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Mathematics Faculty Publications

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Articles 481 - 510 of 562

Full-Text Articles in Mathematics

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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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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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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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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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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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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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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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 Graphs With Equal Algebraic And Vertex Connectivity, Stephen J. Kirkland, Jason J. Molitierno, Michael Neumann, Bryan L. Shader Jan 2002

On Graphs With Equal Algebraic And Vertex Connectivity, Stephen J. Kirkland, Jason J. Molitierno, Michael Neumann, Bryan L. Shader

Mathematics Faculty Publications

No abstract provided.

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Polynomial Continued Fractions, Douglas Bowman, James Mclaughlin Jan 2002

Polynomial Continued Fractions, Douglas Bowman, James Mclaughlin

Mathematics Faculty Publications

Continued fractions whose elements are polynomial sequences have been carefully studied mostly in the cases where the degree of the numerator polynomial is less than or equal to two and the degree of the denominator polynomial is less than or equal to one. Here we study cases of higher degree for both numerator and denominator polynomials, with particular attention given to cases in which the degrees are equal. We extend work of Ramanujan on continued fractions with rational limits and also consider cases where the limits are irrational.

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A Density Property Of The Tori And Duality, Peter Loth Jan 2002

A Density Property Of The Tori And Duality, Peter Loth

Mathematics Faculty Publications

In this note, a short proof of a recent theorem of D. Dikranjan and M. Tkachenko is given, and their result is extended.

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The Method Of Quasilinearization And A Three-Point Boundary Value Problem, Paul W. Eloe, Yang Gao Jan 2002

The Method Of Quasilinearization And A Three-Point Boundary Value Problem, Paul W. Eloe, Yang Gao

Mathematics Faculty Publications

The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green's function is constructed. For nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.

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Generalized Quasilinearization Method For A Second Order Three Point Boundary-Value Problem With Nonlinear Boundary Conditions, Bashir Ahmad, Rahmat Ali Khan, Paul W. Eloe Jan 2002

Generalized Quasilinearization Method For A Second Order Three Point Boundary-Value Problem With Nonlinear Boundary Conditions, Bashir Ahmad, Rahmat Ali Khan, Paul W. Eloe

Mathematics Faculty Publications

The generalized quasilinearization technique is applied to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of three point boundary value problem for second order di_erential equations with nonlinear boundary conditions. Also, we improve the convergence of the sequence of iterates by establishing a convergence of order k.

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Method Of The Quasilinearization For Nonlinear Impulsive Differential Equations With Linear Boundary Conditions, Paul W. Eloe, S. G. Hristova Jan 2002

Method Of The Quasilinearization For Nonlinear Impulsive Differential Equations With Linear Boundary Conditions, Paul W. Eloe, S. G. Hristova

Mathematics Faculty Publications

The method of quasilinearization for nonlinear impulsive differential equations with linear boundary conditions is studied. The boundary conditions include periodic boundary conditions. It is proved that the convergence is quadratic.

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Composition Operators And A Pull-Back Measure Formula, Valentin Matache Sep 2001

Composition Operators And A Pull-Back Measure Formula, Valentin Matache

Mathematics Faculty Publications

A pull-back measure formula obtained in some particular cases by E. A. Nordgren and this author is generalized in the framework of boundary measures for zero-free Nevanlinna class fuctions on the unit polydisk. The formula is used to characterize the zero-free Nevanlinna class functions which are solutions of Schröder's equation induced by a polydisk automorphism ϕ (i.e. to determine the zero-free functionsf belonging to the Nevanlinna class which are solutions of the functional equationf ° π=λf, for some constant λ), thus generalizing earlier results obtained by R. Mortini and this author.

