Mathematics Commons^™

Hypersurfaces In Hyperbolic Space With Support Function, Vincent Bonini, José M. Espinar, Jie Qint

Mathematics

Based on [previous publication*], we develop a global correspondence between immersed hypersurfaces ϕ:Mⁿ→Hⁿ⁺¹ϕ:Mn→Hn+1 satisfying an exterior horosphere condition, also called here horospherically concave hypersurfaces, and complete conformal metrics e^2ρg_Sⁿe2ρgSn on domains Ω in the boundary SⁿSn at infinity of Hⁿ⁺¹Hn+1, where ρ is the horospherical support function, ∂_∞ϕ(Mⁿ)=∂Ω∂∞ϕ(Mn)=∂Ω, and Ω is the image of the Gauss map G:Mⁿ→SⁿG:Mn→Sn. To do so we first establish results on when the Gauss map G:Mⁿ→SⁿG:Mn→Sn is injective. We also …

Homology Over Trivial Extensions Of Commutative Dg Algebras, Luchezar L. Avramov, Srikanth B. Iyengar, Saeed Nasseh, Sean Sather-Wagstaff

Mathematical Sciences: Faculty Publications

Conditions on the Koszul complex of a noetherian local ring R guarantee that TorRi(M,N) is non-zero for infinitely many i, when M and N are finitely generated R-modules of infinite projective dimension. These conditions are obtained from results concerning Tor of differential graded modules over certain trivial extensions of commutative differential graded algebras.

Global Optimized Isothermal And Nonlinear Models Of Earth’S Standard Atmosphere, Nihad E. Daidzic, Ph.D.,

International Journal of Aviation, Aeronautics, and Aerospace

Both, a global isothermal temperature model and a nonlinear quadratic temperature model of the ISA was developed and presented here. Constrained optimization techniques in conjunction with the least-square-root approximations were used to design best-fit isothermal models for ISA pressure and density changes up to 47 geopotential km for NLPAM, and 86 orthometric km for ISOAM respectively. The mass of the dry atmosphere and the relevant fractional-mass scale heights have been computed utilizing the very accurate eight-point Gauss-Legendre numerical quadrature for both ISOAM and NLPAM. Both, the ISOAM and the NLPAM represent viable alternatives to ISA in many practical applications and …

Invariance Explains Multiplicative And Exponential Skedactic Functions, Vladik Kreinovich, Olga Kosheleva, Hung T. Nguyen, Songsak Sriboonchitta

Departmental Technical Reports (CS)

In many situation, we have an (approximately) linear dependence between several quantities y = f(x₁, ..., x_n). The variance v of the corresponding approximation error often depends on the values of the quantities x₁, ..., x_n: v = v(x₁, ..., x_n); the function describing this dependence is known as the skedactic function. Empirically, two classes of skedactic functions are most successful: multiplicative functions v = c * |x₁|^γ₁ * ... * |x_n|^γ_n and exponential functions v = exp(α + …

Smooth Representation Of Functions On Non-Periodic Domains By Means Of The Fourier Continuation Method, Nicholas Rubel, David Bilyeu, Justin Koo

STAR Program Research Presentations

This report examines a new methodology in solving Partial Differential Equations (PDEs) numerically. The report also studies the accuracy of this new method as a PDE solver. This new Fourier Continuation (FC) method is one of a few that avoids the well-known Gibbs Phenomenon, which is the overestimation or underestimation of a function. These estimations are oscillations around a “jump” when a non-periodic function is expressed in terms of sines and cosines. Instead, the FC algorithm creates a smooth, periodic extension of a function over a general domain, as demonstrated by the many examples presented here. The FC algorithm was …

The Integration Of Kinesthetic Learning Through The Math & Movement Program: Pilot Study 2015, Benjamin Ferder

Master's Theses

Purpose: The primary purpose of this pilot study was to verify that the use of kinesthetic learning (Math & Movement Program) in the classroom increases retention of multiplication facts at a greater rate than traditional drill and practice. The Math & Movement Program uses a kinesthetic learning-based approach for practicing, learning, and memorizing mathematics through the incorporation of bodily movement(s). Participants: The directors of the research project for the participating school district selected the sample of convenience. The population size of this study included 213 third and fourth grade students during the second half of the 2011-2012 school years. Data …

Guidelines For Good Mathematical Writing, Francis Su

All HMC Faculty Publications and Research

Communicating mathematics well is an important part of doing mathematics. Many of us know from writing papers or giving talks that communicating effectively not only serves our audience but also clarifies and structures our own thinking. There is an art and elegance to good writing that every writer should strive for. And writing, as a work of art, can bring a person great personal satisfaction.

