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Articles 1  30 of 22376
FullText Articles in Physical Sciences and Mathematics
Ultrametric Diffusion, Rugged Energy Landscapes And Transition Networks, Wilson A. ZunigaGalindo
Ultrametric Diffusion, Rugged Energy Landscapes And Transition Networks, Wilson A. ZunigaGalindo
Mathematical and Statistical Sciences Faculty Publications and Presentations
In this article we introduce the ultrametric networks which are p" role="presentation" style="boxsizing: borderbox; margin: 0px; padding: 0px; display: inlineblock; lineheight: normal; fontsize: 16.2px; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: none; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px; position: relative;">padic continuous analogs of the standard Markov state models constructed using master equations. A p" role="presentation" style="boxsizing: borderbox; margin: 0px; padding: 0px; display: inlineblock; lineheight: normal; fontsize: 16.2px; wordspacing: normal; overflowwrap: normal; whitespace: nowrap; float: none; direction: ltr; maxwidth: none; maxheight: none; minwidth: 0px; minheight: 0px; border: 0px ...
The ZariskiRiemann Space As A Universal Model For The Birational Geometry Of A Function Field, Giovan Battista Pignatti Morano Di Custoza
The ZariskiRiemann Space As A Universal Model For The Birational Geometry Of A Function Field, Giovan Battista Pignatti Morano Di Custoza
Dissertations, Theses, and Capstone Projects
Given a function field $K$ over an algebraically closed field $k$, we propose to use the ZariskiRiemann space $\ZR (K/k)$ of valuation rings as a universal model that governs the birational geometry of the field extension $K/k$. More specifically, we find an exact correspondence between adhoc collections of open subsets of $\ZR (K/k)$ ordered by quasirefinements and the category of normal models of $K/k$ with morphisms the birational maps. We then introduce suitable Grothendieck topologies and we develop a sheaf theory on $\ZR (K/k)$ which induces, locally at once, the sheaf theory of each normal ...
Fractional Bernstein Operational Matrices For Solving IntegroDifferential Equations Involved By Caputo Fractional Derivative, M.H.T. Alshbool, Mutaz Mohammad, Osman Isik, Ishak Hashim
Fractional Bernstein Operational Matrices For Solving IntegroDifferential Equations Involved By Caputo Fractional Derivative, M.H.T. Alshbool, Mutaz Mohammad, Osman Isik, Ishak Hashim
All Works
The present work is devoted to developing two numerical techniques based on fractional Bernstein polynomials, namely fractional Bernstein operational matrix method, to numerically solving a class of fractional integrodifferential equations (FIDEs). The first scheme is introduced based on the idea of operational matrices generated using integration, whereas the second one is based on operational matrices of differentiation using the collocation technique. We apply the Riemann–Liouville and fractional derivative in Caputo’s sense on Bernstein polynomials, to obtain the approximate solutions of the proposed FIDEs. We also provide the residual correction procedure for both methods to estimate the absolute errors ...
Universality And Synchronization In Complex Quadratic Networks (Cqns), Anca R. Radulescu, Danae Evans
Universality And Synchronization In Complex Quadratic Networks (Cqns), Anca R. Radulescu, Danae Evans
Biology and Medicine Through Mathematics Conference
No abstract provided.
Implementation Of A Least Squares Method To A NavierStokes Solver, Jada P. Lytch, Taylor Boatwright, Ja'nya Breeden
Implementation Of A Least Squares Method To A NavierStokes Solver, Jada P. Lytch, Taylor Boatwright, Ja'nya Breeden
RoseHulman Undergraduate Mathematics Journal
The NavierStokes equations are used to model fluid flow. Examples include fluid structure interactions in the heart, climate and weather modeling, and flow simulations in computer gaming and entertainment. The equations date back to the 1800s, but research and development of numerical approximation algorithms continues to be an active area. To numerically solve the NavierStokes equations we implement a least squares finite element algorithm based on work by Roland Glowinski and colleagues. We use the deal.II academic library , the C++ language, and the Linux operating system to implement the solver. We investigate convergence rates and apply the least squares ...
