Physical Sciences and Mathematics Commons^™

The Two Covering Radius Of The Two Error Correcting Bch Code, Andrew Klapper, Andrew Mertz

Andrew Mertz

The m-covering radii of codes are natural generalizations of the covering radii of codes. In this paper we analyze the 2-covering radii of double error correcting BCH code.

Capturing Data Uncertainty In High-Volume Stream Processing, Yanlei Diao, Boduo Li, Anna Liu, Liping Peng, Charles Sutton, Thanh Tran, Michael Zink

Anna Liu

We present the design and development of a data stream system that captures data uncertainty from data collection to query processing to final result generation. Our system focuses on data that is naturally modeled as continuous random variables such as many types of sensor data. To provide an end-to-end solution, our system employs probabilistic modeling and inference to generate uncertainty description for raw data, and then a suite of statistical techniques to capture changes of uncertainty as data propagates through query operators. To cope with high-volume streams, we explore advanced approximation techniques for both space and time efficiency. We are …

Establishing The Quantitative Thinking Program At Macalester, David Bressoud

David Bressoud

No abstract provided.

Maa To Probe Calculus I, David Bressoud

David Bressoud

No abstract provided.

Is The Sky Still Falling?, David Bressoud

David Bressoud

No abstract provided.

Review Of “Continuum Modeling In The Physical Sciences” By Van Groesen And Molenaar, Chad M. Topaz

Chad M. Topaz

No abstract provided.

Mind The Gap, David Bressoud

David Bressoud

No abstract provided.

Pompeiu's Theorem Revisited, Árpád Bényi

Árpád Bényi

Pompeiu's theorem states that if ABC is an equilateral triangle and M a point in its plane, then MA, MB, and MC form a new triangle. In this article, we have a new look at this theorem in the realm of arbitrary triangles. We discover what we call Pompeiu's Area Formula, a neat equality relating areas of triangles determined by the points A, B, C, and M.

Periodic Traveling Waves In Sirs Endemic Models, Tong Li, Yi Li, Herbert W. Hethcote

Yi Li

Mathematical models are used to determine if infection wave fronts could occur by traveling geographically in a loop around a region or continent. These infection wave fronts arise by Hopf bifurcation for some spatial models for infectious disease transmission with distributed-contacts. Periodic traveling waves are shown to exist for the spatial analog of the SIRS endemic model, in which the temporary immunity is described by a delay, but they do not exist in a similar spatial SIRS endemic model without a delay. Specifically, we found that the ratio of the delay ω in the recovered class and the average infectious …

A Note On The Positive Solutions Of An Inhomogeneous Elliptic Equation On Rn, Yinbin Deng, Yi Li, Fen Yang

Yi Li

This paper is contributed to the elliptic equation (0.1) Δu+K(|x|)up+μf(|x|)=0,

where p>1, x∈Rn, n⩾3, and μ⩾0 is a constant. We study the structure of positive radial solutions of (0.1) and obtain the uniqueness of solution decaying faster than r−m at ∞ if μ is small enough under some assumptions on K and f, where m is the slow decay rate.

Optical Tomography For Media With Variable Index Of Refraction, Stephen R. Mcdowall

Mathematics Faculty Publications

Optical tomography is the use of near-infrared light to determine the optical absorption and scattering properties of a medium M ⊂ Rⁿ. If the refractive index is constant throughout the medium, the steady-state case is modeled by the stationary linear transport equation in terms of the Euclidean metric and photons which do not get absorbed or scatter travel along straight lines. In this expository article we consider the case of variable refractive index where the dynamics are modeled by writing the transport equation in terms of a Riemannian metric; in the absence of interaction, photons follow the geodesics …

Modulation Invariant Bilinear T(1) Theorem, Árpád Bényi, Ciprian Demeter, Andrea R. Nahmod, Christoph M. Thiele, Rodolfo H. (Rudolfo Humberto) Torres, Paco Villarroya

Mathematics Faculty Publications

We prove a T(1) theorem for bilinear singular integral operators (trilinear forms) with a one-dimensional modulation symmetry.

Local Well-Posedness Of Nonlinear Dispersive Equations On Modulation Spaces, Árpád Bényi, Kasso A. Okoudjou

Mathematics Faculty Publications

By using tools of time-frequency analysis, we obtain some improved local well-posedness results for the nonlinear Schrödinger, nonlinear wave and nonlinear Klein–Gordon equations with Cauchy data in modulation spaces ℳ_0,s^p,1.

