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On Free-Type Rigid C*-Tensor Categories And Their Annular Representations., B. Madhav Reddy Dr.

Doctoral Theses

No abstract provided.

Introduction Of Infinite Series In High School Level Calculus, Ericka Bella

Masters Essays

No abstract provided.

Algebraic Topics In The Classroom – Gauss And Beyond, Lisa Krance

Masters Essays

No abstract provided.

Calculus Remediation As An Indicator For Success On The Calculus Ap Exam, Ty Stockham

Electronic Theses, Projects, and Dissertations

This study investigates the effects of implementing a remediation program in a high school Advanced Placement Calculus AB course on student class grades and success in passing the AP Calculus AB exam.

A voluntary remediation program was designed to help students understand the key concepts and big ideas in beginning Calculus. Over a period of eight years the program was put into practice and data on student participation and achievement was collected. Students who participated in this program were given individualized recitation activities targeting their specific misunderstandings, and then given an opportunity to retest on chapter exams that they had …

Orbit Spaces Of Unimodular Rows Over Smooth Real Affine Algebras., Soumi Tikader Dr.

Doctoral Theses

Let R be a commutative, Noetherian ring of (Krull) dimension d. It is well known that the set of isomorphism classes of (oriented, if d is even) stably free R-modules of rank d carries the structure of an abelian group. This group can be identified with the orbit space of unimodular rows namely, Umd+1(R)/SLd+1(R). The prime objective of this thesis is to provide the complete computation of this group, when X = Spec(R) be a smooth real affine variety of dimension d ≥ 2 (with the assumption that the set of real points of X is non-empty and orientable). In …

Infinite Mode Quantum Gaussian States., Tiju Cherian John Dr.

Doctoral Theses

No abstract provided.

Barrier Graphs And Extremal Questions On Line, Ray, Segment, And Hyperplane Sensor Networks, Kirk Anthony Boyer

Electronic Theses and Dissertations

A sensor network is typically modeled as a collection of spatially distributed objects with the same shape, generally for the purpose of surveilling or protecting areas and locations. In this dissertation we address several questions relating to sensors with linear shapes: line, line segment, and rays in the plane, and hyperplanes in higher dimensions.

First we explore ray sensor networks in the plane, whose resilience is the number of sensors that must be crossed by an agent traveling between two known locations. The coverage of such a network is described by a particular tripartite graph, the barrier graph of the …

Applications Of Geometric And Spectral Methods In Graph Theory, Lauren Morey Nelsen

Electronic Theses and Dissertations

Networks, or graphs, are useful for studying many things in today’s world. Graphs can be used to represent connections on social media, transportation networks, or even the internet. Because of this, it’s helpful to study graphs and learn what we can say about the structure of a given graph or what properties it might have. This dissertation focuses on the use of the probabilistic method and spectral graph theory to understand the geometric structure of graphs and find structures in graphs. We will also discuss graph curvature and how curvature lower bounds can be used to give us information about …

Decidability For Residuated Lattices And Substructural Logics, Gavin St. John

Electronic Theses and Dissertations

We present a number of results related to the decidability and undecidability of various varieties of residuated lattices and their corresponding substructural logics. The context of this analysis is the extension of residuated lattices by various simple equations, dually, the extension of substructural logics by simple structural rules, with the aim of classifying simple equations by the decidability properties shared by their extensions. We also prove a number of relationships among simple extensions by showing the equational theory of their idempotent semiring reducts coincides with simple extensions of idempotent semirings. On the decidability front, we develop both semantical and syntactical …

Towards Analytical Techniques For Systems Engineering Applications, Griselda Valdepeñas Acosta

Open Access Theses & Dissertations

One of the main objectives of systems engineering is to design, maintain, and analyze systems that help the users. To design an appropriate system for an application domain, we need to know: what are the users' desires and preferences (so that we know in what direction we should aim to change this domain), what is the current state and what is the dynamics of this application domain, and how to use all this information to select the best alternatives for the system design and maintenance. Designing a system includes selecting numerical values for many of the parameters describing the corresponding …

Analysing Flow Free With One Pair Of Dots, Eliot Harris Roske

Senior Projects Spring 2019

Flow Free is a smartphone puzzle game where the player is presented with an m by m grid containing multiple pairs of colored dots. In order to solve the puzzle, the player must draw a path connecting each pair of points so that the following conditions are met: each pair of dots is connected by a path, each square of the grid is crossed by a path, and no paths intersect. Based on these puzzles, this project looks at grids of size m by n with only one pair of dots to determine for which configurations of dots a solution …

Modelling Potential Fluctuations In Double Layer Graphene Systems As A Periodic Oscillation In Electron Density & Its Effect On Coulomb Drag, Ryan Bogucki

Williams Honors College, Honors Research Projects

An expression for the drag transresistivity in a graphene double layer system exhibiting potential fluctuations modelled as a periodic oscillation in electron density is derived. Our model starts from the Coulombic interaction and we derive the correlation between a sinusoidal fluctuation in electron density in the first layer and the induced electron density in the second layer. Previous models in the literature have employed an arbitrary correlation between each layer’s electron density, and the model presented is the first attempt in the literature to explicitly derive this correlation. Recent experiments have found that the drag transresistivity in graphene double layers …

Practical Chaos: Using Dynamical Systems To Encrypt Audio And Visual Data, Julia Ruiter

Scripps Senior Theses

Although dynamical systems have a multitude of classical uses in physics and applied mathematics, new research in theoretical computer science shows that dynamical systems can also be used as a highly secure method of encrypting data. Properties of Lorenz and similar systems of equations yield chaotic outputs that are good at masking the underlying data both physically and mathematically. This paper aims to show how Lorenz systems may be used to encrypt text and image data, as well as provide a framework for how physical mechanisms may be built using these properties to transmit encrypted wave signals.