Gene Drives And The Consequences Of OverSuppression, Cole Butler
Gene Drives And The Consequences Of OverSuppression, Cole Butler
Biology and Medicine Through Mathematics Conference
No abstract provided.
An Even 2Factor In The Line Graph Of A Cubic Graph, Seungjae Eom, Kenta Ozeki
An Even 2Factor In The Line Graph Of A Cubic Graph, Seungjae Eom, Kenta Ozeki
Theory and Applications of Graphs
An even 2factor is one such that each cycle is of even length. A 4 regular graph G is 4edgecolorable if and only if G has two edgedisjoint even 2 factors whose union contains all edges in G. It is known that the line graph of a cubic graph without 3edgecoloring is not 4edgecolorable. Hence, we are interested in whether those graphs have an even 2factor. Bonisoli and Bonvicini proved that the line graph of a connected cubic graph G with an even number of edges has an even 2factor, if G has a perfect matching [Even cycles and even ...
Mathematical Model Of ImmuneInflammatory Response In Covid19 Patients, Quiyana M. Murphy
Mathematical Model Of ImmuneInflammatory Response In Covid19 Patients, Quiyana M. Murphy
Biology and Medicine Through Mathematics Conference
No abstract provided.
Estimating Glutamate Transporter Surface Density In Mouse Hippocampal Astrocytes, Anca R. Radulescu, Annalisa Scimemi
Estimating Glutamate Transporter Surface Density In Mouse Hippocampal Astrocytes, Anca R. Radulescu, Annalisa Scimemi
Biology and Medicine Through Mathematics Conference
No abstract provided.
RealTime Interactive Simulation Of Large Bird Flocks: Toward Understanding Murmurations, Maxfield R. Comstock
RealTime Interactive Simulation Of Large Bird Flocks: Toward Understanding Murmurations, Maxfield R. Comstock
Biology and Medicine Through Mathematics Conference
No abstract provided.
Optimal TimeDependent Classification For Diagnostic Testing, Prajakta P. Bedekar, Paul Patrone, Anthony Kearsley
Optimal TimeDependent Classification For Diagnostic Testing, Prajakta P. Bedekar, Paul Patrone, Anthony Kearsley
Biology and Medicine Through Mathematics Conference
No abstract provided.
On TwoPlayer Pebbling, Garth Isaak, Matthew Prudente, Andrea Potylycki, William Fagley, Joseph Marcinik
On TwoPlayer Pebbling, Garth Isaak, Matthew Prudente, Andrea Potylycki, William Fagley, Joseph Marcinik
Communications on Number Theory and Combinatorial Theory
Graph pebbling can be extended to a twoplayer game on a graph G, called TwoPlayer Graph Pebbling, with players Mover and Defender. The players each use pebbling moves, the act of removing two pebbles from one vertex and placing one of the pebbles on an adjacent vertex, to win. Mover wins if they can place a pebble on a specified vertex. Defender wins if the specified vertex is pebblefree and there are no more pebbling moves on the vertices of G. The TwoPlayer Pebbling Number of a graph G, η(G), is the minimum m such that for every arrangement ...
The Impact Of Academic Tracking And Mathematics SelfConcept On Mathematics Achievement., Kain M. Schow
The Impact Of Academic Tracking And Mathematics SelfConcept On Mathematics Achievement., Kain M. Schow
Dissertations, Theses, and Projects
ABSTRACT
This study examines the effects of academic tracking, in high school math, on students’ mathematics selfconcept (MSC) and how that correlates to students’ mathematics achievement. This study measured students’ MSC through a mathematics selfconcept questionnaire and measured mathematics achievement by the students’ latest grade report. Participants included 60 students in grades 1012 who had been or were currently enrolled in math courses in the researcher’s school district. The data collected will direct the researcher and school administration on the effects of academic tracking on students, allowing for further discussion about continuing tracking in the district.