Within the MAA, we value exposition and mathematical communication. In this column, I’m sharing the advice I give my students to help them write well. There are more extensive treatments (e.g., see Paul Halmos’s How …

Extended Book Review: Really Big Numbers, By Richard Evan Schwartz; The Boy Who Loved Math: The Improbable Life Of Paul Erdös, By Deborah Heiligman; The Short Seller, By Elissa Brent Weissman, Gizem Karaali

Pomona Faculty Publications and Research

The genre of math lit for children is not huge, but it is growing. My kid loves the early reader books by my friend and colleague Julie Glass (A Dollar for Penny (1998), The Fly On the Ceiling (2000)). I found Izolda Fotiyeva’s Math with Mom (2003) too late for my daughter but will definitely read it with my son. For a neat twist on the traditional alphabet book, I recommend The Technical Alphabet (2014) by the engineer sisters Lavanya and Melissa Jawaharlal. More recently a colleague introduced me to Laura Overdeck’s Bedtime Math series; these will soon join …

On The Topology Of The Permutation Pattern Poset, Peter R. W. Mcnamara, Einar Steingrímsson

Faculty Journal Articles

The set of all permutations, ordered by pattern containment, forms a poset. This paper presents the first explicit major results on the topology of intervals in this poset. We show that almost all (open) intervals in this poset have a disconnected subinterval and are thus not shellable. Nevertheless, there seem to be large classes of intervals that are shellable and thus have the homotopy type of a wedge of spheres. We prove this to be the case for all intervals of layered permutations that have no disconnected subintervals of rank 3 or more. We also characterize in a simple way …

Infographics And Mathematics: A Mechanism For Effective Learning In The Classroom, Ivan Sudakov, Thomas Bellsky, Svetlana Usenyuk, Victoria V. Polyakova

Physics Faculty Publications

This work discusses the creation and use of infographies in an undergraduate mathematics course. Infographies are a visualization of information combining data, formulas, and images. This article discusses how to form an infographic and uses infographics on topics within mathematics and climate as examples. It concludes with survey data from undergraduate students on both the general use of infographics and on the specific infographics designed by the authors.

Kdv Solitons In Direct Numerical Simulation Of The Navier-Stokes Equation, Jake Dynes

Theses, Dissertations and Culminating Projects

Tracking the behavior of an interface present between two fluids is critical to a wide array of different fields. Much can be learned through lab work and experimentation, however there are many limitations involved. Solving the Navier-Stokes equations with interfaces is very difficult, and in many cases intractable. One way to combat this is to make assumptions to help reduce the equation (e.g. KdV), and make it more easily studied. An entirely different approach is to use Direct Numerical Simulation on the N-S equation, weather it be by use of front-tracking, VOF, etc. In this thesis, we compare these two …

Dynamic Pricing For Competing Sellers, Liu Zhu

All Theses

To optimize profit, pricing is of great importance for each company, especially when competitors exist. The optimal pricing strategy we are interested in is to achieve Nash equilibrium (NE) to prevent malignant competition. In this work, we study dynamic pricing for a duopoly with two competing sellers, each of which sells one product, using a simple linear model which incorporates the competition effect. Motivated from the modified pricing policy constructed in Liu and Cooper [12], we propose a policy, referred to as randomized certainty equivalent pricing (RCEP) policy, under which each seller applies certainty equivalent pricing (CEP) policy for most …

Thresholding Of Statistical Maps In Functional Neuroimaging Via Independent Filtering, Jaqueline Kwiasowski

All Theses

The high dimension of functional magnetic resonance imaging (fMRI) data causes problems in finding effective thresholds for voxelwise test statistics. Due to the enormous number of voxels, adjustment for multiple testing is necessary. But such an adjustment can lead to low statistical power. It has been shown that filtering the test statistics to reduce the number of tests being performed potentially increases the number of discoveries. However, some filter-test combinations can result in loss of control over the false discovery rate. We present an independent filtering approach which avoids this issue. Independent filtering uses filter-test combinations such that the filter …

Polygon Distances With Applications To High Performance Liquid Chromatography, Vito Capuano

All Theses

Analytical chemistry uses high performance liquid chromatography (HPLC) to separate desired macromolecules from a fluid. This thesis is concerned with monolithic column environments used in HPLC separations. The monolithic column environment under consideration consists of many long polymer fibers suspended in a tube. Between the fibers are voids (interstices) which regulate the separation process. The goal of this thesis is both to identify interstices of a size such that the interstice contributes to the separation process, and to identify the boundaries of the fibers along such interstices. We model the cross section of the column environment with a collection of …

Systems Of Parameters And The Cohen–Macaulay Property, Katharine Shultis

Department of Mathematics: Dissertations, Theses, and Student Research

Let R be a commutative, Noetherian, local ring and M a finitely generated R-module. Consider the module of homomorphisms Hom_R(R/a,M/bM) where b [subset of] a are parameter ideals of M. When M = R and R is Cohen-Macaulay, Rees showed that this module of homomorphisms is isomorphic to R/a, and in particular, a free module over R/a of rank one. In this work, we study the structure of such modules of homomorphisms for a not necessarily Cohen-Macaulay R-module M.

