Ultrametric Diffusion, Rugged Energy Landscapes And Transition Networks, 2022 The University of Texas Rio Grande Valley

#### Ultrametric Diffusion, Rugged Energy Landscapes And Transition Networks, Wilson A. Zuniga-Galindo

*Mathematical and Statistical Sciences Faculty Publications and Presentations*

In this article we introduce the ultrametric networks which are p" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">p-adic continuous analogs of the standard Markov state models constructed using master equations. A p" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px ...

The Zariski-Riemann Space As A Universal Model For The Birational Geometry Of A Function Field, 2022 The Graduate Center, City University of New York

#### The Zariski-Riemann 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 Zariski-Riemann 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 ad-hoc collections of open subsets of $\ZR (K/k)$ ordered by quasi-refinements 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 Integro-Differential Equations Involved By Caputo Fractional Derivative, 2022 Zayed University

#### Fractional Bernstein Operational Matrices For Solving Integro-Differential 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 integro-differential 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), 2022 State University of New York at New Paltz

#### 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 Navier-Stokes Solver, 2022 Francis Marion University

#### Implementation Of A Least Squares Method To A Navier-Stokes Solver, Jada P. Lytch, Taylor Boatwright, Ja'nya Breeden

*Rose-Hulman Undergraduate Mathematics Journal*

The Navier-Stokes 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 Navier-Stokes 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 Over-Suppression, 2022 Virginia Commonwealth University

#### Gene Drives And The Consequences Of Over-Suppression, Cole Butler

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

An Even 2-Factor In The Line Graph Of A Cubic Graph, 2022 Yokohama National University

#### An Even 2-Factor In The Line Graph Of A Cubic Graph, Seungjae Eom, Kenta Ozeki

*Theory and Applications of Graphs*

An even 2-factor is one such that each cycle is of even length. A 4- regular graph G is 4-edge-colorable if and only if G has two edge-disjoint even 2- factors whose union contains all edges in G. It is known that the line graph of a cubic graph without 3-edge-coloring is not 4-edge-colorable. Hence, we are interested in whether those graphs have an even 2-factor. Bonisoli and Bonvicini proved that the line graph of a connected cubic graph G with an even number of edges has an even 2-factor, if G has a perfect matching [Even cycles and even ...

Mathematical Model Of Immune-Inflammatory Response In Covid-19 Patients, 2022 Virginia Polytechnic Institute and State University

#### Mathematical Model Of Immune-Inflammatory Response In Covid-19 Patients, Quiyana M. Murphy

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Estimating Glutamate Transporter Surface Density In Mouse Hippocampal Astrocytes, 2022 State University of New York at New Paltz

#### Estimating Glutamate Transporter Surface Density In Mouse Hippocampal Astrocytes, Anca R. Radulescu, Annalisa Scimemi

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Real-Time Interactive Simulation Of Large Bird Flocks: Toward Understanding Murmurations, 2022 Georgia Institute of Technology

#### Real-Time Interactive Simulation Of Large Bird Flocks: Toward Understanding Murmurations, Maxfield R. Comstock

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Optimal Time-Dependent Classification For Diagnostic Testing, 2022 Johns Hopkins University

#### Optimal Time-Dependent Classification For Diagnostic Testing, Prajakta P. Bedekar, Paul Patrone, Anthony Kearsley

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

On Two-Player Pebbling, 2022 Lehigh University

#### On Two-Player 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 two-player game on a graph G, called *Two-Player 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 pebble-free and there are no more pebbling moves on the vertices of G. The Two-Player Pebbling Number of a graph G, η(G), is the minimum m such that for every arrangement ...

The Impact Of Academic Tracking And Mathematics Self-Concept On Mathematics Achievement., 2022 Minnesota State University Moorhead

#### The Impact Of Academic Tracking And Mathematics Self-Concept 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 self-concept (MSC) and how that correlates to students’ mathematics achievement. This study measured students’ MSC through a mathematics self-concept questionnaire and measured mathematics achievement by the students’ latest grade report. Participants included 60 students in grades 10-12 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, 2022 Minnesota State University Moorhead

#### 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, 2022 Minnesota State University Moorhead

#### 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, 2022 Mississippi State University

#### The Mathematical Foundation Of The Musical Scales And Overtones, Michaela Dubose-Schmitt

*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 2-Deficient Rectangles With L-Pentominoes, 2022 California Lutheran University

#### Tiling Rectangles And 2-Deficient Rectangles With L-Pentominoes, Monica Kane

*Rose-Hulman Undergraduate Mathematics Journal*

We investigate tiling rectangles and 2-deficient rectangles with *L*-pentominoes. First, we determine exactly when a rectangle can be tiled with *L*-pentominoes. We then determine locations for pairs of unit squares that can always be removed from an *m* × *n* rectangle to produce a tileable 2-deficient 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, 2022 University of Southern Mississippi

#### 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 small-scale processes at the seafloor-ocean interface. Commonly used Euler-Lagrange 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, 2022 Duquesne University

#### 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 24-hour 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 K-Rational Groups Of Isogenous Elliptic Curves Over Finite Fields, 2022 University of Rochester

#### On Isomorphic K-Rational Groups Of Isogenous Elliptic Curves Over Finite Fields, Ben Kuehnert, Geneva Schlafly, Zecheng Yi

*Rose-Hulman 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 ...