Mathematics Commons^™

Regularity For A Class Of Quasilinear Degenerate Parabolic Equations In The Heisenberg Group, Luca Capogna, Giovanna Citti, Nicola Garofalo

Mathematics Sciences: Faculty Publications

We extend to the parabolic setting some of the ideas originated with Xiao Zhong's proof in [31] of the Hölder regularity of p-harmonic functions in the Heisenberg group Hn. Given a number p ≥ 2, in this paper we establish the C1 smoothness of weak solutions of a class of quasilinear PDE in Hn modeled on the equation.

Engaging English Learners In Purposeful Discourse In Elementary Mathematics, Karlyn E. Davis-Welton

Walden Dissertations and Doctoral Studies

Teachers are experiencing a change in practice, from teacher-centered to student-centered, which affects their work with English learners (ELs) in third through fifth grade mathematics classrooms. The implementation of student-centered discourse practices is essential to orchestrating productive mathematical discussions. However, the common practice is teacher-centered instruction where teacher talk is prevalent. Although the school district in this study provided professional development (PD) to address student-centered practices, PD for teaching ELs to interact in English in their mathematics classrooms remained to be addressed. The purpose of this study was to gain an understanding of teachers’ experiences with new discourse practices and …

Teacher Understanding Of Instructional Strategies In Elementary Mathematics, Erica Boatwright Glover

Walden Dissertations and Doctoral Studies

Synergizing Elementary School (pseudonym) consistently experiences low state-required mathematics test scores in grades 3 and 4 below district and state proficiency rates in mathematics. The purpose of this qualitative case study was to investigate what instructional practices used by Grade 3 and Grade 4 teachers are, aligned or not aligned, with research-based planning, standards-based instruction, attention to conditions of learning, and professional responsibilities of teachers to support students’ achievement in mathematics. This study's conceptual framework was grounded in Robert Marzano's model of teaching effectiveness called the focus teacher evaluation model. Data for this case study were gathered from semi-structured interviews …

Ranked List Fusion And Re-Ranking With Pre-Trained Transformers For Arqmath Lab, Shaurya Rohatgi, Jian Wu, C. Lee Giles

Computer Science Faculty Publications

This paper elaborates on our submission to the ARQMath track at CLEF 2021. For our submission this year we use a collection of methods to retrieve and re-rank the answers in Math Stack Exchange in addition to our two-stage model which was comparable to the best model last year in terms of NDCG’. We also provide a detailed analysis of what the transformers are learning and why is it hard to train a math language model using transformers. This year’s submission to Task-1 includes summarizing long question-answer pairs to augment and index documents, using byte-pair encoding to tokenize formula and …

Elliptical Fourier Analysis Of Crown Shape In Permanent Mandibular Molars From The Late Neolithic Cave Burials Of Belgium, Frank L'Engle Williams, Juliet K. Brophy, Gregory J. Matthews

Mathematics and Statistics: Faculty Publications and Other Works

Prehistoric remains from caves and rockshelters are known from more than 250 sites situated along the Meuse River Basin of Belgium. Most of these osteological remnants date to the Late Neolithic period beginning after 4,500 years before present (BP), and five of these cave burials have been subject to intensive study, including Hastière Caverne M and Hastière Trou Garçon C from an earlier period of the Late Neolithic (4,345 ± 60 to 4,220 ± 45 years BP), Sclaigneaux and Bois Madame from the final/late Neolithic (4,155 ± 35 to 3,910 ± 40 years BP) and Maurenne Caverne de la Cave …

Bipartite, Size, And Online Ramsey Numbers Of Some Cycles And Paths, Eliyahu Schudrich

Theses, Dissertations and Culminating Projects

The basic premise of Ramsey Theory states that in a sufficiently large system, complete disorder is impossible. One instance from the world of graph theory says that given two fixed graphs F and H, there exists a finitely large graph G such that any red/blue edge coloring of the edges of G will produce a red copy of F or a blue copy of H. Much research has been conducted in recent decades on quantifying exactly how large G must be if we consider different classes of graphs for F and H. In this thesis, we explore several Ramsey- type …

Transitioning To An Active Learning Environment For Calculus At The University Of Florida, Darryl Chamberlain, Amy Grady, Scott Keeran, Kevin Knudson, Ian Manly, Melissa Shabazz, Corey Stone

Publications

In this note, we describe a large-scale transition to an active learning format in first-semester calculus at the University of Florida. Student performance and attitudes are compared across traditional lecture and flipped sections.

