Physical Sciences and Mathematics Commons^™

Elementary Differential Equations With Boundary Value Problems, William F. Trench

William F. Trench

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some prepa- ration in linear algebra. In writing this book I have been guided by the these principles: An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. …

Elementary Differential Equations, William F. Trench

William F. Trench

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra. In writing this book I have been guided by the these principles: An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. An …

Student Solutions Manual For Elementary Differential Equations And Elementary Differential Equations With Boundary Value Problems, William F. Trench

William F. Trench

No abstract provided.

Introduction To Real Analysis, William F. Trench

William F. Trench

This is a text for a two-term course in introductory real analysis for junior or senior math- ematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathe- matical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calcu- lus sequence …

Improvement Of Ifng Elispot Performance Following Overnight Resting Of Frozen Pbmc Samples Confirmed Through Rigorous Statistical Analysis, Radleigh Santos, Alcinette Bunying, Nazila Sabri, John Yu, Anthony Gringeri, James Bender, Sylvia Janetzki, Clemencia Pinilla, Valeria A. Judkowski

Mathematics Faculty Articles

Immune monitoring of functional responses is a fundamental parameter to establish correlates of protection in clinical trials evaluating vaccines and therapies to boost antigen-specific responses. The IFNg ELISPOT assay is a well-standardized and validated method for the determination of functional IFNg-producing T-cells in peripheral blood mononuclear cells (PBMC); however, its performance greatly depends on the quality and integrity of the cryopreserved PBMC. Here, we investigate the effect of overnight (ON) resting of the PBMC on the detection of CD8-restricted peptide-specific responses by IFNg ELISPOT. The study used PBMC from healthy donors to evaluate the CD8 T-cell response to five pooled …

On Dual Toric Complete Intersection Codes, Pinar Celebi Demiraslan, Ivan Soprunov

Mathematics and Statistics Faculty Publications

In this paper we study duality for evaluation codes on intersections of ℓ hypersurfaces with given ℓ-dimensional Newton polytopes, so called toric complete intersection codes. In particular, we give a condition for such a code to be quasi-self-dual. In the case of it reduces to a combinatorial condition on the Newton polygons. This allows us to give an explicit construction of dual and quasi-self-dual toric complete intersection codes. We provide a list of examples over and an algorithm for producing them.

Cartan Subalgebras, Compact Roots And The Satake Diagram For Su(2, 2), Ian M. Anderson

Tutorials on... in 1 hour or less

In this worksheet we use the 15-dimensional real Lie algebra su(2, 2) to illustrate some important points regarding the general structure theory and classification of real semi-simple Lie algebras.

1. Recall that a real semi-simple Lie algebra g is called a compact Lie algebra if the Killing form is negative definite. The Lie algebra g is compact if and only if all the root vectors for any Cartan subalgebra are purely imaginary. However, if the root vectors are purely imaginary for some choice of Cartan subalgebra it is not necessarily true that the Lie algebra is compact.

2. A real …

Jordan Algebras And The Exceptional Lie Algebra F4, Ian M. Anderson

Tutorials on... in 1 hour or less

This worksheet analyzes the structure of the Jordan algebra J(3, O) and its split and exceptional versions. The algebra of derivations is related to the exceptional Lie algebra f4.

Linear Operators That Preserve Graphical Properties Of Matrices: Isolation Numbers, Leroy B. Beasley, Seok-Zun Song, Young Bae Jun

Mathematics and Statistics Faculty Publications

Let A be a Boolean {0, 1} matrix. The isolation number of A is the maximum number of ones in A such that no two are in any row or any column (that is they are independent), and no two are in a 2 × 2 submatrix of all ones. The isolation number of A is a lower bound on the Boolean rank of A. A linear operator on the set of m × n Boolean matrices is a mapping which is additive and maps the zero matrix, O, to itself. A mapping strongly preserves a set, S, if it …

Statistical Partition Problem For Exponential Populations And Statistical Surveillance Of Cancers In Louisiana, Jin Gu

University of New Orleans Theses and Dissertations

In this dissertation, we consider the problem of partitioning a set of

k population with respect

to a control population. For this problem some multistage methodologies are proposed and their

properties are derived. Using the Monte Carlo simulation techniques, the small and moderate

sample size performance of the proposed procedure are studied.

