Energy On Spheres And Discreteness Of Minimizing Measures, 2021 The University of Texas Rio Grande Valley

#### Energy On Spheres And Discreteness Of Minimizing Measures, Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk

*Mathematical and Statistical Sciences Faculty Publications and Presentations*

In the present paper we study the minimization of energy integrals on the sphere with a focus on an interesting clustering phenomenon: for certain types of potentials, optimal measures are discrete or are supported on small sets. In particular, we prove that the support of any minimizer of the *p*-frame energy has empty interior whenever *p* is not an even integer. A similar effect is also demonstrated for energies with analytic potentials which are not positive definite. In addition, we establish the existence of discrete minimizers for a large class of energies, which includes energies with polynomial potentials.

The Edwards Model For Fractional Brownian Loops And Starbursts, 2021 Technische Universität Kaiserslautern, Technomathematics Group, 67663 Kaiserslautern, Germany

#### The Edwards Model For Fractional Brownian Loops And Starbursts, Wolfgang Bock, Torben Fattler, Ludwig Streit

*Journal of Stochastic Analysis*

No abstract provided.

Alòs Type Decomposition Formula For Barndorff-Nielsen And Shephard Model, 2021 Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan

#### Alòs Type Decomposition Formula For Barndorff-Nielsen And Shephard Model, Takuji Arai

*Journal of Stochastic Analysis*

No abstract provided.

Интегрирование Модифицированного Уравнения Кортевега-Де Фриза С Нагруженным Членом И Источником В Виде Суммы, 2021 Каракалпакский государственный университет имени Бердаха

#### Интегрирование Модифицированного Уравнения Кортевега-Де Фриза С Нагруженным Членом И Источником В Виде Суммы, Т.Ж. Алланазарова Ассистент Преподаватель

*Science and Society*

** **This paper considers the method of the inverse spectral problem for integrating the modified Korteweg-de Vries equation (mKdV) with a loaded term and a source in the form of a sum in the class of infinite-gap periodic functions.

** **

Mixed Generalized Fractional Brownian Motion, 2021 Imam Abdulrahman Bin Faisal University, P. O. Box 1982, Dammam, Saudi Arabia

#### Mixed Generalized Fractional Brownian Motion, Shaykhah Alajmi, Ezzedine Mliki

*Journal of Stochastic Analysis*

No abstract provided.

Understanding The Effect Of Adaptive Mutations On The Three-Dimensional Structure Of Rna, 2021 Duquesne University

#### Understanding The Effect Of Adaptive Mutations On The Three-Dimensional Structure Of Rna, Justin Cook

*Undergraduate Research and Scholarship Symposium*

Single-nucleotide polymorphisms (SNPs) are variations in the genome where one base pair can differ between individuals.^{1} SNPs occur throughout the genome and can correlate to a disease-state if they occur in a functional region of DNA.^{1}According to the central dogma of molecular biology, any variation in the DNA sequence will have a direct effect on the RNA sequence and will potentially alter the identity or conformation of a protein product. A single RNA molecule, due to intramolecular base pairing, can acquire a plethora of 3-D conformations that are described by its structural ensemble. One SNP, rs12477830, which ...

Streaming Down The Stern-Brocot Tree: Finding And Expressing Solutions To Pell's Equation In Sl(2,Z), 2021 Jacksonville State University

#### Streaming Down The Stern-Brocot Tree: Finding And Expressing Solutions To Pell's Equation In Sl(2,Z), Marcus L. Shell

*Theses*

This paper explores and elaborates on a method of solving Pell’s equation as introduced by Norman Wildberger. In the first chapters of the paper, foundational topics are introduced in expository style including an explanation of Pell’s equation. An explanation of continued fractions and their ability to express quadratic irrationals is provided as well as a connection to the Stern-Brocot tree and a convenient means of representation for each in terms of 2×2 matrices with integer elements. This representation will provide a useful way of navigating the Stern-Brocot tree computationally and permit us a means of computing continued ...

