Mathematics Commons^™

New Examples Of Self-Dual Near-Extremal Ternary Codes Of Length 48 Derived From 2-(47,23,11) Designs, Sanja Rukavina, Vladimir Tonchev

Michigan Tech Publications, Part 2

In a recent paper (Araya and Harada, 2023), Araya and Harada gave examples of self-dual near-extremal ternary codes of length 48 for 145 distinct values of the number A12 of codewords of minimum weight 12, and raised the question about the existence of codes for other values of A12. In this note, we use symmetric 2-(47,23,11) designs with an automorphism group of order 6 to construct self-dual near-extremal ternary codes of length 48 for 150 new values of A12.

Higher Diffeology Theory, Emilio Minichiello

Dissertations, Theses, and Capstone Projects

Finite dimensional smooth manifolds have been studied for hundreds of years, and a massive theory has been built around them. However, modern mathematicians and physicists are commonly dealing with objects outside the purview of classical differential geometry, such as orbifolds and loop spaces. Diffeology is a new framework for dealing with such generalized smooth spaces. This theory (whose development started in earnest in the 1980s) has started to catch on amongst the wider mathematical community, thanks to its simplicity and power, but it is not the only approach to dealing with generalized smooth spaces. Higher topos theory is another such …

Bifurcations And Resultants For Rational Maps And Dynatomic Modular Curves In Positive Characteristic, Colette Lapointe

Dissertations, Theses, and Capstone Projects

No abstract provided.

Sigma_N-Correct Forcing Axioms, Benjamin P. Goodman

Dissertations, Theses, and Capstone Projects

I introduce a new family of axioms extending ZFC set theory, the Sigma_n-correct forcing axioms. These assert roughly that whenever a forcing name a' can be forced by a poset in some forcing class Gamma to have some Sigma_n property phi which is provably preserved by all further forcing in Gamma, then a' reflects to some small name such that there is already in V a filter which interprets that small name so that phi holds. Sigma_1-correct forcing axioms turn out to be equivalent to classical forcing axioms, while Sigma_2-correct forcing axioms for Sigma_2-definable forcing classes are consistent relative to …

Explicit Composition Identities For Higher Composition Laws In The Quadratic Case, Ajith A. Nair

Dissertations, Theses, and Capstone Projects

The theory of Gauss composition of integer binary quadratic forms provides a very useful way to compute the structure of ideal class groups in quadratic number fields. In addition to that, Gauss composition is also important in the problem of representations of integers by binary quadratic forms. In 2001, Bhargava discovered a new approach to Gauss composition which uses 2x2x2 integer cubes, and he proved a composition law for such cubes. Furthermore, from the higher composition law on cubes, he derived four new higher composition laws on the following spaces - 1) binary cubic forms, 2) pairs of binary quadratic …

Parabolic And Non-Parabolic Surfaces With Small Or Large End Spaces Via Fenchel-Nielsen Parameters, Michael Antony Pandazis

Dissertations, Theses, and Capstone Projects

We consider conditions on the Fenchel-Nielsen parameters of a Riemann surface X that determine whether or not a surface X is parabolic. Fix a geodesic pants decomposition of a surface and call the boundary geodesics in the decomposition cuffs. For a zero or half-twist flute surface, we prove that parabolicity is equivalent to the surface having a covering group of the first kind. Using that result, we give necessary and sufficient conditions on the Fenchel-Nielsen parameters of a half-twist flute surface X with increasing cuff lengths such that X is parabolic. As an application, we determine whether or not each …

Me And Mathematics: “Doing What You’Re Talking About”: In Dialogue With My Family, Eden Morris

Dissertations, Theses, and Capstone Projects

This paper is a philosophically oriented accompaniment to my audio project (accessible through the following link: https://cuny.manifoldapp.org/projects/me-and-mathematics). Working together, the paper and audio collages form a call to action and a resource. My primary finding is the importance of doing what you’re talking about or exploring and implementing your ideas experientially. Doing what you’re talking about is important for effective teaching/learning and feeling in line with oneself. This working concept came to my attention during my research conversation with my oldest living relative, and then, again, with my youngest (non-baby) relative. This doing what you’re talking about is a way …

