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Articles 1  30 of 19829
FullText Articles in Mathematics
Energy On Spheres And Discreteness Of Minimizing Measures, Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk
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 pframe 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.
Alòs Type Decomposition Formula For BarndorffNielsen And Shephard Model, Takuji Arai
Alòs Type Decomposition Formula For BarndorffNielsen And Shephard Model, Takuji Arai
Journal of Stochastic Analysis
No abstract provided.
Интегрирование Модифицированного Уравнения КортевегаДе Фриза С Нагруженным Членом И Источником В Виде Суммы, Т.Ж. Алланазарова Ассистент Преподаватель
Интегрирование Модифицированного Уравнения КортевегаДе 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 Kortewegde Vries equation (mKdV) with a loaded term and a source in the form of a sum in the class of infinitegap periodic functions.
Mixed Generalized Fractional Brownian Motion, Shaykhah Alajmi, Ezzedine Mliki
Mixed Generalized Fractional Brownian Motion, Shaykhah Alajmi, Ezzedine Mliki
Journal of Stochastic Analysis
No abstract provided.
Understanding The Effect Of Adaptive Mutations On The ThreeDimensional Structure Of Rna, Justin Cook
Understanding The Effect Of Adaptive Mutations On The ThreeDimensional Structure Of Rna, Justin Cook
Undergraduate Research and Scholarship Symposium
Singlenucleotide 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 diseasestate 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 3D conformations that are described by its structural ensemble. One SNP, rs12477830, which ...
Streaming Down The SternBrocot Tree: Finding And Expressing Solutions To Pell's Equation In Sl(2,Z), Marcus L. Shell
Streaming Down The SternBrocot 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 SternBrocot 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 SternBrocot tree computationally and permit us a means of computing continued ...
Qualitative Analysis Of Corequisite Instruction In A Quantitative Reasoning Course, Zachary Beamer
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 collegelevel coursework, taught with a paired support course. Initial research suggests that such models yield significant improvements in the number of students passing creditlevel 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, Jose Sanchez, Daanial Ahmad, Satyanand Singh
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, Mario Lefebvre
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, Zachery Trump
Potential Effects Of Autonomous Vehicles On The Insurance Industry, Zachery Trump
Senior Honors Theses
The implementation of autonomous vehicles, or selfdriving 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, Andrea Clark
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 twodimensional 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, Erik Flinn
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, Stephen Wang
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, Abderrahim Elallam
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 nonconvergent 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) upperbound, focusing on the Beta and Gamma integrals ...
Applying Emotional Analysis For Automated Content Moderation, John Shelnutt
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, TingYao Lee
Studies Of Classical Analysis After Whittaker And Watson, TingYao 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 endofchapter exercises and some details within each chapter are often ...
A Weighted Version Of ErdősKac Theorem, Unique Subedi
A Weighted Version Of ErdősKac 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}sKac 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), Samantha O'Rourke
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, Marina Michelle Duchesne
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 ...
Regionalized Models With Spatially Continuous Predictions At The Borders, Jadon S. Wagstaff
Regionalized Models With Spatially Continuous Predictions At The Borders, Jadon S. Wagstaff
All Graduate Theses and Dissertations
Creating maps of continuous variables involves estimating values between measurement locations scattered throughout a geographic region. These maps often leverage observed similarities between geographically close measurements, but may also make predictions using other geographic information such as elevation. The relationship between the available geographic information and the variable of interest can vary with location, especially when mapping large areas like a continent. A simple way to account for the changing relationship is to divide the space into different subregions and model the relationship at each region. The naive implementation of this approach has the side effect of making sudden changes ...
Determining Quantum Symmetry In Graphs Using Planar Algebras, Akshata Pisharody
Determining Quantum Symmetry In Graphs Using Planar Algebras, Akshata Pisharody
Undergraduate Honors Theses
A graph has quantum symmetry if the algebra associated with its quantum automorphism group is noncommutative. We study what quantum symmetry means and outline one specific method for determining whether a graph has quantum symmetry, a method that involves studying planar algebras and manipulating planar tangles. Modifying a previously used method, we prove that the 5cycle has no quantum symmetry by showing it has the generating property.
How RiskRelated Statistics, As Reported In News And Social Media, Are Linked To The Use Of The Public Transit System, Prashiddhi Pokhrel
How RiskRelated Statistics, As Reported In News And Social Media, Are Linked To The Use Of The Public Transit System, Prashiddhi Pokhrel
Thinking Matters Symposium
Due to the pandemic, people have started relying more on televisions, news, social media, and other news outlets for guidance. Moreover, with the increasing amount of news, data, and information there is also an increase in the amount of misleading statistics. People’s opinions and decisions significantly depend on the data, statistics, and information that they are exposed to, as well as their sources. For this project, we want to look at how information and its sources are affecting the decision made by the general public for the usage of the Portland Transit System. It is very important to know ...
Solving Parabolic Interface Problems With A Finite Element Method, Henry Brown
Solving Parabolic Interface Problems With A Finite Element Method, Henry Brown
Mathematics Student Work
Partial differential equations (PDEs) dominate mathematical models given their effectiveness and accuracy at modeling the physical realities which govern the world. Though we have these powerful tools, analytic solutions can only be found in the simplest of cases due to the complexity of PDE models. Thus, efficient and accurate computational methods are needed to approximate solutions to PDE models. One class of these methods are finite element methods which can be used domain to provide close approximations to the PDE model in a finite domain. In this presentation, we discuss the use of a Discontinuous Galerkin (DG) Finite Element Methods ...