Zn Orbifolds Of Vertex Operator Algebras, Daniel Graybill

Electronic Theses and Dissertations

Given a vertex algebra V and a group of automorphisms of V, the invariant subalgebra V^G is called an orbifold of V. This construction appeared first in physics and was also fundamental to the construction of the Moonshine module in the work of Borcherds. It is expected that nice properties of V such as C2-cofiniteness and rationality will be inherited by V^G if G is a finite group. It is also expected that under reasonable hypotheses, if V is strongly finitely generated and G is reductive, V^G will also be strongly finitely generated. This is an analogue …

Quantization For Uniform Distributions On Hexagonal, Semicircular, And Elliptical Curves, Gabriela Pena, Hansapani Rodrigo, Mrinal Kanti Roychowdhury, Josef A. Sifuentes, Erwin Suazo

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, first we have defined a uniform distribution on the boundary of a regular hexagon, and then investigated the optimal sets of n-means and the nth quantization errors for all positive integers n. We give an exact formula to determine them, if n is of the form n = 6k for some positive integer k. We further calculate the quantization dimension, the quantization coefficient, and show that the quantization dimension is equal to the dimension of the object, and the quantization coefficient exists as a finite positive number. Then, we define a mixture of two uniform distributions on …

Internet-Based Cognitive–Behavioural Therapy For Tinnitus: Secondary Analysis To Examine Predictors Of Outcomes, Hansapani Rodrigo, Eldré W. Beukes, Gerhard Andersson, Vinaya Manchaiah

School of Mathematical & Statistical Sciences Faculty Publications

Objectives The current study examined predictors of outcomes of internet-based cognitive–behavioural therapy (ICBT) for individuals with tinnitus.

Design Secondary analysis of intervention studies.

Setting Internet-based guided tinnitus intervention provided in the UK.

Participants 228 individuals who underwent ICBT.

Interventions ICBT.

Primary and secondary outcome measures The key predictor variables included demographic, tinnitus, hearing-related and treatment-related variables as well as clinical factors (eg, anxiety, depression, insomnia), which can have an impact on the treatment outcome. A 13-point reduction in Tinnitus Functional Index (TFI) scores has been defined as a successful outcome.

Results Of the 228 subjects who were included in the …

Semiclassical Backreaction On Asymptotically Anti–De Sitter Black Holes, Peter Taylor, Cormac Breen

Articles

We consider a quantum scalar field on the classical background of an asymptotically anti–de Sitter black hole and the backreaction the field’s stress-energy tensor induces on the black hole geometry. The backreaction is computed by solving the reduced-order semiclassical Einstein field equations sourced by simple analytical approximations for the renormalized expectation value of the scalar field stress-energy tensor. When the field is massless and conformally coupled, we adopt Page’s approximation to the renormalized stress-energy tensor, while for massive fields we adopt a modified version of the DeWitt-Schwinger approximation. The latter approximation must be modified so that it possesses the correct …

Collaborations In Environmental Initiatives For An Effective Gover- Nance Of Social-Ecological Systems: What The Scientific Literature Suggests., Elena Andriollo, Alberto Caimo, Laura Secco, Elena Pisani

