Mathematics Commons^™

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.

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 …

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.

Geometrical Problems In Engineering Mechanics, Feraydune Kashefi, Mostafa Ghandehari

Mathematics Technical Papers - Archive

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.

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 …

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.

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, …

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.

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

Isolation And Component Structure In Spaces Of Composition Operators, Christopher Hammond, Barbara D. Maccluer

Mathematics Faculty Publications

We establish a condition that guarantees isolation in the space of composition operators acting between H ^p (B _N ) and H ^q (B _N ), for 0 < p ≤ ∞, 0 < q < ∞, and N ≥ 1. This result will allow us, in certain cases where 0 < q < p ≤ ∞, completely to characterize the component structure of this space of operators.

Pure Nash Equilibria Of Coordination Matrix Games, David P. Roberts

Mathematics Publications

We give a simple formula for the chance that a random m-by-n coordination game has exactly k pure Nash equilibria and compare the payoffs at the different equilibria.

An Iterated Pseudospectral Method For Functional Partial Differential Equations, J. Mead, B. Zubik-Kowal

Mathematics Faculty Publications and Presentations

Chebyshev pseudospectral spatial discretization preconditioned by the Kosloff and Tal-Ezer transformation [10] is applied to hyperbolic and parabolic functional equations. A Jacobi waveform relaxation method is then applied to the resulting semi-discrete functional systems, and the result is a simple system of ordinary differential equations ^d/_dtU^k+1(t) = M_αU^k+1(t)+f(t,U ^k_t). Here M_α is a diagonal matrix, k is the index of waveform relaxation iterations, U ^k_t is a functional argument computed from the previous iterate and the function f …

Image Registration With Auto-Mapped Control Volumes, Dana Paquin, Eduard Schreibmann, Lei Xing

Mathematics

Abstract of paper presented at the 47th Annual Meeting of the American Society for Therapeutic Radiology and Oncology.

Q.954 And A.954, Quickie Problem And Solution, Arthur T. Benjamin, Michel Bataille

All HMC Faculty Publications and Research

Problem and proof proposed by authors.

Another proof, using lattice paths, can be found in Robert A. Sulanke's article, Objects Counted by the Central Delannoy Numbers, The Journal of Integer Sequences, Vol 6, 2003. A proof by polynomials is in Michel Bataille's paper Some Identities about an Old Combinatorial Sum, The Mathematical Gazette, March 2003, pp. 144-8. A slight change in the above proof leads to m ≥ n, a generalization proved by Li Zhou using lattice paths in The Mathematical Gazette.

Remarks On Risk-Sensitive Control Problems, José Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

The main purpose of this paper is to investigate the asymptotic behavior of the discounted risk-sensitive control problem for periodic diffusion processes when the discount factor α goes to zero. If u_α(θ, x) denotes the optimal cost function, being the risk factor, then it is shown that lim_α→0αu_α(θ, x) = ξ(θ) where ξ(θ) is the average on ]0, θ[ of the optimal cost of the (usual) in nite horizon risk-sensitive control problem.

Improving Pro Forma Analysis Through Better Terminal Value Estimates, Tom Arnold, David S. North, Roy A. Wiggins

Finance Faculty Publications

Basic pro forma analysis often estimates the terminal value input using a simple growing perpetuity assumption. While this assumption is easy to implement, it potentially creates an upward bias in some inputs leading to lower firm or project value outputs. The purpose of this paper is to demonstrate a more accurate way to estimate the terminal value input. Further, by allowing for multiple sales growth rates and by not restricting other input variables to necessarily grow at these same rates, a more accurate, flexible, compact, and thorough analysis is possible.

Dependence, Dispersiveness, And Multivariate Hazard Rate Ordering, Baha-Eldin Khaledi, Subhash C. Kochar

Mathematics and Statistics Faculty Publications and Presentations

To compare two multivariate random vectors of the same dimension, we define a new stochastic order called upper orthant dispersive ordering and study its properties. We study its relationship with positive dependence and multivariate hazard rate ordering as defined by Hu, Khaledi, and Shaked (Journal of Multivariate Analysis, 2002). It is shown that if two random vectors have a common copula and if their marginal distributions are ordered according to dispersive ordering in the same direction, then the two random vectors are ordered according to this new upper orthant dispersive ordering. Also, it is shown that the marginal distributions of …

Regularity Of Digits And Significant Digits Of Random Variables, Theodore P. Hill, Klaus Schürger

