Physical Sciences and Mathematics Commons^™

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.

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 …

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.

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.

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 …

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

Colloquia

Abstracts of the talks given at the 2005 Fall Colloquium

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.

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 …

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.

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

Department of 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 …

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.

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.

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

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

Systems Science 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.

Graduate Student Satisfaction With An Online Discrete Mathematics Course, Amber Settle, Chad Settle

Amber Settle

Dynamics Of Trapped Bright Solitons In The Presence Of Localized Inhomogeneities, G. Herring, Panos Kevrekidis, R. Carretero-Gonzalez, B. A. Malomed, D. J. Frantzeskakis, A. R. Bishop

Panos Kevrekidis

We examine the dynamics of a bright solitary wave in the presence of a repulsive or attractive localized ``impurity'' in Bose-Einstein condensates (BECs). We study the generation and stability of a pair of steady states in the vicinity of the impurity as the impurity strength is varied. These two new steady states, one stable and one unstable, disappear through a saddle-node bifurcation as the strength of the impurity is decreased. The dynamics of the soliton is also examined in all the cases (including cases where the soliton is offset from one of the relevant fixed points). The numerical results are …

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.

Discrete Approximations Of Differential Inclusions In Infinite-Dimensional Spaces, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we study discrete approximations of continuous-time evolution systems governed by differential inclusions with nonconvex compact values in infinite-dimensional spaces. Our crucial result ensures the possibility of a strong Sobolev space approximation of every feasible solution to the continuous-time inclusion by its discrete-time counterparts extended as Euler's "broken lines." This result allows us to establish the value and strong solution convergences of discrete approximations of the Bolza problem for constrained infinite-dimensional differential/evolution inclusions under natural assumptions on the initial data.

Von Neumann And Computers, Steve Humble

The Mathematics Enthusiast

The title of this paper should not be Von Neumann and computers, but Von Neumann and the Von Neumann machine. Von Neumann may be famous for many things but humility was not one of them. Yet no one had anything bad to say about 'good time' Johnny Von Neumann; he just was too likeable. He gave massive parties and loved women, fast cars, jokes, noise, Mexican food, fine wine, and, most of all, mathematics. 'Unbelievable', said one of Von Neumann's old friends, 'He knew how to have a good time. His parties were once if not twice a week at …

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 …

A Comparison Of The Danish And The Virginia Secondary Teacher Education System: Their Values And Emphasis On Mathematics Content Knowledge, Bettina Dahl

The Mathematics Enthusiast

In this paper I will first examine an example of secondary mathematics teacher education in the USA, namely Virginia, then compare it with the secondary teacher education in Denmark. The purpose is both to investigate how much mathematics the students get in the respective systems and secondly to see what this type of teacher education communicates about the values emphasized in the various countries’ education systems. I spent more time on explaining the Danish education system than that of the USA and the single states since it is assumed that the reader is familiar with these systems. One cannot necessarily …

Problem Solving And Problem Posing In A Dynamic Geometry Environment, Constantinos Christou, Nicholas Mousoulides, Marios Pittalis, Demetra Pitta-Pantazi

The Mathematics Enthusiast

In this study, we considered dynamic geometry software (DGS) as the tool that mediates students’ strategies in solving and posing problems. The purpose of the present study was twofold. First, to understand the way in which students can solve problems in the setting of a dynamic geometry environment, and second, to investigate how DGS provides opportunities for posing new problems. Two mathematical problems were presented to six pre-service teachers with prior experience in dynamic geometry. Each student participated in two interview sessions which were video recorded. The results of the study showed that DGS, as a mediation tool, encouraged students …

Call For Papers

The Mathematics Enthusiast

No abstract provided.

Tme Statistics

The Mathematics Enthusiast

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Meet The Authors

The Mathematics Enthusiast

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Editorial: Globalization, History, Technology And Mathematics Education, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Algebraic Insight Underpins The Use Of Cas For Modelling, Robyn Pierce

The Mathematics Enthusiast

Computer Algebra Systems (CAS) performs algorithmic processes quickly and correctly. Concern is commonly expressed that students using CAS will merely be pushing buttons but this paper indicates that, while CAS may assist students, this facility impacts on only one section of the mathematical modeling process: CAS may be used to help find mathematical solutions to mathematically formulated problems. Controlling and monitoring the use of CAS to perform the necessary routine processes requires the mathematical thinking referred to as algebraic insight. This paper sets out a framework of the aspects, and elements of algebraic insight and illustrates the importance of students …

Tme Volume 2, Number 2

The Mathematics Enthusiast

No abstract provided.

Numb3rs: The Intersection Between Mathematics And Hollywood Is Not Empty, Ron Buckmire

Ron Buckmire

No abstract provided.