Mathematics Commons^™

Impulse Formulations Of The Euler Equations For Incompressible And Compressible Fluids, Victor David Pareja

Electronic Theses and Dissertations

The purpose of this paper is to consider the impulse formulations of the Euler equations for incompressible and compressible fluids. Different gauges are considered. In particular, the Kuz'min gauge provides an interesting case as it allows the fluid impulse velocity to describe the evolution of material surface elements. This result affords interesting physical interpretations of the Kuz'min invariant. Some exact solutions in the impulse formulation are studied. Finally, generalizations to compressible fluids are considered as an extension of these results. The arrangement of the paper is as follows: in the first chapter we will give a brief explanation on the …

On Strongly Asymptotic L(P) Spaces And Minimality, S J. Dilworth, V Ferenczi, Denka Kutzarova, E Odell

Faculty Publications

No abstract provided.

Conics In The Hyperbolic Plane, Trent Phillip Naeve

Theses Digitization Project

An affine transformation such as T(P)=Q is a locus of an affine conic. Any affine conic can be produced from this incidence construction. The affine type of conic (ellipse, parabola, hyperbola) is determined by the invariants of T, the determinant and trace of its linear part. The purpose of this thesis is to obtain a corresponding classification in the hyperbolic plane of conics defined by this construction.

S-Toeplitz Composition Operators, Valentin Matache

Mathematics Faculty Publications

Operators on function spaces acting by composition to the right with a fixed selfmap φ of some set are called composition operators of symbol φ.

Modeling Immune Response To Bacterial Infection, Carla Roth

The Journal of Undergraduate Research

Mathematical models have begun to play an important role in the study of biology. We will examine this role further by analyzing a specific model of the innate immune system's response to a bacterial infection. Beginning with the biological background of the model, we will move into an explanation of a specific model of this situation followed by a critique of the model and future work to be done with the topic.

A Comparison Of Three Topologies On Ordered Sets, Joe Mashburn

Mathematics Faculty Publications

We introduce two new topologies on ordered sets: the way below topology and weakly way below topology. These are similar in definition to the Scott topology, but are very different if the set is not continuous. The basic properties of these three topologies are compared. We will show that while domain representable spaces must be Baire, this is not the case with the new topologies.

2007 (Winter), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2007 Winter Colloquium.

A Transform Method In Discrete Fractional Calculus, Ferhan M. Atici, Paul W. Eloe

Mathematics Faculty Publications

We begin with an introduction to a calculus of fractional finite differences. We extend the discrete Laplace transform to develop a discrete transform method. We define a family of finite fractional difference equations and employ the transform method to obtain solutions.

An Euler Trifecta (Abstract), William Dunham

Kenneth C. Schraut Memorial Lectures

To recognize Leonhard Euler’s 300th birthday, we sketch his life and give a brief survey of some of his mathematical achievements.

Garden-Variety Symmetry (Abstract), Colleen Hoover

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

After a gentle introduction to the topic of symmetry, we will explore the symmetry groups of bounded plane figures, pulling examples from the garden.

2007 Program And Abstracts, University Of Dayton. Department Of Mathematics

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

No abstract provided.

The Topology Of Surface Mediatrices, James Bernhard, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

Given a pair of distinct points p and q in a metric space with distance d, the mediatrix is the set of points x such that d(x,p)=d(x,q). In this paper, we examine the topological structure of mediatrices in connected, compact, closed 2-manifolds whose distance function is inherited from a Riemannian metric. We determine that such mediatrices are, up to homeomorphism, finite, closed simplicial 1-complexes with an even number of incipient edges emanating from each vertex. Using this and results from [J.J.P. Veerman, J. Bernhard, Minimally separating sets, mediatrices and Brillouin spaces, Topology Appl., in press], we give the classification …

On The Kauffman Bracket Skein Module Of The Quaternionic Manifold, Patrick M. Gilmer, John M. Harris

Faculty Publications

We use recoupling theory to study the Kauffman bracket skein module of the quaternionic manifold over Z[A(+/- 1)] localized by inverting all the cyclotomic polynomials. We prove that the skein module is spanned by five elements. Using the quantum invariants of these skein elements and the Z(2)-homology of the manifold, we determine that they are linearly independent.