A Thesis, Or Digressions On Sculptural Practice: In Which, Concepts & Influences Thereof Are Explained, Set Forth, Catalogued, Or Divulged By Way Of Commentaries To A Poem, First Conceived By The Artist, Fed Through Chatg.P.T., And Re-Edited By The Artist, To Which Are Added, Annotated References, Impressions And Ruminations Thereof, Also Including Private Thoughts & Personal Accounts Of The Artist, Jaimie An

Masters Theses

This thesis is an exercise in, perhaps a futile, attempt to trace just some of the ideas, stories, and musings I might meander through in my process. It’s not quite a map, nor is it a neat catalogue; it is a haphazard collection of tickets and receipts from a travel abroad, carelessly tossed in a carry-on, only to be stashed upon returning home. These ideas are derived from much greater thinkers and authors than myself; I am a mere collector or a translator, if that, and not a very good one, for much is lost. I do not claim comprehensive …

Linear Ode Systems Having A Fundamental Matrix Of The Form F(Mt), Kevin L. Shirley, Vicky W. Klima

CODEE Journal

We interweave scaffolded problem statements with exposition and examples to support the reader as they explore specific linear systems of differential equations with variable coefficients, $\vec{x}'(t)=A(t)\vec{x}(t)$ and initial value $\vec{x}(0)$. We begin with a constant $n\times n$ matrix $M$ and a real or complex-valued function $f$, analytic at the eigenvalues of $M$ with $f(0) = 1$, and construct a linear system of differential equations with solutions $x(t)=f(Mt)\vec{x}(0)$, where $t$ is a parameter in some interval including zero. In general, the solutions to the resulting non-autonomous system are more difficult to analyze than solutions to the constant coefficient case. However, some …

A Novel Consumer-Centric Metric For Evaluating Hearing Device Audio Performance, Vinaya Manchaiah, Steve Taddei, Abram Bailey, De Wet Swanepoel, Hansapani Rodrigo

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Background and Aim: The emergence of direct-to-consumer hearing devices has introduced confusion in making appropriate choices, highlighting the need for users to be well-informed for optimal device selection. Currently, no established metric offers insights into the sound performance of these devices. This study aimed to introduce and assess a novel consumer-centric metric (i.e., SoundScore) for hearing device audio performance.

Method: The SoundScore metric was created based on five dimensions of hearing device audio performance (i.e., speech benefit in quiet and moderate, speech benefit in loud, own voice perception, feedback control, streamed music sound quality). Tests were conducted under lab conditions …

Numerical Simulations For A Non-Newtonian Power Law Fluids In Oscillating Lid-Driven Square Cavity, Nusrat Rehman, Rashid Mahmood, Sara Fatima

International Journal of Emerging Multidisciplinaries: Mathematics

Fluid flows in cavities has been one of the important benchmark problems in Computational Fluid Dynamics to test and validate open source and commercial codes. Fluid mixing plays a pivotal role in Chemical and Process engineering research. Cavities have emerged as valuable assets in facilitating mixing processes. Enhancement of mixing within cavities can be achieved through various means, including the installation of baffles within the domain, utilization of stirrers, and implementation of an oscillating lid. We focus on oscillating lid driven flows in cavities in this thesis including the non-Newtonian fluid (Power law model). Numerical simulations are performed for top …

Differential Equations For Modeling Pathways Leading To Diabetes Onset, Viktoria Savatorova, Aleksei Talonov

CODEE Journal

This paper presents a mathematical model that explains potential pathways leading to diabetes onset. By utilizing a system of nonlinear differential equations to describe the dynamics of the glucose regulatory system, the model can serve as a pedagogical tool for teaching and learning differential equations, dynamical systems, mathematical modeling, and introduction to biomathematics. Within this framework, students can analyze equilibrium solutions, investigate stability, assess parameter sensitivity, and explore the potential for bifurcations. Theoretical analysis is complemented by illustrative numerical examples. Instructors have the flexibility to adapt and incorporate suggested activities according to their teaching preferences and objectives.

