Physical Sciences and Mathematics Commons^™

Looking Beyond The Curriculum In Jamaica, Jon T. Jacobsen, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

In August 2004, we had the opportunity to travel to Jamaica to lead a pilot workshop for Jamaican high school math teachers. The workshop focused on the importance of mathematical context in the teaching of mathematics. It was sponsored by the Gibraltar Institute, a Jamaica-based nongovernmental organization led by Trevor Campbell (Pomona College) and Reginald Nugent (Cal State Pomona), Jamaica’s College of Agriculture, Science and Education, and Harvey Mudd College.

Pythagorean Primes And Palindromic Continued Fractions, Arthur T. Benjamin, Doron Zeilberger

All HMC Faculty Publications and Research

In this note, we prove that every prime of the form 4m + 1 is the sum of the squares of two positive integers in a unique way. Our proof is based on elementary combinatorial properties of continued fractions. It uses an idea by Henry J. S. Smith ([3], [5], and [6]) most recently described in [4] (which provides a new proof of uniqueness and reprints Smith's paper in the original Latin). Smith's proof makes heavy use of nontrivial properties of determinants. Our purely combinatorial proof is self-contained and elementary.

Recounting The Odds Of An Even Derangement, Arthur T. Benjamin, Curtis D. Bennet, Florence Newberger

All HMC Faculty Publications and Research

No abstract provided in this article.

Parity Theorems For Combinatorial Statistics, Mark A. Shattuck

Doctoral Dissertations

A q-generalization Gn(q) of a combinatorial sequence Gn which reduces to that sequence when q = 1 is obtained by q-counting a statistic defined on a sequence of finite discrete structures enumerated by Gn. In what follows, we evaluate Gn(−1) for statistics on several classes of discrete structures, giving both algebraic and combinatorial proofs. For the latter, we define appropriate sign-reversing involutions on the associated structures. We shall call the actual algebraic result of such an evaluation at q = −1 a parity theorem (for the …

On Sequential And Fixed Designs For Estimation With Comparisons And Applications, Mekki Terbeche, Broderick O. Oluyede, Ahmed Barbour

Department of Mathematical Sciences Faculty Publications

A fully sequential approach to the estimation of the difference of two population means for distributions belonging to the exponential family of distributions is adopted and compared with the best fixed design. Results on the lower bound for the Bayes risk due to estimation and expected cost are presented and shown to be of first order efficiency. Applications involving the Poisson and exponential distributions with gamma priors as well as the Bernoulli distribution with beta priors are given. Finally, some numerical results are presented.

Some New Orthogonal Arrays Oa (4r;R (1) 2(P);2), Warren F. Kuhfeld, Chung Yi Suen

Mathematics and Statistics Faculty Publications

We developed an algorithm to search for new orthogonal arrays, OA(4rOA(4r, r12pr12p, 2), for odd r . With it, we found new orthogonal arrays with 4r=364r=36 through 124 runs. Many other new arrays can be obtained from these new arrays.

Neutrosophic Methods In General Relativity, Florentin Smarandache, Dmitri Rabounski, Larissa Borissova

Branch Mathematics and Statistics Faculty and Staff Publications

In this work the authors apply concepts of Neutrosophic Logic to the General Theory of Relativity to obtain a generalisation of Einstein’s fourdimensional pseudo-Riemannian differentiable manifold in terms of Smarandache Geometry (Smarandache manifolds), by which new classes of relativistic particles and non-quantum teleportation are developed. Fundamental features of Neutrosophic Logic are its denial of the Law of Excluded Middle, and open (or estimated) levels of truth, falsity and indeterminancy. Both Neutrosophic Logic and Smarandache Geometry were invented some years ago by one of the authors (F. Smarandache). The application of these purely mathematical theories to General Relativity reveals hitherto unknown …

The Application Of Category Theory And Analysis Of Receiver Operating Characteristics To Information Fusion, Steven N. Thorsen

Theses and Dissertations

Multisensor data fusion is presented in a rigorous mathematical format, with definitions consistent with the desires of the data fusion community. A model of event-state fusion is developed and described. Definitions of fusion rules and fusors are introduced, along with the functor categories of which they are objects. Defining fusors and competing fusion rules involves the use of an objective function of the researcher's choice. One such objective function, a functional on families of classification systems, and in particular, receiver operating characteristics (ROCs), is introduced. Its use as an objective function is demonstrated in that the argument that minimizes it …

Mathematical Functions: An Interactive Emodule, Sarah Jean Moody

Undergraduate Honors Capstone Projects

The National Library of Virtual Manipulatives (NLVM, http://nlvm.usu.edu/) is a widely used and highly praised teaching/learning resource for school mathematics. The NLVM is the result of a four-year USU project, funded primarily by the National Science Foundation, Award #9819107, to create a web-based, freely accessible, library of interactive virtual manipulatives to help students learn basic mathematics concepts. During a typical school day, the NLVM server receives more than 3 million hits.

