Publications - 2002

A hierarchical 3-{D} {P}oisson modified {F}ourier solver by domain decomposition

A Kolmogorov-Smirnov Type Test of Changing Conditional Variances for Threshold Autoregressive Models

A New Test for Normality in Linear Autoregressive Models

A nonholonomic oscillator

A Note on the Parallelogram Method for Computing the On-level Premium

Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation

In this paper, we refine work of Beukers, applying results from the theory of Padé approximation to $(1 - z)^{1/2}$ to the problem of restricted rational approximation to quadratic irrationals. As a result, we derive effective lower bounds for rational approximation to $\sqrt{m}$ (where m is a positive nonsquare integer) by rationals of certain types. For example, we have $\left|\sqrt{2}-\frac{p}{q}\right|\gg q^{-1.47}\quad {\rm and}\quad\left|\sqrt{3}-\frac{p}{q}\right|\gg q^{-1.62},$ provided q is a power of 2 or 3, respectively. We then use this approach to obtain sharp bounds for the number of solutions to certain families of polynomial-exponential Diophantine equations. In particular, we answer a question of Beukers on the maximal number of solutions of the equation $x^2 + D = p^n$ where D is a nonzero integer and p is an odd rational prime, coprime to D.

Art galleries with guards of uniform range of vision

Beepers, creepers, and sleepers

Coloring finite substructures of countable structures

Convergence Rates of Estimators in Partial Linear Regression Models With MA($\infty$) Error Process

Criteria for the asphericity of 2-complexes

Dynamic and self-stabilizing distributed matching

Filter games on {$\omega$} and the dual ideal

Forty-four years with {P}eter {L}ancaster

Functional Data Analysis of Human Gait

High-resolution stereoscopic digital fundus photography versus contact-lens biomicroscopy for the detection of clinically significant macular edema

I{BN} and related properties for rings

Illumination in the presence of opaque line segments in the plane

Improving {R}ogers' upper bound for the density of unit ball packings via estimating the surface area of {V}oronoi cells from below in {E}uclidean {$d$}-space for all {$d\ge8$}

Isogeny classes of Hilbert-Blumenthal abelian varieties over finite fields

Line graphs of complete multipartite graphs have small cycle double covers

Modular arithmetic on elements of small norm in quadratic fields

Multivariate simultaneous approximation

My thanks to {E}rd{\H o}s {P}\'al

Nonholonomic reduction for free and proper actions

On a BMO-property for subharmonic functions

On cop-win graphs

On oscillation of a differential equation with infinite number of delays

On oscillation properties of delay differential equations with positive and negative coefficients

On the asymptotics of {F}ekete-type points for univariate radial basis interpolation

On the limit under scaling of polynomial {L}agrange interpolation on analytic manifolds

On two ODE models for HIV/AIDS development in Canada and a logistic SEIR model

Pellian polynomials and period lengths of continued fractions

Preliminary Test Prediction of Population Total under Regression Models with Measurement Error

Pushing disks apart-the {K}neser-{P}oulsen conjecture in the plane

Recent advances in randomized quasi-{M}onte {C}arlo methods

Repeated eigenvectors and the numerical range of self-adjoint quadratic operator polynomials

Separation in neighbourly 4-polytopes

Solving the {P}ell equation 

Spectral asymptotics for {S}turm-{L}iouville equations with indefinite weight

Sturm-{L}iouville problems with boundary conditions rationally dependent on the eigenparameter. {I}

Tests for a general two-sample problem using weighted spacings

The {D}iophantine equation {$ax\sp 2-by\sp 2=c$} and simple continued fractions

The Dirac Equation in Geometric Quantization

The elementary solution of triple series equations involving series of {L}egendre polynomials and their application to an electrostatic problem

The k most frequent distances in the palne

Topology of the maximal ideal space of H^\infty