We have also considered at statistical surveillance of various cancers in Louisiana.

Finite Symmetries Of S^4, Weimin Chen Chen, Slawomir Kwasik, Reinhard Shultz

Weimin Chen

This paper discusses topological and locally linear actions of finite groups on S4. Local linearity of the orientation preserving actions on S4 forces the group to be a subgroup of SO(5). On the other hand, orientation reversing topological actions of “exotic” groups G (i.e. G 6⊂ O(5)) on S4 are constructed, and local linearity and stable smoothability of the actions are studied.

Elliptic Curve Cryptography, Kerrie Pratt

Honors Program Theses and Projects

In the present day, security is essential for sending and receiving information. There are always stories about bank accounts being hacked, credit card numbers being stolen, and secret information being decoded. With the technology of the Internet age growing at a rapid pace, security is essential to keep privileged information safe. In order to ensure this information is kept private, so that information can be sent and received without being hacked and decoded, organizations employ different types of encryption. One of the current encoding systems is Elliptic Curve Cryptography (ECC). ECC uses elliptic curves over finite fields to send information …

Computing Intersection Multiplicity Via Triangular Decomposition, Paul Vrbik

Electronic Thesis and Dissertation Repository

Fulton’s algorithm is used to calculate the intersection multiplicity of two plane curves about a rational point. This work extends Fulton’s algorithm first to algebraic points (encoded by triangular sets) and then, with some generic assumptions, to l many hypersurfaces.

Out of necessity, we give a standard-basis free method (i.e. practically efficient method) for calculating tangent cones at points on curves.

Integrating Path-Dependent Functionals On Yeh-Wiener Space, Ian Pierce, David Skough

Department of Mathematics: Faculty Publications

Denote by Ca,b(Q) the generalized two-parameter Yeh-Wiener space with associated Gaussian measure. We investigate several scenarios in which integrals of functionals on this space can be reduced to integrals of related functionals over an appropriate single-parameter generalized Wiener space Cˆa,ˆb[0, T ]. This extends some interesting results of R. H. Cameron and D. A. Storvick.

Applications Of Nonlinear Optimization, Yao Xie

Arts & Sciences Electronic Theses and Dissertations

We apply an interior point algorithm to two nonlinear optimization problems and achieve improved results. We also devise an approximate convex functional alternative for use in one of the problems and estimate its accuracy.

The first problem is maximum variance unfolding in machine learning. The traditional method to solve this problem is to convert it to a semi-definite optimization problem by defining a kernel matrix. We obtain better unfolding and higher speeds with the interior point algorithm on the original non-convex problem for data with less than 10,000 points.

The second problem is a multi-objective dose optimization for intensity modulated …

Modeling The Progress And Retention Of International Students Using Markov Chains, Lucas Gagne

Lucas Gagne

Some Observations On Scientific Epistemology With Applications To Conflict Resolution And Constructive Controversy, Judith Puncochar, Don Faust

Other Presentations

An overview, by Judy and Don (published in 2013 in the BULLETIN OF SYMBOLIC LOGIC):

Explorationism is a perspective wherein all of our knowledge is (so far) less than certain, and naturally would come equipped with a base logic entailing machinery for representing and processing evidential knowledge. One such base logic is Evidence Logic, which strives to deal with the phenomenon of the gradational presence of both confirmatory and refutatory evidence. From this perspective, we will address questions surrounding sociological problem areas that we see as deeply infused with substantial epistemological factors. By defining a framework as any theory, …

On The Indispensable Premises Of The Indispensability Argument, Andrea Sereni, Marco Panza