Research Scholars in Residence

A random variable X is digit-regular (respectively, significant-digit-regular) if the probability that every block of k given consecutive digits (significant digits) appears in the b-adic expansion of X approaches b^-k as the block moves to the right, for all integers b>1 and k≥1. Necessary and sufficient conditions are established, in terms of convergence of Fourier coefficients, and in terms of convergence in distribution modulo 1, for a random variable to be digit-regular (significant-digit-regular), and basic relationships between digit-regularity and various classical classes of probability measures and normal numbers are given. These results provide a theoretical basis for analyses …

2005 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2005 Fall Colloquium

The Effect Of The Hiv/Aids Epidemic On Africa's Truck Drivers, Christopher Kribs, Melanie Lee, Christine Roman, Shari Wiley, Carlos M. Hernandez-Suarez

Mathematics Faculty Publications - Archive

The AIDS epidemic is having a growing impact on the transport sector of the economy of sub-Saharan Africa, where long-distance truck drivers are at an increased risk of infection due to their frequent contacts with com- mercial sex workers. The spread of AIDS in the transport industry is especially signi¯cant to the economy, as truck drivers are largely responsible for trans- porting crops and supplies needed for daily subsistence. In this paper we analyze these e®ects via two models, one employing a switch and the other a Verhulst saturation function, to describe the rate at which new drivers are recruited …

Application Of Information-Theoretic Data Mining Techniques In A National Ambulatory Practice Outcomes Research Network, Adam Wright, Thomas N. Ricciardi, Martin Zwick

Complex Systems Faculty Publications and Presentations

The Medical Quality Improvement Consortium data warehouse contains de-identified data on more than 3.6 million patients including their problem lists, test results, procedures and medication lists. This study uses reconstructability analysis, an information-theoretic data mining technique, on the MQIC data warehouse to empirically identify risk factors for various complications of diabetes including myocardial infarction and microalbuminuria. The risk factors identified match those risk factors identified in the literature, demonstrating the utility of the MQIC data warehouse for outcomes research, and RA as a technique for mining clinical data warehouses.

Conjugacy Classes And Finite P-Groups, Edith Adan-Bante

Faculty Publications

Let G be a finite p-group, where p is a prime number, and a ∈ G. Denote by Cl(a) = {gag⁻¹| g ∈ G} the conjugacy class of a in G. Assume that |Cl(a)| = p ⁿ . Then Cl(a) Cl(a⁻¹) = {xy | x ∈ Cl(a), y ∈ Cl(a⁻¹)} is the union of at least n(p − 1) + 1 distinct conjugacy classes of G.

Vertices Of Self-Similar Tiles, Da-Wen Deng, Sze-Man Ngai

Mathematical Sciences: Faculty Publications

The set V_n of n-vertices of a tile T in \R^d is the common intersection of T with at least n of its neighbors in a tiling determined by T. Motivated by the recent interest in the topological structure as well as the associated canonical number systems of self-similar tiles, we study the structure of V_n for general and strictly self-similar tiles. We show that if T is a general self-similar tile in \R² whose interior consists of finitely many components, then any tile in any self-similar tiling generated by T has a finite …

Discretisation For Odd Quadratic Twists, J. Brian Conrey, Michael O. Rubinstein, Nina C. Snaith, Mark Watkins

Mathematics - All Scholarship

The discretisation problem for even quadratic twists is almost understood, with the main question now being how the arithmetic Delaunay heuristic interacts with the analytic random matrix theory prediction. The situation for odd quadratic twists is much more mysterious, as the height of a point enters the picture, which does not necessarily take integral values (as does the order of the Shafarevich-Tate group). We discuss a couple of models and present data on this question.

Rank Distribution In A Family Of Cubic Twists, Mark Watkins

Mathematics - All Scholarship

In 1987, Zagier and Kramarz published a paper in which they presented evidence that a positive proportion of the even-signed cubic twists of the elliptic curve x³+y³=1 should have positive rank. We extend their data, showing that it is more likely that the proportion goes to zero.

Instrumented Techniques And Reflective Thinking In Analytic Geometry, Nurit Zehavi, Giora Mann

The Mathematics Enthusiast

In a previous study that explored epistemological perspectives on solving problems with Computer Algebra Systems (CAS) we concluded that awareness of the special ways that the software utilizes symbols in algebraic manipulations and in implicit plotting should be encouraged (Zehavi, 2004). Such awareness is required for, and encouraged by treating geometry analytically with a symbolic-graphical system. In this paper we compare a traditional solution of a problem in analytic geometry with CAS-based solutions to the same problem. The discussion will focus on the role of reflective thinking, namely selection of techniques, monitoring of the solution process, insight, and conceptualization, play …