Mathematics Commons^™

Newton's Electromagnetic Bucket, Angelina Georg

Mathematics Colloquium Series

We examine Newton’s thought experiment: Newton’s Bucket. We replace the bucket with a charged infinite cylindrical shell in order to extend the analysis to an electromagnetic one. We show that Newton’s mechanical conclusions are equally valid electromagnetically.

Exclusion Tests For Approximating All Solutions Of Nonlinear Equations, Yasmeen Omar Hamida

Thesis/ Dissertation Defenses

The exclusion test is a mathematical technique used to isolate and approximate solutions of nonlinear equations within a defined interval. This thesis introduces a new exclusion test-based approach that aims to accelerate convergence to the zeros of nonlinear equations within a compact domain. By selecting Taylor, series, and Lipschitz test and solving nonlinear equations, the proposed method substantially reduces the number of subintervals necessary for accurate approximation. The primary contribution of this research is the development of a more efficient algorithm, which significantly improves the speed of convergence. These findings have meaningful implications for the field of numerical analysis, presenting …

On Fractional Dunkl-Type Laplacian, Saba Ibrahim Aldan

Thesis/ Dissertation Defenses

This thesis provides a comprehensive study of the fractional Dunkl-type Laplacian operator (—llxllΔ_k) ^σ for 0 < σ < 1, focusing on four key equivalent characterizations: the heat semigroup approach, the pointwise formulation, the spherical mean representation, and through an extension theorem. A significant part of the thesis is devoted to the extension theorem, where, following the approach of Caffarelli and Silvestre for the Euclidean Laplacian, we prove that (—llxllΔ_k) ^σ can be characterized as an operator that maps a Dirichlet boundary condition to a Neumann-type condition via an extension PDE problem. Further, a Poisson formula for the extension was established. These four characterizations provide distinct perspectives on the operator llxllΔ_k, extending Euclidean Laplacian results to include reflection symmetries and revealing connections between the fractional operator (—llxllΔ_k) ^σ, harmonic analysis, and applications in mathematical physics and PDEs.

Shevtsov: Teaching Modeling To First-Year Life Science Students: The Ucsc Experience, Martin H. Weissman

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Opioid Addiction In Hand Surgery Patients, Eli Goldwyn, Grace Bowman, Kathryn Montovan, Julie Blackwood

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Identifiability And Convergence Behavior For Markov Chain Monte Carlo Using Multivariate Probit Models, Xiao Zhang

Michigan Tech Publications

Multivariate probit models have been popularly utilized to analysis multivariate ordinal data. However, the identifiable multivariate probit models entail the covariance matrix for the underlying multivariate normal variables to be a correlation matrix, which brings a rigorous task to conduct efficient statistical analysis. Parameter expansion to make the identifiable model to be non-identifiable has been inevitably explored. However, the effect of the expanded parameters on the convergence of Markov chain Monte Carlo (MCMC) is seldomly investigated; in addition, the comparison of MCMC developed based on the identifiable model and that based on the non-identifiable model is hardly ever explored, especially …

Telu Activation Function For Fast And Stable Deep Learning, Alfredo Fernandez

USF Tampa Graduate Theses and Dissertations

We propose the Hyperbolic Tangent Exponential Linear Unit (TeLU), a neural network hidden activation function defined as $TeLU(x)=x \cdot tanh(e^x)$. TeLU’s design is grounded in the core principles of key activation functions, achieving strong convergence by closely approximating the identity function in its active region while effectively mitigating the vanishing gradient problem in its saturating region. Its simple formulation enhances computational efficiency, leading to improvements in scalability and convergence speed. Unlike many modern activation functions, TeLU seamlessly combines the simplicity and effectiveness of ReLU with the smoothness and analytic properties essential for learning stability in deep neural networks. TeLU’s ability …

Preservative Splitting Numerical Schemes For Solving A Variable Coefficient Quenching Problem, Julienne Kabre

Mathematics Colloquium Series

Physical processes are modelled mathematically using Partial Differential Equations(PDEs). An insight into these processes requires solving those PDEs. Since these equations most of the time do not have analytical solutions, delicate numerical methods are required. In this talk, we will explore the numerical solution of the two-dimensional quenching type nonlinear reaction-diffusion problem via dimensional splitting. The differential equation possesses a variable diffusion coefficient and a nonlinear forcing term that leads to a strong quenching singularity. Our current investigation focuses on the construction of a finite difference implementation of a Peaceman- Rachford and a Glowinski-Le Tallec splitting procedures for solving the …