Qualitative Analysis Of Corequisite Instruction In A Quantitative Reasoning Course, 2021 Piedmont Virginia Community College

#### Qualitative Analysis Of Corequisite Instruction In A Quantitative Reasoning Course, Zachary Beamer

*Inquiry: The Journal of the Virginia Community Colleges*

In corequisite models of instruction, marginally prepared students are placed directly into college-level coursework, taught with a paired support course. Initial research suggests that such models yield significant improvements in the number of students passing credit-level mathematics when compared to previous models of prerequisite remediation. The present study employs qualitative methods to investigate methods of instruction at one community colleges to understand how instructors identify and respond to student needs. It concludes with recommendations for practice and highlights advantages of small format corequisite classes taught by the same instructor.

Application Of Randomness In Finance, 2021 CUNY New York City College of Technology

#### Application Of Randomness In Finance, Jose Sanchez, Daanial Ahmad, Satyanand Singh

*Publications and Research*

Brownian Motion which is also considered to be a Wiener process and can be thought of as a random walk. In our project we had briefly discussed the fluctuations of financial indices and related it to Brownian Motion and the modeling of Stock prices.

Exact Solutions To Optimal Control Problems For Wiener Processes With Exponential Jumps, 2021 Polytechnique Montréal, Montréal, Québec H3C 3A7, Canada

#### Exact Solutions To Optimal Control Problems For Wiener Processes With Exponential Jumps, Mario Lefebvre

*Journal of Stochastic Analysis*

No abstract provided.

Potential Effects Of Autonomous Vehicles On The Insurance Industry, 2021 Liberty University

#### Potential Effects Of Autonomous Vehicles On The Insurance Industry, Zachery Trump

*Senior Honors Theses*

The implementation of autonomous vehicles, or self-driving cars, promises to radically change much of the normal way of life. While it may seem inconsequential to start small with a vehicle of relatively low level of automation, there are many factors to consider. Some of these factors include security, moral dilemmas, and even the insurance field. One can look back at previous implementations of new technology, such as air bags, and see that it can be difficult to predict consequences and adapt. However, actuaries have been suggesting solutions to make autonomous vehicles a safe reality. While the solutions may vary, one ...

Visualizing Geometric Structures On Topological Surfaces, 2021 Northern Michigan University

#### Visualizing Geometric Structures On Topological Surfaces, Andrea Clark

*All NMU Master's Theses*

We study an interplay between topology, geometry, and algebra. Topology is the study of properties unchanged by bending, stretching or twisting space. Geometry measures space through concepts such as length, area, and angles. In the study of two-dimensional surfaces one can go back and forth between picturing twists as either distortions of the geometric properties of the surface or as a wrinkling of the surface while leaving internal measures unchanged. The language of groups gives us a way to distinguish geometric structures. Understanding the mapping class group is an important and hard problem. This paper contributes to visualizing how the ...

Algebraic Structures And Variations: From Latin Squares To Lie Quasigroups, 2021 Northern Michigan University

#### Algebraic Structures And Variations: From Latin Squares To Lie Quasigroups, Erik Flinn

*All NMU Master's Theses*

In this Master's Thesis we give an overview of the algebraic structure of sets with a single binary operation. Specifically, we are interested in quasigroups and loops and their historical connection with Latin squares; considering them in both finite and continuous variations. We also consider various mappings between such algebraic objects and utilize matrix representations to give a negative conclusion to a question concerning isotopies in the case of quasigroups.

Zeta Function Regularization And Its Relationship To Number Theory, 2021 East Tennessee State University

#### Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang

*Electronic Theses and Dissertations*

While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to ...

Constructions & Optimization In Classical Real Analysis Theorems, 2021 East Tennessee State University

#### Constructions & Optimization In Classical Real Analysis Theorems, Abderrahim Elallam

*Electronic Theses and Dissertations*

This thesis takes a closer look at three fundamental Classical Theorems in Real Analysis. First, for the Bolzano Weierstrass Theorem, we will be interested in constructing a convergent subsequence from a non-convergent bounded sequence. Such a subsequence is guaranteed to exist, but it is often not obvious what it is, e.g., if an = sin n. Next, the H¨older Inequality gives an upper bound, in terms of p ∈ [1,∞], for the the integral of the product of two functions. We will find the value of p that gives the best (smallest) upper-bound, focusing on the Beta and Gamma integrals ...

