Mathematics Commons^™

Uniform Lipschitz Continuity Of The Isoperimetric Profile Of Compact Surfaces Under Normalized Ricci Flow, Yizhong Zheng

Dissertations, Theses, and Capstone Projects

We show that the isoperimetric profile h_{g(t)}(\xi) of a compact Riemannian manifold (M,g) is jointly continuous when metrics g(t) vary continuously. We also show that, when M is a compact surface and g(t) evolves under normalized Ricci flow, h^2_{g(t)}(\xi) is uniform Lipschitz continuous and hence h_{g(t)}(\xi) is uniform locally Lipschitz continuous.

Convexity And Curvature In Hierarchically Hyperbolic Spaces, Jacob Russell-Madonia

Dissertations, Theses, and Capstone Projects

Introduced by Behrstock, Hagen, and Sisto, hierarchically hyperbolic spaces axiomatized Masur and Minsky's powerful hierarchy machinery for the mapping class groups. The class of hierarchically hyperbolic spaces encompasses a number of important and seemingly distinct examples in geometric group theory including the mapping class group and Teichmueller space of a surface, virtually compact special groups, and the fundamental groups of 3-manifolds without Nil or Sol components. This generalization allows the geometry of all of these important examples to be studied simultaneously as well as providing a bridge for techniques from one area to be applied to another.

This thesis presents …

Symmetric Rigidity For Circle Endomorphisms With Bounded Geometry And Their Dual Maps, John Adamski

Dissertations, Theses, and Capstone Projects

Let $f$ be a circle endomorphism of degree $d\geq2$ that generates a sequence of Markov partitions that either has bounded nearby geometry and bounded geometry, or else just has bounded geometry, with respect to normalized Lebesgue measure. We define the dual symbolic space $\S^*$ and the dual circle endomorphism $f^*=\tilde{h}\circ f\circ{h}^{-1}$, which is topologically conjugate to $f$. We describe some properties of the topological conjugacy $\tilde{h}$. We also describe an algorithm for generating arbitrary circle endomorphisms $f$ with bounded geometry that preserve Lebesgue measure and their corresponding dual circle endomorphisms $f^*$ as well as the conjugacy $\tilde{h}$, and implement it …

Pemahaman Ungkapan Algebra Dalam Kalangan Murid Tingkatan Dua, Hamid Azizah

Student Works (2020-2029)

Pemahaman tentang konsep ungkapan algebra penting bagi murid sekolah menengah kerana ia merupakan asas kepada pembelajaran matematik di peringkat menengah dan peringkat pengajian tinggi memandangkan kesukaran dalam pembelajaran algebra menjadi semakin kritikal. Kajian ini adalah untuk mengenal pasti pemahaman murid Tingkatan Dua tentang ungkapan algebra dengan berlandaskan konstruktivisme radikal. Penyelidikan ini menggunakan kajian kes sebagai reka bentuk kajian, yang membabitkan data berbentuk kualitatif. Peserta kajian membabitkan enam murid dari tiga kategori pencapaian akademik dengan menggunakan teknik persampelan bertujuan. Data kajian terkumpul melalui tiga sesi temu duga klinikal dengan menggunakan perakam video, catatan murid dan pengkaji. Data kajian dianalisis dengan menggunakan …

Pemahaman Murid Tingkatan Lima Tentang Konsep Dalam Topik Janjang Aritmetik, Edwar Siti Zaharah

Student Works (2020-2029)

Janjang Aritmetik merupakan tajuk yang sangat penting bagi murid Tingkatan Lima yang mengambil matapelajaran elektif Matematik Tambahan. Tujuan kajian ini dijalankan adalah untuk mengetahui pemahaman murid Tingkatan Lima tentang konsep dalam topik janjang aritmetik. Seramai empat orang murid Tingkatan Lima dipilih dalam kajian ini menggunakan kaedah persampelan bertujuan. Mereka belajar di sebuah sekolah menengah di Selangor. Kajian ini dijalankan berlandaskan teori konstruktivisme radikal. Kajian kes digunakan bagi mengumpulkan data melalui empat sesi temu bual klinikal yang melibatkan gambaran mental, perwakilan, makna dan penyelesaian masalah. Setiap sesi temu duga dirakam dengan alat perakam video. Data kajian dalam bentuk jawapan bertulis dan …

Optimal Control Of A Rumor Propagation Model With Different Propagation Degrees In Social Network, Yingfeng Tang

Student Works (2020-2029)

Rumor is a social interaction of information, and its development is of great significance to human beings. In this paper, by studying the D K model and a rumor model spreading with rumor latent period, deduces the rumor model with differe nt propagation degrees of the spreaders. The two equilibrium points in the system are found through derivation. In real life, enterprises often ignore the reasonable planning of the cost of rumor control. By means of public education and media technology u sing by the authorities to debunk rumors, an optimal control problem i s established. The Pontryagin’s maximum principle …

