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Articles 91 - 120 of 475
Full-Text Articles in Mathematics
Topological And H^Q Equivalence Of Cyclic N-Gonal Actions On Riemann Surfaces - Part Ii, Sean A. Broughton
Topological And H^Q Equivalence Of Cyclic N-Gonal Actions On Riemann Surfaces - Part Ii, Sean A. Broughton
Mathematical Sciences Technical Reports (MSTR)
We consider conformal actions of the finite group G on a closed Riemann surface S, as well as algebraic actions of G on smooth, complete, algebraic curves over an arbitrary, algebraically closed field. There are several notions of equivalence of actions, the most studied of which is topological equivalence, because of its close relationship to the branch locus of moduli space. A second important equivalence relation is that induced by representation of G on spaces of holomorphic q-differentials. The notion of topological equivalence does not work well in positive characteristic. We shall discuss an alternative to topological equivalence, …
Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya
Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya
Department of Mathematics Facuty Scholarship and Creative Works
We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the …
Spectral Sequences For Almost Complex Manifolds, Qian Chen
Spectral Sequences For Almost Complex Manifolds, Qian Chen
Dissertations, Theses, and Capstone Projects
In recent work, two new cohomologies were introduced for almost complex manifolds: the so-called J-cohomology and N-cohomology [CKT17]. For the case of integrable (complex) structures, the former cohomology was already considered in [DGMS75], and the latter agrees with de Rham cohomology. In this dissertation, using ideas from [CW18], we introduce spectral sequences for these two cohomologies, showing the two cohomologies have natural bigradings. We show the spectral sequence for the J-cohomology converges at the second page whenever the almost complex structure is integrable, and explain how both fit in a natural diagram involving Bott-Chern cohomology and the Frolicher spectral sequence. …
The Künneth Formula And Applications, Melissa Sugimoto
The Künneth Formula And Applications, Melissa Sugimoto
SURF Posters and Papers
The de Rham cohomology of a manifold is a homotopy invariant that expresses basic topological information about smooth manifolds. The q-th de Rham cohomology of the n-dimensional Euclidean space is the vector space defined by the closed q-forms over the exact q-forms. Furthermore, the support of a continuous function f on a topological space X is the closure of the set on which f is nonzero. The result of restricting the definition of the de Rham cohomology to functions with compact support is called the de Rham cohomology with compact support, or the compact cohomology. The concept of cohomology can …
Analyzing Network Topology For Ddos Mitigation Using The Abelian Sandpile Model, Bhavana Panchumarthi, Monroe Ame Stephenson
Analyzing Network Topology For Ddos Mitigation Using The Abelian Sandpile Model, Bhavana Panchumarthi, Monroe Ame Stephenson
altREU Projects
A Distributed Denial of Service (DDoS) is a cyber attack, which is capable of triggering a cascading failure in the victim network. While DDoS attacks come in different forms, their general goal is to make a network's service unavailable to its users. A common, but risky, countermeasure is to blackhole or null route the source, or the attacked destination. When a server becomes a blackhole, or referred to as the sink in the paper, the data that is assigned to it "disappears" or gets deleted. Our research shows how mathematical modeling can propose an alternative blackholing strategy that could improve …
Harmony Amid Chaos, Drew Schaffner
Harmony Amid Chaos, Drew Schaffner
Pence-Boyce STEM Student Scholarship
We provide a brief but intuitive study on the subjects from which Galois Fields have emerged and split our study up into two categories: harmony and chaos. Specifically, we study finite fields with elements where is prime. Such a finite field can be defined through a logarithm table. The Harmony Section is where we provide three proofs about the overall symmetry and structure of the Galois Field as well as several observations about the order within a given table. In the Chaos Section we make two attempts to analyze the tables, the first by methods used by Vladimir Arnold as …
A Differential-Algebraic Criterion For Obtaining A Small Maximal Cohen-Macaulay Module, Hans Schoutens
A Differential-Algebraic Criterion For Obtaining A Small Maximal Cohen-Macaulay Module, Hans Schoutens
Publications and Research
We show how for a three-dimensional complete local ring in positive characteristic, the existence of an F-invariant, differentiable derivation implies Hochster’s small MCM conjecture. As an application we show that any three-dimensional pseudo-graded ring in positive characteristic satisfies Hochster’s small MCM conjecture.
