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Mathematics Faculty Publications

2003

Articles 1 - 13 of 13

Full-Text Articles in Physical Sciences and Mathematics

Deconstructing Bases: Fair, Fitting, And Fast Bases, Thomas Q. Sibley Dec 2003

Deconstructing Bases: Fair, Fitting, And Fast Bases, Thomas Q. Sibley

Mathematics Faculty Publications

No abstract provided.

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Orthogonal Macroelement Scaling Vectors And Wavelets In 1-D, Douglas P. Hardin, Bruce Kessler Jun 2003

Orthogonal Macroelement Scaling Vectors And Wavelets In 1-D, Douglas P. Hardin, Bruce Kessler

Mathematics Faculty Publications

We develop a {\em macroelement} based technique for constructing orthogonal univariate multiwavelets. We illustrate the technique with two examples. In the first example we provide a new construction of the symmetric, orthogonal, continuous scaling vector given in \cite{GHM}. In the second example, we construct a continuous orthogonal scaling vector with three components. The components of this scaling vector are symmetric or antisymmetric and provide approximation order 3, (equivalently, the components of $\Psi$ are orthogonal to polynomials of degree 2 or less.) We believe this second example to be new.

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Taking The Sting Out Of Wasp Nests: A Dialogue On Modeling In Mathematical Biology, Jennifer C. Klein, Thomas Q. Sibley May 2003

Taking The Sting Out Of Wasp Nests: A Dialogue On Modeling In Mathematical Biology, Jennifer C. Klein, Thomas Q. Sibley

Mathematics Faculty Publications

Wasps in hot climates build elongated nests, while in colder areas they tend to be circular. Mathematics cannot explain that, but there are questions about numbers of cells that can be answered.

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Paths Of Length Four, Béla Bollobás, Amites Sarkar Apr 2003

Paths Of Length Four, Béla Bollobás, Amites Sarkar

Mathematics Faculty Publications

For each sufficiently large m, we determine the unique graph of size m with the maximum number of paths of length four. If m is even, this is the complete bipartite graph K(m/2,2).

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Fixed Points Of Holomorphic Mappings For Domains In Banach Spaces, Lawrence A. Harris Jan 2003

Fixed Points Of Holomorphic Mappings For Domains In Banach Spaces, Lawrence A. Harris

Mathematics Faculty Publications

We discuss the Earle-Hamilton fixed-point theorem and show how it can be applied when restrictions are known on the numerical range of a holomorphic function. In particular, we extend the Earle-Hamilton theorem to holomorphic functions with numerical range having real part strictly less than 1. We also extend the Lumer-Phillips theorem estimating resolvents to dissipative holomorphic functions.

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Finite Element Solutions Of Heat Transfer In Molten Polymer Flow In Tubes With Viscous Dissipation, Dongming Wei, Haibiao Luo Jan 2003

Finite Element Solutions Of Heat Transfer In Molten Polymer Flow In Tubes With Viscous Dissipation, Dongming Wei, Haibiao Luo

Mathematics Faculty Publications

This paper presents the results of finite element analysis of a heat transfer problem of flowing polymer melts in a tube with constant ambient temperature. The rheological behavior of the melt is described by a temperature dependent power-law model. Aviscous dissipation term is included in the energy equation. Temperature profiles are obtained for different tube lengths and different entrance temperatures. The results are compared with some similar results in the literature.

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On The Location Of Critical Points Of Polynomials, Branko Ćurgus, Vania Mascioni Jan 2003

On The Location Of Critical Points Of Polynomials, Branko Ćurgus, Vania Mascioni

Mathematics Faculty Publications

Given a polynomial p of degree n ≥ 2 and with at least two distinct roots let Z(p) = { z: p(z) = 0}. For a fixed root α ∈ Z(p) we define the quantities ω(p, α) := min (formula) and (formula). We also define ω (p) and τ (p) to be the corresponding minima of ω (p,α) and τ (p,α) as α runs over Z(p). Our main results show that the ratios τ (p,α)/ω (p,α) and τ (p)/ω (p) are bounded above and below by constants that only depend on the degree of p. In particular, …

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Continuous Embeddings, Completions And Complementation In Krein Spaces, Branko Ćurgus, H. Langer Jan 2003

