Mathematics Commons^™

The Wright Message, 2010, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- 2010 - 2011 Tenure-Stream Faculty
-- Spotlight on Undergraduates
-- Projects and Grants
-- Secondary Mathematics Education Programs
-- UNI I-Teach
-- Crane Scholarship
-- Actuarial Science and the Actuarial Science Fund
-- Alliance Project
-- Mathematics Contribution Form
-- Additional Mathematics Funds
-- Around Wright Hall
-- In Memoriam
-- Dr. Ridenhour Retires

The Fundamental Gap For Hyperbolic Triangles, Dennis Stuart Fillebrown

Honors Theses

In 1983, M. van den Berg made his Fundamental Gap Conjecture about the difference between the first two Dirichlet eigenvalues (the fundamental gap) of any convex domain in the Euclidean plane. Recently, progress has been made in the case where the domains are polygons and, in particular, triangles. We examine the conjecture for triangles in hyperbolic geometry, though we seek an for an upper bound for the fundamental gap rather than a lower bound.

Hydraulic Geometry Relationships And Regional Curves For The Inner And Outer Bluegrass Regions Of Kentucky, Ruth Roseann Brockman

University of Kentucky Master's Theses

Hydraulic geometry relationships and regional curves are used in natural channel design to assist engineers, biologists, and fluvial geomorphologists in the efforts undertaken to ameliorate previous activities that have diminished, impaired or destroyed the structure and function of stream systems. Bankfull channel characteristics were assessed for 14 United States Geological Survey (USGS) gaged sites in the Inner Bluegrass and 15 USGS gaged sites in the Outer Bluegrass Regions of Kentucky. Hydraulic geometry relationships and regional curves were developed for the aforementioned regions.

Analysis of the regression relationships showed that bankfull discharge is a good explanatory variable for bankfull parameters such …

Light Attenuation At Molasses Reef, Ashley Earls

Undergraduate Journal of Mathematical Modeling: One + Two

Estimating the amount of light available at different depths of the ocean is important for gaining a better understanding of coral reefs. It is especially useful to be able to get such estimates without having to perform direct measurements. Although accurate, the direct measurements are costly, time consuming, and usually limited to relatively small areas of interest.

One statistic that could be useful for estimating the amount of available light is the rate at which it declines with depth (the rate of light attenuation). In this project, this rate is calculated for four different wavelengths using data for 30m water …

Mathematical Reasoning In Service Courses: Why Students Need Mathematical Modeling Problems, Kris H. Green, Allen Emerson

The Mathematics Enthusiast

In this paper we argue that conventional mathematics word problems are not aligned with the typical learning goals and expectations partner disciplines, especially business, have in requiring that their students take mathematics courses. Using the taxonomy of educational objectives presented by Anderson and Krathwohl (2001) we show how mathematical modeling problems can be used to promote the needed alignment and contrast two examples to illustrate the differences. We then demonstrate how the more conventional word problem can be rewritten as a modeling problem. Sample assessment materials and instructional activities are included to support teachers in making the transition to the …

When Is .999... Less Than 1?, Karin Usadi Katz, Mikhail G. Katz

The Mathematics Enthusiast

We examine alternative interpretations of the symbol described as nought, point, nine recurring. Is "an infinite number of 9s" merely a figure of speech? How are such alternative interpretations related to infinite cardinalities? How are they expressed in Lightstone's "semicolon" notation? Is it possible to choose a canonical alternative interpretation? Should unital evaluation of the symbol .999... be inculcated in a pre-limit teaching environment? The problem of the unital evaluation is hereby examined from the pre-R, pre-lim viewpoint of the student.

Positive Solutions For A System Of Singular Second Order Nonlocal Boundary Value Problems, Naseer Ahmad Asif, Paul W. Eloe, Rahmat Ali Khan

Mathematics Faculty Publications

Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type (see PDF for details) are obtained. The nonlinearities (see PDF) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. … An example is provided to illustrate the results.

Periodic Solutions Of Neutral Delay Integral Equations Of Advanced Type, Muhammad Islam, Nasrin Sultana, James Booth

Mathematics Faculty Publications

We study the existence of continuous periodic solutions of a neutral delay integral equation of advanced type. In the analysis we employ three fixed point theorems: Banach, Krasnosel'skii, and Krasnosel'skii-Schaefer. Krasnosel'skii-Schaefer fixed point theorem requires an a priori bound on all solutions. We employ a Liapunov type method to obtain such bound.