New Fueter-Type Variables Associated To The Global Operator In The Quaternionic Case, Daniel Alpay, Kamal Diki, Mihaela Vajiac

Mathematics, Physics, and Computer Science Faculty Articles and Research

The purpose of this paper is to develop a new theory of three non-commuting quaternionic variables and its related Schur analysis theory for a modified version of the quaternionic global operator.

Using Academic Librarians And The Academic Library: Survey Results From Mathematics Faculty In United States And Canada, Elizabeth Novosel, Daniel G. Kipnis, Jenni Burke, Rasitha Jayesekera

Libraries Scholarship

Presented at STEM Librarian South Conference, November 6, 2024

Despite our diligent outreach and relationship-building efforts, certain groups of faculty within STEM disciplines remain hesitant to engage with academic librarians and utilize library resources. This challenge raises a critical question: How can librarians effectively support a department when faculty members are unresponsive?

Our research team, composed of three frustrated mathematics librarians and one mathematics faculty member, recognized the need for a fresh approach. Mathematics, a department known for its independence, has received limited attention in scholarly Library and Information Science (LIS) literature. To address this gap, we embarked on a …

On The Work Of Cartan And Münzner On Isoparametric Hypersurfaces, Thomas E. Cecil, Patrick J. Ryan

Mathematics and Computer Science Department Faculty Scholarship

A hypersurface Mⁿ in a real space form Rⁿ⁺¹, Sⁿ⁺¹, or Hⁿ⁺¹ is isoparametric if it has constant principal curvatures. This paper is a survey of the fundamental work of Cartan and Münzner on the theory of isoparametric hypersurfaces in real space forms, in particular, spheres. This work is contained in four papers of Cartan [3]–[6] published during the period 1938–1940, and two papers of Münzner [47]–[48] that were published in preprint form in the early 1970’s, and as journal articles in 1980–1981. These papers of Cartan and Münzner have been the …

Smooth And Proper Maps With Respect To A Fibration, Mathieu Anel, Jonathan Weinberger

Engineering Faculty Articles and Research

This paper explain how the geometric notions of local contractibility and properness are related to the Σ-types and Π-types constructors of dependent type theory. We shall see how every Grothendieck fibration comes canonically with such a pair of notions—called smooth and proper maps—and how this recovers the previous examples and many more. This paper uses category theory to reveal a common structure between geometry and logic, with the hope that the parallel will be beneficial to both fields. The style is mostly expository, and the main results are proved in external references.

Purely Pseudo-Anosov Subgroups Of The Genus Two Handlebody Group, Marissa E. Chesser, Christiopher J. Leininger

Faculty Work Comprehensive List

We prove that finitely generated, purely pseudo-Anosov subgroups of the genus 2 handlebody group are convex cocompact.

Quantization Dimensions For The Bi-Lipschitz Recurrent Iterated Function Systems, Amit Priyadarshi, Mrinal Kanti Roychowdhury, Manuj Verma

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, the quantization dimensions of the Borel probability measures supported on the limit sets of the bi-Lipschitz recurrent iterated function systems under the strong open set condition in terms of the spectral radius have been estimated.

Non-Vanishing Modulo P Of Hecke L-Values Over Imaginary Quadratic Fields, Debanjana Kundu, Antonio Lei

School of Mathematical & Statistical Sciences Faculty Publications

Let p and q be two distinct odd primes. Let K be an imaginary quadratic field over which p and q are both split. Let Ψ be a Hecke character over K of infinity type (k, j) with 0 ≤ − j < k. Under certain technical hypotheses, we show that for a Zariski dense set of finite-order characters κ over K which factor through the Z2q -extension of K, the p-adic valuation of the algebraic part of the L-value L(κΨ¯¯¯¯¯¯¯,k+j) is a constant independent of κ. In addition, when j = 0 and certain technical hypothesis holds, this constant is zero.

Math Is Good, Elisa Benthem

Student Work

"There are endless ways we can explore creation, each revealing something wonderfully distinct."

