Physical Sciences and Mathematics Commons^™

Modeling Nonintersective Adjectives Using Operator Logics, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

Our topic is one that involves the interface between natural language and mathematical logic. First-order predicate language/logic does a good job approximating many parts of (English) speech, i.e., nouns, verbs and prepositions, but fails decidedly when it comes to, say, adjectives. In particular, it cannot account for the quite different ways in which the adjectives green and big modify a noun such as chair. In the former case, we can easily view a world in which the class of green chairs is the intersection of the class of green things with the class of chair-things. By contrast, the way …

Stone Coalgebras, Clemens Kupke, Alexander Kurz, Yde Venema

Engineering Faculty Articles and Research

In this paper we argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue to the power set functor. We prove that the so-called descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. This yields a duality between the category of modal algebras and that of coalgebras over the Vietoris functor. Building on this idea, we introduce the notion of a Vietoris polynomial functor over the category of Stone spaces. …

Prediction Intervals For The Binomial Distribution With Dependent Trials, Florian Sebastian Rueck

Masters Theses

"A generalization of a prediction interval procedure for the binomial distribution to the case of the binomial distribution with dependent trials is considered. Several different methods have been developed for obtaining prediction intervals for the binomial distribution. An unpublished study by Vlieger and Samaranayake has shown that two of these methods achieve coverage probabilities close to nominal levels. The proposed method is an extension of one of these methods and is based on the maximum likelihood predictive density proposed by Lejeune and Faulkenberry. A simulation study was carried out to investigate the coverage probabilities of the proposed prediction bounds.

This …

Notes On Interpolation In The Generalized Schur Class. Ii. Nudelman's Problem, Daniel Alpay, T. Constantinescu, A. Dijksma, J. Rovnyak, A. Dijksma

Mathematics, Physics, and Computer Science Faculty Articles and Research

An indefinite generalization of Nudel′man’s problem is used in a systematic approach to interpolation theorems for generalized Schur and Nevanlinna functions with interior and boundary data. Besides results on existence criteria for Pick-Nevanlinna and Carath´eodory-Fej´er interpolation, the method yields new results on generalized interpolation in the sense of Sarason and boundary interpolation, including properties of the finite Hilbert transform relative to weights. The main theorem appeals to the Ball and Helton almost-commutant lifting theorem to provide criteria for the existence of a solution to Nudel′man’s problem.

Am I Too Fat? Bulimia As An Epidemic, Christopher Kribs, Beverly Gonzalez, Emilia Huerta-Sanchez, Angela Ortiz-Nieves, Terannie Vazquez-Alvarez

Mathematics Faculty Publications

For at least the past ten years, eating disorders have had a major impact in the physical and mental health of women, particularly young women. Anorexia and bulimia nervosa are closely linked eating disorders. Anorexia often precedes bulimia. However, there are about 2 million women in college that have been exclusively bulimic. In this article, we focus on the role of college-peer pressure on the dynamics of anorexia-free bulimia. The model looks at bulimia as a progressive disease and explores the impact of intervention (treatment) at two stages of disease progression. The impact of relapse (a common occurrence among bulimics) …

Working Across Cultures, John Hooker

John Hooker

No abstract provided.

Graphs Of Essentially Equivalent Lattice Paths, Lara Pudwell, Marjorie Brewer, Adam Hughes

Lara K. Pudwell

No abstract provided.

On Abel-Gontscharoff-Gould's Polynomials, Tian-Xiao He, Leetsch Hsu, Peter Shiue

Tian-Xiao He

In this paper a connective study of Gould’s annihilation coefficients and Abel-Gontscharoff polynomials is presented. It is shown that Gould’s annihilation coefficients and Abel-Gontscharoff polynomials are actually equivalent to each other under certain linear substitutions for the variables. Moreover, a pair of related expansion formulas involving Gontscharoff’s remainder and a new form of it are demonstrated, and also illustrated with several examples.

Boundary-Type Quadrature And Boundary Element Method, Tian-Xiao He

Tian-Xiao He

In this paper, we apply a boundary-type quadrature technique to derive a type of boundary element scheme, which is used to solve the boundary-value problems of partial differential equations.Numerical examples for solving the exterior boundary-value problem of Helmholtz equation by using the spline approximation and the spline wavelet approximation are given.

Analytical Upstream Collocation Solution Of A Forced Steady-State Convection-Diffusion Equation, Stephen Brill

Stephen H. Brill

We give herein formulas for the solution of the Hermite collocation discretization of a nonhomogeneous steady-state convection-diffusion equation in one spatial dimension and with constant coefficients, defined on a uniform mesh, with Dirichlet boundary conditions. The accuracy of the method is enhanced by employing "upsteam weighting" of the convective term in an optimal way. We discuss also the issue of where to optimally sample the forcing function. Computational examples illustrate the efficacy of the optimal upstream weighting technique combined with optimal sampling of the forcing function.

Length-Preserving Transformations On Polygons, Brad Ballinger

Brad Ballinger

Spectral Distribution Of Hermitian Toeplitz Matrices Formally Generated By Rational Functions, William F. Trench

William F. Trench

No abstract provided.

A Note On Asymptotic Zero Distribution Of Orthogonal Polynomials, William F. Trench

William F. Trench

No abstract provided.

A Family Of Isomorphic Fusion Algebras Of Twisted Quantum Doubles Of Finite Groups, Christopher Goff

Christopher Goff

Absolute Equal Distribution Of The Spectra Of Hermitian Matrices, William F. Trench

William F. Trench

No abstract provided.

Absolute Equal Distribution Of Families Of Finite Sets, William F. Trench

William F. Trench

No abstract provided.

Open Problems From The Linz2000 Closing Session, Lawrence N. Stout

Lawrence N. Stout

No abstract provided.

