissa Sugimoto

Mathematics, Physics, and Computer Science Faculty Articles and Research

We show that every locally integral involutive partially ordered semigroup (ipo-semigroup) A=(A,≤,⋅,∼,−), and in particular every locally integral involutive semiring, decomposes in a unique way into a family {Ap:p∈A+} of integral ipo-monoids, which we call its integral components. In the semiring case, the integral components are unital semirings. Moreover, we show that there is a family of monoid homomorphisms Φ={φpq:Ap→Aq:p≤q}, indexed over the positive cone (A+,≤), so that the structure of A can be recovered as a glueing ∫ΦAp of its integral components along Φ. Reciprocally, we give necessary and sufficient conditions so that the Płonka sum of any family …

An Exploratory Approach For Teaching Systems Of Linear Odes With Real Repeated Eigenvalues, Biyong Luo, Li Zhang

CODEE Journal

In this paper, we present a project that aims to pique students' interest and facilitate their engagement in learning. Students will be encouraged to take an active role in their learning of systems of linear ODEs with real repeated Eigenvalues. Through discussion and completion of a set of guided questions given in the project, students will gain a deeper understanding of the topic. Also, students will use the technology tool Bluffton App to draw solution trajectories in a phase plane, and then learn necessary skills for explaining the movements of the trajectories and their long term behaviors. This project may …

Integrable Discrete Massive Thirring Model, Junchao Chen, Bao-Feng Feng

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we are concerned with integrable semi- and fully discrete analogues of the massive Thirring model in light core coordinates. By using the Hirota’s bilinear approach and the Kadomtsev-Petviashvili (KP) hierarchy reduction method, we propose both the semi- and fully discrete massive Thirring models and construct their multi-bright soliton solutions.