A Quantitative Study Of An Online Learning Platform’S Impact On High School Students' Engagement, Academic Achievement, And Student Satisfaction In A Mathematics Class, Mariah Minkkinen
Dissertations, Theses, and Projects
The present study investigated the impact using the online learning platform Pear Deck had on an online high school math class. The study measured student engagement, academic achievement, and students’ overall satisfaction with using the online learning platform. The participants in this study were online Algebra 2 students. The study was conducted during synchronous online lessons using an online learning system. Data was collected from two different live classes. One class used the online learning platform Pear Deck and the other did not. Engagement was measured by charting the number of student responses for each question posed. Students’ academic achievement ...
Sheltered Math Curriculum For Middle School English Learners, Jasmine Ercink
Sheltered Math Curriculum For Middle School English Learners, Jasmine Ercink
Dissertations, Theses, and Projects
Language barriers have shown a need for differentiation and sheltered instruction in the classroom for English Learners (ELs) to be successful in the United States public school system. This project proposes a mathematics curriculum using SIOP so that both groups of students in the middle school level can increase their proficiency in the mathematics content area as well as experience opportunities for academic and social language development. The purpose of this report is to describe the processes, methods, data, and intent of the mathematics curriculum for these learners. The curriculum acts as an effective intervention to fill gaps in both ...
The Mathematical Foundation Of The Musical Scales And Overtones, Michaela DuboseSchmitt
The Mathematical Foundation Of The Musical Scales And Overtones, Michaela DuboseSchmitt
Theses and Dissertations
This thesis addresses the question of mathematical involvement in music, a topic long discussed going all the way back to Plato. It details the mathematical construction of the three main tuning systems (Pythagorean, just intonation, and equal temperament), the methods by which they were built and the mathematics that drives them through the lens of a historical perspective. It also briefly touches on the philosophical aspects of the tuning systems and whether their differences affect listeners. It further details the invention of the Fourier Series and their relation to the sound wave to explain the concept of overtones within the ...
Tiling Rectangles And 2Deficient Rectangles With LPentominoes, Monica Kane
Tiling Rectangles And 2Deficient Rectangles With LPentominoes, Monica Kane
RoseHulman Undergraduate Mathematics Journal
We investigate tiling rectangles and 2deficient rectangles with Lpentominoes. First, we determine exactly when a rectangle can be tiled with Lpentominoes. We then determine locations for pairs of unit squares that can always be removed from an m × n rectangle to produce a tileable 2deficient rectangle when m ≡ 1 (mod 5), n ≡ 2 (mod 5) and when m ≡ 3 (mod 5), n ≡ 4 (mod 5).
A New Model For Predicting The Drag And Lift Forces Of Turbulent Newtonian Flow On Arbitrarily Shaped Shells On The Seafloor, Carley R. Walker, James V. Lambers, Julian Simeonov
A New Model For Predicting The Drag And Lift Forces Of Turbulent Newtonian Flow On Arbitrarily Shaped Shells On The Seafloor, Carley R. Walker, James V. Lambers, Julian Simeonov
Dissertations
Currently, all forecasts of currents, waves, and seafloor evolution are limited by a lack of fundamental knowledge and the parameterization of smallscale processes at the seafloorocean interface. Commonly used EulerLagrange models for sediment transport require parameterizations of the drag and lift forces acting on the particles. However, current parameterizations for these forces only work for spherical particles. In this dissertation we propose a new method for predicting the drag and lift forces on arbitrarily shaped objects at arbitrary orientations with respect to the direction of flow that will ultimately provide models for predicting the sediment sorting processes that lead to ...
Impact Of Treatment Length On Individuals With Substance Use Disorders In Allegheny County, Cassie Dibenedetti, Kate Rosello
Impact Of Treatment Length On Individuals With Substance Use Disorders In Allegheny County, Cassie Dibenedetti, Kate Rosello
Undergraduate Research and Scholarship Symposium
Auberle social services is opening the Family Healing Center (FHC), a level 3.5 treatment program in Pittsburgh, PA that provides housing and 24hour support for families struggling with opioid addiction. We partnered with Auberle to study characteristics of individuals receiving level 3.5 treatment and to determine whether longer treatment lengths correlate with fewer adverse outcomes. We obtained data from the Allegheny County Department of Human Services on 2,016 individuals admitted to level 3.5 treatment in 2019. The data included birth year, race, gender, admittance date, discharge date, and Children Youth and Family (CYF) incidents before and ...