Articles

Moving from the scientific literature on evaluation of environmental projects and programs, this study identifies how and under which conditions collaborations are considered effective for adaptive gover- nance of SES. The method adopted is a systematic literature review based on the quantitative and qualitative analysis of 56 articles selected through specific queries on the SCOPUS database and published from 2004 to 2020. Results of the quantitative analysis underline conditions able to make collaborations effective for adaptive governance of SES: the importance of transdisciplinary research tackling both environmental and social sciences, the perceived urgency of stakeholders to tackle environmental challenges and …

Numerical Simulations Of Capsule Deformation Using A Dual Time-Stepping Lattice Boltzmann Method, Charles Armstrong, Yan Peng

Mathematics & Statistics Faculty Publications

In this work a quasisteady, dual time-stepping lattice Boltzmann method is proposed for simulation of capsule deformation. At each time step the steady-state lattice Boltzmann equation is solved using the full approximation storage multigrid scheme for nonlinear equations. The capsule membrane is modeled as an infinitely thin shell suspended in an ambient fluid domain with the fluid structure interaction computed using the immersed boundary method. A finite element method is used to compute the elastic forces exerted by the capsule membrane. Results for a wide range of parameters and initial configurations are presented. The proposed method is found to reduce …

Interaction Between Genetic Risk Scores For Reduced Pulmonary Function And Smoking, Asthma And Endotoxin, Sinjini Sikdar, Annah B. Wyss, Mi Kyeong Lee, Thanh T. Hoang, Marie Richards, Laura E. Beane Freeman, Christine Parks, Peter S. Thorne, John L. Hankinson, David M. Umbach, Alison Motsinger-Reif, Stephanie J. London

Mathematics & Statistics Faculty Publications

Rationale Genome-wide association studies (GWASs) have identified numerous loci associated with lower pulmonary function. Pulmonary function is strongly related to smoking and has also been associated with asthma and dust endotoxin. At the individual SNP level, genome-wide analyses of pulmonary function have not identified appreciable evidence for gene by environment interactions. Genetic Risk Scores (GRSs) may enhance power to identify gene–environment interactions, but studies are few.

Methods We analysed 2844 individuals of European ancestry with 1000 Genomes imputed GWAS data from a case–control study of adult asthma nested within a US agricultural cohort. Pulmonary function traits were FEV₁, …

Em Estimation For Zero- And K-Inflated Poisson Regression Model, Monika Arora, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

Count data with excessive zeros are ubiquitous in healthcare, medical, and scientific studies. There are numerous articles that show how to fit Poisson and other models which account for the excessive zeros. However, in many situations, besides zero, the frequency of another count k tends to be higher in the data. The zero- and k-inflated Poisson distribution model (ZkIP) is appropriate in such situations The ZkIP distribution essentially is a mixture distribution of Poisson and degenerate distributions at points zero and k. In this article, we study the fundamental properties of this mixture distribution. Using stochastic representation, we …

Morphology-Dependent Resonances In Two Concentric Spheres With Variable Refractive Index In The Outer Layer: Analytic Solutions, Umaporn Nuntaplook, John A. Adam

Mathematics & Statistics Faculty Publications

In many applications constant or piecewise constant refractive index profiles are used to study the scattering of plane electromagnetic waves by a spherical object. When the structured media has variable refractive indices, this is more of a challenge. In this paper, we investigate the morphology dependent resonances for the scattering of electromagnetic waves from two concentric spheres when the outer shell has a variable refractive index. The resonance analysis is applied to the general solutions of the radial Debye potential for both transverse magnetic and transverse electric modes. Finally, the analytic conditions to determine the resonance locations for this system …

Using Sentiment Analysis To Find The Public's Opinion On Iowa's Three State Schools, Alexa Ryan Bullock

Honors Program Theses

The purpose of this project was to create my own sentiment analysis that would allow me to analyze reviews of the three Iowa state schools: University of Iowa, Iowa State, and University of Northern Iowa, and organize them in a way that showed the strong and weak points of each university. I accomplished this by researching how sentiment analysis works, applying that to the construction of my own sentiment analysis, and then using it on reviews about these three schools. The goal of this project was to give my audience a greater understanding of how sentiment analysis works by creating …