Posting about ­­­­­­­­the beauty of mathematics from In All Things, an online hub that offers insight into maintaining and faithful and orthodox Reformed Christian worldview while fearlessly engaging in every aspect of contemporary life – until all is made new.

Math is Good

Book V Of The Mathematical Collection Of Pappus Of Alexandria, Translated By John B. Little, Pappus Of Alexandria, John B. Little

Holy Cross Bookshelf

John B. Little is the translator.

Book V of the Mathematical Collection is addressed to a certain Megethion, about whom we know nothing else. From the context he may have been a student or patron of Pappus in Alexandria. In a heading at the start, Pappus says that the general theme will be comparisons between different geometric figures. The overall structure brings interesting relations and connections to the fore. The book opens with a very well-known and charming discussion of how the importance of such comparisons can be seen by considering the structures built by non-human creatures such as bees. …

Magpy: A Python Package For Magmas, Skylar Korf

All NMU Master's Theses

There exist a multitude of computational tools available to mathematicians, such as interactive and automated theorem provers, finite counter-example generators, and computer algebra systems, most of which have a complicated installation process, unintuitive syntax, a lack of comprehensiveness for mathematical structures, or some combination of these. Computer algebra systems are indispensable tools due to their capacity for creating mathematical objects and performing computations on them. However, there is a lack of computational resources that focus on dealing with explicit examples, and extracting the properties thereof, especially for the most basic algebraic structures. Here, we will dive into several prominent computer …

Why Geological Angular Unconformity Is Usually Horizontal: A Geometric Explanation, Julio C. Urenda, Aaron Velasco, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In several locations, geologists have observed the presence of two differently oriented rock masses, one horizonal (or almost horizontal) and the other somewhat inclined; this phenomenon is known as angular unconformity. Based on the detailed analysis of geophysical processes, geologists conclude that usually, horizontal rock masses are much newer. This is known as the law of original horizontality. From the fundamental viewpoint, it is desirable to take into account that geophysics is a developing science, its models get modified and adjusted as time progresses. It is therefore desirable to come up with an explanation of this phenomenon that would be …

Codes From Incidence Matrices Of Hypergraphs, Sudipta Mallik, Bahattin Yildiz

Mathematics Faculty Research

Binary codes are constructed from incidence matrices of hypergraphs. A combinatorial description is given for the minimum distances of such codes via a combinatorial tool called “eonv”. This combinatorial approach provides a faster alternative method of finding the minimum distance, which is known to be a hard problem. This is demonstrated on several classes of codes from hypergraphs. In particular the “eonv” method is used to prove that the minimum distance of codes from incidence matrices of complete 3-partite 3-uniform hypergraphs with partite set size of n is n2. A lower bound on the minimum distances of codes from …

A Complete Invariant For Shift Equivalence For Boolean Matrices And Finite Relations, Ethan Akin, Marian Mrozek, Mateusz Przybylski, Jim Wiseman

Mathematics and Statistics Faculty Research & Creative Works

We give a complete invariant for shift equivalence for Boolean matrices (equivalently finite relations), in terms of the period, the induced partial order on recurrent components, and the cohomology class of the relation on those components.

Exploring The Human Side Of Math, Mike Janssen

Faculty Work Comprehensive List

"Abstract mathematics is an important way to better understand and marvel at the beauty and intricacy of God’s creation."

Posting about ­­­­­­­­experiences in math research from In All Things, an online hub that offers insight into maintaining and faithful and orthodox Reformed Christian worldview while fearlessly engaging in every aspect of contemporary life – until all is made new.

Exploring the Human Side of Math

Exclusion Tests For Approximating All Solutions Of Nonlinear Equations, Yasmeen Omar Hamida

Theses

The exclusion test is a mathematical technique used to isolate and approximate the solutions of nonlinear equations within a specified interval. This thesis aims to construct a new test leveraging the principles of the exclusion test to achieve faster convergence to the zeros of any given interval within a compact domain. By selecting an alternative objective function and employing nonlinear equations, the proposed method significantly reduces the number of subintervals required for accurate approximation. The key finding of this research is the development of a more efficient algorithm that enhances the speed of convergence. The implications of these findings are …

