Physical Sciences and Mathematics Commons^™

2006 Alumni Presenters, University Of Dayton. Department Of Mathematics

Biennial Alumni Seminar

No abstract provided.

2006 (Winter), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2006 Winter Colloquium.

A Database Of Local Fields, John W. Jones, David P. Roberts

Mathematics Publications

We describe our online database of finite extensions of Q_p, and how it can be used to facilitate local analysis of number fields.

Algebraic Characterizations Of Graph Imbeddability In Surfaces And Pseudosurfaces, Lowell Abrams, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a finite connected graph G and specifications for a closed, connected pseudosurface, we characterize when G can be imbedded in a closed, connected pseudosurface with the given specifications. The specifications for the pseudosurface are: the number of face-connected components, the number of pinches, the number of crosscaps and handles, and the dimension of the first Z2-homology group. The characterizations are formulated in terms of the existence of a dual graph G ∗ on the same set of edges as G which satisfies algebraic conditions inspired by homology groups and their intersection products.

Bias Matroids With Unique Graphical Representations, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a 3-connected biased graph Ω with three node-disjoint unbalanced circles, at most one of which is a loop, we describe how the bias matroid of Ω is uniquely represented by Ω.

Electrical Properties Of Unintentionally Doped Semi-Insulating And Conducting 6h-Sic, William C. Mitchel, W. D. Mitchell, Z. Q. Fang, S. R. Smith, Helen Smith, Igor Khlebnikov, Y. I. Khlebnikov, C. Basceri, C. Balkas

Mathematics and Statistics Faculty Publications

Temperature dependent Hall effect (TDH), low temperature photoluminescence (LTPL), secondary ion mass spectrometry (SIMS), optical admittance spectroscopy (OAS), and thermally stimulated current (TSC) measurements have been made on 6H-SiC grown by the physical vapor transport technique without intentional doping. n- and p-type as well semi-insulating samples were studied to explore the compensation mechanism in semi-insulating high purity SiC. Nitrogen and boron were found from TDH and SIMS measurements to be the dominant impurities that must be compensated to produce semi-insulating properties. The electrical activation energy of the semi-insulating sample determined from the dependence of the resistivity …

On Adaptive Testing In Orthogonal Saturated Designs, Daniel T. Voss, Weizhen Wang

Mathematics and Statistics Faculty Publications

Adaptive, size-a step-down tests are provided for the analysis of orthogonal saturated designs. The tests work effectively under effect sparsity, and include as special cases the individual nonadaptive tests of Berk and Picard (1991) and the simultaneous nonadaptive tests of Voss (1988). The approach is similar to that used by Wang and Voss (2003) to construct adaptive confidence intervals, but testing is simpler because one can use the same denominator for all statistics. Step-down tests also have a clear power advantage over simultaneous confidence intervals and analogous single-step tests, as is demonstrated theoretically and assessed via simulation.

Vertically Iterated Classical Enrichment, Stefan Forcey

Mathematical Sciences Faculty Research

Lyubashenko has described enriched 2-categories as categories enriched over V-Cat, the 2-category of categories enriched over a symmetric monoidal V. This construction is the strict analogue for V-functors in V-Cat of Brian Day’s probicategories for V-modules in V-Mod. Here I generalize the strict version to enriched n-categories for k-fold monoidal V. The latter is defined as by Balteanu, Fiedorowicz, Schw¨anzl and Vogt but with the addition of making visible the coherent associators αi. The symmetric case can easily be recovered. This paper proposes a recursive definition of V-n …

Operads In Iterated Monoidal Categories, Stefan Forcey, Jacob Siehler, E. Seth Sowers

Mathematical Sciences Faculty Research

The structure of a k-fold monoidal category as introduced by Balteanu, Fiedorowicz, Schw¨anzl and Vogt in [2] can be seen as a weaker structure than a symmetric or even braided monoidal category. In this paper we show that it is still sufficient to permit a good definition of (n-fold) operads in a k-fold monoidal category which generalizes the definition of operads in a braided category. Furthermore, the inheritance of structure by the category of operads is actually an inheritance of iterated monoidal structure, decremented by at least two iterations. We prove that the category of n-fold operads in a k-fold …