Multiparty Non-Interactive Key Exchange And More From Isogenies On Elliptic Curves, Dan Boneh, Darren B. Glass, Daniel Krashen, Kristin Lauter, Shahed Sharif, Alice Silverberg, Mehdi Tibouchi, Mark Zhandry
Multiparty Non-Interactive Key Exchange And More From Isogenies On Elliptic Curves, Dan Boneh, Darren B. Glass, Daniel Krashen, Kristin Lauter, Shahed Sharif, Alice Silverberg, Mehdi Tibouchi, Mark Zhandry
Math Faculty Publications
We describe a framework for constructing an efficient non-interactive key exchange (NIKE) protocol for n parties for any n ≥ 2. Our approach is based on the problem of computing isogenies between isogenous elliptic curves, which is believed to be difficult. We do not obtain a working protocol because of a missing step that is currently an open mathematical problem. What we need to complete our protocol is an efficient algorithm that takes as input an abelian variety presented as a product of isogenous elliptic curves, and outputs an isomorphism invariant of the abelian variety.
Our framework builds a cryptographic …
Hyperbolic Triangle Groups, Sergey Katykhin
Hyperbolic Triangle Groups, Sergey Katykhin
Electronic Theses, Projects, and Dissertations
This paper will be on hyperbolic reflections and triangle groups. We will compare hyperbolic reflection groups to Euclidean reflection groups. The goal of this project is to give a clear exposition of the geometric, algebraic, and number theoretic properties of Euclidean and hyperbolic reflection groups.
Evolution Of Computational Thinking Contextualized In A Teacher-Student Collaborative Learning Environment., John Arthur Underwood
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 …
An Analysis And Comparison Of Knot Polynomials, Hannah Steinhauer
An Analysis And Comparison Of Knot Polynomials, Hannah Steinhauer
Senior Honors Projects, 2020-current
Knot polynomials are polynomial equations that are assigned to knot projections based on the mathematical properties of the knots. They are also invariants, or properties of knots that do not change under ambient isotopy. In other words, given an invariant α for a knot K, α is the same for any projection of K. We will define these knot polynomials and explain the processes by which one finds them for a given knot projection. We will also compare the relative usefulness of these polynomials.
Hyperbolic Endomorphisms Of Free Groups, Jean Pierre Mutanguha
Hyperbolic Endomorphisms Of Free Groups, Jean Pierre Mutanguha
Graduate Theses and Dissertations
We prove that ascending HNN extensions of free groups are word-hyperbolic if and only if they have no Baumslag-Solitar subgroups. This extends Brinkmann's theorem that free-by-cyclic groups are word-hyperbolic if and only if they have no Z2 subgroups. To get started on our main theorem, we first prove a structure theorem for injective but nonsurjective endomorphisms of free groups. With the decomposition of the free group given by this structure theorem, we (more or less) construct representatives for nonsurjective endomorphisms that are expanding immersions relative to a homotopy equivalence. This structure theorem initializes the development of (relative) train track theory …
Syllabus For Semester Bridge Course: Fundamental Concepts Of Math For Educators: Fundamental Concepts Of Algebra And Geometry & Problem Solving Through Theory And Practice (Math 301a Qbr), Lamies Nazzal, Joyce Ahlgren
Syllabus For Semester Bridge Course: Fundamental Concepts Of Math For Educators: Fundamental Concepts Of Algebra And Geometry & Problem Solving Through Theory And Practice (Math 301a Qbr), Lamies Nazzal, Joyce Ahlgren
Q2S Enhancing Pedagogy
The Quarter-to-Semester transition at CSUSB brought a number of challenges for many courses or course series. One of those included the math requirement for Liberal Studies series, Math 30x courses. The challenge here is that the 30x series includes four courses, yet the transition to semesters will yield three courses. In the Fall of 2020, the fourth 2-unit course in the series, Math 308 (Problem Solving Through Theory and Practice), will no longer be offered. Instead, it will be embedded into the first three courses. Students beginning the series after Fall 2019, will not have enough time to complete the …
Fern Or Fractal... Or Both?, Christina Babcock
Fern Or Fractal... Or Both?, Christina Babcock
Research and Scholarship Symposium Posters
Fractals are series of self similar sets and can be found in nature. After researching the Barnsley Fern and the iterated function systems using to create the fractal, I was able to apply what I learned to create a fractal shell. This was done using iterated function systems, matrices, random numbers, and Python coding.
Compactifications Of Cluster Varieties Associated To Root Systems, Feifei Xie
Compactifications Of Cluster Varieties Associated To Root Systems, Feifei Xie
Doctoral Dissertations
In this thesis we identify certain cluster varieties with the complement of a union of closures of hypertori in a toric variety. We prove the existence of a compactification $Z$ of the Fock--Goncharov $\mathcal{X}$-cluster variety for a root system $\Phi$ satisfying some conditions, and study the geometric properties of $Z$. We give a relation of the cluster variety to the toric variety for the fan of Weyl chambers and use a modular interpretation of $X(A_n)$ to give another compactification of the $\mathcal{X}$-cluster variety for the root system $A_n$.