MPP Published Research

We identify four different minimal versions of the indispensability argument, falling under four different varieties: an epistemic argument for semantic realism, an epistemic argument for platonism and a non-epistemic version of both. We argue that most current formulations of the argument can be reconstructed by building upon the suggested minimal versions. Part of our discussion relies on a clarification of the notion of (in)dispensability as relational in character. We then present some substantive consequences of our inquiry for the philosophical significance of the indispensability argument, the most relevant of which being that both naturalism and confirmational holism can be dispensed …

Motivation For Achievement And Attitudes Toward Mathematics Instruction In A Required Calculus Course At The Norwegian University Of Science And Technology, Donna Sundre, Carol Barry, Vidar Gynnild, Erin Tangen Ostgard

Donna L. Sundre

This study from the Norwegian University of Science and Technology (NTNU) examines students’ learning goals and attitudes toward mathematics in a first-year calculus course in undergraduate engineering education. Achievement motivation research using the Achievement Goal Questionnaire (AGQ) is advanced from current literature with two additions: (1) a course specific context using introductory college calculus students, and (2) participation of Norwegian students. Pre- and posttest measures of attitudes indicate that students do change learning goals over time, unfortunately opposite to the instructors’ aspirations. A significant increase in “Mastery Avoidance” and “Work Avoidance” was accompanied with a drop in “Mastery Approach” and …

Computing Singular Values Of Large Matrices With An Inverse-Free Preconditioned Krylov Subspace Method, Qiao Liang, Qiang Ye

Mathematics Faculty Publications

We present an efficient algorithm for computing a few extreme singular values of a large sparse m×n matrix C. Our algorithm is based on reformulating the singular value problem as an eigenvalue problem for C^TC. To address the clustering of the singular values, we develop an inverse-free preconditioned Krylov subspace method to accelerate convergence. We consider preconditioning that is based on robust incomplete factorizations, and we discuss various implementation issues. Extensive numerical tests are presented to demonstrate efficiency and robustness of the new algorithm.

A Statistical Analysis Of The Role Of Critical-Thinking Games In College Students' Quantitative Reasoning, Melissa Radevicz

Honors Program Theses and Projects

Improving college students' quantitative reasoning is crucial to increase STEM-field retention rates. The National Survey of Student Engagement (NSSE), results indicate that "college students don't always get exposure to activities that develop [quantitative reasoning]" (Berrett & Sander, 2013). This study aimed to engage college students in quantitative reasoning through critical-thinking games. Phase 1, conducted in summer 2014 with a university research grant, involved a correlation analysis of the work of 133 college students enrolled in Elementary Statistics I, Chemical Principles II, Elements of Calculus, Pre-Calculus with Trigonometry, Multivariable Calculus, and Differential Equations. Participants held a variety of 39 different majors, …

Ropelength Criticality, Jason Cantarella, Joseph H.G. Fu, Robert B. Kusner, John M. Sullivan

Robert Kusner

The ropelength problem asks for the minimum-length configuration of a knotted diameter-one tube embedded in Euclidean three-space. The core curve of such a tube is called a tight knot, and its length is a knot invariant measuring complexity. In terms of the core curve, the thickness constraint has two parts: an upper bound on curvature and a self-contact condition.

We give a set of necessary and sufficient conditions for criticality with respect to this constraint, based on a version of the Kuhn–Tucker theorem that we established in previous work. The key technical difficulty is to compute the derivative of thickness …

Cohomology Of Absolute Galois Groups, Claudio Quadrelli

Electronic Thesis and Dissertation Repository

The main problem this thesis deals with is the characterization of profinite groups which are realizable as absolute Galois groups of fields: this is currently one of the major problems in Galois theory. Usually one reduces the problem to the pro-p case, i.e., one would like to know which pro-p groups occur as maximal pro-p Galois groups, i.e., maximal pro-p quotients of absolute Galois groups. Indeed, pro-p groups are easier to deal with than general profinite groups, yet they carry a lot of information on the whole absolute Galois group.