Data Assimilation For Conductance-Based Neuronal Models, Matthew Moye

Dissertations

This dissertation illustrates the use of data assimilation algorithms to estimate unobserved variables and unknown parameters of conductance-based neuronal models. Modern data assimilation (DA) techniques are widely used in climate science and weather prediction, but have only recently begun to be applied in neuroscience. The two main classes of DA techniques are sequential methods and variational methods. Throughout this work, twin experiments, where the data is synthetically generated from output of the model, are used to validate use of these techniques for conductance-based models observing only the voltage trace. In Chapter 1, these techniques are described in detail and the …

Analysis Of Gameplay Strategies In Hearthstone: A Data Science Approach, Connor W. Watson

Theses

In recent years, games have been a popular test bed for AI research, and the presence of Collectible Card Games (CCGs) in that space is still increasing. One such CCG for both competitive/casual play and AI research is Hearthstone, a two-player adversarial game where players seeks to implement one of several gameplay strategies to defeat their opponent and decrease all of their Health points to zero. Although some open source simulators exist, some of their methodologies for simulated agents create opponents with a relatively low skill level. Using evolutionary algorithms, this thesis seeks to evolve agents with a higher skill …

Price Vs Quantity: Essays On Strategic Choice In Differentiated Oligopoly., Arindam Paul Dr.

Doctoral Theses

Industrial economists are often interested in comparing different market structures which are primarily based on their market outcomes and then try to determine the best market structure considering either the society’s welfare or the firm’s profit and sometimes considering both. In this context, the "Cournot-Bertrand comparison" is one such important comparison that has often been analyzed in the literature of industrial economics. The main structural difference between Cournot competition and Bertrand competition arises due to the strategic variable through which firms interact with each other in the market. To be more specific, in case of Cournot competition, firms compete with …

Acoustic Versus Electromagnetic Field Theory: Scalar, Vector, Spinor Representations And The Emergence Of Acoustic Spin, Lucas Burns, Konstantin Y. Bliokh, Franco Nori, Justin Dressel

Mathematics, Physics, and Computer Science Faculty Articles and Research

We construct a novel Lagrangian representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian representation with a scalar potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement vector potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether …

Radio Graceful Labelling Of Graphs, Laxman Saha, Alamgir Rahaman Basunia

Theory & Applications of Graphs

Radio labelling problem of graphs have their roots in communication problem known as Channel Assignment Problem. For a simple connected graph G=(V(G), E(G)), a radio labeling is a mapping f : V(G) →{0,1,2,…} such that |f(u)-f(v)|≥ diam(G)+1-d(u,v) for each pair of distinct vertices u,v ∈ V(G), where diam(G) is the diameter of G and d(u,v) is the distance between u and v. A radio labeling f of a graph G is a radio graceful labeling of G if f(V(G)) = {0,1,… |V(G)|-1}. A graph for which a radio graceful labeling exists is called radio graceful. …

"Fireworks And Quadratic Functions”, Kelly W. Remijan

Teacher Resources

No abstract provided.

Evolution Of Computational Thinking Contextualized In A Teacher-Student Collaborative Learning Environment., John Arthur Underwood

LSU Doctoral Dissertations

The discussion of Computational Thinking as a pedagogical concept is now essential as it has found itself integrated into the core science disciplines with its inclusion in all of the Next Generation Science Standards (NGSS, 2018). The need for a practical and functional definition for teacher practitioners is a driving point for many recent research endeavors. Across the United States school systems are currently seeking new methods for expanding their students’ ability to analytically think and to employee real-world problem-solving strategies (Hopson, Simms, and Knezek, 2001). The need for STEM trained individuals crosses both the vocational certified and college degreed …

A Decision Tree Model To Predict Marginalized Zero-Inflated Poisson Mean, Philip Amewudah

LSU New Orleans Theses and Dissertations

No abstract provided.

On Dc And Local Dc Functions, Liam Jemison

University Honors Theses

In this project we investigate the class of functions which can be represented by a difference of convex functions, hereafter referred to simply as 'DC' functions. DC functions are of interest in optimization because they allow the use of convex optimization techniques in certain non-convex problems. We present known results about DC and locally DC functions, including detailed proofs of important theorems by Hartman and Vesely.

We also investigate the DCA algorithm for optimizing DC functions and implement it to solve the support vector machine problem.

"Sheet Metal And Polynomials At Work”, Kelly W. Remijan

Teacher Resources

No abstract provided.

A Note On Eulerian Numbers And Toeplitz Matrices, Tian-Xiao He, Peter J.-S. Shiue

Mathematical Sciences Faculty Research

This note presents a new formula of Eulerian numbers derived from Toeplitz matrices via Riordan array approach.

"Dancing Fountains”, Kelly W. Remijan

Teacher Resources

No abstract provided.

“Product Development: Model Rockets As Toys”, Kelly W. Remijan

Teacher Resources

No abstract provided.

