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2021

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Articles 931 - 960 of 1314

Full-Text Articles in Mathematics

On Domination And Bondage Numbers Of Some Classes Of Graphs, Andrew Pham Jan 2021

On Domination And Bondage Numbers Of Some Classes Of Graphs, Andrew Pham

Electronic Theses and Dissertations

Given a simple finite graph G=(V,E), a vertex subset D ? V(G) is said to be a dominating set of G if every vertex v ? V(G)-D is adjacent to a vertex in D. The domination number of G, denoted ?(G), is the minimum cardinality among all dominating sets of G. In a network, the domination number determines the minimum number of sites required to dominate the entire network at a minimum cost. The bondage number of a graph G is the minimum cardinality among all edge sets B such that ?(G-B) > ?(G). The bondage number may serve as a …

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A Gompertz Distribution For Time Scales, Tom Cuchta, Robert Jon Nichel, Sabrina Streipert Jan 2021

A Gompertz Distribution For Time Scales, Tom Cuchta, Robert Jon Nichel, Sabrina Streipert

Mathematics Faculty Research

We investigate a family of probability distributions, with three parameters associated with the dynamic Gompertz function. We prove its existence for various parameter sets and discuss the existence of its time scale moments. Afterwards, we investigate the special case of discrete time scales, where it is shown that the discrete Gompertz distribution is a q -geometric distribution of the second kind. Further, we find their q -binomial moments, we bound their expected value, and we show how a classical Gompertz distribution is obtained from them.

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The Hatcher-Quinn Invariant And Differential Forms, Joshua Lenwood Turner Jan 2021

The Hatcher-Quinn Invariant And Differential Forms, Joshua Lenwood Turner

Wayne State University Dissertations

An intersection problem consists of submanifolds $P, Q \subset M$ having non-empty intersection. In 1974, Hatcher and Quinn introduced a bordism-theoretic obstruction to finding a deformation of $P$ off of $Q$ by an isotopy. This dissertation studies the problem of finding an analytical expression for the Hatcher-Quinn obstruction---one which involves the language of differential forms. We first introduce the notion of a smooth structure on a set by introducing a system of mappings called plots. By generalizing this to the fibered setting, we use the concept to give a model for the homology of the generalized path space $E$ i.e., …

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Multivariate Distributions Of Correlated Binary Variables Generated By Pair-Copulas, Huihui Lin, N. Rao Chaganty Jan 2021

Multivariate Distributions Of Correlated Binary Variables Generated By Pair-Copulas, Huihui Lin, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

Correlated binary data are prevalent in a wide range of scientific disciplines, including healthcare and medicine. The generalized estimating equations (GEEs) and the multivariate probit (MP) model are two of the popular methods for analyzing such data. However, both methods have some significant drawbacks. The GEEs may not have an underlying likelihood and the MP model may fail to generate a multivariate binary distribution with specified marginals and bivariate correlations. In this paper, we study multivariate binary distributions that are based on D-vine pair-copula models as a superior alternative to these methods. We elucidate the construction of these binary distributions …

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A Class Of Copula-Based Bivariate Poisson Time Series Models With Applications, Mohammed Alqawba, Dimuthu Fernando, Norou Diawara Jan 2021

A Class Of Copula-Based Bivariate Poisson Time Series Models With Applications, Mohammed Alqawba, Dimuthu Fernando, Norou Diawara

Mathematics & Statistics Faculty Publications

A class of bivariate integer-valued time series models was constructed via copula theory. Each series follows a Markov chain with the serial dependence captured using copula-based transition probabilities from the Poisson and the zero-inflated Poisson (ZIP) margins. The copula theory was also used again to capture the dependence between the two series using either the bivariate Gaussian or “t-copula” functions. Such a method provides a flexible dependence structure that allows for positive and negative correlation, as well. In addition, the use of a copula permits applying different margins with a complicated structure such as the ZIP distribution. Likelihood-based inference was …

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Representer Theorems In Banach Spaces: Minimum Norm Interpolation, Regularized Learning And Semi-Discrete Inverse Problems, Rui Wang, Yusheng Xu Jan 2021

Representer Theorems In Banach Spaces: Minimum Norm Interpolation, Regularized Learning And Semi-Discrete Inverse Problems, Rui Wang, Yusheng Xu

