Other Mathematics Commons^™

Subfitness In Distributive (Semi)Lattices, G. Bezhanishvili, J. Madden, M. A. Moshier, M. Tressl, Joanne Walters-Wayland

Mathematics, Physics, and Computer Science Faculty Articles and Research

We investigate whether the set of subfit elements of a distributive semilattice is an ideal. This question was raised by the second author at the BLAST conference in 2022. We show that in general it has a negative solution, however if the semilattice is a lattice, then the solution is positive. This is somewhat unexpected since, as we show, a semilattice is subfit if and only if so is its distributive lattice envelope.

Ornstein-Uhlenbeck Type Operators Induced By Some Geometric Structures On Complex Domains, Souheyl Jendoubu

Journal of Stochastic Analysis

No abstract provided.

Quantum Extensions Of The Exotic Laplacians And Associated Quantum Heat Semigroups, Luigi Accardi, Un Cig Ji, Kimiaki Saito

Journal of Stochastic Analysis

No abstract provided.

Preface, José Luis Da Silva, Un Cig Ji, Aurel Stan

Journal of Stochastic Analysis

No abstract provided.

Hypergraph Association With Lie Algebra Of Upper Triangular Matrices And Its Application To Wireless Networks, Supriya S

Theses and Dissertations

A hypergraph is a generalized graph characterized by edges spanning more than one vertices describing multiple relationships among them. It provides a mathematical framework for comprehending and learning about a wide range of real-world challenges. On the other side, the theory of non-associative algebras, such as Jordan, Octonions, Malcev, and Lie, has found significant impetus in recent years. These structures proved intriguing from an algebraic standpoint; they generated novel concepts and approaches that aided in solving specific classic algebraic problems, also progressing towards application.

A preeminent observation that galvanizes this thesis is that hypergraph association is still unexplored in Lie …

Weak Solutions Of Spdes In The Space Of Tempered Distributions, Suprio Bhar, Barun Sarkar

Journal of Stochastic Analysis

No abstract provided.

Revisiting The Hidden Symmetries Of The Multiplication Table, Zoheir Barka

Journal of Humanistic Mathematics

In previous work, we have explored some of the symmetries hidden in the multiplication tables of natural numbers and integers. In this article, we dive deeper into the hidden symmetries within the distribution of positive and negative integers. We also share various ideas to explore these symmetries in a classroom setting, encouraging active engagement and deeper understanding among students.

A Family Of Markov Chains, Schur Functions, And Exterior Powers, Philip Feinsilver, John P. Mcsorley

Journal of Stochastic Analysis

No abstract provided.

On An Asset Model Of Merton Type: Long-Term Observations In Financial Time-Series, Shuya Kanagawa, Narn-Rueih Shieh

Journal of Stochastic Analysis

No abstract provided.

Malliavin Calculus On The Clifford Algebra, Takayoshi Watanabe

Journal of Stochastic Analysis

No abstract provided.

Modelling Uncertain Volatility Using Quantum Stochastic Calculus: Unitary Vs Non-Unitary Time Evolution, Will Hicks

Journal of Stochastic Analysis

No abstract provided.

Gompertz Distribution On Time Scales, Wasiu Sule

Theses, Dissertations and Capstones

We shall investigate Gompertz dynamic equations within the context of time scales calculus, by exploring the mathematical foundations and applications of the Gompertz model, which is commonly used to describe growth phenomena in various fields such as biology and economics. This research seeks to analyze the Gompertz cumulative distribution functions (CDF) and probability density functions (PDF) across different time scales, including the real numbers R and integer multiples hN. Probability techniques will be used to derive the CDF and PDF associated with the Gompertz dynamic equations, and we will examine how varying the time scale impacts the characteristics …

A Numerical Method For Coefficient Reconstruction Of A Periodic Inverse Source Problem, Robert Ireri

Theses, Dissertations and Capstones

This thesis investigates a numerical method for solving the periodic inverse source problem governed by the Helmholtz equation. The problem involves reconstructing an unknown periodic source term from boundary measurements, which is inherently ill-posed. To address this challenge, we employ a quasi-reversibility method (QRM) combined with a basis function expansion to stabilize the inverse reconstruction. The forward problem is solved using the Lippmann-Schwinger equation, discretized via the trapezoidal rule, and the inverse problem is formulated as a constrained least-squares minimization. The discretized system is efficiently solved using sparse matrix techniques and regularization strategies. Numerical experiments demonstrate the robustness of the …