On Isomorphic KRational Groups Of Isogenous Elliptic Curves Over Finite Fields, Ben Kuehnert, Geneva Schlafly, Zecheng Yi
On Isomorphic KRational Groups Of Isogenous Elliptic Curves Over Finite Fields, Ben Kuehnert, Geneva Schlafly, Zecheng Yi
RoseHulman Undergraduate Mathematics Journal
It is well known that two elliptic curves are isogenous if and only if they have same number of rational points. In fact, isogenous curves can even have isomorphic groups of rational points in certain cases. In this paper, we consolidate all the current literature on this relationship and give a extensive classification of the conditions in which this relationship arises. First we prove two ordinary isogenous elliptic curves have isomorphic groups of rational points when they have the same $j$invariant. Then, we extend this result to certain isogenous supersingular elliptic curves, namely those with equal $j$invariant of ...
An Overview Of Monstrous Moonshine, Catherine E. Riley
An Overview Of Monstrous Moonshine, Catherine E. Riley
Channels: Where Disciplines Meet
The ConwayNorton monstrous moonshine conjecture set off a quest to discover the connection between the Monster and the Jfunction. The goal of this paper is to give an overview of the components of the conjecture, the conjecture itself, and some of the ideas that led to its solution. Special focus is given to Klein's Jfunction.
John Horton Conway: The Man And His Knot Theory, Dillon Ketron
John Horton Conway: The Man And His Knot Theory, Dillon Ketron
Electronic Theses and Dissertations
John Horton Conway was a British mathematician in the twentieth century. He made notable achievements in fields such as algebra, number theory, and knot theory. He was a renowned professor at Cambridge University and later Princeton. His contributions to algebra include his discovery of the Conway group, a group in twentyfour dimensions, and the Conway Constellation. He contributed to number theory with his development of the surreal numbers. His Game of Life earned him longlasting fame. He contributed to knot theory with his developments of the Conway polynomial, Conway sphere, and Conway notation.
Extremal Problems In Graph Saturation And Covering, Adam Volk
Extremal Problems In Graph Saturation And Covering, Adam Volk
Dissertations, Theses, and Student Research Papers in Mathematics
This dissertation considers several problems in extremal graph theory with the aim of finding the maximum or minimum number of certain subgraph counts given local conditions. The local conditions of interest to us are saturation and covering. Given graphs F and H, a graph G is said to be Fsaturated if it does not contain any copy of F, but the addition of any missing edge in G creates at least one copy of F. We say that G is Hcovered if every vertex of G is contained in at least one copy of H. In the former setting, we ...
On Uniqueness And Stability For The BoltzmannEnskog Equation, Martin Friesen, Barbara Ruediger, Padmanabhan Subdar
On Uniqueness And Stability For The BoltzmannEnskog Equation, Martin Friesen, Barbara Ruediger, Padmanabhan Subdar
Faculty Publications
The timeevolution of a moderately dense gas in a vacuum is described in classical mechanics by a particle density function obtained from the BoltzmannEnskog equation. Based on a McKeanVlasov equation with jumps, the associated stochastic process was recently constructed by modified Picard iterations with the meanfield interactions, and more generally, by a system of interacting particles. By the introduction of a shifted distance that exactly compensates for the free transport term that accrues in the spatially inhomogeneous setting, we prove in this work an inequality on the Wasserstein distance for any two measurevalued solutions to the BoltzmannEnskog equation. As a ...