Co-Taught Inclusive Classrooms And Algebra I Achievement Of Students With Disabilities, Valeree Williams

Walden Dissertations and Doctoral Studies

Co-teaching has become an increasingly important topic for students with disabilities (SWDs) to access to the general education curriculum. The purpose of this quantitative study was to determine the instructional effectiveness of co-teaching versus inclusive non-co-teaching classroom instruction for SWDs using Algebra I End of Course (EOC) scores and whether these effects differed by gender. Cook and Friend’s principles of co-teaching provided the framework for the study. The first research question was: is there a significant difference in EOC scores for male SWDs enrolled in Grade 9 Algebra I who receive instruction in co-taught Algebra I classes as compared to …

Mathematics Teachers’ Pedagogical Content Knowledge And Its Relation To Student Achievement, Michelle Emmalyn Peters-George

Walden Dissertations and Doctoral Studies

Students' performance in national assessments of mathematics at Grades 2, 4, and 6 has been a cause for concern in the Eastern Caribbean. Researchers have called for studies to focus on primary mathematics teachers' pedagogies rather than on laptops and curriculum; however, it is unclear how primary mathematics teachers' pedagogical knowledge influences these student’s achievement. The purpose of this quantitative study was to investigate the relationship between primary mathematics teachers' pedagogical content knowledge (mathematical knowledge for teaching, quality of instruction, and pedagogical qualifications) and student achievement, measured by national assessment scores in Grenada, controlling for teachers’ age, gender, and experience. …

Numerical Approximation Of Lyapunov Exponents And Its Applications In Control Systems, Nakita K. Andrews

College of Graduate Studies: Theses & Dissertations

The progression of state trajectories with respect to time, and its stability properties can be described by a system of nonlinear differential equations. However, since most nonlinear dynamical systems cannot be solved by hand, one must rely on computer simulations to observe the behavior of the system. This work focuses on chaotic systems. The Lyapunov Exponent (LE) is frequently used in the quantitative studies of a chaotic system. Lyapunov exponents give the average rate of separation of nearby orbits in phase space, which can be used to determine the state of a system, e.g. stable or unstable. The objective of …

On The Lagrangian Description And Uniqueness For The One-Dimensional Pressureless Euler System, Mark David Suder

Graduate Theses, Dissertations, and Problem Reports (ETD)

In this work we show that the one-dimensional pressureless Euler system admits a Lagragian characterization under fairly general initial conditions, extending recent results by Hynd [7]. Moreover, we show that if the initial velocity is right-continuous and bounded, then we have uniqueness of this Lagrangian solution (called Sticky Particles Flow, or SPF solution), which coincides with the Scalar Conservation Laws (or SCL) solution. An important tool we employed in order to prove existence is a result by Gangbo et al. [5], which establishes a canonical (i.e. the flow is given by the optimal maps pushing the Lebesgue measure restricted to …

Heterogeneous Generalizations Of Vertex Coloring, Lucia Ciletti Mazza

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation proves a collection of results in some heterogeneous generalizations of vertex coloring, i.e. generalizations in which the relationship between the colors of two adjacent vertices may differ throughout the graph. For the most part, the results are from group coloring, group list coloring, and DP coloring. The main results are as follows: a group list coloring analogue of Brooks' Theorem for multigraphs, a result linking group structure (rather than only group size) with group coloring, some results involving coloring edge-disjoint unions, and an examination of the relationship between the group and DP coloring numbers of a multigraph and …

Question 1: Chess Moves; Question 2: Cat Litter, Larry Weinstein

Physics Faculty Publications

How many chess moves are made by Americans each year?

How much cat litter did Americans scoop last year?