Improving The Solution Time Of Integer Programs By Merging Knapsack Constraints With Cover Inequalities, Fabio Vitor

Mathematics Faculty Publications

Integer Programming is used to solve numerous optimization problems. This class of mathematical models aims to maximize or minimize a cost function restricted to some constraints and the solution must be integer. One class of widely studied Integer Program (IP) is the Multiple Knapsack Problem (MKP). Unfortunately, both IPs and MKPs are NP-hard, potentially requiring an exponential time to solve these problems.

Utilization of cutting planes is one common method to improve the solution time of IPs. A cutting plane is a valid inequality that cuts off a portion of the linear relaxation space. This thesis presents a new class …

Inverse Problem For Non-Viscous Mean Field Control: Example From Traffic, Shaurya Agarwal

UNLV Theses, Dissertations, Professional Papers, and Capstones

This thesis presents an inverse problem for mean field games where we find the

mean field problem statement for which the given dynamics is the solution. We use

distributed traffic as an example and derive the classic Lighthill Whitham Richards

(LWR) model as a solution of the non-viscous mean field game. We also derive

the same model by choosing a different problem where we use travel time, which

is a distributed parameter, as the cost for the optimal control. We then study the

stationary versions of these two problems and provide numerical solutions for the

same.

The Impact Of A Quantitative Reasoning Instructional Approach To Linear Equations In Two Variables On Student Achievement And Student Thinking About Linearity, Paul Thomas Belue

Boise State University Theses and Dissertations

A control group and an experimental group of college students at a community college in the Pacific Northwest were taught a unit on linear equations in two variables. The control group was taught using a traditional instructional approach that focused on learning procedures and the experimental group was taught using a quantitative reasoning instructional approach that focused on learning proportional and functional reasoning. Both groups were then given the same unit assessment that had 10 procedural understanding items and 10 conceptual understanding items related to linear equations in two variables. The assessment was given to determine the impact of the …

A Nonabelian Landau-Ginzburg B-Model Construction, Ryan Thor Sandberg

Theses and Dissertations

The Landau-Ginzburg (LG) B-Model is a significant feature of singularity theory and mirror symmetry. Krawitz in 2010, guided by work of Kaufmann, provided an explicit construction for the LG B-model when using diagonal symmetries of a quasihomogeneous, nondegenerate polynomial. In this thesis we discuss aspects of how to generalize the LG B-model construction to allow for nondiagonal symmetries of a polynomial, and hence nonabelian symmetry groups. The construction is generalized to the level of graded vector space and the multiplication developed up to an unknown factor. We present complete examples of nonabelian LG B-models for the polynomials x^2y + y^3, …

Prognostic Role Of Serum Chloride Levels In Acute Decompensated Heart Failure, Justin L. Grodin, Jennifer Simon, Rory Hachamovitch, Yuping Wu, Gregory Jackson, Meghana Halkar, Randall C. Starling, Jeffrey M. Testani, W.H. Wilson Tang

Mathematics and Statistics Faculty Publications

BACKGROUND: Acute decompensated heart failure (ADHF) can be complicated by electrolyte abnormalities, but the major focus has been concentrated on the clinical significance of serum sodium levels.

Lorentz Invariant Spacelike Surfaces Of Constant Mean Curvature In Anti-De Sitter 3-Space, Jamie Patrick Lambert

Master's Theses

In this thesis, I studied Lorentz invariant spacelike surfaces with constant mean curvature H = c in the anti-de Sitter 3-space H³₁(−c²) of constant curvature −c². In particular, I construct Lorentz invariant spacelike surfaces of constant mean curvature c and maximal Lorentz invariant spacelike surfaces in H³₁(−c²). I also studied the limit behavior of those constant mean curvature c surfaces in H³₁(−c²). It turns out that they approach a maximal catenoid in Minkowski 3-space E³₁ as c → …

The Strict Higher Grothendieck Integral, Scott W. Dyer

Department of Mathematics: Dissertations, Theses, and Student Research

This thesis generalizes A. Grothendieck’s construction, denoted by an integral, of a fibered category from a contravariant pseudofunctor, to a construction for n- and even ∞-categories. Only strict higher categories are considered, the more difficult theory of weak higher categories being neglected. Using his axioms for a fibered category, Grothendieck produces a contravariant pseudofunctor from which the original fibered category can be reconstituted by integration. In applications, the integral is often most efficient, constructing the fibered category with its structure laid bare. The situation generalizes the external and internal definitions of the semidirect product in group theory: fibration is …