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A Construction Of Compactly-Supported Biorthogonal Scaling Vectors And Multiwavelets On $R^2$, Bruce Kessler Jul 2001

A Construction Of Compactly-Supported Biorthogonal Scaling Vectors And Multiwavelets On $R^2$, Bruce Kessler

Mathematics Faculty Publications

In \cite{K}, a construction was given for a class of orthogonal compactly-supported scaling vectors on $\R^{2}$, called short scaling vectors, and their associated multiwavelets. The span of the translates of the scaling functions along a triangular lattice includes continuous piecewise linear functions on the lattice, although the scaling functions are fractal interpolation functions and possibly nondifferentiable. In this paper, a similar construction will be used to create biorthogonal scaling vectors and their associated multiwavelets. The additional freedom will allow for one of the dual spaces to consist entirely of the continuous piecewise linear functions on a uniform subdivision of the …

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Numerical Ranges Of Composition Operators, Valentin Matache Jan 2001

Numerical Ranges Of Composition Operators, Valentin Matache

Mathematics Faculty Publications

Composition operators on the Hilbert Hardy space of the unit disk are considered. The shape of their numerical range is determined in the case when the symbol of the composition operator is a monomial or an inner function fixing 0. Several results on the numerical range of composition operators of arbitrary symbol are obtained. It is proved that 1 is an extreme boundary point if and only if 0 is a fixed point of the symbol. If 0 is not a fixed point of the symbol 1 is shown to be interior to the numerical range. Some composition operators whose …

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Iteration Of Λ-Complete Forcing Notions Not Collapsing Λ+, Andrzej Roslanowski Jan 2001

Iteration Of Λ-Complete Forcing Notions Not Collapsing Λ+, Andrzej Roslanowski

Mathematics Faculty Publications

We look for a parallel to the notion of “proper forcing” among λ-complete forcing notions not collapsing λ+. We suggest such a definition and prove that it is preserved by suitable iterations.

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Topologically Pure Extensions, Peter Loth Jan 2001

Topologically Pure Extensions, Peter Loth

Mathematics Faculty Publications

A proper short exact sequence 0→H →G→K→0 (*) in the category of locally compact abelian groups is said to be topologically pure if the induced sequence 0→nH→nG→nK→0 is proper short exact for all positive integers n. Some characterizations of topologically pure sequences in terms of direct decompositions, pure extensions and tensor products are established. A simple proof is given for a theorem on pure subgroups by Hartman and Hulanickl. Using topologically pure extensions, we characterize those splitting locally compact abelian groups whose torsion part is a direct sum of a compact …

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A Penalty Method For Approximations Of The Stationary Power-Law Stokes Problem, Lew Lefton, Dongming Wei Jan 2001

A Penalty Method For Approximations Of The Stationary Power-Law Stokes Problem, Lew Lefton, Dongming Wei

Mathematics Faculty Publications

We study approximations of the steady state Stokes problem governed by the power-law model for viscous incompressible non-Newtonian flow using the penalty formulation. We establish convergence and find error estimates

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Decay Estimates Of Heat Transfer To Melton Polymer Flow In Pipes With Viscous Dissipation, Dongming Wei, Zhenbu Zhang Jan 2001

Decay Estimates Of Heat Transfer To Melton Polymer Flow In Pipes With Viscous Dissipation, Dongming Wei, Zhenbu Zhang

Mathematics Faculty Publications

In this work, we compare a parabolic equation with an elliptic equation both of which are used in modeling temperature profile of a power-law polymer flow in a semi-infinite straight pipe with circular cross section. We show that both models are well-posed and we derive exponential rates of convergence of the two solutions to the same steady state solution away from the entrance. We also show estimates for difference between the two solutions in terms of physical data.

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The Possibility Of Impossible Pyramids, Thomas Q. Sibley Jun 2000

The Possibility Of Impossible Pyramids, Thomas Q. Sibley

Mathematics Faculty Publications

No abstract provided.

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Rhombic Penrose Tilings Can Be 3-Colored, Thomas Q. Sibley, Stan Wagon Mar 2000

Rhombic Penrose Tilings Can Be 3-Colored, Thomas Q. Sibley, Stan Wagon

Mathematics Faculty Publications

No abstract provided.

