Nonlocal Helmholtz Decompositions And Connections To Classical Counterparts,
2020
University of Nebraska-Lincoln
Nonlocal Helmholtz Decompositions And Connections To Classical Counterparts, Andrew Haar, Petronela Radu
UCARE: Research Products
In recent years nonlocal models have been successfully introduced in a variety of applications, such as dynamic fracture, nonlocal diffusion, flocking, and image processing. Thus, the development of a nonlocal calculus theory, together with the study of nonlocal operators has become the focus of many theoretical investigations. Our work focuses on a Helmholtz decomposition in the nonlocal (integral) framework. In the classical (differential) setting the Helmholtz decomposition states that we can decompose a three dimensional vector field as a sum of an irrotational function and a solenoidal function. We will define new nonlocal gradient and curl operators that allow us …
From Branches To Fibers - Investigating F-Actin Networks With Biochemistry And Mathematical Modeling,
2020
James Madison University
From Branches To Fibers - Investigating F-Actin Networks With Biochemistry And Mathematical Modeling, Melissa A. Riddle
Senior Honors Projects, 2020-current
F-actin networks have different structures throughout the cell depending on their location or mechanical role. For example, at the leading edge of a migrating cell, F-actin is organized in a region called the lamellipodia as a branched network responsible for pushing the membrane outwards. Behind the lamellipodia is a lamellar actin network where focal adhesions and stress fibers originate, and then within the cell cortex, actin is arranged in a gel-like network. Stress fibers are an important organization of F-actin and how they arise from either the branched lamellipodia network or the gel-like cortex network is poorly understood. Our approach …
Bridge To Bulldogs: A Student And Financial Analysis,
2020
Louisiana Tech University
Bridge To Bulldogs: A Student And Financial Analysis, Rebekah Moss
Mathematics Senior Capstone Papers
In this paper, we discuss the statistical analysis of the Bridge to Bulldogs program. The Bridge to Bulldogs program provides prospective students, who do not meet all of the admission requirements, an alternate route of admission to Louisiana Tech University. The program is offered over two consecutive quarters, either summer/fall or fall/winter. During the program, students focus on building their math skills through tutoring and special advising. We compare the Bridge students to other first-time freshman in relation to scores in Freshman level math classes. We also compare composite and Math ACT scores. Finally, we perform a financial analysis, including …
An Analysis And Comparison Of Knot Polynomials,
2020
James Madison University
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.
Conjugation By Circulant Matrices In Non-Commutative Cryptography,
2020
University of Mary Washington
Conjugation By Circulant Matrices In Non-Commutative Cryptography, Hannah B. Frederick
Departmental Honors & Graduate Capstone Projects
We introduce a procedure in which two trusted individuals, Alice and Bob, may share a secret matrix K from the non-abelian general linear group of matrices. In this procedure, the matrix K is concealed from an eavesdropper, Eve, by a sequence of conjugations by elements from a pre-determined abelian subgroup of the general linear group. We demonstrate that the group of invertible circulant matrices is one abelian subgroup that may be able to withstand a brute force attack. To analyze this we need a technique to determine the order of this group, and to do this we make use of …
Lattice Paths In Diagonals And Dimensions,
2020
Coastal Carolina University
Lattice Paths In Diagonals And Dimensions, Freya Bennett
Honors Theses
The Lattice Paths of Combinatorics have been used in many applications, normally under the guise of a different name, due to its versatility in surface variety and specificity of answer. The Lattice Path’s of game development, in finding paths around barriers in mazes, is called Path Finder with the A∗ algorithms as its method of solving.
