Physical Sciences and Mathematics Commons^™

Limit Theorems For L-Functions In Analytic Number Theory, Asher Roberts

Dissertations, Theses, and Capstone Projects

We use the method of Radziwill and Soundararajan to prove Selberg’s central limit theorem for the real part of the logarithm of the Riemann zeta function on the critical line in the multivariate case. This gives an alternate proof of a result of Bourgade. An upshot of the method is to determine a rate of convergence in the sense of the Dudley distance. This is the same rate Selberg claims using the Kolmogorov distance. We also achieve the same rate of convergence in the case of Dirichlet L-functions. Assuming the Riemann hypothesis, we improve the rate of convergence by using …

The Product Of Distributions And Stochastic Differential Equations Arising From Powers Of Infinite Dimensional Brownian Motions, Un Cig Ji, Hui-Hsiung Kuo, Hara-Yuko Mimachi, Kimiaki Saitô

Journal of Stochastic Analysis

In this paper, we introduce a new locally convex space of distributions, as a generalization of the space from [15] and [11], in which we have the product of any distributions as a series expansion. Then we discuss an extension of the Lévy and Volterra Laplacians to operators on the locally convex space including distribution-coefficient polynomials and distribution valued exponentials on distributions, and give an infinite dimensional Brownian motion associated with the Lévy Laplacian. Moreover, we give an integral expression of the Lévy Laplacian. Based on those results, we obtain white noise distribution-valued stochastic differential equations for the delta distributions …

`The Very Beautiful Principles Of Natural Philosophy': Michael Faraday, Paper Marbling And The Physics Of Natural Forms, Robert Pepperell

LASER Journal

In 1854, Michael Faraday wrote to thank the author who had sent him a book on the art of paper marbling. In the letter, Faraday referred to `the very beautiful principles of natural philosophy' involved in the process of dropping ink on thickened water. What are the `beautiful principles' that Faraday referred to, and how are they involved in the art of paper marbling? Here I consider some of the physical processes that occur in paper marbling and how the patterns that emerge represent `dissipative structures' that are governed by fundamental principles of nature, in particular the tendency for physical …

Are All Weakly Convex And Decomposable Polyhedral Surfaces Infinitesimally Rigid?, Jilly Kevo

Rose-Hulman Undergraduate Mathematics Journal

It is conjectured that all decomposable (that is, interior can be triangulated without adding new vertices) polyhedra with vertices in convex position are infinitesimally rigid and only recently has it been shown that this is indeed true under an additional assumption of codecomposability (that is, the interior of the difference between the convex hull and the polyhedron itself can be triangulated without adding new vertices). One major set of tools for studying infinitesimal rigidity happens to be the (negative) Hessian M_T of the discrete Hilbert-Einstein functional. Besides its theoretical importance, it provides the necessary machinery to tackle the problem …

Big Two And N-Card Poker Probabilities, Brian Wu, Chai Wah Wu

Communications on Number Theory and Combinatorial Theory

Between the poker hands of straight, flush, and full house, which hand is more common? In standard 5-card poker, the order from most common to least common is straight, flush, full house. The same order is true for 7-card poker such as Texas hold'em. However, is the same true for n-card poker for larger n? We study the probability of obtaining these various hands for n-card poker for various values of n≥5. In particular, we derive closed expressions for the probabilities of flush, straight and full house and show that the probability of a flush is less than a straight …

Supplementary Files For: "Interactive Modeling Of Bear Lake Elevations In A Future Climate", Benjamin D. Shaw, Scout Jarman, Brennan Bean, Kevin R. Moon, Wei Zhang, Nathan Butler, Tommy Bolton, April Knight, Emeline Haroldsen, Abby Funk, Rebecca Higbee