3Uniform 4Path Decompositions Of Complete 3Uniform Hypergraphs, Rachel Mccann
3Uniform 4Path Decompositions Of Complete 3Uniform Hypergraphs, Rachel Mccann
Mathematical Sciences Undergraduate Honors Theses
The complete 3uniform hypergraph of order v is denoted as K_{v} and consists of vertex set V with size v and edge set E, containing all 3element subsets of V. We consider a 3uniform hypergraph P_{7}, a path with vertex set {v_{1}, v_{2}, v_{3}, v_{4}, v_{5}, v_{6}, v_{7}} and edge set {{v_{1}, v_{2}, v_{3}}, {v_{2}, v_{3}, v_{4}}, {v_{4}, v_{5}, v_{6}}, {v_{5}, v_{6}, v_{7}}}. We provide the necessary and sufficient conditions for the existence of a decomposition of K_{v ...}
Error Terms For The Trapezoid, Midpoint, And Simpson's Rules, Jessica E. Coen
Error Terms For The Trapezoid, Midpoint, And Simpson's Rules, Jessica E. Coen
Electronic Theses, Projects, and Dissertations
When it is not possible to integrate a function we resort to Numerical Integration. For example the ubiquitous Normal curve tables are obtained using Numerical Integration. The antiderivative of the defining function for the normal curve involves the formula for antiderivative of e^{x}^{^2} which can't be expressed in the terms of basic functions.
Simpson's rule is studied in most Calculus books, and in all undergraduate Numerical Analysis books, but proofs are not provided. Hence if one is interested in a proof of Simpson's rule, either it can be found in advanced Numerical Analysis books as ...
Dynamical Systems Analysis In Adaptive And Metapopulation Ecology With Applications To Conservation Management, Guenchik Grosklos
Dynamical Systems Analysis In Adaptive And Metapopulation Ecology With Applications To Conservation Management, Guenchik Grosklos
All Graduate Theses and Dissertations
The ability for a species to persist largely relies on how well they adapt to the environment and their interactions with local and global communities. Specifically, if adaptation occurs quickly enough or nearby communities sufficiently promote growth rates, populations at risk of extinction may persist. In this dissertation, we first develop a method that estimates and compares rates of change in time series data of population densities and measurable traits (phenotypes). Additionally, we compare between genetic (evolutionary) and nongenetic (plastic) trait change to determine whether phenotypes change faster when driven by evolutionary or plastic change. We then focus on metapopulation ...
The Influence Of A Course On Assessment For Inservice Secondary Mathematics Teachers, Natalie M. Anderson
The Influence Of A Course On Assessment For Inservice Secondary Mathematics Teachers, Natalie M. Anderson
All Graduate Theses and Dissertations
Many mathematics teachers are not prepared to design valid and usable measurements of their students’ mathematical achievements. There are relatively few opportunities for mathematics teachers to improve their assessment literacy. The purpose of this study is to (1) design a course on assessment for inservice mathematics teachers and (2) evaluate the effectiveness of the course. This paper recounts the development of the course and its influence on 16 teachers. Teachers who completed the course submitted a unit outline with learning objectives, a test blueprint, and a unit test. These artifacts influenced my evaluation on the effectiveness of the course. All ...
The Butterfly Effect Of Fractals, Cody Watkins
The Butterfly Effect Of Fractals, Cody Watkins
Honors College Theses
This thesis applies concepts in fractal geometry to the relatively new field of mathematics known as chaos theory, with emphasis on the underlying foundation of the field: the butterfly effect. We begin by reviewing concepts useful for an introduction to chaos theory by defining terms such as fractals, transformations, affine transformations, and contraction mappings, as well as proving and demonstrating the contraction mapping theorem. We also show that each fractal produced by the contraction mapping theorem is unique in its fractal dimension, another term we define. We then show and demonstrate iterated function systems and take a closer look at ...
Data And Algorithmic Modeling Approaches To Count Data, Andraya Hack
Data And Algorithmic Modeling Approaches To Count Data, Andraya Hack
Honors College Theses
Various techniques are used to create predictions based on count data. This type of data takes the form of a nonnegative integers such as the number of claims an insurance policy holder may make. These predictions can allow people to prepare for likely outcomes. Thus, it is important to know how accurate the predictions are. Traditional statistical approaches for predicting count data include Poisson regression as well as negative binomial regression. Both methods also have a zeroinflated version that can be used when the data has an overabundance of zeros. Another procedure is to use computer algorithms, also known as ...