Mathematics & Statistics Faculty Publications

Learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation (MNI) problem, a regularized learning problem or, in general, a semi discrete inverse problem (SDIP), in either Hilbert spaces or Banach spaces. The goal of this paper is to systematically study solutions of these problems in Banach spaces. We aim at obtaining explicit representer theorems for their solutions, on which convenient solution methods can then be developed. For the MNI problem, the explicit representer theorems enable us to express the infimum …

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Dynamics Of The Meromorphic Families $F_\Lambda=\Lambda \Tan^Pz^Q$, Tao Chen, Linda Keen Jan 2021

Dynamics Of The Meromorphic Families $F_\Lambda=\Lambda \Tan^Pz^Q$, Tao Chen, Linda Keen

Publications and Research

This paper continues our investigation of the dynamics of families of transcendental meromorphic functions with finitely many singular values all of which are finite. Here we look at a generalization of the family of polynomials Pa(z) =zd−1(z−da/(d−1)), the family fλ=λtanpzq. These functions have a super-attractive fixed point, and, depending on p, one or two asymptotic values. Although many of the dynamical properties generalize, the existence of an essential singularity and of poles of multiplicity greater than one implies that significantly different techniques are required here. Adding transcendental methods to standard …

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Random Matrix Theory: A Combinatorial Proof Of Wigner's Semicircle Law, Vanessa Wolf Jan 2021

Random Matrix Theory: A Combinatorial Proof Of Wigner's Semicircle Law, Vanessa Wolf

Scripps Senior Theses

A combinatorial proof of Wigner’s semicircle law for the Gaussian Unitary Ensemble (GUE) is presented using techniques from free probability. Motivating examples taken from the symmetric Bernoulli ensemble and the GUE show the distribution of eigenvalues of sample n x n matrices approaching Wigner’s semicircle as n get large. The concept of crossing and non-crossing pairings is developed, along with proofs of Wick’s Formula for real and complex Gaussians. It is shown that Wigner’s semicircle distribution has moments given by the Catalan numbers. Wick’s Formula and several additional lemmas (proved in sequence) lead to a "method of moments" proof that …

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Using Semialgebraic Parametric Analysis By Metaprogramming In Portfolio Optimization, Philip Blaine Meersman Jan 2021

Using Semialgebraic Parametric Analysis By Metaprogramming In Portfolio Optimization, Philip Blaine Meersman

Lewis Honors College Capstone Collection

One classic problem in quantitative finance is portfolio optimization, which consists of assigning weights to assets in a portfolio to maximize one’s expected return while keeping the level of risk at a desired level. This problem can be modeled as a linear program (LP), using a risk aversion parameter mu. For a given single value of mu, the LP can be solved using any standard LP solver. In this work, however, the problem is considered parametrically: the optimal solution is sought for every possible value of mu. This describes how weights to the portfolio assets would be assigned from the …

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The Dangers Of Lift On Parked Planes: General Aviation Airport Safety, Robert Malloy Jan 2021

The Dangers Of Lift On Parked Planes: General Aviation Airport Safety, Robert Malloy

Undergraduate Journal of Mathematical Modeling: One + Two

The focus of this paper is to investigate proper aircraft management for safety on an airfield. This is accomplished by looking at lift caused by powerful winds to the aircrafts stored on an airfield, and the tension it places on the rope that secures them. This work could be used to determine when aircrafts are in high-risk and need to be stored either in hangars or moved to other airports prior to storms. The calculations used to determine these conclusions are also explored in the paper.

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Area Of Irregular Shaped Roof, Omar Alkhawaldeh Jan 2021

Area Of Irregular Shaped Roof, Omar Alkhawaldeh

Undergraduate Journal of Mathematical Modeling: One + Two

This project makes use of calculus, specifically integration, to find the exact area of a roof garden to minimize the cost of material used in flooring it. Since the roof is of irregular shape, it is divided into four sections, the integral of each section is taken, and a relationship between the integrals is generated. Positive results are found, and the data reveal that the area of the grass floor is 175.3 m2 while the area of the wooden floor is 23.4 m2 with the total price being 2472 US dollars.

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Calculating Probable Theoretical Offspring Genotype In Fruit Flies, Megan Keller Jan 2021

Calculating Probable Theoretical Offspring Genotype In Fruit Flies, Megan Keller

Undergraduate Journal of Mathematical Modeling: One + Two

Being able to calculate an offspring's theoretical genotype is critical in genetic sciences. We calculate the theoretical genotype and phenotype of fruit fly offspring. Using the product rule, we determine the probability for each trait and then for each genotype. In conclusion, we calculate 64 different genotypes that are supposed to be possible, but only 8 phenotypes are possible.

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Mathematical Reconstruction Of A Traffic Crash, Benjamin Covert Jan 2021

Mathematical Reconstruction Of A Traffic Crash, Benjamin Covert

Undergraduate Journal of Mathematical Modeling: One + Two

The objective is to find the impact speeds of two motor vehicles involved in a traffic crash. The calculations take into account the approach (pre-collision) and departure (post collision) angles, as well as weights and post collision speeds of both vehicles. The data is provided by Timothy Sleyzack who investigated this traffic collision. The conclusions confirm the validity of the use of Conservation of Linear Momentum in the field of traffic crash reconstruction.

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Emergency Communications Deficiency Locator, Austin Collins Jan 2021

Emergency Communications Deficiency Locator, Austin Collins

Undergraduate Journal of Mathematical Modeling: One + Two

The Bi-Directional Amplifier (BDA) is the newest edition to Life Safety in the state of Florida. The Florida Fire Prevention Code (NFPA 1) section 11.10.1 states that “In all new and existing buildings, minimum radio signal strength for fire department communications shall be maintained at a level determined by the authority having jurisdiction (Committee NFPA 1: Fire Code 2018). That authority having jurisdiction for our local Tampa Bay area is the Hillsborough County Fire Rescue department and they have posted their own requirements along with the Florida Senate for emergency communication standards. All existing “Hi-rise” buildings, 75 feet tall …

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Evaluating The Improvement In Dna Fingerprinting, Dani Dray Jan 2021

Evaluating The Improvement In Dna Fingerprinting, Dani Dray

Undergraduate Journal of Mathematical Modeling: One + Two

DNA fingerprinting is a forensic technique used to create patterns that are unique to a person’s DNA. Previously, these fingerprints were made from 13 different segments of DNA, but today they are made from the 20 ones. The fundamental principle of counting is used to determine how much of an improvement was made after adding the 7 additional DNA segments. It is found that this addition greatly reduces the likelihood of two people having the same exact fingerprint, therefore improving the accuracy and reliability of DNA fingerprinting.

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Predicting The Cost Of Dental Care Using A Probability Model, Nadine Wehbe Jan 2021

Predicting The Cost Of Dental Care Using A Probability Model, Nadine Wehbe

Undergraduate Journal of Mathematical Modeling: One + Two

This paper uses survey data to present a probability model that allows dental offices to predict patient costs. The quantitative model is useful for developing and accepting capitation rates. It accounts for whether the care is initial care or maintenance care, the type of dental care (such as operative, prosthetics, or periodontics), and different age groups, all of which affect the cost of dental treatment.

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Using Calculus To Plan An Open-Air Concert, Timur Kalandarov Jan 2021

Using Calculus To Plan An Open-Air Concert, Timur Kalandarov

Undergraduate Journal of Mathematical Modeling: One + Two

A concert is a mass entertainment event held indoors, at concert halls, or outdoors (open-air festivals). These two formats differ greatly from each other. However, the goal of both events remains the same – to allow the audience to enjoy the musical performance. Indoor halls are designed for the best acoustics of sound. They are often circular and let sound waves travel around the inside of the building, like an echo bouncing back and forth. This makes the audience feel like they are surrounded by sound. Such places already have outlined spots for mounting music equipment with the highest efficiency. …

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Calculating The Probability Of Constitutional Isomers Of Pentane, Mary-Margaret Dare Jan 2021

Calculating The Probability Of Constitutional Isomers Of Pentane, Mary-Margaret Dare

Undergraduate Journal of Mathematical Modeling: One + Two

Depending on the reagent, and orientation of collisions within a chemical reaction, organic molecules can be present as different constitutional isomers of the same molecule. We can analyze the likelihood of getting a mixture of pentane with certain conformers. Based on this, we find that there are 16 potential conformers, but 13 are identical structures, meaning only three are distinct from each other. Using the product rule, we then demonstrate how to go about calculating the probability of specific conformers, including specific identical structures, being present in a mixture, and then we demonstrate that process is strictly within the three …

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Surge Functions And Drug Interactions, Olta Tarko Jan 2021

Surge Functions And Drug Interactions, Olta Tarko

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this project is to analyze how surge functions work to understand the way drug concentration levels in the bloodstream of a human body vary over time after an initial dose. A surge function increases rapidly at the beginning of the dosage and drops slowly after it reaches its peak. It is important to realize when a certain drug reaches its peak and how long the effects will last on a patient, so a second drug can be administered without risking negative interactions. We explain the calculations used in order to properly understand the curve of a drug’s …

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Volume And Cost Of Cylindrical Shaped Silo With Conical Roof, Gabriel Mitzakoff Parola Jan 2021

Volume And Cost Of Cylindrical Shaped Silo With Conical Roof, Gabriel Mitzakoff Parola

Undergraduate Journal of Mathematical Modeling: One + Two

This project utilizes integral calculus to find the exact volume of a non-uniform cylindrical-shaped silo used to store wheat and calculate the cost of material utilized to build such silo. Due to its non-uniform shape, the silo is divided into two sections and the volume of each is calculated. The final volume for the silo with the measurements provided is approximately 2330.02 meters cubic and surface area of 1074.96 meters squared, which is considered to be a large capacity silo. With such a large capacity silo there are costs to be considered, such as the material cost which is calculated …

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Some Special Cases Of The Andrews-Bowman Continued Fraction, Bryan Thomas Zollinger Jan 2021

Some Special Cases Of The Andrews-Bowman Continued Fraction, Bryan Thomas Zollinger

Graduate Research Theses & Dissertations

One of the most famous results from q-series is that of the Rogers-Ramanujan continued fraction, given by [special characters omitted]. G.E. Andrews and D. Bowman gave a full extension of this continued fraction using G.N. Watson’s nonterminating very well-poised 8φ7 function. As opposed to Ramanujan’s generalization that only used four variables, this generalization is given in seven variables, and certain q-series identities naturally arise from it. As a special case of their theorem, Andrews and Bowman gave the following identity: [special characters omitted]. This thesis will give a full proof of Andrews and Bowman’s result, as well as investigate other …

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Possible Contamination From Rainwater In Community Pool, David Mcgregor Jan 2021

Possible Contamination From Rainwater In Community Pool, David Mcgregor

Undergraduate Journal of Mathematical Modeling: One + Two

The project is meant to create an equation that can be used to estimate the amount of organic pollutant – bacteria - that is present in a swimming pool per day from rainwater. This equation is derived through a differential equation of the rate in minus the rate out. The created differential equation is an ordinary linear differential equation and is solved using an integration factor. The general solution is then converted into a specific equation using an initial condition. The resulting equation provides an approximate number of organic contaminants x(t) present in the pool after an …

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Moment Of Inertia In Applied Calculus, Saad Habib Jan 2021

Moment Of Inertia In Applied Calculus, Saad Habib

Undergraduate Journal of Mathematical Modeling: One + Two

This paper demonstrates the usefulness of calculus in structural/continuum mechanics. Calculus in structural/continuum mechanics is used to calculate mass, volume, centre of mass, moment of inertia and in solutions of differential equations. In this paper, we will use calculus to calculate moment of inertia. The area moment of inertia of a surface measures the resistance to deflection of the cross section to bending or buckling. Moment of inertia is used by engineers of inertia to determine the state of stress in a cross section and the amount of inertia. It represents a mathematical concept that depends on the size and …

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Cayley Map Embeddings Of Complete Graphs, Miriam Scheinblum Jan 2021

Cayley Map Embeddings Of Complete Graphs, Miriam Scheinblum

Honors Program Theses

This paper looks at Cayley map embeddings of complete graphs on orientable surfaces. Cayley maps constrain graph embeddings to those with cyclical edge rotations, so optimal embeddings on surfaces with the minimum genus may not always be possible. We explore instances when Cayley maps succeed at optimally embedding complete graphs, and when optimal embeddings are not possible, we determine how close to optimal they can get by finding vertex rotations that result in the smallest possible genus. Many of the complete graphs we consider have prime numbers of vertices, so for each complete graph Kn we focus on mappings with …

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Combinatorial Invariants Of Rational Polytopes, Andrés R. Vindas Meléndez Jan 2021

Combinatorial Invariants Of Rational Polytopes, Andrés R. Vindas Meléndez

Theses and Dissertations--Mathematics

The first part of this dissertation deals with the equivariant Ehrhart theory of the permutahedron. As a starting point to determining the equivariant Ehrhart theory of the permutahedron, Ardila, Schindler, and I obtain a volume formula for the rational polytopes that are fixed by acting on the permutahedron by a permutation, which generalizes a result of Stanley’s for the volume for the standard permutahedron. Building from the aforementioned work, Ardila, Supina, and I determine the equivariant Ehrhart theory of the permutahedron, thereby resolving an open problem posed by Stapledon. We provide combinatorial descriptions of the Ehrhart quasipolynomial and Ehrhart series …

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A Partition Of Unity Method For Divergence-Free Or Curl-Free Radial Basis Function Approximation, Kathryn P. Drake, Edward J. Fuselier, Grady B. Wright Jan 2021

A Partition Of Unity Method For Divergence-Free Or Curl-Free Radial Basis Function Approximation, Kathryn P. Drake, Edward J. Fuselier, Grady B. Wright

Mathematics Faculty Publications and Presentations

Divergence-free (div-free) and curl-free vector fields are pervasive in many areas of science and engineering, from fluid dynamics to electromagnetism. A common problem that arises in applications is that of constructing smooth approximants to these vector fields and/or their potentials based only on discrete samples. Additionally, it is often necessary that the vector approximants preserve the div-free or curl-free properties of the field to maintain certain physical constraints. Div/curl-free radial basis functions (RBFs) are a particularly good choice for this application as they are meshfree and analytically satisfy the div-free or curl-free property. However, this method can be computationally expensive …

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Coloring Permutation-Gain Graphs, Daniel Slilaty Jan 2021

Coloring Permutation-Gain Graphs, Daniel Slilaty

Mathematics and Statistics Faculty Publications

Correspondence colorings of graphs were introduced in 2018by Dvoˇr ́ak and Postle as a generalization of list colorings of graphswhich generalizes ordinary graph coloring. Kim and Ozeki observed thatcorrespondence colorings generalize various notions of signed-graph col-orings which again generalizes ordinary graph colorings. In this notewe state how correspondence colorings generalize Zaslavsky’s notionof gain-graph colorings and then formulate a new coloring theory ofpermutation-gain graphs that sits between gain-graph coloring and cor-respondence colorings. Like Zaslavsky’s gain-graph coloring, our newnotion of coloring permutation-gain graphs has well defined chromaticpolynomials and lifts to colorings of the regular covering graph of apermutation-gain graph

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Math 111: Introduction To Statistics And Probability, Yu Wang Jan 2021

Math 111: Introduction To Statistics And Probability, Yu Wang

Open Educational Resources

Introduce the different linear statistical models and develop critical thinking for statistical modeling in scientific and policy contexts; Apply statistical computer software tools to develop useful data analysis skills based on the use of linear regression models. Topics to be covered: simple linear regression, multiple regression, nonlinear regression and logistic regression models; Random and mixed effects models; The application of statistical software tools.

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Dynamically Weighted Balanced Loss: Class Imbalanced Learning And Confidence Calibration Of Deep Neural Networks, K. Ruwani M. Fernando, Chris P. Tsokos Jan 2021

Dynamically Weighted Balanced Loss: Class Imbalanced Learning And Confidence Calibration Of Deep Neural Networks, K. Ruwani M. Fernando, Chris P. Tsokos

Mathematics and Statistics Faculty Publications

Imbalanced class distribution is an inherent problem in many real-world classification tasks where the minority class is the class of interest. Many conventional statistical and machine learning classification algorithms are subject to frequency bias, and learning discriminating boundaries between the minority and majority classes could be challenging. To address the class distribution imbalance in deep learning, we propose a class rebalancing strategy based on a class-balanced dynamically weighted loss function where weights are assigned based on the class frequency and predicted probability of ground-truth class. The ability of dynamic weighting scheme to self-adapt its weights depending on the prediction scores …

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About Automorphisms Of Some Finite Groups, Sarah Emery Jan 2021

About Automorphisms Of Some Finite Groups, Sarah Emery

West Chester University Master’s Theses

This thesis gives an introduction to some topics from group theory, with a focus on automorphism groups of finite groups. Chapter one introduces the basic definitions and properties of groups and subgroups. In chapter two, the different classifications of functions between groups are defined and some properties thereof are given. Here we define automorphisms which are the focus of the paper. Chapters three and four deal with permutation groups and Sylow theorems respectively, and are discussions of some important groups, subgroups, and theorems pertaining thereto. The topics of these chapters help with our discussion of automorphism groups in the final …

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