Algebraic Structures On Parallelizable Manifolds, Sergey Grigorian

School of Mathematical & Statistical Sciences Faculty Publications

In this paper we explore algebraic and geometric structures that arise on parallelizable manifolds. Given a parallelizable manifold L , there exists a global trivialization of the tangent bundle, which defines a map ρ p : l ⟶ T p L for each point p ∈ L , where l is some vector space. This allows us to define a particular class of vector fields, known as fundamental vector fields, that correspond to each element of l . Furthermore, flows of these vector fields give rise to a product between elements of l and L , which in turn induces …

The Near Normality Of The Commutant Of A Moufang Loop, Evan Phillips

All NMU Master's Theses

We investigate conditions under which the commutant of a Moufang loop is normal and related topics. We begin by giving relevant background on Moufang loops and normality. We then prove a theorem showing how close the commutant is to being normal: cR(x, y)R(x, y)R(x, y) = c. We then prove a couple of theorems emphasizing the importance of cubes in Moufang loops. Finally we prove a decomposition theorem for the multiplication group of a finite commutative Moufang loop.

Topology And The Quantum Hall Effects, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

The quantum Hall effects are an excellent example of physical systems where topology plays a major role in accounting for the physical observations. It is shown that the conductivity that appears in the quantum Hall effect is a topological invariant. It is illustrated how a fiber bundle over a torus can be constructed producing a geometry in which the system can be referred. The fractional effect can be studied by introducing homotopy and associated braid groups. Filling fractions can be obtained as a consequence of commensurability relations.

The Implementation Of Stream In Mathematics Classrooms In Abu Dhabi Primary Schools: Prospects, Priorities, Processes, And Problems, Nadeia Rashed Alalawi

Dissertations

This study shed light on implementing science, technology, reading and writing, engineering, art, and mathematics (STREAM) in mathematics classrooms in Abu Dhabi primary schools. The study aimed to explore mathematics teachers’ views on the prospects, priorities, processes, and problems of the implementation of STREAM in their classrooms. The study employed qualitative methods to collect and analyze data to support the findings using interviews, classroom observations, and document analysis. Fifteen in-service mathematics teachers were interviewed to explore their views about the application of STREAM in their classrooms regarding prospects, priorities, processes, and problems (4 Ps). Then, three of them were observed …

On Fractional Dunkl-Type Laplacian, Saba Ibrahim Aldan

Theses

This thesis presents a comprehensive study of the fractional Dunkl-type Laplacian operator (−∥x∥ Δ𝑘)^σ for 0<σ<1, through four equivalent key characterizations: the heat semigroup characterization, the pointwise characterization, the spherical mean characterization, and through an extension theorem. These characterizations offer different perspectives on the operator ∥x∥Δ_𝑘, generalizing known results for the Euclidean Laplace operator by incorporating reflection symmetries, making it highly relevant in the harmonic analysis of root systems.

By exploring these characterizations, the thesis highlights the deep connections between the fractional operator (−∥x∥Δ_𝑘)^σ and harmonic analysis, as well as its broader applicability in mathematical physics and partial differential equations.

Substitution Tilings With Transcendental Inflation Factor, Dirk Frettlöh, Alexey Garber, Neil Mañibo

School of Mathematical & Statistical Sciences Faculty Publications

For any λ>2, we construct a substitution on an infinite alphabet which gives rise to a substitution tiling with inflation factor λ. In particular, we obtain the first class of examples of substitutive systems with transcendental inflation factors. We also show that both the associated subshift and tiling dynamical systems are strictly ergodic, which is related to the quasicompactness of the underlying substitution operator.

Cp Decomposition Initialization Schemes For Speeding-Up Of Convolutional Neural Networks, Mollee M. Swift

LSU Master's Theses

While machine learning and convolutional neural networks (CNNs) are making strides, a persistent effort remains to optimize classification techniques and target redundancies from a large number of parameters naturally present in CNNs. While CNNs have become more accessible across machine learning, the aim is to make their use optimal for central processing unit (CPU) schemes with varying degrees of computational power. Tensor decomposition methods, specifically canonical polyadic (CP) decomposition, look to reduce parameters by compressing specific layers in a CNN. However, they have certain inconsistencies, and their full potential remains untouched as decomposition research is endless, with many facets one …