Continuous Embeddings, Completions And Complementation In Krein Spaces, Branko Ćurgus, H. Langer

Mathematics Faculty Publications

Let the Krein space (A,[. , . ]A) be continuously embedded in the Krein space (K,[.,.]K ). A unique self-adjoint operator A in K can be associated with(A,[. , . ]A) via the adjoint of the inclusion mapping of A in K. Then (A,[. , . ]A) is a Krein space completion of R(A) equipped with an A-inner product. In general this completion is not unique. If, additionally, the embedding of A …

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A Continuation Of The Discussion On Cross Symmetry Of Solutions, Paul W. Eloe, Qin Sheng Jan 2003

A Continuation Of The Discussion On Cross Symmetry Of Solutions, Paul W. Eloe, Qin Sheng

Mathematics Faculty Publications

In this paper we continue to explore cross-symmetry properties of the solutions of second-order nonlinear boundary value problems on time scales. Dynamic equations under delta and nabla differentiations are considered. It is proven that, by introducing a proper companion problem, the solution of a dynamic equation is cross-symmetric to the solution of the companion problem. Proper jump functions on time scales are utilized. Computational examples are given to further illustrate our conclusions.

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On The Divergence In The General Sense Of Q-Continued Fractions On The Unit Circle, Douglas Bowman, James Mclaughlin Jan 2003

On The Divergence In The General Sense Of Q-Continued Fractions On The Unit Circle, Douglas Bowman, James Mclaughlin

Mathematics Faculty Publications

We show, for each q-continued fraction G(q) in a certain class of continued fractions, that there is an uncountable set of points on the unit circle at which G(q) diverges in the general sense. This class includes the Rogers-Ramanujan continued fraction and the three Ramanujan-Selberg continued fraction. We discuss the implications of our theorems for the general convergence of other q-continued fractions, for example the G¨ollnitz-Gordon continued fraction, on the unit circle.

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Multi-Variable Polynomial Solutions To Pell's Equation And Fundamental Units In Real Quadratic Fields, James Mclaughlin Jan 2003

Multi-Variable Polynomial Solutions To Pell's Equation And Fundamental Units In Real Quadratic Fields, James Mclaughlin

Mathematics Faculty Publications

Solving Pell’s equation is of relevance in finding fundamental units in real quadratic fields and for this reason polynomial solutions are of interest in that they can supply the fundamental units in infinite families of such fields. In this paper an algorithm is described which allows one to construct, for each positive integer n, a finite collection, {Fi}, of multi-variable polynomials (with integral coefficients), each satisfying a multi-variable polynomial Pell’s equation C 2 i − FiH 2 i = (−1)n−1 , where Ci and Hi are multi-variable polynomials with integral coefficients. Each positive integer whose square-root has a regular continued …

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Polynomial Solutions To Pell's Equation And Fundamental Units In Real Quadratic Fields, James Mclaughlin Jan 2003

Polynomial Solutions To Pell's Equation And Fundamental Units In Real Quadratic Fields, James Mclaughlin

Mathematics Faculty Publications

Finding polynomial solutions to Pell’s equation is of interest as such solutions sometimes allow the fundamental units to be determined in an infinite class of real quadratic fields. In this paper, for each triple of positive integers (c, h, f) satisfying c 2 − f h2 = 1, where (c, h) are the smallest pair of integers satisfying this equation, several sets of polynomials (c(t), h(t), f(t)) which satisfy c(t) 2 − f(t) h(t) 2 = 1 and (c(0), h(0), f(0)) = (c, h, f) are derived. Moreover, it is shown that the pair (c(t), h(t)) constitute the fundamental polynomial …

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The Structure Of Residuated Lattices, Kevin K. Blount, Constantine Tsinakis Jan 2003

The Structure Of Residuated Lattices, Kevin K. Blount, Constantine Tsinakis

Mathematics Faculty Publications

A residuated lattice is an ordered algebraic structure [formula] such that is a lattice, is a monoid, and \ and / are binary operations for which the equivalences [formula] hold for all a,b,c ∈ L. It is helpful to think of the last two operations as left and right division and thus the equivalences can be seen as "dividing" on the right by b and "dividing" on the left by a. The class of all residuated lattices is denoted by ℛℒ The study of such objects originated in the context of the theory of ring ideals in the 1930s. The …

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