Weakly Pseudo Primary 2-Absorbing Submodules, Omar Hisham Taha, Marrwa Abdulla Salih

Al-Bahir Journal for Engineering and Pure Sciences

Let be a commutative ring with identity. In this paper, we introduce the notion of a weakly pseudo primary 2-absorbing sub-module as a generalization of a 2-absorbing sub-module and a pseudo 2-absorbing sub-module. Moreover, we give many basic properties, examples, and characterizations of these notions.

Constructible Sandwich Cut, Philip A. Son

FIU Undergraduate Research Journal

In mathematical measure theory, the “Ham-Sandwich” theorem states that any n objects in an n-dimensional Euclidean space can be simultaneously divided in half with a single cut by an (n-1)-dimensional hyperplane. While it guarantees its existence, the theorem does not provide a way of finding this halving hyperplane, as it is only an existence result. In this paper, we look at the problem in dimension 2, more in the style of Euclid and the antique Greeks, that is from a constructible point of view, with straight edge and compass. For two arbitrary regions in the plane, there is certainly no …

Canonical Extensions Of Quantale Enriched Categories, Alexander Kurz

MPP Research Seminar

No abstract provided.

A Mceliece Cryptosystem, Using Permutation Error-Correcting Codes, Fiona Smith

CSB and SJU Distinguished Thesis

Using existing methods of cryptography, we can encrypt messages through the internet. However, these methods are vulnerable to attacks done by a quantum computer, which are a rising threat to security. In this thesis I discuss a possible method of encryption, secure against quantum attacks, using permutation groups and coding theory.

Representations Of Gender In Math-Related Films, Jacob Gathje

CSB and SJU Distinguished Thesis

This project analyzes how four popular math-related films - Hidden Figures, Mean Girls, Good Will Hunting, and A Beautiful Mind - either follow, resist, or reconfigure gender stereotypes in mathematics. It includes close readings of specific scenes in each of the films, along with broader analysis of the effects of how women and men are represented differently. It concludes forward-looking focus, providing suggestions for how future math-related movies can depict a more realistic and inclusive version of the field of mathematics. Ideally, this will help improve one part of the larger issue of gender disparities in math.

Calculations From On The Existence Of Periodic Traveling-Wave Solutions To Certain Systems Of Nonlinear, Dispersive Wave Equations, Jacob Daniels

Mathematics and Statistics Student Research and Class Projects

In the field of nonlinear waves, particular interest is given to periodic traveling-wave solutions of nonlinear, dispersive wave equations. This thesis aims to determine the existence of periodic traveling-wave solutions for several systems of water wave equations. These systems are the Schr¨odinger KdV-KdV, Schr¨odinger BBM-BBM, Schr¨odinger KdV-BBM, and Schr¨odinger BBM-KdV systems, and the abcd-system. In particular, it is shown that periodic traveling-wave solutions exist and are explicitly given in terms of cnoidal, the Jacobi elliptic function. Certain solitary-wave solutions are also established as a limiting case of the periodic traveling-wave solutions, that is, as the elliptic modulus approaches one.

Boolean Group Structure In Class Groups Of Positive Definite Quadratic Forms Of Primitive Discriminant, Christopher Albert Hudert Jr.

Student Research Submissions

It is possible to completely describe the representation of any integer by binary quadratic forms of a given discriminant when the discriminant’s class group is a Boolean group (also known as an elementary abelian 2-group). For other discriminants, we can partially describe the representation using the structure of the class group. The goal of the present project is to find whether any class group with 32 elements and a primitive positive definite discriminant is a Boolean group. We find that no such class group is Boolean.

Approval Gap Of Weighted K-Majority Tournaments, Jeremy Coste, Breeann Flesch, Joshua D. Laison, Erin Mcnicholas, Dane Miyata

Theory and Applications of Graphs

A $k$-majority tournament $T$ on a finite set of vertices $V$ is defined by a set of $2k-1$ linear orders on $V$, with an edge $u \to v$ in $T$ if $u>v$ in a majority of the linear orders. We think of the linear orders as voter preferences and the vertices of $T$ as candidates, with an edge $u \to v$ in $T$ if a majority of voters prefer candidate $u$ to candidate $v$. In this paper we introduce weighted $k$-majority tournaments, with each edge $u \to v$ weighted by the number of voters preferring $u$.

We define the …