Recounting The Odds Of An Even Derangement, Arthur T. Benjamin, Curtis T. Bennett, Florence Newberger

Mathematics, Statistics and Data Science Faculty Works

No abstract provided.

The Stochastic Dance Of Early Hiv Infection, Stephen J. Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

The stochastic nature of early HIV infection is described in a series of models, each of which captures aspects of the dance of HIV during the early stages of infection. It is to this highly variable target that the immune response must respond. The adaptability of the various components of the immune response is an important aspect of the system's operation, as the nature of the pathogens that the response will be required to respond to and the order in which those responses must be made cannot be known beforehand. As HIV infection has direct influence over cells responsible for …

Fibonacci Determinants — A Combinatorial Approach, Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn

All HMC Faculty Publications and Research

In this paper, we provide combinatorial interpretations for some determinantal identities involving Fibonacci numbers. We use the method due to Lindström-Gessel-Viennot in which we count nonintersecting n-routes in carefully chosen digraphs in order to gain insight into the nature of some well-known determinantal identities while allowing room to generalize and discover new ones.

Classifcation Of Conics In The Tropical Projective Plane, Amanda Ellis

Theses and Dissertations

This paper defines tropical projective space, TP^n, and the tropical general linear group TPGL(n). After discussing some simple examples of tropical polynomials and their hypersurfaces, a strategy is given for finding all conics in the tropical projective plane. The classification of conics and an analysis of the coefficient space corresponding to such conics is given.

Identity Configurations Of The Sandpile Group, William Chen '06

Distinguished Student Work

The abelian sandpile model on a connected graph yields a finite abelian group Q of recurrent configurations which is closely related to the combinatorial Laplacian. We consider the identity configuration of the sandpile group on graphs with large edge multiplicities, called “thick” graphs. We explicitly compute the identity configuration for all thick paths using a recursion formula. We then analyze the thick cycle and explicitly compute the identity configuration for the three-cycle, the four-cycle, and certain types of symmetric cycles. The latter is a special case of a more general symmetry theorem we prove that applies to an arbitrary graph.

Mathematics And The Divine (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Teun Koetsier and Luc Bergmans, editors. Mathematics and the Divine. Boston: Elsevier, 2005. 701 pages. ISBN 0-444-50328-5

A Reduced-Order Partial Differential Equation Model For Dynamics Of The Flow In Athermosyphon, Evangelos A. Coutsias, Elisabeth A. Burroughs, L. Romero

Branch Mathematics and Statistics Faculty and Staff Publications

Flow in a closed loop thermosyphon heated from below exhibits a sequence of bifurcations with increasing Grashof number. Using the Navier-Stokes equations in the Boussinesq approximation we have derived a model where, in the case of a slender circular loop, the first Fourier modes exactly decouple from all other Fourier modes, leaving a system of three coupled nonlinear partial differential equations that completely describes the flow in the thermosyphon. We have characterized the flow through two bifurcations, identifying stable periodic solutions for flows of Prandtl number greater than 18.5, a much lower value than predicted previously. Because of the quadratic …

Totally Real Galois Representations In Characteristic 2 And Arithmetic Cohomology, Heather Aurora Florence De Melo

Theses and Dissertations

The purpose of this paper is to provide new examples supporting a conjecture of Ash, Doud, and Pollack. This conjecture involves Galois representations taking Gal(Q bar/Q) to the general linear group of 3 x 3 matrices in characterisic 2, and our examples are where complex conjugation is mapped to the identity. Since this case has not yet been examined, the results of this paper are quite significant.

On The Action Of Weight-Preserving Sets, Matthew Badger

Mathematical Sciences Technical Reports (MSTR)

We introduce weight-preserving sets of binary words. Any transformation that respects the row and column weights of a 0-1 matrix can be decomposed as a composition of two types of action on the matrix. We conjecture that weight-preserving sets perform only one type of action, permutations of rows and columns; i.e., weight-preserving sets are cwatsets.

Statistical Pronouncements Iv, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

No abstract provided.