Graph Centers, Hypergraph Degree Sequences, And Induced-Saturation, Sarah Lynne Behrens

Department of Mathematics: Dissertations, Theses, and Student Research

The center of a graph is the set of vertices whose distance to other vertices is minimal. The centralizing number of a graph G is the minimum number of additional vertices in any graph H where V(G) is the center of H. Buckley, Miller, and Slater and He and Liu provided infinite families of graphs with each centralizing number. We show the number of graphs with each nonzero centralizing number grows super-exponentially with the number of vertices. We also provide a method of altering graphs without changing the centralizing number and give results about the centralizing …

Higgs Boson Equation In De Sitter Spacetime: Numerical Investigation Of Bubbles Using Gpus, Jacob N. Banda

Theses and Dissertations - UTB/UTPA

The Higgs field, along with its corresponding boson, represent a milestone for modern day particle physics. In this work we consider the Higgs boson equation in de Sitter spacetime. Previous work by K. Yagdjian [23] has formulated sufficient conditions for the existence of the zeros of global solutions in the interior of their supports. In searching for such solutions, we turn to heterogeneous parallel computing, which allows for faster computation through graphical processing units (GPUs). Armed with general-purpose computation on graphics hardware (GPGPU) techniques and explicit numerical schemes, we approximate solutions of the equation for the Higgs boson along with …

On Various Solutions To A (2+1) Dimensional General Camassa-Holm Equation, Eric J. Tovar

Theses and Dissertations - UTB/UTPA

We study a (2+1)-dimensional generalized Camassa-Holm (2dgCH) equation with both quadratic and cubic nonlinearity. We derive a peaked soliton (peakon) solution and multi-peakon solutions. In particular, the two-peakon dynamical system is explicitly presented and their collisions are investigated in detail. We also find weak kink and kink-peakon interactional solutions. Furthermore, we study all possible smooth one-soliton solutions for the system.

Financial Market And Pricing Of Emerging Financial Derivatives: A Mathematical Approach, Haicheng Gu

Theses and Dissertations - UTB/UTPA

Pricing has been one of the key problems of financial market theory. With the development of the modern financial market, various new financial derivatives have been created and need to be priced properly. In the thesis, we are going to use several mathematical tools to investigate the essential structure of the financial market and models for financial derivatives.

Nonparametric Regression In Natural Exponential Families: A Simulation Study, Yijun Chen

All Theses

Nonparametric regression has been particularly well developed. Base on the asymptotic equivalence theory, there are some procedures that can turn more complicated nonparametric estimation problems into a standard nonparametric regression, especially in natural exponential families. This procedure is described in detail with a wavelet thresholding estimator for Gaussian nonparametric regression and simulation study shed light on the behavior of this method under different sample sizes and parameterizations of exponential distribution. The resulting estimators have a high degree of adaptivity in [2].

Monodromy Representation Of The Braid Group, Phillip W. Hart

Boise State University Theses and Dissertations

In the mid 1980s, it was realized that solutions to what is known as the Knizhnik- Zamolodchikov equation, or KZ equation, provided a pathway to representations of the braid group B_n on n strands, with early mathematical treatments of the topic by Kohno and Drinfel'd. Such representations are typically referred to as monodromy representations of the braid group along solutions of the KZ equation. These linear representations are of great interest within topology, integral to the construction of isotopy invariants of knots and links, such as the well known Jones polynomial. More current discussions of the KZ equation and …

The Robinson-Schensted Correspondence And A2-Web Bases, Matthew Housley, Heather M. Russell, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

We study natural bases for two constructions of the irreducible representation of the symmetric group corresponding to [n, n, n]: the reduced web basis associated to Kuperberg’s combinatorial description of the spider category; and the left cell basis for the left cell construction of Kazhdan and Lusztig. In the case of [n, n], the spider category is the Temperley-Lieb category; reduced webs correspond to planar matchings, which are equivalent to left cell bases. This paper compares the image of these bases under classical maps: the Robinson–Schensted algorithm between permutations and Young tableaux and Khovanov–Kuperberg’s bijection between Young tableaux and reduced …

Quantum Mechanical Derivation Of The Wallis Formula For Π, Tamar Friedmann, C. R. Hagen

Mathematics Sciences: Faculty Publications

A famous pre-Newtonian formula for π is obtained directly from the variational approach to the spectrum of the hydrogen atom in spaces of arbitrary dimensions greater than one, including the physical three dimensions.