Numerical Solution For Solving Two-Points Boundary Value Problems Using Orthogonal Boubaker Polynomials, Imad Noah Ahmed
Numerical Solution For Solving Two-Points Boundary Value Problems Using Orthogonal Boubaker Polynomials, Imad Noah Ahmed
Emirates Journal for Engineering Research
In this paper, a new technique for solving boundary value problems (BVPs) is introduced. An orthogonal function for Boubaker polynomial was utilizedand by the aid of Galerkin method the BVP was transformed to a system of linear algebraic equations with unknown coefficients, which can be easily solved to find the approximate result. Some numerical examples were added with illustrations, comparing their results with the exact to show the efficiency and the applicability of the method.
Classification Of Torsion Subgroups For Mordell Curves, Zachary Porat
Classification Of Torsion Subgroups For Mordell Curves, Zachary Porat
Honors Theses
Elliptic curves are an interesting area of study in mathematics, laying at the intersection of algebra, geometry, and number theory. They are a powerful tool, having applications in everything from Andrew Wiles’ proof of Fermat’s Last Theorem to cybersecurity. In this paper, we first provide an introduction to elliptic curves by discussing their geometry and associated group structure. We then narrow our focus, further investigating the torsion subgroups of elliptic curves. In particular, we will examine two methods used to classify these subgroups. We finish by employing these methods to categorize the torsion subgroups for a specific family of elliptic …
Isoperimetric Problems On The Line With Density |𝑥|ᵖ, Juiyu Huang, Xinkai Qian, Yiheng Pan, Mulei Xu, Lu Yang, Junfei Zhou
Isoperimetric Problems On The Line With Density |𝑥|ᵖ, Juiyu Huang, Xinkai Qian, Yiheng Pan, Mulei Xu, Lu Yang, Junfei Zhou
Rose-Hulman Undergraduate Mathematics Journal
On the line with density |x|^p, we prove that the best single bubble is an interval with endpoint at the origin and that the best double bubble is two adjacent intervals that meet at the origin.
Geogebra Activities: Tracing Points, Jeremy Aikin, Corey Dunn, Jeffrey Meyer, Rolland Trapp
Geogebra Activities: Tracing Points, Jeremy Aikin, Corey Dunn, Jeffrey Meyer, Rolland Trapp
Q2S Enhancing Pedagogy
In this activity, we will learn how to use GeoGebra (www.geogebra.org) to trace the movement of points, which depend on the movement of other objects. The paths of these points determine curves and we will provide algebraic descriptions of these curves.
Pascal's Mystic Hexagon In Tropical Geometry, Hanna Hoffman
Pascal's Mystic Hexagon In Tropical Geometry, Hanna Hoffman
HMC Senior Theses
Pascal's mystic hexagon is a theorem from projective geometry. Given six points in the projective plane, we can construct three points by extending opposite sides of the hexagon. These three points are collinear if and only if the six original points lie on a nondegenerate conic. We attempt to prove this theorem in the tropical plane.
Phylogenetic Networks And Functions That Relate Them, Drew Scalzo
Phylogenetic Networks And Functions That Relate Them, Drew Scalzo
Williams Honors College, Honors Research Projects
Phylogenetic Networks are defined to be simple connected graphs with exactly n labeled nodes of degree one, called leaves, and where all other unlabeled nodes have a degree of at least three. These structures assist us with analyzing ancestral history, and its close relative - phylogenetic trees - garner the same visualization, but without the graph being forced to be connected. In this paper, we examine the various characteristics of Phylogenetic Networks and functions that take these networks as inputs, and convert them to more complex or simpler structures. Furthermore, we look at the nature of functions as they relate …
A Multi Centerpoint Theorem Via Fourier Analysis On The Torus, Yan Chen
A Multi Centerpoint Theorem Via Fourier Analysis On The Torus, Yan Chen
Senior Projects Spring 2020
The Centerpoint Theorem states that for any set $S$ of points in $\mathbb{R}^d$, there exists a point $c$ such that any hyperplane goes through that point divides the set. For any half-space containing the point $c$, the amount of points in that half-space is no bigger than $\frac{1}{d+1}$ of the whole set. This can be related to how close can any hyperplane containing the point $c$ comes to equipartitioning for a given shape $S$. For a function from unit circle to real number, it has a Fourier interpretation. Using Fourier analysis on the Torus, I will try to find a …
Gröbner Bases And Systems Of Polynomial Equations, Rachel Holmes
Gröbner Bases And Systems Of Polynomial Equations, Rachel Holmes
All Graduate Theses, Dissertations, and Other Capstone Projects
This paper will explore the use and construction of Gröbner bases through Buchberger's algorithm. Specifically, applications of such bases for solving systems of polynomial equations will be discussed. Furthermore, we relate many concepts in commutative algebra to ideas in computational algebraic geometry.