Enrichment As Categorical Delooping I: Enrichment Over Iterated Monoidal Categories, Stefan Forcey

Mathematical Sciences Faculty Research

Joyal and Street note in their paper on braided monoidal categories [10] that the 2–category V–Cat of categories enriched over a braided monoidal category V is not itself braided in any way that is based upon the braiding of V. What is meant by “based upon” here will be made more clear in the present paper. The exception that they mention is the case in which V is symmetric, which leads to V–Cat being symmetric as well. The symmetry in V–Cat is based upon the symmetry of V. The motivation behind this paper is in part to describe how these …

Higher Dimensional Enrichment, Stefan Forcey

Mathematical Sciences Faculty Research

Lyubashenko has described enriched 2–categories as categories enriched over V–Cat, the 2–category of categories enriched over a symmetric monoidal V. Here I generalize this to a k–fold monoidal V. The latter is defined as by Balteanu, Fiedorowicz, Schw¨anzl and Vogt but with the addition of making visible the coherent associators _i. The symmetric case can easily be recovered. The introduction of this paper proposes a recursive definition of V–n–categories and their morphisms. Then I consider the special case of V–2–categories and give the details of the proof that with their morphisms these form the structure of a 3–category.

Probabilisticmodel-Based Cell Tracking, Nezamoddin Nezamoddini-Kachouie, Paul Fieguth, Eric Jervis

Mathematics and System Engineering Faculty Publications

The study of cell behavior is of crucial importance in drug and disease research. The fields of bioinformatics and biotechnology rely on the collection, processing, and analysis of huge numbers of biocellular images, including cell features such as cell size, shape, and motility. However manual methods of inferring these values are so onerous that automated methods of cell tracking and segmentation are in high demand. In this paper, a novel model-based cell tracker is designed to locate and track individual cells. The proposed cell tracker has been successfully applied to track hematopoietic stem cells (HSCs) based on identified cell locations …

On A Class Of Two-Point Boundary Value Problems With Singular Boundary Conditions, Ravi P. Agarwal, To Fu Ma

Mathematics and System Engineering Faculty Publications

A new existence theory for a class of second order two-point boundary value problems with nonlinear boundary conditions which can blow up in finite intervals is established. The proofs are based on the dual variational principle and the critical point theory.

A Positive Solution For Singular Discrete Boundary Value Problems With Sign-Changing Nonlinearities, Haishen Lü, Donal O'Regan, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

This paper presents new existence results for the singular discrete boundary value problem - Δ²u(k - 1) = g(k, u(k)) + λh(k,u(k)), k ∈ [1,T], u(0) = 0 = u(T + 1). In particular, our nonlinearity may be singular in its dependent variable and is allowed to change sign.

Application Of The Empirical Likelihood Method In Proportional Hazards Model, Bin He

Electronic Theses and Dissertations

In survival analysis, proportional hazards model is the most commonly used and the Cox model is the most popular. These models are developed to facilitate statistical analysis frequently encountered in medical research or reliability studies. In analyzing real data sets, checking the validity of the model assumptions is a key component. However, the presence of complicated types of censoring such as double censoring and partly interval-censoring in survival data makes model assessment difficult, and the existing tests for goodness-of-fit do not have direct extension to these complicated types of censored data. In this work, we use empirical likelihood (Owen, 1988) …

A Comparative Study Of Ant Colony Optimization, Matthew Becker

Electronic Theses and Dissertations

Ant Colony Optimization (ACO) belongs to a class of biologically-motivated approaches to computing that includes such metaheuristics as artificial neural networks, evolutionary algorithms, and artificial immune systems, among others. Emulating to varying degrees the particular biological phenomena from which their inspiration is drawn, these alternative computational systems have succeeded in finding solutions to complex problems that had heretofore eluded more traditional techniques. Often, the resulting algorithm bears little resemblance to its biological progenitor, evolving instead into a mathematical abstraction of a singularly useful quality of the phenomenon. In such cases, these abstract computational models may be termed biological metaphors. Mindful …