Combinatorial And Asymptotic Statistical Properties Of Partitions And Unimodal Sequences,
2020
Louisiana State University and Agricultural and Mechanical College
Combinatorial And Asymptotic Statistical Properties Of Partitions And Unimodal Sequences, Walter Mcfarland Bridges
LSU Doctoral Dissertations
Our main results are asymptotic zero-one laws satisfied by the diagrams of unimodal sequences of positive integers. These diagrams consist of columns of squares in the plane; the upper boundary is called the shape. For various types of unimodal sequences, we show that, as the number of squares tends to infinity, 100% of shapes are near a certain curve---that is, there is a single limit shape. Similar phenomena have been well-studied for integer partitions, but several technical difficulties arise in the extension of such asymptotic statistical laws to unimodal sequences. We develop a widely applicable method for obtaining these limit …
The Sir Models, Their Applications, And Approximations Of Their Rates,
2020
Louisiana Tech University
The Sir Models, Their Applications, And Approximations Of Their Rates, Christopher Cano
Mathematics Senior Capstone Papers
The SIR (Susceptible-Infected-Recovered) models are used to help predict the spread of diseases. The goals of this paper are: elaborating on the methods of approximating the recovery rate, infection rate, and loss of immunity rate, comparing the SIR models with these approximation methods to real world data, and determining the most accurate combination of the approximation methods for each SIR model. There are several SIR models such as the Kermack-McKendrick, SIRS, and SI models that are designed for specific diseases. Understanding the parameters of these models will assist us in maximizing their accuracy. For example, there is no explicit formula …
Pattern-Avoiding (0,1)-Matrices,
2020
University of Wisconsin - Madison
Pattern-Avoiding (0,1)-Matrices, Richard Brualdi, Lei Cao
Mathematics Faculty Articles
We investigate pattern-avoiding (0,1)-matrices as generalizations of pattern-avoiding permutations. Our emphasis is on 123-avoiding and 321-avoiding patterns for which we obtain exact results as to the maximum number of 1's such matrices can have. We also give algorithms when carried out in all possible ways, construct all of the pattern-avoiding matrices of these two types.
Exploration Of Solvable Quintic Polynomials,
2020
University of Mary Washington
Exploration Of Solvable Quintic Polynomials, Stephen Tivenan
Departmental Honors & Graduate Capstone Projects
A polynomial f(x) with rational coefficients is solvable by radicals if its roots (in the field of complex numbers C) can be expressed in terms of its coefficients using the basic operations and radicals. It is known that for quintic polynomials there is no generic formula for the roots. That is, some quintic polynomials are solvable and some are not. In this paper, we address the mathematical theory that makes the formula for the roots of a polynomial. Primarily we will focus on our methodology of generating and examining quintic polynomials. In one case study, we will examine quintic polynomials …
Anticommutative Associative Algebras And The Binomial Theorem,
2020
University of Mary Washington
Anticommutative Associative Algebras And The Binomial Theorem, Ashley Scurlock
Departmental Honors & Graduate Capstone Projects
We examine the binomial theorem and its components in a noncommutative associative algebra. Specifically, we examine the relationship between the 1-binomial and -1-binomial coefficient, as well as exploring alternatives for the exponential identity for non-commutative and anticommutative elements. Through this investigation we found that the 1-binomial can be mapped to the -1-binomial and that the relationship could be used to prove a defined alternative for the exponential identity for anticommutative elements.
Singular Value Decomposition,
2020
Coastal Carolina University
Singular Value Decomposition, Krystal Bonaccorso, Andrew Incognito
Honors Theses
A well-known theorem is Diagonalization, where one of the factors is a diagonal matrix. In this paper we will be describing a similar way to factor/decompose a non-square matrix. The key to both of these ways to factor is eigenvalues and eigenvectors.
A Review Of Major Role Of Vitamin D3 In Human Immune System And Its Possible Use For Novel Corona Virus Treatment,
2020
University of New Mexico
A Review Of Major Role Of Vitamin D3 In Human Immune System And Its Possible Use For Novel Corona Virus Treatment, Florentin Smarandache, Victor Christianto
Branch Mathematics and Statistics Faculty and Staff Publications
the evidences showing major role of Vitamin D3 in human immune system and its potential use for novel corona virus treatment. Our argument is based on research finding that corona virus has viral envelope glycoproteins. In this regard, Vitamin D3 proves to offer various beneficial effects, including immunomodulatory effect, in order to break the glycoproteins envelope of the virus. One of the greatest benefit of vitamin D3 is the fact that it is easy to get 10,000 - 20,000 IU of daily intake requirement, by sunbathing for more or less twenty minutes. Such a method is likely applicable in many …
The T, T*, Vi, Vni Model For Human Immunodeficiency Virus Type 1 (Hiv-1) Dynamics,
2020
University of Mary Washington
The T, T*, Vi, Vni Model For Human Immunodeficiency Virus Type 1 (Hiv-1) Dynamics, Amy Creel
Departmental Honors & Graduate Capstone Projects
