Other Mathematics Commons^™

Covariant Anyons Via Mackey Machinery, Radhakrishnan Balu

Journal of Stochastic Analysis

No abstract provided.

Nonlinear Filtering Of Classical And Quantum Spin Systems, Sivaguru S. Sritharan, Saba Mudaliar

Journal of Stochastic Analysis

No abstract provided.

Bounded Point Derivations On Roadrunner Sets, Evan Abshire

Theses, Dissertations and Capstones

This paper is concerned primarily with a type of subset of the complex plane known as a Roadrunner set, and its admittance of a bounded point derivation with respect to a given norm on the complex plane. The four norms we are concerned with are the Uniform norm, Lipschitz norm, L^p norm, and Campanato semi-norm. The purpose of this thesis is to provide researchers in approximation theory with more tools for them to accomplish their goals such as the proof of theorems regarding generalized derivatives. A connection has historically been established between the existence of bounded point derivations and …

Cats, Dogs, And Roll Waves: Solutions For Fermi Questions, April 2024, John Adam

Mathematics & Statistics Faculty Publications

On a hot afternoon in western North Carolina, the heavens opened and (to mix metaphors) it started raining “cats and dogs.” The rain was torrential, and soon a river of water was flowing downhill into the parking lot. In rivers and dam spillways, these are known as flood waves. The picture shows a particular type of flood waves known s roll waves—shock-like patterns separated by smooth profiles. In a steady-state situation, the drag forces on the water in the channel are balanced by the down-slope gravitational force. The dimensionless friction coefficient is C, the stream depth is h, v is …

Sky Smiley Face: Solutions For Fermi Questions, November 2024, John Adam

Mathematics & Statistics Faculty Publications

Question 2(a): By rotating Fig. 2 counterclockwise by 90°, explain why circumhorizontal arcs (CHAs) [Figs. 1(b) and (c)] form (under favorable conditions) only when the solar altitude exceeds 58° of arc. (In this case, the incoming ray enters a vertical face of an ice crystal and exits via the lower horizontal face.)Question 2(b): By considering the tilt of Earth’s imaginary N–S axis toward the plane of its orbit around the Sun (∼23.5°), explain why in the northern hemisphere CHAs cannot be seen above about latitude 56° N.

Manifold Learning In Robotics: A Tutorial And Survey, Marcus Hawkins

Computer Science and Engineering Theses - Archive

In this article, we hope to represent the current state of the art of manifold learning in an understandable and approachable way. The authors will present a general overview core algorithms associated with linear and nonlinear dimensionality reduction techniques, give rudimentary definitions from differential geometry, and tenets of robotic perception, manipulation and path planning. Some of the historical applications of these algorithms will be presented, as well as conjectures about future uses, through examples from peer-reviewed journals.

Calculus Students’ Problem-Solving Strategies On Related Rates Of Change Problems Appearing In Online Versus Paper-And-Pencil Format, Tyson Bailey

Mathematics Dissertations - Archive

This study explores first-semester calculus students’ use of mathematical problem-solving strategies while working related rates of change problems in both an online homework format and a traditional pencil-paper format. We address two research questions: (1) How do students’ mathematical problem-solving strategies when working online homework on related rates of change problems compare with their problem-solving strategies when working paper-and-pencil homework related rates of change problems? (2) What influence does the ‘view an example’ feature in online homework have on a student’s problem-solving strategies when working an online RRC homework problem? Using scores on free-response midterm exam problems on related rates …

Fundamental Computational Problems And Algorithms For Superhypergraphs, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Hypergraphs extend traditional graphs by allowing edges (known as hyperedges) to connect more than two vertices, rather than just pairs. This paper explores fundamental problems and algorithms in the context of SuperHypergraphs, an advanced extension of hypergraphs enabling modeling of hierarchical and complex relationships. Topics covered include constructing SuperHyperGraphs, recognizing SuperHyperTrees, and computing SuperHyperTree-width. We address a range of optimization problems, such as the SuperHy-pergraph Partition Problem, Reachability, Minimum Spanning SuperHypertree, and Single-Source Shortest Path. Furthermore, adaptations of classical problems like the Traveling Salesman Problem, Chinese Postman Problem, and Longest Simple Path Problem are presented in the SuperHypergraph framework.