Scrollar Invariants Of Tropical Chains Of Loops, Kalila Joelle Sawyer
Scrollar Invariants Of Tropical Chains Of Loops, Kalila Joelle Sawyer
Theses and Dissertations--Mathematics
We define scrollar invariants of tropical curves with a fixed divisor of rank 1. We examine the behavior of scrollar invariants under specialization, and compute these invariants for a much-studied family of tropical curves. Our examples highlight many parallels between the classical and tropical theories, but also point to some substantive distinctions.
Algebraic And Geometric Properties Of Hierarchical Models, Aida Maraj
Algebraic And Geometric Properties Of Hierarchical Models, Aida Maraj
Theses and Dissertations--Mathematics
In this dissertation filtrations of ideals arising from hierarchical models in statistics related by a group action are are studied. These filtrations lead to ideals in polynomial rings in infinitely many variables, which require innovative tools. Regular languages and finite automata are used to prove and explicitly compute the rationality of some multivariate power series that record important quantitative information about the ideals. Some work regarding Markov bases for non-reducible models is shown, together with advances in the polyhedral geometry of binary hierarchical models.
Codes, Cryptography, And The Mceliece Cryptosystem, Bethany Matsick
Codes, Cryptography, And The Mceliece Cryptosystem, Bethany Matsick
Senior Honors Theses
Over the past several decades, technology has continued to develop at an incredible rate, and the importance of properly securing information has increased significantly. While a variety of encryption schemes currently exist for this purpose, a number of them rely on problems, such as integer factorization, that are not resistant to quantum algorithms. With the reality of quantum computers approaching, it is critical that a quantum-resistant method of protecting information is found. After developing the proper background, we evaluate the potential of the McEliece cryptosystem for use in the post-quantum era by examining families of algebraic geometry codes that allow …
Heat Kernel Voting With Geometric Invariants, Alexander Harr
Heat Kernel Voting With Geometric Invariants, Alexander Harr
All Graduate Theses, Dissertations, and Other Capstone Projects
Here we provide a method for comparing geometric objects. Two objects of interest are embedded into an infinite dimensional Hilbert space using their Laplacian eigenvalues and eigenfunctions, truncated to a finite dimensional Euclidean space, where correspondences between the objects are searched for and voted on. To simplify correspondence finding, we propose using several geometric invariants to reduce the necessary computations. This method improves on voting methods by identifying isometric regions including shapes of genus greater than 0 and dimension greater than 3, as well as almost retaining isometry.
The Neutrosophic Triplet Of ����-Algebras, Florentin Smarandache, Akbar Rezaei
The Neutrosophic Triplet Of ����-Algebras, Florentin Smarandache, Akbar Rezaei
Branch Mathematics and Statistics Faculty and Staff Publications
In this paper, the concepts of a Neutro-����-algebra and Anti-����-algebra are introduced, and some related properties are investigated. We show that the class of Neutro-����-algebra is an alternative of the class of ����-algebras.
Neutro-Bck-Algebra, Florentin Smarandache, Mohammad Hamidi
Neutro-Bck-Algebra, Florentin Smarandache, Mohammad Hamidi
Branch Mathematics and Statistics Faculty and Staff Publications
This paper introduces the novel concept of Neutro-BCK-algebra. In Neutro-BCK-algebra, the outcome of any given two elements under an underlying operation (neutro-sophication procedure) has three cases, such as: appurtenance, non-appurtenance, or indeterminate. While for an axiom: equal, non-equal, or indeterminate. This study investigates the Neutro-BCK-algebra and shows that Neutro-BCK-algebra are different from BCK-algebra. The notation of Neutro-BCK-algebra generates a new concept of NeutroPoset and Neutro-Hass-diagram for NeutroPosets. Finally, we consider an instance of applications of the Neutro-BCK-algebra.
A New Trend To Extensions Of Ci-Algebras, Florentin Smarandache, Akbar Rezaei, Hee Sik Kim
A New Trend To Extensions Of Ci-Algebras, Florentin Smarandache, Akbar Rezaei, Hee Sik Kim
Branch Mathematics and Statistics Faculty and Staff Publications
In this paper, as an extension of CI-algebras, we discuss the new notions of Neutro-CI-algebras and Anti-CI-algebras. First, some examples are given to show that these definitions are different. We prove that any proper CI-algebra is a Neutro-BE-algebra or Anti-BE-algebra. Also, we show that any NeutroSelf-distributive and AntiCommutative CI-algebras are not BE-algebras.