In this research project, I investigated deterministic and stochastic versions of a model for Human Immunodeficiency Virus Type 1 (HIV-1) dynamics. First, an analytical solution to a simplified version of the deterministic model is found. Then, numerical techniques are used to obtain an approximate solution to the deterministic model. Finally, a stochastic version of the model is discussed, and numerical methods are used to find an approximate solution to the stochastic system. These results demonstrate the behavior of HIV-1 in an infected patient under the effects of reverse transcriptase and protease inhibitors, and illustrate how the addition of randomness to …
Legendrian Dga Representations And The Colored Kauffman Polynomial,
2020
Department of Mathematics, 303 Lockett Hall, Louisiana State University, Baton Rouge, LA
Legendrian Dga Representations And The Colored Kauffman Polynomial, Justin Murray, Dan Rutherford
Faculty Publications
For any Legendrian knot K in standard contact R-3 we relate counts of ungraded (1-graded) representations of the Legendrian contact homology DG-algebra (A(K), partial derivative) with the n-colored Kauffman polynomial. To do this, we introduce an ungraded n-colored ru-ling polynomial, R-n,K(1)(q), as a linear combination of reduced ruling polynomials of positive permutation braids and show that (i) R-n,K(1)(q) arises as a specialization F-n,F-K(a, q)vertical bar(a-1) = 0 of the n-colored Kauffman polynomial and (ii) when q is a power of two R-n,K(1)(q) agrees with the total ungraded representation number, Rep(1) (K, F-q(n)), which is a normalized count of n-dimensional representations …
Structure Theorems For Idempotent Residuated Lattices,
2020
University of Bern
Structure Theorems For Idempotent Residuated Lattices, José Gil-Férez, Peter Jipsen, George Metcalfe
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we study structural properties of residuated lattices that are idempotent as monoids. We provide descriptions of the totally ordered members of this class and obtain counting theorems for the number of finite algebras in various subclasses. We also establish the finite embeddability property for certain varieties generated by classes of residuated lattices that are conservative in the sense that monoid multiplication always yields one of its arguments. We then make use of a more symmetric version of Raftery’s characterization theorem for totally ordered commutative idempotent residuated lattices to prove that the variety generated by this class has …
Life Insurance Purchase Behavior Analysis For Retired People,
2020
Bryant University
Life Insurance Purchase Behavior Analysis For Retired People, Connor Frauendorf
Honors Projects in Mathematics
Life insurance is an important need for many people in the United States. It is an insurance that the purchaser will never get to receive the benefit, instead, upon death, their beneficiaries will receive it to supplement their income. This study will be analyzing the Health and Retirement Study dataset in order to identify and model the variables that are most related and/or correlated to the purchasing behavior of life insurance in the United States. Using different mathematical applications, such as linear modeling through R and correlations through Excel, the data has been scanned thoroughly to isolate potential significant variables. …
The Game Of Life On The Hyperbolic Plane,
2020
Rose-Hulman Institute of Technology
The Game Of Life On The Hyperbolic Plane, Yuncong Gu
Mathematical Sciences Technical Reports (MSTR)
In this paper, we work on the Game of Life on the hyperbolic plane. We are interested in different tessellations on the hyperbolic plane and different Game of Life rules. First, we show the exponential growth of polygons on the pentagon tessellation. Moreover, we find that the Group of 3 can keep the boundary of a set not getting smaller. We generalize the existence of still lifes by computer simulations. Also, we will prove some propositions of still lifes and cycles. There exists a still life under rules B1, B2, and S3.
On Quantum Effects Of Vector Potentials And Generalizations Of Functional Analysis,
2020
Chapman University
On Quantum Effects Of Vector Potentials And Generalizations Of Functional Analysis, Ismael L. Paiva
Computational and Data Sciences (PhD) Dissertations
This is a dissertation in two parts. In the first one, the Aharonov-Bohm effect is investigated. It is shown that solenoids (or flux lines) can be seen as barriers for quantum charges. In particular, a charge can be trapped in a sector of a long cavity by two flux lines. Also, grids of flux lines can approximate the force associated with continuous two-dimensional distributions of magnetic fields. More, if it is assumed that the lines can be as close to each other as desirable, it is explained how the classical magnetic force can emerge from the Aharonov-Bohm effect. Continuing, the …
A Dynamic F5 Algorithm,
2020
The University of Southern Mississippi
A Dynamic F5 Algorithm, Candice Mitchell
Dissertations
Gröbner bases are a “nice” representation for nonlinear systems of polynomials, where by “nice” we mean they have good computation properties. They have many useful applications, including decidability (whether the system has a solution or not), ideal membership (whether a given polynomial is in the system or not), and cryptography. Traditional Gröbner basis algorithms require as input an ideal and an admissible term ordering. They then determine a Gröbner basis with respect to the given ordering. Some term orderings lead to a smaller basis, but finding them traditionally requires testing many orderings and hoping for better results. A dynamic algorithm …