Modeling The Problem Of Integral Geometry On A Family Of Hyperbolic And Spherical Curves, Azamat Pirimbetov, N. Uteuliev, G. Djaykov
Modeling The Problem Of Integral Geometry On A Family Of Hyperbolic And Spherical Curves, Azamat Pirimbetov, N. Uteuliev, G. Djaykov
Karakalpak Scientific Journal
The problems of integral geometry in a strip on a family of curves of hyperbolic and spherical type are considered which have numerous applications in problems of geophysics, thermoacoustic and photoacoustic tomography. Explicit formulas are obtained for the Fourier image of the solution of integral geometry problems in the class of smooth compactly supported functions. Further, the obtained formulas are investigated for stability using numerical methods. To solve the problems, algorithms are constructed. Numerical and graphical results of applying these algorithms to solving the problems are presented.
Markov Chains And Their Applications, Fariha Mahfuz
Markov Chains And Their Applications, Fariha Mahfuz
Math Theses
Markov chain is a stochastic model that is used to predict future events. Markov chain is relatively simple since it only requires the information of the present state to predict the future states. In this paper we will go over the basic concepts of Markov Chain and several of its applications including Google PageRank algorithm, weather prediction and gamblers ruin.
We examine on how the Google PageRank algorithm works efficiently to provide PageRank for a Google search result. We also show how can we use Markov chain to predict weather by creating a model from real life data.
Classification Of Cayley Rose Window Graphs, Angsuman Das, Arnab Mandal
Classification Of Cayley Rose Window Graphs, Angsuman Das, Arnab Mandal
Theory and Applications of Graphs
Rose window graphs are a family of tetravalent graphs, introduced by Steve Wilson. Following it, Kovacs, Kutnar and Marusic classified the edgetransitive rose window graphs and Dobson, Kovacs and Miklavic characterized the vertex transitive rose window graphs. In this paper, we classify the Cayley rose window graphs.
Social Distancing And Testing As Optimal Strategies Against The Spread Of Covid19 In The Rio Grande Valley Of Texas, Kristina P. Vatcheva, Josef A. Sifuentes, Tamer Oraby, Jose Campo Maldonado, Timothy Huber, Cristina Villalobos
Social Distancing And Testing As Optimal Strategies Against The Spread Of Covid19 In The Rio Grande Valley Of Texas, Kristina P. Vatcheva, Josef A. Sifuentes, Tamer Oraby, Jose Campo Maldonado, Timothy Huber, Cristina Villalobos
Mathematical and Statistical Sciences Faculty Publications and Presentations
At the beginning of August 2020, the Rio Grande Valley (RGV) of Texas experienced a rapid increase of coronavirus disease 2019 (abbreviated as COVID19) cases and deaths. This study aims to determine the optimal levels of effective social distancing and testing to slow the virus spread at the outset of the pandemic. We use an agestratified eight compartment epidemiological model to depict COVID19 transmission in the community and within households. With a simulated 120day outbreak period data we obtain a post 180days period optimal control strategy solution. Our results show that easing social distancing between adults by the end of ...
Normality Properties Of Composition Operators, Grace Weeks, Hallie Kaiser, Katy O'Malley
Normality Properties Of Composition Operators, Grace Weeks, Hallie Kaiser, Katy O'Malley
Celebration of Scholarship 2021
We explore two main concepts in relation to truncated composition matrices: the conditions required for the binormal and commutative properties. Both of these topics are important in linear algebra due to their connection with diagonalization.
We begin with the normal solution before moving onto the more complex binormal solutions. Then we cover conditions for the composition matrix to commute with the general matrix. Finally, we end with ongoing questions for future work.
Developing Better Instruction, Better Instructors, And New Investigators, Clay Vander Kolk, Abigail Pyle
Developing Better Instruction, Better Instructors, And New Investigators, Clay Vander Kolk, Abigail Pyle
Celebration of Scholarship 2021
This research discusses how HAMTE and future educators collaborated to use the Principles to Action Professional Learning Toolkit in their classes and the tools they used to measure and gather conclusions about the development in the future teachers.
An AgentBased Model To Evaluate The Effect Of Socioeconomic Status And Demographic Factors On Covid19 Prevalence And Mortality, Jonathan Huang, Berke Nouri
An AgentBased Model To Evaluate The Effect Of Socioeconomic Status And Demographic Factors On Covid19 Prevalence And Mortality, Jonathan Huang, Berke Nouri
Arts & Sciences Student Symposium
The purpose of the project is to discover how the prevalence and mortality of a pandemic change depending on a population’s demographic factors as well as various intervention policies through a NetLogo agentbased model. This model will simulate how demographic factors affect the course of COVID19 (infection rate, recovery rate, and death rate). Demographic factors of interest will include population density, income distribution, age distribution, and number of hospital beds per capita. Intervention policies include vaccination, social distancing, mask wearing, mass testing, and quarantining. Conclusions about the effect of demographic factors on the infection, recovery, and death rate will ...