Applying Emotional Analysis For Automated Content Moderation, 2021 University of Arkansas, Fayetteville

#### Applying Emotional Analysis For Automated Content Moderation, John Shelnutt

*Computer Science and Computer Engineering Undergraduate Honors Theses*

The purpose of this project is to explore the effectiveness of emotional analysis as a means to automatically moderate content or flag content for manual moderation in order to reduce the workload of human moderators in moderating toxic content online. In this context, toxic content is defined as content that features excessive negativity, rudeness, or malice. This often features offensive language or slurs. The work involved in this project included creating a simple website that imitates a social media or forum with a feed of user submitted text posts, implementing an emotional analysis algorithm from a word emotions dataset, designing ...

Studies Of Classical Analysis After Whittaker And Watson, 2021 Utah State University

#### Studies Of Classical Analysis After Whittaker And Watson, Ting-Yao Lee

*All Graduate Theses and Dissertations*

The goal of this thesis is to solve problems from the first four chapters of the book, titled *A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions with an Account of the Principal Transcendental Functions *by E.T. Whittaker and G.N. Watson. The titles of the first four chapters are “Complex Numbers,” “The Theory of Convergence,” “Continuous Functions and Uniform Convergence,” and “The Theory of Riemann Integration,” respectively. This book is a classic mathematical analysis textbook that contains some challenging end-of-chapter exercises and some details within each chapter are often ...

A Weighted Version Of Erdős-Kac Theorem, 2021 University of Mississippi

#### A Weighted Version Of Erdős-Kac Theorem, Unique Subedi

*Honors Theses*

Let $\omega(n)$ denote the number of distinct prime factors of a natural number $n$. A celebrated result of Erd{\H o}s and Kac states that $\omega(n)$ as a Gaussian distribution. In this thesis, we establish a weighted version of Erd{\H o}s-Kac Theorem. Specifically, we show that the Gaussian limiting distribution is preserved, but shifted, when $\omega(n)$ is weighted by the $k-$fold divisor function $\tau_k(n)$. We establish this result by computing all positive integral moments of $\omega(n)$ weighted by $\tau_k(n)$.

We also provide a proof of the classical identity of $\zeta ...

Visual Analysis Of Historical Lessons Learned During Exercises For The United States Air Force Europe (Usafe), 2021 University of Nebraska at Omaha

#### Visual Analysis Of Historical Lessons Learned During Exercises For The United States Air Force Europe (Usafe), Samantha O'Rourke

*Theses/Capstones/Creative Projects*

Within the United States Air Force, there are repeated patterns of differences observed during exercises. After an exercise is completed, forms are filled out detailing observations, successes, and recommendations seen throughout the exercise. At the most, no two reports are identical and must be analyzed by personnel and then categorized based on common themes observed. Developing a computer application will greatly reduce the time and resources used to analyze each After Action Report. This application can visually represent these observations and optimize the effectiveness of these exercises. The visualization is done through graphs displaying the frequency of observations and recommendations ...

Symmetric Presentation Of Finite Groups, And Related Topics, 2021 California State University, San Bernardino

#### Symmetric Presentation Of Finite Groups, And Related Topics, Marina Michelle Duchesne

*Electronic Theses, Projects, and Dissertations*

We have discovered original symmetric presentations for several finite groups, including 2^{2}:^{.}(2^{4}:(2^{.}S_{3})), M_{11}, 3:(PSL(3,3):2), S_{8}, and 2^{.}M_{12}. We have found homomorphic images of several progenitors, including 2^{*18}:((6x2):6), 2^{*24}:(2^{.}S_{4}), 2^{*105}:A_{7}, 3^{*3}:_{m}(2^{3}:3), 7^{*8}:_{m}(PSL(2,7):2), 3^{*4}:_{m}(4^{2}:2^{2}), 7^{*5}:(2xA_{5}), and 5^{*6}:_{m}S_{5}. We have provided the isomorphism type of all of the finite images that we have discovered. We ...