Slow Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert

Articles

This paper considers the low-Reynolds-number flow of an incompressible fluid contained in the gap between two coaxial cones with coincident apices and bounded by a spherical lid. The two cones and the lid are allowed to rotate independently about their common axis, generating a swirling motion. The swirl induces a secondary, meridional circulation through inertial effects. For specific configurations complex eigenmodes representing an infinite sequence of eddies, analogous to those found in two-dimensional corner flows and some three-dimensional geometries, form a component of this secondary circulation. When the cones rotate these eigenmodes, arising from the geometry, compete with the forced …

Krylov Subspaces From Bilinear Representations Of Nonlinear Systems, Marissa Condon, Rossen Ivanov

Articles

For efficient simulation of state-of-the-art dynamical systems as arise in all aspects of engineering, the development of reduced-order models is of paramount importance. While linear reduction techniques have received considerable study, increasingly nonlinear model reduction is becoming a significant field of interest. From a circuits and systems viewpoint, systems involving micromachined devices or systems involving mixed technologies necessitate the development of reduced-order nonlinear models. From a control systems viewpoint, the design of controllers for nonlinear systems is greatly facilitated by nonlinear model reduction strategies. To this end, the paper proposes two novel model-reduction strategies for nonlinear systems. The first involves …

Generalised Fourier Transform For The Camassa-Holm Hierarchy, Adrian Constantin, Vladimir Gerdjikov, Rossen Ivanov

Articles

The squared eigenfunctions of the spectral problem associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform for the Camassa-Holm hierarchy as a Generalised Fourier transform. The main result of this work is the derivation of the completeness relation for the squared solutions of the Camassa-Holm spectral problem. We show that all the fundamental properties of the Camassa-Holm equation such as the integrals of motion, the description of the equations of the whole hierarchy and their Hamiltonian structures can be naturally expressed making use of the completeness relation and the recursion …

Projectional Entropy In Higher Dimensional Shifts Of Finite Type, Aimee S. A. Johnson, S. Kass, K. M. Madden

Mathematics & Statistics Faculty Works

Any higher dimensional shift space (X, ℤᵈ) contains many lower dimensional shift spaces obtained by projection onto r-dimensional sublattices L of ℤᵈ where r < d. We show here that any projectional entropy is bounded below by the ℤᵈ entropy and, in the case of certain shifts of finite type satisfying a mixing condition, equality is achieved if and only if the shift of finite type is the infinite product of a lower dimensional projection.

Periodic Solution To The Time-Inhomogeneous Multi-Server Poisson Queue, Barbara Haas Margolius

Mathematics and Statistics Faculty Publications

We derive the periodic family of asymptotic distributions and the periodic moments for number in the queue for the multi-server queue with Poisson arrivals and exponential service for time-varying periodic arrival and departure rates, and time-varying periodic number of servers. The method is a straight-forward application of generating functions.

Some Transitivity Results For Torsion Abelian Groups, Brendan Goldsmith, Lutz Strungmann

Articles

We introduce a new class of fully transitive and transitive Abelian p-groups and study the new concept of weak transitivity which is the missing link between full transitivity and transitivity.

The Wright Message, 2007, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- 2007 - 2008 Tenure or Tenure-Track Faculty
-- New Faces in the Mathematics Department
-- Faculty Notes
-- Alumni Survey Conducted
-- Actuarial Program Thrives
-- Board of Regents Collaborative Mathematics and Science Initiative
-- TEAM News
-- DoDEA/UNI Project
-- Online Course Development
-- Math Day at UNI
-- First Millar Scholarship Awarded
-- In Memory of Paul Trafton
-- Major Gifts to the Department

Asymptotic Properties Of Estimators For The Linear Panel Regression Model With Individual Effects And Serially Correlated Errors: The Case Of Stationary And Non-Stationary Regressors And Residuals, Badi H. Baltagi, Chihwa Kao, Long Liu

Center for Policy Research

This paper studies the asymptotic properties of standard panel data estimators in a simple panel regression model with error component disturbances. Both the regressor and the remainder disturbance term are assumed to be autoregressive and possibly non-stationary. Asymptotic distributions are derived for the standard panel data estimators including ordinary least squares, fixed effects, first-difference, and generalized least squares (GLS) estimators when both T and n are large. We show that all the estimators have asymptotic normal distributions and have different convergence rates dependent on the non-stationarity of the regressors and the remainder disturbances. We show using Monte Carlo experiments that …

Modelling And Testing For Structural Changes In Panel Cointegration Models With Common And Idiosyncratic Stochastic Trend, Chihwa Kao, Lorenzo Trapani, Giovanni Urga

Center for Policy Research

In this paper, we propose an estimation and testing framework for parameter instability in cointegrated panel regressions with common and idiosyncratic trends. We develop tests for structural change for the slope parameters under the null hypothesis of no structural break against the alternative hypothesis of (at least) one common change point, which is possibly unknown. The limiting distributions of the proposed test statistics are derived. Monte Carlo simulations examine size and power of the proposed tests. We are grateful for discussions with Robert De Jong, Long-Fei Lee, Zongwu Cai, and Yupin Hu. We would also like to thank participants in …

Forecasting With Panel Data, Badi H. Baltagi

Center for Policy Research

This paper gives a brief survey of forecasting with panel data. Starting with a simple error component regression model and surveying best linear unbiased prediction under various assumptions of the disturbance term. This includes various ARMA models as well as spatial autoregressive models. The paper also surveys how these forecasts have been used in panel data applications, running horse races between heterogeneous and homogeneous panel data models using out of sample forecasts.