Super Hiper Funcion Y Super Hiper Estructura Y Sus Correspondientes Super Hiper Funcion Neutrosofica Y Super Hiper Estructura Neutrosofica, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

El n-ésimo Conjunto Potencia de un Conjunto {o Pn(S)} describe mejor nuestro mundo real, porque un sistema S (que puede ser una empresa, institución, asociación, país, sociedad, conjunto de objetos/plantas/animales/seres, conjunto de conceptos/ideas/proposiciones, etc.) está formado por subsistemas, que a su vez están formados por sub-subsistemas, y así sucesivamente. Demostramos que la Super Hiper Función es una generalización de la Función clásica, Super Función y la Hiper Función. Y el Super Hiper Álgebra, Super Hiper Gráfico son parte de la Super Hiper Estructura. Casi todas las estructuras en nuestro mundo real son Super Hiper Estructuras Neutrosóficas ya que tienen …

A Reconsideration Of Advanced Concepts In Neutrosophic Graphs: Smart, Zero Divisor, Layered, Weak, Semi, And Chemical Graphs, Takaaki Fujita, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

One of the most powerful tools in graph theory is the classification of graphs into distinct classes based on shared properties or structural features. Over time, many graph classes have been introduced, each aimed at capturing specific behaviors or characteristics of a graph. Neutrosophic Set Theory, a method for handling uncertainty, extends fuzzy logic by incorporating degrees of truth, indeterminacy, and falsity. Building on this framework, Neutrosophic Graphs [9,84,135] have emerged as significant generalizations of fuzzy graphs. In this paper, we extend several classes of fuzzy graphs to Neutrosophic graphs and analyze their properties.

Recreational Mathematics: Where Is The Error?, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This short note is a funny problem for the trigonometry students!.

The Direct And Inverse Scattering Problems For The Third-Order Operator, Ivan Toledo

Mathematics Dissertations - Archive

We consider the full-line direct and inverse scattering problems for the third-order ordinary differential equation containing two potentials decaying sufficiently fast at infinity. The direct scattering problem consists of the determination of the scattering data set when the two potentials are known. The scattering data set is made up of the corresponding scattering coefficients and the bound-state information. On the other hand, the inverse scattering problem involves the recovery of the two potentials when the scattering data set is available. We formulate the inverse scattering problem via a related Riemann--Hilbert problem on the complex plane. We describe the recovery of …

The Computational Search For Unidentified Central Configurations Of The Newtonian N-Body Problem, Hannah G. Havel

CURE Proceedings

The N-body problem is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It is vital in celestial mechanics, such as planning collision-free satellite orbit trajectories. When beginning to understand the N-body problem, we can start by looking at equal masses of these particles or celestial bodies. As particles move, their position and velocity change, both energy and angular momentum are conserved. Sets of constant energy and angular momentum, known as integral manifolds, are higher-dimensional figures that represent constraints of movement to a system. Integral manifolds are described …

The Cardinal Of The M-Powerset Of A Set Of N Elements Used In The Superhyperstructures And Neutrosophic Superhyperstructures, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we find a formula for computing the cardinal of the m-th powerset of a set of n elements, which is needed in the SuperHyperStructures.

An Investigation Of Students' Modes Of Thinking Concerning Linearity In Linear Algebra, Noa Levy

Honors Undergraduate Theses

The intent of this thesis is to investigate student approaches to linearity within a linear algebra context, focusing on definitional, computational, and theoretical skills. Linear algebra’s abstract nature constitutes a major challenge for a significant sector of STEM students, with the course often serving as undergraduates’ first encounter with mathematical proofs and extrapolations. The current student struggle is reflected through the prominent gap in knowledge derived from a lack of a concrete understanding of rudimentary concepts (like linearity), pivotal to student success. As such, this investigation aimed to bridge this gap by considering students’ modes of thinking regarding the elementary …

Paley Graphs, Prime Graphs, And Crossword Puzzles, Robert D. Jacobs Jr.

Theses and Dissertations

In this paper, we will talk about many different mathematical concepts. We will prove theorems about Paley graphs, prime graphs, and crossword puzzles. It will be very fun.

The results in the section about Paley graphs include structure theorems about the subgraph induced by the quadratic residues, the subgraph induced by the non-residues and a few related subgraphs. The main is to better understand the “independence structure” of the Paley graph itself. No good upper bound on the independence number of Paley graphs is known. Theorems about these subgraphs, and various counts aim at future improvement of upper bounds for …

Snow Spheres And Ice Cubes, John Adam

Mathematics & Statistics Faculty Publications

This article, titled "Snow spheres and ice cubes," discusses the melting of snowballs and ice cubes. It explains that in standard calculus textbooks, it is shown that a snowball melting at a rate proportional to its surface area will have its radius decrease at a constant rate, assuming it remains spherical as it melts. The article then poses several questions related to this concept, including the proportion of a smaller snow sphere that remains when half of a larger one has melted, the value of p for which the smaller sphere first melts, and the volume reduction factor for cubes …

Snow Spheres And Ice Cubes: Solutions For Fermi Questions, February 2024, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Sky Smiley Face, John Adam

Mathematics & Statistics Faculty Publications

The article discusses the formation of a circumzenithal arc (CZA) in the sky, caused by specific light ray paths through hexagonal ice crystals in cirrus clouds. The CZA is visible when the Sun's altitude is about 32° or less. The text includes questions for readers to explore the physics behind the formation of CZAs and circumhorizontal arcs (CHAs). The author acknowledges photographers for providing images and invites readers to find answers online.

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …