Mathematics Commons^™

Alcohol Perceptions And Behavior In A Residential Peer Social Network, Shannon R. Kenney, Miles Q. Ott, Matthew Meisel, Nancy P. Barnett

Statistical and Data Sciences: Faculty Publications

Personalized normative feedback is a recommended component of alcohol interventions targeting college students. However, normative data are commonly collected through campus-based surveys, not through actual participant-referent relationships. In the present investigation, we examined how misperceptions of residence hall peers, both overall using a global question and those designated as important peers using person-specific questions, were related to students’ personal drinking behaviors. Participants were 108 students (88% freshman, 54% White, 51% female) residing in a single campus residence hall. Participants completed an online baseline survey in which they reported their own alcohol use and perceptions of peer alcohol use using both …

Curriculum Guidelines For Undergraduate Programs In Data Science, Richard D. De Veaux, Mahesh Agarwal, Maia Averett, Benjamin Baumer, Andrew Bray, Thomas C. Bressoud, Lance Bryant, Lei Z. Cheng, Amanda Francis, Robert Gould, Albert Y. Kim, Matt Kretchmar, Qin Lu, Ann Moskol, Deborah Nolan, Roberto Pelayo, Sean Raleigh, Ricky J. Sethi, Mutiara Sondjaja, Neelesh Tiruviluamala, Paul X. Uhlig, Talitha M. Washington, Curtis L. Wesley, David White, Ping Ye

Statistical and Data Sciences: Faculty Publications

The Park City Math Institute 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in data science. The group consisted of 25 undergraduate faculty from a variety of institutions in the United States, primarily from the disciplines of mathematics, statistics, and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in data science.

Asymptotic Properties Of Polynomials Orthogonal Over Multiply Connected Domains, James A. Henegan

Electronic Theses and Dissertations

We investigate the asymptotic behavior of polynomials orthogonal over certain multiply connected domains. Each domain that we consider has an analytic boundary and is, in a strong sense, conformally equivalent to a canonical type of multiply connected domain called a circular domain. The two most general results involve the construction of a series expansion and an integral representation for these polynomials. We show that the integral representation can be utilized to derive more specific results when the domain of orthogonality is circular. In this case, we shed light on the manner in which the holes in the domain of orthogonality …

Generalized Interval Valued Neutrosophic Graphs Of First Type, Florentin Smarandache, Said Broumi, Mohamed Talea, Assia Bakali, Ali Hassan

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, motivated by the notion of generalized single valued neutrosophic graphs of first type, we defined a new neutrosophic graphs named generalized interval valued neutrosophic graphs of first type (GIVNG1) and presented a matrix representation for it and studied few properties of this new concept. The concept of GIVNG1 is an extension of generalized fuzzy graphs (GFG1) and generalized single valued neutrosophic of first type (GSVNG1).

Fast Multipole Method Using Cartesian Tensor In Beam Dynamic Simulation, He Zhang, He Huang, Rui Li, Jie Chen, Li-Shi Luo

Mathematics & Statistics Faculty Publications

The fast multipole method (FMM) using traceless totally symmetric Cartesian tensor to calculate the Coulomb interaction between charged particles will be presented. The Cartesian tensor based FMM can be generalized to treat other non-oscillating interactions with the help of the differential algebra or the truncated power series algebra. Issues on implementation of the FMM in beam dynamic simulations are also discussed. © 2017 Author(s).

Mock Theta Function Identities Deriving From Bilateral Basic Hypergeometric Series, James Mclaughlin

Mathematics Faculty Publications

The bilateral series corresponding to many of the third-, fifth-, sixth- and eighth order mock theta functions may be derived as special cases of 2ψ2 series ∞ ∑n=−∞ (a, c;q)n (b,d;q)n z n . Three transformation formulae for this series due to Bailey are used to derive various transformation and summation formulae for both these mock theta functions and the corresponding bilateral series. New and existing summation formulae for these bilateral series are also used to make explicit in a number of cases the fact that for a mock theta function, say χ(q), and a root of unity in a …

Sampling And Reconstruction Of Spatial Signals, Cheng Cheng

Electronic Theses and Dissertations

Digital processing of signals f may start from sampling on a discrete set Γ, f →(f(ϒη))ϒηεΓ. The sampling theory is one of the most basic and fascinating topics in applied mathematics and in engineering sciences. The most well known form is the uniform sampling theorem for band-limited/wavelet signals, that gives a framework for converting analog signals into sequences of numbers. Over the past decade, the sampling theory has undergone a strong revival and the standard sampling paradigm is extended to non-bandlimited signals including signals in reproducing kernel spaces (RKSs), signals with finite rate of innovation (FRI) and sparse signals, and …

11: Eulers Method, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

EulersMethod.nb asks for a differential equation, an x-interval, a specific point, and the step size. It shows the graphical approximation given by Euler's Method. This notebook has setups that allow it to be used with one DE or with a system of two DE's.

10: Roots Of Unity, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

RootsOfUnity.nb offers some solutions to x⁶ -1=0 and then graphs and labels the complex roots of unity up through x⁸ -1=0 .

03: Derivative Signs, Ruth Dover

Mathematica Notebooks for Pre-Calculus and Calculus

DerivativeSigns.nb asks the user to input a function and a domain. It will color the graph to show where the derivative is positive and where it's negative. The second part colors the graph to show where the function is concave up and down.

An Optimal A Posteriori Error Estimates Of The Local Discontinuous Galerkin Method For The Second-Order Wave Equation In One Space Dimension, Mahboub Baccouch

Mathematics Faculty Publications

In this paper, we provide the optimal convergence rate of a posteriori error estimates for the local discontinuous Galerkin (LDG) method for the second-order wave equation in one space dimension. One of the key ingredients in our analysis is the recent optimal superconvergence result in [W. Cao, D. Li and Z. Zhang, Commun. Comput. Phys. 21 (1) (2017) 211-236]. We first prove that the LDG solution and its spatial derivative, respectively, converge in the L 2 -norm to (p + 1)-degree right and left Radau interpolating polynomials under mesh refinement. The order of convergence is proved to be p + …

A Flexible Distribution Class For Count Data, Kimberly F. Sellers, Andrew W. Swift, Kimberly S. Weems

Mathematics Faculty Publications

The Poisson, geometric and Bernoulli distributions are special cases of a flexible count distribution, namely the Conway-Maxwell-Poisson (CMP) distribution – a two-parameter generalization of the Poisson distribution that can accommodate data over- or under-dispersion. This work further generalizes the ideas of the CMP distribution by considering sums of CMP random variables to establish a flexible class of distributions that encompasses the Poisson, negative binomial, and binomial distributions as special cases. This sum-of-Conway-Maxwell-Poissons (sCMP) class captures the CMP and its special cases, as well as the classical negative binomial and binomial distributions. Through simulated and real data examples, we demonstrate this …

Nonminimal Cyclic Invariant Subspaces Of Hyperbolic Composition Operators, Valentin Matache

Mathematics Faculty Publications

Operators on function spaces acting by composition to the right with a fixed self-map ϕ are called composition operators. We denote them Cϕ. Given ϕ, a hyperbolic disc automorphism, the composition operator Cϕ on the Hilbert Hardy space H2 is considered. The bilateral cyclic invariant subspaces Kf, f ∈ H2, of Cϕ are studied, given their connection with the invariant subspace problem, which is still open for Hilbert space operators. We prove that nonconstant inner functions u induce non–minimal cyclic subspaces Ku if they have unimodular, orbital, cluster points. Other results about Ku when u is inner are obtained. If …

Integrals Of Frullani Type And The Method Of Brackets, Sergio Bravo, Ivan Gonzalez, Karen T. Kohl, Victor H. Moll

Faculty Publications

The method of brackets is a collection of heuristic rules, some of which have being made rigorous, that provide a flexible, direct method for the evaluation of definite integrals. The present work uses this method to establish classical formulas due to Frullani which provide values of a specific family of integrals. Some generalizations are established.

Compactness Of Isoresonant Potentials, Robert G. Wolf

Theses and Dissertations--Mathematics

Bruning considered sets of isospectral Schrodinger operators with smooth real potentials on a compact manifold of dimension three. He showed the set of potentials associated to an isospectral set is compact in the topology of smooth functions by relating the spectrum to the trace of the heat semi-group. Similarly, we can consider the resonances of Schrodinger operators with real valued potentials on Euclidean space of whose support lies inside a ball of fixed radius that generate the same resonances as some fixed Schrodinger operator, an ``isoresonant" set of potentials. This isoresonant set of potentials is also compact in the topology …

Orbital Stability Results For Soliton Solutions To Nonlinear Schrödinger Equations With External Potentials, Joseph B. Lindgren

Theses and Dissertations--Mathematics

For certain nonlinear Schroedinger equations there exist solutions which are called solitary waves. Addition of a potential $V$ changes the dynamics, but for small enough $||V||_{L^\infty}$ we can still obtain stability (and approximately Newtonian motion of the solitary wave's center of mass) for soliton-like solutions up to a finite time that depends on the size and scale of the potential $V$. Our method is an adaptation of the well-known Lyapunov method.

For the sake of completeness, we also prove long-time stability of traveling solitons in the case $V=0$.

On P-Adic Fields And P-Groups, Luis A. Sordo Vieira

Theses and Dissertations--Mathematics

The dissertation is divided into two parts. The first part mainly treats a conjecture of Emil Artin from the 1930s. Namely, if f = a_1x_1^d + a_2x_2^d +...+ a_{d^2+1}x^d where the coefficients a_i lie in a finite unramified extension of a rational p-adic field, where p is an odd prime, then f is isotropic. We also deal with systems of quadratic forms over finite fields and study the isotropicity of the system relative to the number of variables. We also study a variant of the classical Davenport constant of finite abelian groups and relate it to the isotropicity of diagonal …

Approximation Of Solutions To The Mixed Dirichlet-Neumann Boundary Value Problem On Lipschitz Domains, Morgan F. Schreffler

Theses and Dissertations--Mathematics

We show that solutions to the mixed problem on a Lipschitz domain Ω can be approximated in the Sobolev space H¹(Ω) by solutions to a family of related mixed Dirichlet-Robin boundary value problems which converge in H¹(Ω), and we give a rate of convergence. Further, we propose a method of solving the related problem using layer potentials.

The Partition Lattice In Many Guises, Dustin G. Hedmark

Theses and Dissertations--Mathematics

This dissertation is divided into four chapters. In Chapter 2 the equivariant homology groups of upper order ideals in the partition lattice are computed. The homology groups of these filters are written in terms of border strip Specht modules as well as in terms of links in an associated complex in the lattice of compositions. The classification is used to reproduce topological calculations of many well-studied subcomplexes of the partition lattice, including the d-divisible partition lattice and the Frobenius complex. In Chapter 3 the box polynomial B_{m,n}(x) is defined in terms of all integer partitions that fit in an m …

Colorings Of Hamming-Distance Graphs, Isaiah H. Harney

Theses and Dissertations--Mathematics

Hamming-distance graphs arise naturally in the study of error-correcting codes and have been utilized by several authors to provide new proofs for (and in some cases improve) known bounds on the size of block codes. We study various standard graph properties of the Hamming-distance graphs with special emphasis placed on the chromatic number. A notion of robustness is defined for colorings of these graphs based on the tolerance of swapping colors along an edge without destroying the properness of the coloring, and a complete characterization of the maximally robust colorings is given for certain parameters. Additionally, explorations are made into …

Some Take-Away Games On Discrete Structures, Kristen M. Barnard

Theses and Dissertations--Mathematics

The game of Subset Take-Away is an impartial combinatorial game posed by David Gale in 1974. The game can be played on various discrete structures, including but not limited to graphs, hypergraphs, polygonal complexes, and partially ordered sets. While a universal winning strategy has yet to be found, results have been found in certain cases. In 2003 R. Riehemann focused on Subset Take-Away on bipartite graphs and produced a complete game analysis by studying nim-values. In this work, we extend the notion of Take-Away on a bipartite graph to Take-Away on particular hypergraphs, namely oddly-uniform hypergraphs and evenly-uniform hypergraphs whose …

Positive Solutions Of Boundary Value Problems For Ordinary Differential Equations With Dependence On Higher Order Derivatives, Ahlam Abid, Paul Eloe

Mathematics Faculty Publications

In this paper, the compression contraction fixed point theorem is applied to a right focal boundary value problem for a second order ordinary differential equation to provide sufficient conditions for existence of solutions in a cone. The nonlinear term is a function of three variables and singularities are allowed. A cone is defined in the Banach space C1[0, 1] and concavity of derivatives of solutions plays a key role. A family of examples is provided in which explicit sufficient conditions are exhibited.

An Updated Survey On Rainbow Connections Of Graphs - A Dynamic Survey, Xueliang Li, Yuefang Sun

Theory & Applications of Graphs

The concept of rainbow connection was introduced by Chartrand, Johns, McKeon and Zhang in 2008. Nowadays it has become a new and active subject in graph theory. There is a book on this topic by Li and Sun in 2012, and a survey paper by Li, Shi and Sun in 2013. More and more researchers are working in this field, and many new papers have been published in journals. In this survey we attempt to bring together most of the new results and papers that deal with this topic. We begin with an introduction, and then try to organize the …

Triple Non-Negative Matrix Factorization Technique For Sentiment Analysis And Topic Modeling, Alexander A. Waggoner

CMC Senior Theses

Topic modeling refers to the process of algorithmically sorting documents into categories based on some common relationship between the documents. This common relationship between the documents is considered the “topic” of the documents. Sentiment analysis refers to the process of algorithmically sorting a document into a positive or negative category depending whether this document expresses a positive or negative opinion on its respective topic. In this paper, I consider the open problem of document classification into a topic category, as well as a sentiment category. This has a direct application to the retail industry where companies may want to scour …

The Qq–Bit (Ii): Functional Central Limits And Monotone Representation Of The Azema Martingale, Luigi Accardi, Yun-Gang Lu

Communications on Stochastic Analysis

No abstract provided.

The Subcritical Phase For A Homopolymer Model, Iddo Ben-Ari, Hugo Panzo

Communications on Stochastic Analysis

No abstract provided.

Near-Martingale Property Of Anticipating Stochastic Integration, C R. Hwang, Hui-Hsiung Kuo, Kimiaki Saitô, Jiayu Zhai

Communications on Stochastic Analysis

No abstract provided.

An Option Pricing Model With Memory, Flavia Sancier, Salah Mohammed

Communications on Stochastic Analysis

No abstract provided.

Using The Pert Exponential Growth Model: Predicting Past And Future Chinese Populations Involving Their Famous Population Control Policies, Greg Gancarz

A with Honors Projects

This project serves to examine the hypothetical effects of the implementation and repeal of China’s famous One Child Policy on the rate of population growth in that country through the use and applications of the basic exponential growth model. Calculates growth in three different scenarios and estmates the population for China in the year 2045.

Disrupted Superior Collicular Activity May Reveal Cervical Dystonia Disease Pathomechanisms, Eavan M. Mcgovern, Owen Killian, Shruti Narashimham, Brendan Quinlivan, John Butler, Rebecca Beck, Ines Beiser, Laura W. Williams, Ronan P. Killeen, Michael Farrell, Sean O'Riordan, Richard B. Reilly, Michael Hutchinson

Articles

Cervical dystonia is a common neurological movement disorder characterised by muscle contractions causing abnormal movements and postures affecting the head and neck. The neural networks underpinning this condition are incompletely understood. While animal models suggest a role for the superior colliculus in its pathophysiology, this link has yet to be established in humans. The present experiment was designed to test the hypothesis that disrupted superior collicular processing is evident in affected patients and in relatives harbouring a disease-specific endophenotype (abnormal temporal discrimination). The study participants were 16 cervical dystonia patients, 16 unaffected first-degree relatives with abnormal temporal discrimination, 16 unaffected …