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Nonlinear Eigenvalue Problems For Higher Order Lidstone Boundary Value Problems, Paul W. Eloe Jan 2000

Nonlinear Eigenvalue Problems For Higher Order Lidstone Boundary Value Problems, Paul W. Eloe

Mathematics Faculty Publications

In this paper, we consider the Lidstone boundary value problem y(t) = λa(t)f(y(t), . . . , y(t), . . . y(t)), 0 < t < 1, y(0) = 0 = y(1), i = 0, . . . , m − 1, where (−1)f > 0 and a is nonnegative. Growth conditions are imposed on f and inequalities involving an associated Green’s function are employed which enable us to apply a well-known cone theoretic fixed point theorem. This in turn yields a λ interval on which there exists a nontrivial solution in a cone for each λ in that interval. The methods of the paper are known. The emphasis here is that f depends upon higher order derivatives. Applications are made to …

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Tight Bounds On The Algebraic Connectivity Of A Balanced Binary Tree, Jason J. Molitierno, Michael Neumann, Bryan L. Shader Jan 2000

Tight Bounds On The Algebraic Connectivity Of A Balanced Binary Tree, Jason J. Molitierno, Michael Neumann, Bryan L. Shader

Mathematics Faculty Publications

In this paper, quite tight lower and upper bounds are obtained on the algebraic connectivity, namely, the second-smallest eigenvalue of the Laplacian matrix, of an unweighted balanced binary tree with k levels and hence n = 2k - 1 vertices. This is accomplished by considering the inverse of a matrix of order k - 1 readily obtained from the Laplacian matrix. It is shown that the algebraic connectivity is 1/(2k - 2k + 3) + 0(1/22k).

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Oif Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, Joe D. Mashburn Jan 2000

Oif Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, Joe D. Mashburn

Mathematics Faculty Publications

A base β of a space X is called an OIF base when every element of B is a subset of only a finite number of other elements of β. We will explore the fundamental properties of spaces having such bases. In particular, we will show that in T2 spaces, strong OIF bases are the same as uniform bases, and that in T3 spaces where all subspaces have OIF bases, compactness, countable compactness, or local compactness will give metrizability.

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Countable Positive Solutions Of A Conjugate Boundary Value Problem, Paul W. Eloe, Johnny Henderson, Nickolai Kosmatov Jan 2000

Countable Positive Solutions Of A Conjugate Boundary Value Problem, Paul W. Eloe, Johnny Henderson, Nickolai Kosmatov

Mathematics Faculty Publications

In this paper we consider the conjugate type nonlinear boundary value problem (-1) n-k u (n) (t)=f(u(t)), 0

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A Construction Of Orthogonal Compactly-Supported Multiwavelets On $\R^{2}$, Bruce Kessler Nov 1999

A Construction Of Orthogonal Compactly-Supported Multiwavelets On $\R^{2}$, Bruce Kessler

Mathematics Faculty Publications

This paper will provide the general construction of the continuous, orthogonal, compactly-supported multiwavelets associated with a class of continuous, orthogonal, compactly-supported scaling functions that contain piecewise linears on a uniform triangulation of $\R^2$. This class of scaling functions is a generalization of a set of scaling functions first constructed by Donovan, Geronimo, and Hardin. A specific set of scaling functions and associated multiwavelets with symmetry properties will be constructed.

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Classroom Capsules: Additivity ⊕ Homogeneity, Michael J. Bradley, Michael St. Vincent, David L. Finn Mar 1999

Classroom Capsules: Additivity ⊕ Homogeneity, Michael J. Bradley, Michael St. Vincent, David L. Finn

Mathematics Faculty Publications

A Classroom Capsule is a short article that contains a new insight on a topic taught in the earlier years of undergraduate mathematics.

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