We define a new class of pro-p groups, called Bloch-Kato …

On The Data Of Images, Lori Ziegelmeier

Lori Beth Ziegelmeier

No abstract provided.

K-Theory Of Quadratic Modules: A Study Of Roy's Elementary Orthogonal Group., A. A. Ambily Dr.

Doctoral Theses

This thesis discusses the K-theory of quadratic modules by studying Roys elementary orthogonal group of the quadratic space Q1H(P) over a commutative ring A. We estab- lish a set of commutator relations among the elementary generators of Roys elementary orthogonal group and use this to prove Quillens local-global principle for this elementary group. We also obtain a result on extendability of quadratic modules. We establish nor- mality of the elementary orthogonal group under certain conditions and prove stability results for the Ki group of this orthogonal group. We also prove that Roys elementary orthogonal group and Petrovs odd hyperbolic unitary …

Polynomials With Prescribed Bad Primes, David P. Roberts

Mathematics Publications

We tabulate polynomials in ℚ[t] with a given factorization partition, bad reduction entirely within a given set of primes, and satisfying auxiliary conditions associated to 0, 1, and ∞. We explain how these polynomials are of particular interest because of their role in the construction of nonsolvable number fields of arbitrarily large degree and bounded ramification.

A Price-Volume Model For A Single-Period Stock Market, Yun Chen-Shue

HIM 1990-2015

The intention of this thesis is to provide a primitive mathematical model for a financial market in which tradings affect the asset prices. Currently, the idea of a price-volume relationship is typically used in the form of empirical models for specific cases. Among the theoretical models that have been used in stock markets, few included the volume parameter. The thesis provides a general theoretical model with the volume parameter for the intention of a broader use. The core of the model is the correlation between trading volume and stock price, indicating that volume should be a function of the stock …

Scattering Amplitudes In Flat Space And Anti-De Sitter Space, Savan Kharel

Doctoral Dissertations

We calculate gauge theory one-loop amplitudes with the aid of the complex shift used in the Britto- Cachazo-Feng-Witten (BCFW) recursion relations of tree amplitudes. We apply the shift to the integrand and show that the contribution from the limit of infinite shift vanishes after integrating over the loop momentum, with a judicious choice of basis for polarization vectors. This enables us to write the one-loop amplitude in terms of on-shell tree and lower-point one-loop amplitudes. Some of the tree amplitudes are forward amplitudes. We show that their potential singularities do not contribute and the BCFW recursion relations can be applied …

A Markov Model For Baseball With Applications, Daniel Joseph Ursin

Theses and Dissertations

In this work we confirm a Markov chain model of baseball for 2013 Major League Baseball batting data. We describe the transition matrices for individual player data and their use in generating single and nine-inning run distributions for a given lineup. The run distribution is used to calculate the expected number of runs produced by a lineup over nine innings. We discuss batting order optimization heuristics to avoid computation of distributions for the 9! = 362, 880 distinct lineups for 9 players. Finally, we describe an implementation of the algorithms and review their performance against actual game data.

Mixed Variational Formulation For The Wellposedness And Numerical Approximation Of A Pde Model Arising In A 3-D Fluid-Structure Interaction, George Avalos, Tom Clark

Faculty Work Comprehensive List

We present qualitative and numerical results on a partial differential equation (PDE) system which models a certain fluid-structure dynamics. Wellposedness is established by constructing for it a nonstandard semigroup generator representation; this representation is accomplished by an appropriate elimination of the pressure. This coupled PDE model involves the Stokes system which evolves on a three dimensional domain O coupled to a fourth order plate equation, possibly with rotational inertia parameter ρ>0. This plate PDE evolves on a flat portion Ω of the boundary of O. The coupling on Ω is implemented via the Dirichlet trace of the Stokes system …