Browse all Datasets

The water level, or elevation, of Bear Lake has a significant impact on agriculture, power, infrastructure, and recreation for communities around the lake. Climatological variables, such as precipitation, temperature, and snowfall, all have an impact on the elevation of Bear Lake. As the climate changes due to greenhouse gas emissions, the typical behaviors of these climate variables change, leading to new behaviors in Bear Lake elevation. Because of the importance of Bear Lake, it is vital to be able to model and understand how Bear Lake's elevation may change in the face of different climate scenarios and to gain further …

Oscillations In Neuronal Activity: A Neuron-Centered Spatiotemporal Model Of The Unfolded Protein Response In Prion Diseases, Elliot M. Miller, Tat Chung D. Chan, Carlos Montes-Matamoros, Omar Sharif, Laurent Pujo-Menjouet, Michael R. Lindstrom

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Many neurodegenerative diseases (NDs) are characterized by the slow spatial spread of toxic protein species in the brain. The toxic proteins can induce neuronal stress, triggering the Unfolded Protein Response (UPR), which slows or stops protein translation and can indirectly reduce the toxic load. However, the UPR may also trigger processes leading to apoptotic cell death and the UPR is implicated in the progression of several NDs. In this paper, we develop a novel mathematical model to describe the spatiotemporal dynamics of the UPR mechanism for prion diseases. Our model is centered around a single neuron, with representative proteins P …

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 …

(R2067) Solutions Of Hyperbolic System Of Time Fractional Partial Differential Equations For Heat Propagation, Sagar Sankeshwari, Vinayak Kulkarni

Applications and Applied Mathematics: An International Journal (AAM)

Hyperbolic linear theory of heat propagation has been established in the framework of a Caputo time fractional order derivative. The solution of a system of integer and fractional order initial value problems is achieved by employing the Adomian decomposition approach. The obtained solution is in convergent infinite series form, demonstrating the method’s strengths in solving fractional differential equations. Moreover, the double Laplace transform method is employed to acquire the solution of a system of integer and fractional order boundary conditions in the Laplace domain. An inversion of double Laplace transforms has been achieved numerically by employing the Xiao algorithm in …

(R2074) A Comparative Study Of Two Novel Analytical Methods For Solving Time-Fractional Coupled Boussinesq-Burger Equation, Jyoti U. Yadav, Twinkle R. Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a comparative study between two different methods for solving nonlinear timefractional coupled Boussinesq-Burger equation is conducted. The techniques are denoted as the Natural Transform Decomposition Method (NTDM) and the Variational Iteration Transform Method (VITM). To showcase the efficacy and precision of the proposed approaches, a pair of different numerical examples are presented. The outcomes garnered indicate that both methods exhibit robustness and efficiency, yielding approximations of heightened accuracy and the solutions in a closed form. Nevertheless, the VITM boasts a distinct advantage over the NTDM by addressing nonlinear predicaments without recourse to the application of Adomian polynomials. …

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 …

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.

A Brief Introduction To General Topology, Richard P. Millspaugh

Open Educational Resources

The material in this text is intended to be accessible to undergraduates who have had an introduction to elementary set theory and proof techniques. It includes sufficient material from general topology to prove the two main topological results found in a standard first semester calculus course: the Intermediate Value Theorem and the Extreme Value Theorem. This material can be found in Chapters 2 through 6 and makes up the bulk of the text. Rather than approaching these topics through use of the standard euclidean metric, it defines the standard topology on R in terms of the usual order on R. …

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 …

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 …

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 …

A Computational Investigation Of Wood Selection For Acoustic Guitar, Jonah Osterhus

Senior Honors Theses

The acoustic guitar is a stringed instrument, often made of wood, that transduces vibrational energy of steel strings into coupled vibrations of the wood and acoustic pressure waves in the air. Variations in wood selection and instrument geometry have been shown to affect the timbre of the acoustic guitar. Computational methods were utilized to investigate the impact of material properties on acoustic performance. Sitka spruce was deemed the most suitable wood for guitar soundboards due to its acoustic characteristics, strength, and uniform aesthetic. Mahogany was deemed to be the best wood for the back and sides of the guitar body …

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.