Discrete Fractional Gompertz Models, Rebecca Oduro

Theses, Dissertations and Capstones

This thesis explores the theory and application of discrete fractional Gompertz models—systems that integrate fractional difference operators into the classical Gompertz growth paradigm. By doing so, these models capture both discrete time steps and the long-range memory effects characteristic of fractional calculus. After outlining the fundamental notions of discrete calculus, discrete fractional sums and differences, and related special functions such as the discrete Mittag–Leffler function, we derive various fractional Gompertz-type equations. We prove the existence and uniqueness of solutions to these fractional difference equations, often employing discrete analogues of standard solution methods like variation of constants. We also investigate the …

Möbius Transformations And Hyperbolic Geometry In The Upper Half-Plane, Emma Bunch

Mahurin Honors College Capstone Experience/Thesis Projects

In this thesis, we discuss several properties of Möbius transformations and hyperbolic geometry, a type of non-Euclidean geometry, in the upper half-plane using tools of complex analysis. We begin with preliminaries for our work, comprising the stereographic projection, the representation of circles and lines in the complex plane, conformal maps, and a result on cross-products, which we include for further development. We proceed to Möbius transformations and discuss their properties, cross-ratios, and various mappings. We additionally provide useful calculations. Lastly, we conclude with the hyperbolic metric in the upper half-plane and explore hyperbolic distance, including its invariance under Möbius transformations. …

Examining Student Understanding Of Series Convergence Using Script Writing, Eduardo Torres Manzanarez

Mathematics Dissertations - Archive

This exploratory study investigates second-semester calculus students’ understanding of series convergence using both nonscripting and scripting-based tasks. Researchers recognize that students encounter difficulties with learning series, including series convergence, and that there is a need for more meaningful tasks that aid students’ learning of series. Script writing, used mainly with prospective mathematics teachers, can be used to explore mathematical understandings. Thus, this study examines how script writing, in the form of a scripting task, elicits students’ understanding of series convergence in contrast to nonscripting-based tasks to determine the potential of script writing in assessing this student understanding. We examine students’ …

A Bridge Too Low, John Adam

Mathematics & Statistics Faculty Publications

The article "A bridge too low" in the Physics Teacher journal discusses a low bridge near the River Greta in Keswick, England, with an arch shaped like a semiellipse. It presents questions about the maximum height a person of a certain height can walk under the bridge without hitting their head, the cross-sectional area of the arch, its eccentricity, and perimeter. The article also mentions the approximation by Indian mathematician Srinivasa Ramanujan for the perimeter of an ellipse and invites readers to find the answers online.

Strong Neighborhood-Prime Labelings Under Ordinary & Gaussian Integers, Micheal Arnal-Brown

Murray State Theses and Dissertations

This thesis introduces and studies the notion of a strong neighborhood-prime labeling, a strengthening of the neighborhood-prime labeling where the label 1 can be assigned to any vertex in a graph. We prove that several graph families—including paths, cycles (excluding those congruent to 2 modulo 4), caterpillars, helm graphs, closed helm graphs, gear graphs, and graphs with universal vertices—admit such labelings, and also provide results to more general classes of graphs. We extend this new labeling concept to the Gaussian integers using a spiral order- ing on Z[i] and define a Gaussian analogue of strongly neighborhood-primeness. To support this extension, …

Novel Generative And Language Model Architectures With Applications, Edison Mucllari

Theses and Dissertations--Mathematics

This dissertation investigates novel architectures to address fundamental challenges in machine learning, particularly focusing on transformer models, recurrent neural networks, GAN and continual learning and their applications in natural language processing and computer vision. We propose the Neumann-Cayley Gated Recurrent Unit (NC-GRU), which leverages a Neumann series-based Scaled Cayley transformation to maintain orthogonal weight matrices, effectively mitigating exploding gradients problems while improving long-term memory retention across prediction tasks. We demonstrate the practical applications of NC-GRU by implementing our proposed architecture into an autoencoder to derive neural molecular fingerprints. Building upon these advancements, we turn our attention to the transformer architecture, …

Mathematics And Determinism: Chaos, Quantum Mechanics, And The Limits Of Predictive Structure, Jackson T. Salumbides

CMC Senior Theses

This thesis examines the relationship between mathematics and determinism by analyzing how chaos theory, quantum mechanics, and formal mathematical limits challenge traditional conceptions of predictability and causal structure. Chaos theory shows that deterministic systems can exhibit practical unpredictability due to sensitivity to initial conditions. Quantum mechanics introduces probabilistic outcomes that complicate deterministic interpretation, though alternative frameworks such as Bohmian mechanics and superdeterminism attempt to restore determinism at conceptual cost. Additionally, results from mathematical logic, including Gödel’s incompleteness theorems and Turing’s undecidability, demonstrate intrinsic limitations on what can be deduced or computed, even in fully deterministic systems. By synthesizing these areas, …