"American Football: Field Goals And Quadratic Functions”, Kelly W. Remijan

Teacher Resources

No abstract provided.

"Crash Reconstruction: Stopping Distance”, Kelly W. Remijan

Teacher Resources

No abstract provided.

Phase-Adjusted Estimation Of The Covid-19 Outbreak In South Korea Under Multi-Source Data And Adjustment Measures: A Modelling Study, Xiaomei Feng, Jing Chen, Kai Wang, Lei Wang, Fengqin Zhang, Zhen Jin, Lan Zou, Xia Wang

Mathematics Faculty Articles

Based on the reported data from February 16, 2020 to March 9, 2020 in South Korea including confirmed cases, death cases and recovery cases, the control reproduction number was estimated respectively at different control measure phases using Markov chain Monte Carlo method and presented using the resulting posterior mean and 95% credible interval (C_rI). At the early phase from February 16 to February 24, we estimate the basic reproduction number R₀ of COVID-19 to be 4.79(95% C_rI 4.38 - 5.2). The estimated control reproduction number dropped rapidly to R_c ≈ 0.32(95% C_rI …

An Effective Method To Obtain Contour Of Fisheye Images Based On Explicit Level Set Method, Xuegang Wu, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

Obtaining the effective contour from an image taken by fisheye lens is important for the following transactions. Many studies try to develop suitable methods to get accurate contours of fisheye images. Using the traditional level set method (CV model) is hard to meet the desire task that the final segmentation region is a circle. Therefore, the preprocessing of fisheye images and the improvement of traditional level set method are redesigned to get a final circular segmentation which may be suitable to other applications. In this paper, we use the local entropy method to make the value of pixels be even …

The Distribution Of The Greatest Common Divisor Of Elements In Quadratic Integer Rings, Asimina S. Hamakiotes

Student Theses and Dissertations

For a pair of quadratic integers n and m chosen randomly, uniformly, and independently from the set of quadratic integers of norm x or less, we calculate the probability that the greatest common divisor of (n,m) is k. We also calculate the expected norm of the greatest common divisor (n,m) as x tends to infinity, with explicit error terms. We determine the probability and expected norm of the greatest common divisor for quadratic integer rings that are unique factorization domains. We also outline a method to determine the probability and expected norm of the greatest …

The Perceptions And Experiences Of Math Anxiety, Bradley Baas

Education | Master's Theses

Math anxiety has the potential to negatively impact a student’s knowledge and awareness of themselves. This anxiety leaves students with feelings of incapability in learning math because of their existing beliefs they received in their early years in their educations. The purpose of this research was to better understand the development of middle school eighth grade students and their teachers’ math anxiety while also exploring the obstacles that anxiety creates preventing and/or inhibiting teachers from teaching the required standardized lessons. My research shows that without a trusting relationship between the teacher and student, students experience a decline in mathematics performance …

Oscillations Via Excitable Cells, Derek Orr, Bard Ermentrout

Biology and Medicine Through Mathematics Conference

No abstract provided.

Modeling Vaccination Strategies To Control White-Nose Syndrome In Little Brown Bat Colonies, Eva Cornwell, David Elzinga, Shelby R. Stowe, Alex Capaldi

Biology and Medicine Through Mathematics Conference

No abstract provided.

Emergence, Mechanics, And Development: How Behavior And Geometry Underlie Cowrie Seashell Form, Michael G. Levy, Michael R. Deweese

Biology and Medicine Through Mathematics Conference

No abstract provided.

Network Mediation Of Pathology Pattern In Sporadic Creutzfeldt–Jakob Disease, Benjamin Freeze, Pedro Maia, Sneha Pandya, Ashish Raj

Mathematics Faculty Publications - Archive

Sporadic Creutzfeldt–Jakob disease is a rare fatal rapidly progressive dementia caused by the accumulation and spread of pathologically misfolded prions. Evidence from animal models and in vitro experiments suggests that prion pathology propagates along neural connectivity pathways, with the transmission of misfolded prions initiating a corruptive templating process in newly encountered brain regions. Although particular regional patterns of disease have been recognized in humans, the underlying mechanistic basis of these patterns remains poorly understood. Here, we demonstrate that the spatial pattern of disease derived from publicly available human diffusion-weighted MRI data demonstrates stereotypical features across patient cohorts and can be …

Dynamic Portfolio Optimization With A Noisy Observation Of The Hidden Economic Regime, Siqi Peng

Arts & Sciences Graduate Student Theses and Dissertations

In this thesis, we aim to maximize the expected utility of a risk-averse investor by allocating her wealth in a risk-free bank account, a stock, and a defaultable security. The securities' rates of return depend on a hidden continuous-time finite-state Markov chain representing the economic regime. The securities' price volatilities are determined by an observable process, which can be considered as a noisy observation of the hidden economic regime. We use a two dimensional Markov chain, with a special construction of its generator matrix, to model the joint dynamics of the hidden process and the observable process. Our model is …