Strukturationen Der Interaktivität, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

Linear Perturbations Of A Nonoscillatory Second Order Differential Equation Ii, William F. Trench

William F. Trench

No abstract provided.

Uniform Convergence Of Cesàro Means Of Negative Order Of Double Walsh-Fourier Series, Ushangi Goginava

Ushangi Goginava

No abstract provided.

Hyperbolic Billiard Paths, Rebecca Lehman, Chad White

Mathematical Sciences Technical Reports (MSTR)

A useful way to investigate closed geodesics on a kaleidoscopically tiled surface is to look at the billiard path described by a closed geodesic on a single tile. When looking at billiard paths it is possible to ignore surfaces and restrict ourselves to the tiling of the hyperbolic plane. We classify the smallest billiard paths by wordlength and parity. We also demonstrate the existence of orientable paths and investigate conjectures about the billiard spectrum for the (2, 3, 7)-tiling.

Pigeon-Holing Monodromy Groups, Niles G. Johnson

Mathematical Sciences Technical Reports (MSTR)

A simple tiling on a sphere can be used to construct a tiling on a d-fold branched cover of the sphere. By lifting a so-called equatorial tiling on the sphere, the lifted tiling is locally kaleidoscopic, yielding an attractive tiling on the surface. This construction is via a correspondence between loops around vertices on the sphere and paths across tiles on the cover. The branched cover and lifted tiling give rise to an associated monodromy group in the symmetric group on d symbols. This monodromy group provides a beautiful connection between the cover and its base space. Our investigation …

Invariant Sets And Inverse Limits, William Thomas Ingram

Mathematics and Statistics Faculty Research & Creative Works

In this paper we investigate the nature of inverse limits from the point of view of invariant sets. We then introduce a special class of examples of inverse limits on [0,1] using Markov bonding maps determined by members of the group of permutations on n elements. © 2002 Elsevier Science B.V. All rights reserved.

Sign-Changing And Multiple Solutions For The P-Laplacian, Siegfried Carl, Kanishka Perera

Mathematics and System Engineering Faculty Publications

We obtain a positive solution, a negative solution, and a sign-changing solution for a class of p-Laplacian problems with jumping nonlinearities using variational and super-subsolution methods.

Normal Forms For Two-Inputs Nonlinear Control Systems, Issa Amadou Tall, Witold Respondek

Miscellaneous (presentations, translations, interviews, etc)

We study the feedback group action on two-inputs non-linear control systems. We follow an approach proposed by Kang and Krener which consists of analyzing the system and the feedback group step by step. We construct a normal form which generalizes that obtained in the single-input case. We also give homogeneous m-invariants of the action of the group of homogeneous transformations on the homogeneous systems of the same degree. We illustrate our results by analyzing the normal form and invariants of homogeneous systems of degree two.

On Choosing And Bounding Probability Metrics, Alison L. Gibbs, Francis E. Su

All HMC Faculty Publications and Research

When studying convergence of measures, an important issue is the choice of probability metric. We provide a summary and some new results concerning bounds among some important probability metrics/distances that are used by statisticians and probabilists. Knowledge of other metrics can provide a means of deriving bounds for another one in an applied problem. Considering other metrics can also provide alternate insights. We also give examples that show that rates of convergence can strongly depend on the metric chosen. Careful consideration is necessary when choosing a metric.

Individual-Based Modeling: Comparing Model Outputs To Telemetry Data With Application To The Florida Panther, Dinesh Raj Sharma

Masters Theses

Mean distance of the locations of an animal from the boundaries of its home range was presented as a measure of its space-use preference. Methods for evaluating the predictive ability of an individual-based model were also presented. These methods were applied to data on the Florida panther and some interesting results were obtained.

A strong negative correlation was observed between age and home range size of the panther, indicating constrained mobility of the panther during its old age. Space-use preference was also highly dependent on age of the panther. A general trend was found for panthers, which indicates they stay …

Calculating The Conformal Modulus Of Complex Tori And An Application To Graph Theory, Jason Howard

Masters Theses

In 1985 William Thurston conjectured that conformal mappings could be approximated using infintessimal circles. With this, the area of mathematics called Cirle Packing was born. The advantage of this technique is that it gives a computational method of understanding manifolds. In particular, we attempt to gain some insight of complex tori via Circle Packing. In practice, it is difficult to imagine what these tori look like. Computational techniques of Circle Packing will help us visualise these tori as points in moduli space by beginning with an initial triangulation of the torus. We then experiment with triangulations on a set number …

Theoretical Issues In The Economics Of International Trade And Environment., Meeta Keswani Mehra Dr.

Doctoral Theses

In the wake of substantial trade liberalization in the world economy over the last two decades and growing environmental consciousness, the issues of the impacts of international goods trade and foreign direct investment (FDI) on local and global environment are becoming increasingly contentious. Whilst trade and FDI have been said to bring higher incomes and well-being for all, these are seen to act as "magnifiers" of environmental deterioration - especially in the developing countries. On the other hand, growing environmentalism is perceived to act as an impediment to freer trade and investment flows across countries. Hence, the central issues are …

The Galois Correspondence For Branched Covering Spaces And Its Relationship To Hecke Algebras, Matthew Ong

Mathematical Sciences Technical Reports (MSTR)

There is a very beautiful correspondence between branched covers of the Riemann sphere P¹ and subgroups of the fundamental group π₁(P¹ − {branch points}), exactly analogous to the correspondence between subfields of an algebraic extension E/F and subgroups of the Galois group Gal(E/F). This paper explores the concept of a Hecke algebra, which in this context is a generalization of the Galois group to the case of non- Galois covers S/P¹. Specifically, we show that the isomorphism type of a Hecke algebra C[H\G/H] is completely determined by the decomposition of …