On The Use Of Gaussian Filter Functions For Adaptive Optics, Merfit Assad

Electronic Theses and Dissertations

For adaptive optic systems, the use of aperture filter functions calculated using various Zernike modes can be useful in removing lower-order aberrations caused by atmospheric turbulence. Traditionally, these filter functions are calculated using the step function depicting a hard aperture that introduces integrals that are sometimes difficult to integrate and must be done numerically. The Gaussian method can be used in place of the conventional method for calculating the aperture filter functions. Evaluation of the Gaussian approximation for modeling a finite receiver aperture can be made by comparison of reduction in phase variance with results achieved using the conventional method. …

Epidemiological Models For Mutating Pathogens With Temporary Immunity, Neeta Singh

Electronic Theses and Dissertations

Significant progress has been made in understanding different scenarios for disease transmissions and behavior of epidemics in recent years. A considerable amount of work has been done in modeling the dynamics of diseases by systems of ordinary differential equations. But there are very few mathematical models that deal with the genetic mutations of a pathogen. In-fact, not much has been done to model the dynamics of mutations of pathogen explaining its effort to escape the host's immune defense system after it has infected the host. In this dissertation we develop an SIR model with variable infection age for the transmission …

The Stable Manifold Theorem For Semilinear Stochastic Evolution Equations And Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang, Huaizhong Zhao

Articles and Preprints

The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. Such characterization is realized through the long-term behavior of the solution field near stationary points. The analysis falls in two parts 1, 2.

In Part 1, we prove general existence and compactness theorems for C^k-cocycles of semilinear see’s and spde’s. Our results cover a large class of semilinear see’s as well as certain semilinear spde’s with Lipschitz and non-Lipschitz terms such as stochastic reaction diffusion equations and the …

A Q-Continued Fraction, Douglas Bowman, James Mclaughlin, Nancy Wyshinksi

Mathematics Faculty Publications

Let a, b, c, d be complex numbers with d 6= 0 and |q| < 1. Define H1(a, b, c, d, q) := 1 1 + −abq + c (a + b)q + d + · · · + −abq2n+1 + cqn (a + b)q n+1 + d + · · · . We show that H1(a, b, c, d, q) converges and 1 H1(a, b, c, d, q) − 1 = c − abq d + aq P∞ j=0 (b/d) j (−c/bd)j q j(j+3)/2 (q)j (−aq2/d)j P∞ j=0 (b/d) j (−c/bd)j q j(j+1)/2 (q)j (−aq/d)j . We then use this result to deduce various corollaries, including the following: 1 1 − q 1 + q − q 3 1 + q 2 − q 5 1 + q 3 − · · · − q 2n−1 1 + q n − · · · = (q 2 ; q 3 )∞ (q; q 3)∞ , (−aq)∞ X∞ j=0 (bq) j (−c/b)j q j(j−1)/2 (q)j (−aq)j = (−bq)∞ X∞ j=0 (aq) j (−c/a)j q j(j−1)/2 (q)j (−bq)j , and the Rogers-Ramanujan identities, X∞ n=0 q n 2 (q; q)n = 1 (q; q 5)∞(q 4; q 5)∞ , X∞ n=0 q n 2+n (q; q)n = 1 (q 2; q 5)∞(q 3; q 5)∞.

The Convergence Behavior Of Q-Continued Fractions On The Unit Circle, Douglas Bowman, James Mclaughlin

Mathematics Faculty Publications

In a previous paper, we showed the existence of an uncountable set of points on the unit circle at which the Rogers-Ramanujan continued fraction does not converge to a finite value. In this present paper, we generalise this result to a wider class of qcontinued fractions, a class which includes the Rogers-Ramanujan continued fraction and the three Ramanujan-Selberg continued fractions. We show, for each q-continued fraction, G(q), in this class, that there is an uncountable set of points, YG, on the unit circle such that if y ∈ YG then G(y) does not converge to a finite value. We discuss …

Continued Fractions And Generalizations With Many Limits: A Survey, Douglas Bowman, James Mclaughlin

Mathematics Faculty Publications

There are infinite processes (matrix products, continued fractions, (r, s)-matrix continued fractions, recurrence sequences) which, under certain circumstances, do not converge but instead diverge in a very predictable way. We give a survey of results in this area, focusing on recent results of the authors.