Misconceptions Leading To Choosing The T Test Over The Wilcoxon Mann-Whitney Test For Shift In Location Parameter, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

There exist many misconceptions in choosing the t over the Wilcoxon Rank-Sum test when testing for shift. Examples are given in the following three groups: (1) false statement, (2) true premise, but false conclusion, and (3) true statement irrelevant in choosing between the t test and the Wilcoxon Rank Sum test.

The Rényi-Ulam Pathological Liar Game With A Fixed Number Of Lies, Robert B. Ellis, Vadim Ponomarenko, Catherine H. Yan

Mathematics Faculty Research

The q-round Rényi-Ulam pathological liar game with k lies on the set [n] := {1,..., n} is a 2-player perfect information zero sum game. In each round Paul chooses a subset A ⊆ [n] and Carole either assigns 1 lie to each element of A or to each element of [n]\A. Paul wins if after q rounds there is at least one element with k or fewer lies. The game is dual to the original Rényi-Ulam liar game for which the winning condition is that at most one element has …

Self-Adaptive Scheduler Parameterization, Barry Lawson, Evgenia Smirni

Department of Math & Statistics Technical Report Series

High-end parallel systems present a tremendous research challenge on how to best allocate their resources to match dynamic workload characteristics and user habits that are often unique to each system. Although thoroughly investigated, job scheduling for production systems remains an inexact science, requiring significant experience and intuition from system administrators to properly configure batch schedulers. State-of-the-art schedulers provide many parameters for their configuration, but tuning these to optimize performance and to appropriately respond to the continuously varying characteristics of the workloads can be very difficult — the effects of different parameters and their interactions are often unintuitive.

In this paper, …

Proof Without Words: Alternating Sums Of Odd Numbers, Arthur T. Benjamin

All HMC Faculty Publications and Research

Proof for alternating sums of odd numbers in two figures.

Particular Solutions For Axisymmetric Helmholtz-Type Operators, A.S. Muleshkov, M.A. Golberg, C.S. Chen

Faculty Publications

In this paper, we consider the solution of the axisymmetric heat equation with axisymmetric data in an axisymmetric domain in R-3. To solve this problem, we remove the time-dependence by various transform or time-stepping methods. This converts the problem to one of a sequence of modified inhomogeneous Helmholtz equations. Generalizing previous work, we consider solving these equations by boundary-type methods. In order to do this, one needs to subtract off a particular solution, so that one obtains a sequence of modified homogeneous Helmholtz equations. We do this by modifying the usual Dual Reciprocity Method (DRM) and approximating the right-hand sides …

Geometrical Problems In Engineering Mechanics, Feraydune Kashefi, Mostafa Ghandehari

Mathematics Technical Papers

Four problems in two dimensional geometry are presented, which are applicable to education of the basic courses, statics. These problems represent geometrical concepts that are understandable by engineering students. For example, consider a triangle made from a uniform rod. If we draw the inscribed circle of this triangle, and concentrate the weight of each side on the point at which in circle touches the side, center of the gravity of the three concentrated masses is located at the center.

A Pair Of General Series-Transformation Formulas, Tian-Xiao He, Leetsch Hsu, Peter Shiue

Tian-Xiao He

No abstract provided.

On Some Inequalities For Beta And Gamma Functions Via Some Classical Inequalities, Ravi P. Agarwal, Neven Elezović, Josip Pecaric

Mathematics and System Engineering Faculty Publications

We improve several results recently established by Dragomir et al. in (2000) for the Gamma and Beta functions. All we need is some clever applications of classical inequalities. Copyright © 2005 Hindawi Publishing Corporation.

The Simple Random Walk On A Random Voronoi Tiling, Amites Sarkar, Louigi Addario-Berry

Amites Sarkar

Let P be a Poisson point process in ℝ^d with intensity 1. We show that the simple random walk on the cells of the Voronoi diagram of P is almost surely recurrent in dimensions d = 1 and d = 2 and is almost surely transient in dimension d ≥ 3.

Big Cwatsets And Hamming Code, Matthew Davis, Thomas M. Langley, Norah Mazel

Mathematical Sciences Technical Reports (MSTR)

In contrast to Lagrange's Theorem in Finite Group Theory, we show that the ratio of the largest proper cwatset of degree d to the size of binary d-space approaches 1 as d approaches infinity. We show how to explicitly construct large cwatsets as cosets of Hamming Codes, and discuss many open questions that arise.

Noncompact Manifolds With Nonnegative Ricci Curvature, William Wylie

Mathematics - All Scholarship

Let (M,d) be a metric space. For 0