Pi-Calculus In Logical Form, Marcello M. Bonsangue, Alexander Kurz

Engineering Faculty Articles and Research

Abramsky’s logical formulation of domain theory is extended to encompass the domain theoretic model for picalculus processes of Stark and of Fiore, Moggi and Sangiorgi. This is done by defining a logical counterpart of categorical constructions including dynamic name allocation and name exponentiation, and showing that they are dual to standard constructs in functor categories. We show that initial algebras of functors defined in terms of these constructs give rise to a logic that is sound, complete, and characterises bisimilarity. The approach is modular, and we apply it to derive a logical formulation of pi-calculus. The resulting logic is a …

Locally Conservative Fluxes For The Continuous Galerkin Method, Bernardo Cockburn, Jay Gopalakrishnan, Haiying Wang

Mathematics and Statistics Faculty Publications and Presentations

The standard continuous Galerkin (CG) finite element method for second order elliptic problems suffers from its inability to provide conservative flux approximations, a much needed quantity in many applications. We show how to overcome this shortcoming by using a two step postprocessing. The first step is the computation of a numerical flux trace defined on element inter- faces and is motivated by the structure of the numerical traces of discontinuous Galerkin methods. This computation is non-local in that it requires the solution of a symmetric positive definite system, but the system is well conditioned independently of mesh size, so it …

Some Recent Results On Stochastic Comparisons And Dependence Among Order Statistics In The Case Of Phr Model, Subhash C. Kochar, Maochao Xu

Mathematics and Statistics Faculty Publications and Presentations

This paper reviews some recent results on stochastic orders and dependence among order statistics when the observations are independent and follow the proportional hazard rates model.

Restricted Colored Permutations And Chebyshev Polynomials, Eric S. Egge

Mathematics and Statistics Faculty Work

Several authors have examined connections between restricted permutations and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for colored permutations. First we define a distinguished set of length two and length three patterns, which contains only 312 when just one color is used. Then we give a recursive procedure for computing the generating function for the colored permutations which avoid this distinguished set and any set of additional patterns, which we use to find a new set of signed permutations counted by the Catalan numbers and a new set of signed permutations counted …

Microscopic-Macroscopic Simulations Of Rigid-Rod Polymer Hydrodynamics: Heterogeneity And Rheochaos, M. Gregory Forest, Ruhai Zhou, Qi Wang

Mathematics & Statistics Faculty Publications

Rheochaos is a remarkable phenomenon of nematic (rigid-rod) polymers in steady shear, with sustained chaotic fluctuations of the orientational distribution of the rod ensemble. For monodomain dynamics, imposing spatial homogeneity and linear shear, rheochaos is a hallmark prediction of the Doi-Hess theory [M. Doi, J. Polym. Sci. Polym. Phys. Ed., 19 (1981), pp. 229-243; M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Oxford University Press, London, New York, 1986; S. Hess, Z. Naturforsch., 31 (1976), pp. 1034-1037. The model behavior is robust, captured by second-moment tensor approximations G. Rienäcker, M. Kröger, and S. Hess, Phys. Rev. …

The Center Of Some Braid Groups And The Farrell Cohomology Of Certain Pure Mapping Class Groups, Craig A. Jensen, Yu Qing Chen, Henry H. Glover

Mathematics Faculty Publications

In this paper we first show that many braid groups of low genus surfaces have their centers as direct factors. We then give a description of centralizers and normalizers of prime order elements in pure mapping class groups of surfaces with spherical quotients using automorphism groups of fundamental groups of the quotient surfaces. As an application, we use these to show that the primary part of the Farrell cohomology groups of certain mapping class groups are elementary abelian groups. At the end we compute the primary part of the Farrell cohomology of a few pure mapping class groups.

The Euler Characteristic Of The Whitehead Automorphism Group Of A Free Product, Craig A. Jensen, Jon Mccammond, John Meier

Mathematics Faculty Publications

A combinatorial summation identity over the lattice of labelled hypertrees is established that allows one to gain concrete information on the Euler characteristics of various automorphism groups of free products of groups. In particular, we establish formulae for the Euler characteristics of: the group of Whitehead automorphisms...