Further Combinatorial Identities Deriving From The N-Th Power Of A 2 X 2 Matrix, James Mclaughlin, Nancy Wyshinski

Mathematics Faculty Publications

In this paper we use a formula for the n-th power of a 2×2 matrix A (in terms of the entries in A) to derive various combinatorial identities. Three examples of our results follow. 1) We show that if m and n are positive integers and s ∈ {0, 1, 2, . . . , b(mn − 1)/2c}, then X i,j,k,t 2 1+2t−mn+n (−1)nk+i(n+1) 1 + δ(m−1)/2, i+k m − 1 − i i ! m − 1 − 2i k ! × n(m − 1 − 2(i + k)) 2j ! j t − n(i + k) ! n …

The Convergence And Divergence Of Q-Continued Fractions Outside The Unit Circle, Douglas Bowman, James Mclaughlin

Mathematics Faculty Publications

We consider two classes of q-continued fraction whose odd and even parts are limit 1-periodic for |q| > 1, and give theorems which guarantee the convergence of the continued fraction, or of its odd- and even parts, at points outside the unit circle.

Some General Notions Of Stochastic Orderings For Weighted Reliability And Uncertainty Measures With Applications, Broderick O. Oluyede

Department of Mathematical Sciences Faculty Publications

In this note, stochastic comparisons of reliability measures and related functions are presented. Inequalities for uncertainty of a residual life distribution and certain modified cross-entropy or discrimination information measures under weighted models are established. Comparisons of the expected uncertainty about the remaining lifetime of a component for weighted conditional distributions and unweighted conditional distributions are presented.

Monte Carlo Random Walk Simulations Based On Distributed Order Differential Equations With Applications In Cell Biology, Erik Andries, Sabir Umarov, Stanly Steinberg

Mathematics Faculty Publications

In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a diffusion process in the sense of distributions is proved. Simulations based upon multi-term fractional order differential equations are performed.

Inequality For Ricci Curvature Of Slant Submanifolds In Cosymplectic Space Forms, Dae Won Yoon

Turkish Journal of Mathematics

In this article, we establish inequalities between the Ricci curvature and the squared mean curvature, and also between the k-Ricci curvature and the scalar curvature for a slant, semi-slant and bi-slant submanifold in a cosymplectic space form of constant \varphi-sectional curvature with arbitrary codimension.

Remarks About Some Weierstrass Type Results, Mihai Turinici

Turkish Journal of Mathematics

The Weierstrass type results of Gajek and Zagrodny [7] are not in general retainable in the precise context. Our first aim in this exposition is to show that a completion of the imposed conditions may be offered so that these results be true. As a second aim, alternate proofs of the statements in question are performed, via ordering principles comparable with the one in Brezis and Browder [3].

Monodomain Dynamics For Rigid Rod And Platelet Suspensions In Strongly Coupled Coplanar Linear Flow And Magnetic Fields. Ii. Kinetic Theory, M. Gregory Forest, Sarthok Sircar, Qi Wang, Ruhai Zhou

Mathematics & Statistics Faculty Publications

We establish reciprocity relations of the Doi-Hess kinetic theory for rigid rod macromolecular suspensions governed by the strong coupling among an excluded volume potential, linear flow, and a magnetic field. The relation provides a reduction of the flow and field driven Smoluchowski equation: from five parameters for coplanar linear flows and magnetic field, to two field parameters. The reduced model distinguishes flows with a rotational component, which map to simple shear (with rate parameter) subject to a transverse magnetic field (with strength parameter), and irrotational flows, for which the reduced model consists of a triaxial extensional flow (with two extensional …

Spectral Analysis Of The Supreme Court, Brian L. Lawson, Michael E. Orrison, David T. Uminsky

All HMC Faculty Publications and Research

The focus of this paper is the linear algebraic framework in which the spectral analysis of voting data like that above is carried out. As we will show, this framework can be used to pinpoint voting coalitions in small voting bodies like the United States Supreme Court. Our goal is to show how simple ideas from linear algebra can come together to say something interesting about voting. And what could be more simple than where our story begins— with counting.