Exponential Random Graphs And A Generalization Of Parking Functions, Ryan Demuse

Electronic Theses and Dissertations

Random graphs are a powerful tool in the analysis of modern networks. Exponential random graph models provide a framework that allows one to encode desirable subgraph features directly into the probability measure. Using the theory of graph limits pioneered by Borgs et. al. as a foundation, we build upon the work of Chatterjee & Diaconis and Radin & Yin. We add complexity to the previously studied models by considering exponential random graph models with edge-weights coming from a generic distribution satisfying mild assumptions. In particular, we show that a large family of two-parameter, edge-weighted exponential random graphs display a phase …

A Deep Learning Model To Predict Traumatic Brain Injury Severity And Outcome From Mr Images, Dacosta Yeboah, Hung Nguyen, Daniel B. Hier, Gayla R. Olbricht, Tayo Obafemi-Ajayi

Chemistry Faculty Research & Creative Works

For Many Neurological Disorders, Including Traumatic Brain Injury (TBI), Neuroimaging Information Plays a Crucial Role Determining Diagnosis and Prognosis. TBI is a Heterogeneous Disorder that Can Result in Lasting Physical, Emotional and Cognitive Impairments. Magnetic Resonance Imaging (MRI) is a Non-Invasive Technique that Uses Radio Waves to Reveal Fine Details of Brain Anatomy and Pathology. Although MRIs Are Interpreted by Radiologists, Advances Are Being Made in the Use of Deep Learning for MRI Interpretation. This Work Evaluates a Deep Learning Model based on a Residual Learning Convolutional Neural Network that Predicts TBI Severity from MR Images. the Model Achieved a …

On Coloring Oriented Graphs Of Large Girth, Michael Morris

Graduate Student Theses, Dissertations, & Professional Papers

No abstract provided.

Solving Neutrosophic Linear Equations Systems Using Symbolic Computation (Resolucion De Sistemas De Ecuaciones Lineales Neutrosóficas Mediante Computación Simbólica), Maykel Leyva-Vazquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we apply the concept of neutrosophic numbers to solve a systems of neutrophic linear equations using symbolic computation. Also, we utilize Jupyter, which is supported in Google Colaboratory for performing symbolic computation. The sympy library of Python is used to perform the process of neutrosophic computation. Systems of neutrosophic linear equations are solved through symbolic computation in Python. A case study was developed for the determination of vehicular traffic with indeterminacy. This king of computation opens new ways to deal with indeterminacy in real-world problems.

Indeterminacy In Neutrosophic Theories And Their Applications, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Indeterminacy makes the main distinction between fuzzy / intuitionistic fuzzy (and other extensions of fuzzy) set / logic vs. neutrosophic set / logic, and between classical probability and neutrosophic probability. Also, between classical statistics vs. neutrosophic and plithogenic statistics, between classical algebraic structures vs. neutrosophic algebrais structures, between crisp numbers vs. neutrosophic numbers. We present a broad definition of indeterminacy, various types of indeterminacies, and many practical applications.

Techno-Art Of Selariu Supermathematics Functions, Vol. Iii, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The name of supermathematics (SM) was coined by the late mathematician Prof. em. Dr. doc. eng. Gheorghe Silaş who, at the presentation of the first works in this field, at the First National Conference of Vibrations in Machine Construction, Timişoara, 1978, entitled “EXCENTRIC CIRCULAR FUNCTIONS” declared: “Young man, you didn't just discover some new functions, but a new mathematics, a supermathematics”. Then, at my age of 40, I was as happy as I was when a teenager. And I found, with great satisfaction, that he might be right! In 1978! In 2000, after 22 years, he offered me to write …

A Review On Electroculture, Magneticulture And Laserculture To Boostplant Growth, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

While several reviews on potential applications of electroculture are available, in this survey, we discuss these issues from history, starting from earliest experiments by Ross. And in the last section, we discuss possible application of laserculture, another form of potential improvement. It is our hope that what we present here may be found useful for improving agricultural performance in many countries, as well as reducing dependence on fertilizer.