A First-Year Teacher’S Implementation Of Short-Cycle Formative Assessment Through The Use Of A Classroom Response System And Flexible Grouping, Adrienne Irving Dumas

Electronic Theses and Dissertations

As teachers we are tasked with ensuring that our students are equipped with the skills necessary to not only perform with proficiency on local state and national assessments but also to provide our students with opportunities to develop confidence and competence as learners of mathematics through meaningful challenging and worthwhile activities. As such many teachers have turned to technology and cooperative groups as staples in the classroom. The purpose of this study was to understand how one first-year teacher implemented what she was taught in her undergraduate coursework in teaching two specific units of instruction in two sections of high …

Coarse Geometric Coherence, Jonathan Lee Grossman

Legacy Theses & Dissertations (2009 - 2024)

This dissertation establishes three coarse geometric analogues of algebraic coherence: geometric coherence, coarse coherence, and relative coarse coherence. Each of these coarse geometric coherence notions is a coarse geometric invariant. Several permanence properties of these coarse invariants are demonstrated, elementary examples are computed, and the relationships that these properties have with one another and with other previously established coarse geometric invariants are investigated. Significant results include that the straight finite decomposition complexity of A. Dranishnikov and M. Zarichnyi implies coarse coherence, and that M. Gromov’s finite asymptotic dimension implies coherence, coarse coherence, and relative coarse coherence. Further, as a consequence …

Teachers' Perceptions About Instructing Underachieving K-5 Students On Mathematical Word Problem-Solving, Crystal Yvette Baldwindouglas

Walden Dissertations and Doctoral Studies

The state of Maryland has implemented the Common Core State Standards for Mathematics (CCSSM) operations & algebraic thinking and number & operations-fractions with emphasis on students in Grades K-5 acquiring the ability to solve word problems for state and curriculum math assessments. However, since the implementation of CCSSM, 30% of elementary students in a Maryland school district have demonstrated underachievement (basic or below basic level) on problem-solving sections of the state and school standardized tests. This qualitative case study, guided by Polya's model of the four phases of mathematical problem-solving, was conducted to address this problem. The research questions addressed …

Beta Invariant And Variations Of Chain Theorems For Matroids, Sooyeon Lee

Electronic Theses and Dissertations

The beta invariant of a matroid was introduced by Crapo in 1967. We first find the lower bound of the beta invariant of 3-connected matroids with rank r and the matroids which attain the lower bound. Second we characterize the matroids with beta invariant 5 and 6. For binary matroids we characterize matroids with beta invariant 7. These results extend earlier work of Oxley. Lastly we partially answer an open question of chromatic uniqueness of wheels and prove a splitting formula for the beta invariant of generalized parallel connection of two matroids. Tutte's Wheel-and-Whirl theorem and Seymour's Splitter theorem give …

Cantor Sets, Cantorvals, And Their Topological Structure, Ángel Adrián Agüero

Open Access Theses & Dissertations

With interesting topological properties, the Cantor set is worth studying for itself. In other areas, topological structures arise that are in fact homeomorphic to the Cantor set. In particular, we see sets that are homeomorphic to the Cantor set which result from the subsums of particular series, as well as linear combinations of algebraic sums of Cantor sets. These also result in what has been termed a Cantorval, which we also investigate.

Cramer Type Moderate Deviations For Random Fields And Mutual Information Estimation For Mixed-Pair Random Variables, Aleksandr Beknazaryan

Electronic Theses and Dissertations

In this dissertation we first study Cramer type moderate deviation for partial sums of random fields by applying the conjugate method. In 1938 Cramer published his results on large deviations of sums of i.i.d. random variables after which a lot of research has been done on establishing Cramer type moderate and large deviation theorems for different types of random variables and for various statistics. In particular results have been obtained for independent non-identically distributed random variables for the sum of independent random to estimate the mutual information between two random variables. The estimates enjoy a central limit theorem under some …

Efficient Numerical Methods For Chemotaxis And Plasma Modulation Instability Studies, Truong B. Nguyen

Browse all Theses and Dissertations

In this thesis, we develop efficient numerical solvers for nonlinear systems of partial differential equations (PDEs). These systems of PDEs concern two different sets of physical problems. The first set includes chemotaxis models such as Keller-Segel models and cancer cell invasion models. Solutions of these models are observed to experience the blow-up phenomenon or the development of sharp and spiky features. Therefore, efficient and accurate numerical techniques must be employed in order to capture the solutions' behaviors. For this research, we design efficient solvers for these systems in the one and two spatial dimensions. In particular, we plan to apply …