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Articles 1 - 30 of 44
Full-Text Articles in Physical Sciences and Mathematics
So How Were The Tents Of Israel Placed? A Bible-Inspired Geometric Problem, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
So How Were The Tents Of Israel Placed? A Bible-Inspired Geometric Problem, Julio Urenda, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In one of the Biblical stories, prophet Balaam blesses the tents of Israel for being good. But what can be so good about the tents? A traditional Rabbinical interpretation is that the placement of the tents provided full privacy: from each entrance, one could not see what is happening at any other entrance. This motivates a natural geometric question: how exactly were these tents placed? In this paper, we provide an answer to this question.
Introduce Gâteaux And Frêchet Derivatives In Riesz Spaces, Abdullah Aydın, Erdal Korkmaz
Introduce Gâteaux And Frêchet Derivatives In Riesz Spaces, Abdullah Aydın, Erdal Korkmaz
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the Gâteaux and Frêchet differentiations of functions on Riesz space are introduced without topological structure. Thus, we aim to study Gâteaux and Frêchet differentiability functions in vector lattice by developing topology-free techniques, and also, we give some relations with other kinds of operators.
Sum Of Cubes Of The First N Integers, Obiamaka L. Agu
Sum Of Cubes Of The First N Integers, Obiamaka L. Agu
Electronic Theses, Projects, and Dissertations
In Calculus we learned that Sum^{n}_{k=1} k = [n(n+1)]/2 , that Sum^{n}_{k=1} k^2 = [n(n+1)(2n+1)]/6 , and that Sum^{n}_{k=1} k^{3} = (n(n+1)/2)^{2}. These formulas are useful when solving for the area below quadratic or cubic function over an interval [a, b]. This tedious process, solving for areas under a quadratic or a cubic, served as motivation for the introduction of Riemman integrals. For the overzealous math student, these steps were replaced by a simpler method of evaluating antiderivatives at the endpoints a and b. From my recollection, a former instructor informed us to do the value of memorizing these formulas. …
Estimating The Number Of Discrete Models Of Biological Networks, Brandilyn Stigler
Estimating The Number Of Discrete Models Of Biological Networks, Brandilyn Stigler
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Application Of Tda Mapper To Water Data And Bird Data, Wako Bungula
Application Of Tda Mapper To Water Data And Bird Data, Wako Bungula
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Weaving Mathematics, Ma. Louise Antonette N. De Las Peñas
Weaving Mathematics, Ma. Louise Antonette N. De Las Peñas
Magisterial Lectures
In this lecture, Dr. De las Peñas talks about the intersection of mathematics and Philippine indigenous weaving.
Speaker:
Ma. Louise Antonette N. De Las Peñas is a Professor at the Department of Mathematics and currently the Associate Dean for Research and Creative Work, Loyola Schools, Ateneo De Manila University, Philippines. Her research interests are discrete geometry, mathematical crystallography, group theory, and technology in mathematics education.
She is a recipient of several research awards including the National Research Council of the Philippines (NRCP) Achievement Award in the Mathematical Sciences and the Philippine Commission on Higher Education Republica National Research Award. She …
Dupin Submanifolds In Lie Sphere Geometry (Updated Version), Thomas E. Cecil, Shiing-Shen Chern
Dupin Submanifolds In Lie Sphere Geometry (Updated Version), Thomas E. Cecil, Shiing-Shen Chern
Mathematics and Computer Science Department Faculty Scholarship
A hypersurface Mn-1 in Euclidean space En is proper Dupin if the number of distinct principal curvatures is constant on Mn-1, and each principal curvature function is constant along each leaf of its principal foliation. This paper was originally published in 1989 (see Comments below), and it develops a method for the local study of proper Dupin hypersurfaces in the context of Lie sphere geometry using moving frames. This method has been effective in obtaining several classification theorems of proper Dupin hypersurfaces since that time. This updated version of the paper contains the original exposition together …
Intrinsic Curvature For Schemes, Pat Lank
Intrinsic Curvature For Schemes, Pat Lank
Mathematics & Statistics ETDs
This thesis develops an algebraic analog of psuedo-Riemannian geometry for relative schemes whose cotangent sheaf is finite locally free. It is a generalization of the algebraic differential calculus proposed by Dr. Ernst Kunz in an unpublished manuscript to the non-affine case. These analogs include the psuedo-Riemannian metric, Levi-Civit´a connection, curvature, and various existence theorems.
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.
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 …
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.
Introduction To Neutroalgebraic Structures And Antialgebraic Structures (Revisited), Florentin Smarandache
Introduction To Neutroalgebraic Structures And Antialgebraic Structures (Revisited), Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
In all classical algebraic structures, the Laws of Compositions on a given set are well-defined. But this is a restrictive case, because there are many more situations in science and in any domain of knowledge when a law of composition defined on a set may be only partially-defined (or partially true) and partially-undefined (or partially false), that we call NeutroDefined, or totally undefined (totally false) that we call AntiDefined. Again, in all classical algebraic structures, the Axioms (Associativity, Commutativity, etc.) defined on a set are totally true, but it is again a restrictive case, because similarly there are numerous situations …