A Critical Constant For The K Nearest-Neighbour Model, Paul Balister, Béla Bollobás, Amites Sarkar, Mark Walters

Mathematics Faculty Publications

Let P be a Poisson process of intensity 1 in a square S_n of area n. For a fixed integer k, join every point of P to its k nearest neighbours, creating an undirected random geometric graph G_n,k. We prove that there exists a critical constant c_crit such that, for c‹c_crit, G_{n,⌊clogn⌋} is disconnected with probability tending to 1 as n →∞ and, for c‹c_crit, G_{n,⌊clogn⌋} is connected with probability tending to 1 as n →∞. This answers a question …

Numerical Bifurcation Of Separable Parameterized Equations, Yun-Qiu Shen, Tjalling Ypma

Mathematics Faculty Publications

Many applications give rise to separable parameterized equations, which have the form A(y, µ)z + b(y, µ) = 0, where z ∈ R^N , y ∈ Rⁿ, µ ∈ R^s, and the (N + n) × N matrix A(y, µ) and (N + n) vector b(y, µ) are C² -Lipschitzian in (y, µ) ∈ Ω ⊂ Rⁿ × R^s. We present a technique which reduces the original equation to the form …

Maintenance In Single-Server Queues: A Game-Theoretic Approach, Najeeb Al-Matar, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

We use antagonistic stochastic games and fluctuation analysis to examine a single-server queue with bulk input and secondary work during server's multiple vacations. When the buffer contents become exhausted the server leaves the system to perform some diagnostic service of a minimum of jobs clustered in packets of random sizes (event A). The server is not supposed to stay longer than units of time (event B). The server returns to the system when A or B occurs, whichever comes first. On the other hand, he may not break service of a packet in a middle even if A or B …

Generalized First-Order Nonlinear Evolution Equations And Generalized Yosida Approximations Based On H-Maximal Monotonicity Frameworks, Ram U. Verma

Mathematics and System Engineering Faculty Publications

First a general framework for the Yosida approximation is introduced based on the relative H-maximal monotonicity model, and then it is applied to the solvability of a general class of first-order nonlinear evolution equations. The obtained results generalize and unify a wide range of results to the context of the solvability of first-order nonlinear evolution equations in several settings.© 2009 Texas State University-San Marcos.

Diversity Graphs, P Blain, C Davis, Allen G. Holder, J Silva, C Vinzant

Mathematics Faculty Research

Bipartite graphs have long been used to study and model matching problems, and in this paper we introduce the bipartite graphs that explain a recent matching problem in computational biology. The problem is to match haplotypes to genotypes in a way that minimizes the number of haplotypes, a problem called the Pure Parsimony problem. The goal of this work is not to address the computational or biological issues but rather to explore the mathematical structure through a study of the underlying graph theory.

Radiotherapy Optimal Design: An Academic Radiotherapy Treatment Design System, Ryan Acosta, William Brick, A Hanna, Allen G. Holder, D Lara, G Mcquilen, D Nevin, P Uhlig, B Salter

Mathematics Faculty Research

Optimally designing radiotherapy and radiosurgery treatments to increase the likelihood of a successful recovery from cancer is an important application of operations research. Researchers have been hindered by the lack of academic software that supports head-to-head comparisons of different techniques, and this article addresses the inherent difficulties of designing and implementing an academic treatment planning system. In particular, this article details the algorithms and the software design of Radiotherapy optimAl Design (RAD).

11443, Eugen J. Ionascu

Faculty Bibliography

No abstract provided.

A Characterization Of Regular Tetrahedra In Z3, Eugen J. Ionascu

Faculty Bibliography

In this note we characterize all regular tetrahedra whose vertices in R 3 have integer coordinates. The main result is a consequence of the characterization of all equilateral triangles having integer coordinates ([3]). Previous work on this topic began in [4]. We will use this characterization to point out some corollaries. The number of such tetrahedra whose vertices are in the finite set {0, 1, 2, ..., n} 3 , n ∈ N, is related to the sequence A103158 in the Online Encyclopedia of Integer Sequences ([9]).

Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga

Theses, Dissertations and Capstones

This thesis is on the study of dynamic equations on time scale. Most often, the derivatives and anti-derivatives of functions are taken on the domain of real numbers, which cannot be used to solve some models like insect populations that are continuous while in season and then follow a difference scheme with variable step-size. They die out in winter, while the eggs are incubating or dormant; and then they hatch in a new season, giving rise to a non overlapping population. The general idea of my thesis is to find the conditions for having a positive solution of any boundary …

Twin Solutions Of Even Order Boundary Value Problems For Ordinary Differential Equations And Finite Difference Equations, Xun Sun

Theses, Dissertations and Capstones

The Avery-Henderson fixed-point theorem is first applied to obtain the existence of at least two positive solutions for the boundary value problem

(-1)ⁿy⁽²ⁿ⁾ = f(y); n = 1; 2; 3 ... and t 2 [0; 1];

with boundary conditions

y(2k)(0) = 0

y^(2k+1)(1) = 0 for k = 0; 1; 2 ... n - 1:

This theorem is subsequently used to obtain the existence of at least two positive solutions for the dynamic boundary value problem

(-1)^{n (2n)}u(k)g(u(k)); n = 1; 2; 3 .... and k (0; ... N);

with boundary conditions

(2k)u(0) …

Variable Shape Parameter Strategies In Radial Basis Function Methods, Derek Sturgill

Theses, Dissertations and Capstones

The Radial Basis Function (RBF) method is an important tool in the interpolation of multidimensional scattered data. The method has several important properties. One is the ability to handle sparse and scattered data points. Another property is its ability to interpolate in more than one dimension. Furthermore, the Radial Basis Function method provides phenomenal accuracy which has made it very popular in many fields. Some examples of applications using the RBF method are numerical solutions to partial differential equations, image processing, and cartography. This thesis involves researching Radial Basis Functions using different shape parameter strategies. First, we introduce the Radial …

Preface [Honoring The Career Of John Graef On The Occasion Of His Sixty-Seventh Birthday], Paul W. Eloe, Johnny Henderson

Mathematics Faculty Publications

John R. Graef did not retire from Mississippi State University in order to retire. Rather, he was seeking ways to add to his overfilled schedule . . . which he found in Fall 1999 in the form of position of Head of the Department of Mathematics at the University of Tennessee at Chattanooga. He currently remains in that position, and during his time in that position, he has become a strong proponent in upgrading the visibility of the department, in improving the level of the department faculty, in seeking out benefactors for the department, in obtaining external funding for the …

Periodic Traveling Waves In Sirs Endemic Models, Tong Li, Yi Li, Herbert W. Hethcote

Mathematics and Statistics Faculty Publications

Mathematical models are used to determine if infection wave fronts could occur by traveling geographically in a loop around a region or continent. These infection wave fronts arise by Hopf bifurcation for some spatial models for infectious disease transmission with distributed-contacts. Periodic traveling waves are shown to exist for the spatial analog of the SIRS endemic model, in which the temporary immunity is described by a delay, but they do not exist in a similar spatial SIRS endemic model without a delay. Specifically, we found that the ratio of the delay ω in the recovered class and the average infectious …

A Direct Solution Of The Robin Inverse Problem, Weifu Fang, Suxing Zeng

Mathematics and Statistics Faculty Publications

We present a direct, linear boundary integral equation method for the inverse problem of recovering the Robin coefficient from a single partial boundary measurement of the solution to the Laplace equation.

A Note On The Positive Solutions Of An Inhomogeneous Elliptic Equation On Rn, Yinbin Deng, Yi Li, Fen Yang

Mathematics and Statistics Faculty Publications

This paper is contributed to the elliptic equation

(0.1) Δu+K(|x|)up+μf(|x|)=0,

where p>1, x∈Rn, n⩾3, and μ⩾0 is a constant. We study the structure of positive radial solutions of (0.1) and obtain the uniqueness of solution decaying faster than r−m at ∞ if μ is small enough under some assumptions on K and f, where m is the slow decay rate.

On The Number Of K-Gons In Finite Projective Planes, Felix Lazebnik, Keith Mellinger, Oscar Vega

Mathematics

Let π = πq denote a finite projective plane of order q, and let G = Levi(π) be the bipartite point-line incidence graph of π. For k ≥ 3, let c2k(π) denote the number of cycles of length 2k in G. Are the numbers c2k(π) the same for all πq? We prove that this is the case for k = 3, 4, 5, 6 by computing these numbers.

Logistic Models With Missing Categorical Covariates, Jeremiah Rounds

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

We present an EM based solution to missing categorical covariates in Binomial models with logit links using an assumption that experimental units are drawn from a Multinomial population of infinite size. We further address the problem of separation of points inducing large variances on parameter estimates by the use of a novel score-modification based on Firth's bias-reduction score-modification. We simulate to address questions about estimate bias, distribution, and appropriate parameter coverage by Wald intervals.