2010 Alumni Presenters, University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

Foliations And Global Inversion, Eduardo C. Balreira

Mathematics Faculty Research

We consider topological conditions under which a locally invertible map admits a global inverse. Our main theorem states that a local diffeomorphism f : M → Rⁿ is bijective if and only if H_n−1(M) = 0 and the pre-image of every affine hyperplane is non-empty and acyclic. The proof is based on some geometric constructions involving foliations and tools from intersection theory. This topological result generalizes in finite dimensions the classical analytic theorem of Hadamard-Plastock, including its recent improvement by Nollet-Xavier. The main theorem also relates to a conjecture of the aforementioned authors, involving the well known …

General Flips And The Cd-Index, Daniel J. Wells

University of Kentucky Doctoral Dissertations

We generalize bistellar operations (often called flips) on simplicial manifolds to a notion of general flips on PL-spheres. We provide methods for computing the cd-index of these general flips, which is the change in the cd-index of any sphere to which the flip is applied. We provide formulas and relations among flips in certain classes, paying special attention to the classic case of bistellar flips. We also consider questions of "flip-connecticity", that is, we show that any two polytopes in certain classes can be connected via a sequence of flips in an appropriate class.

Algorithms For Upper Bounds Of Low Dimensional Group Homology, Joshua D. Roberts

University of Kentucky Doctoral Dissertations

A motivational problem for group homology is a conjecture of Quillen that states, as reformulated by Anton, that the second homology of the general linear group over R = Z[1/p; ζ_p], for p an odd prime, is isomorphic to the second homology of the group of units of R, where the homology calculations are over the field of order p. By considering the group extension spectral sequence applied to the short exact sequence 1 → SL₂ → GL₂ → GL₁ → 1 we show that the calculation of the homology …

The Norm Of A Truncated Toeplitz Operator, William T. Ross, Stephan Ramon Garcia

Math and Computer Science Faculty Publications

We prove several lower bounds for the norm of a truncated Toeplitz operator and obtain a curious relationship between the H² and H^∞ norms of functions in model spaces.

Spatial Isomorphisms Of Algebras Of Truncated Toeplitz Operators, William T. Ross, Stephan Ramon Garcia, Warren R. Wogen

Math and Computer Science Faculty Publications

We examine when two maximal abelian algebras in the truncated Toeplitz operators are spatially isomorphic. This builds upon recent work of N. Sedlock, who obtained a complete description of the maximal algebras of truncated Toeplitz operators.

Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, And Similarity, William T. Ross, Joseph A. Cima, Stephan Ramon Garcia, Warren R. Wogen

Math and Computer Science Faculty Publications

A truncated Toeplitz operator Aᵩ : K_Ɵ → K_Ɵ is the compression of a Toeplitz operator Tᵩ : H² → H² to a model space K_Ɵ := H² ⊖ ^ƟH². For Ɵ inner, let T_Ɵ denote the set of all bounded truncated Toeplitz operators on K_Ɵ. Our main result is a necessary and sufficient condition on inner functions Ɵ₁ and Ɵ₂ which guarantees that T_Ɵ1 and T_Ɵ2 are spatially isomorphic. (i.e., UT_Ɵ1 = T_Ɵ2 U for some unitary U : K_{Ɵ1 …}

Analysis Of The Consistency Of A Mixed Integer Programming-Based Multi-Category Constrained Discriminant Model, J. Paul Brooks, Eva K. Lee

Statistical Sciences and Operations Research Publications

Classification is concerned with the development of rules for the allocation of observations to groups, and is a fundamental problem in machine learning. Much of previous work on classification models investigates two-group discrimination. Multi-category classification is less-often considered due to the tendency of generalizations of two-group models to produce misclassification rates that are higher than desirable. Indeed, producing “good” two-group classification rules is a challenging task for some applications, and producing good multi-category rules is generally more difficult. Additionally, even when the “optimal” classification rule is known, inter-group misclassification rates may be higher than tolerable for a given classification model. …

Homomorphic Images Of Progenitors Of Order Three, Mark Gutierrez

Theses Digitization Project

The main purpose of this thesis is to construct finite groups as homomorphic images of infinite semi-direct products, 2*n : N, 3*n : N, and 3*n :m N, where 2*n and 3*n are free products of n copies of the cyclic group C₂ extended by N, a group of permutations on n letters.

On The Convergence Of Greedy Algorithms For Initial Segments Of The Haar Basis, S J. Dilworth, E Odell, Th Schlumprecht, Andras Zsak

Faculty Publications

We consider the X-Greedy Algorithm and the Dual Greedy Algorithm in a finite-dimensional Banach space with a strictly monotone basis as the dictionary. We show that when the dictionary is an initial segment of the Haar basis in Lp[0, 1] (1< p < 1) then the algorithms terminate after finitely many iterations and that the number of iterations is bounded by a function of the length of the initial segment. We also prove a more general result for a class of strictly monotone bases.

Curvature Measures For Nonlinear Regression Models Using Continuous Designs With Applications To Optimal Design, Timothy O'Brien, Somsri Jamroenpinyo, Chinnaphong Bumrungsup

Mathematics and Statistics: Faculty Publications and Other Works

We present and illustrate the methodology to calculate curvature measures for continuous designs, and extend design criteria to incorporate continuous designs. These design algorithms include quadratic design procedures, a subset design criterion, a second-order mean-square error design criterion, and a marginal curvature design methodology. A discussion of confidence intervals is also provided for continuous designs.

2010 Vol. 4 Table Of Contents, University Of Dayton. Department Of Mathematics

Proceedings of Undergraduate Mathematics Day

No abstract provided.