Publications - 2004

A continued fraction approach to the {D}iophantine equation {$ax\sp 2-by\sp 2=\pm1$}

A Description of Continued Fraction Expansions of Quadratic Surds Represented by Polynomials

An algebraic model for the center problem

A New EWMA Control Chart for Monitoring both Location and Dispersion

A note on asymptotic distribution of products of sums

Asset allocation with regime-switching: discrete-time case

A symmetry completeness criterion for second-order differential equations

Bayesian Reserving Models Inspired by Chain Ladder Methods and Implemented Using WinBUGS

Bounds for the independent domination number of graphs and planar graphs

Canonical partitions of universal structures

Let $\mathbb{U}=(U,\mathfrak{L})$ be a universal binary countable homogeneous structure and $n\in \omega$. We determine the equivalence relation $\mathcal{C}(n)(\mathbb{U})$ on $[U]^n$ with the smallest number of equivalence classes $r$ so that each one of the classes is indivisible. As a consequence we obtain \[ \mathbb{U}\to (\mathbb{U})^n_{<\omega/r} \] and a characterization of the smallest number $r$ so that the arrow relation above holds. For the case of infinitely many colors we determine the canonical set of equivalence relations, extending the result of Erd\H{o}s and Rado for the integers to countable universal binary homogeneous structures.

Class numbers, quadratics, and exponential Diphantine equations

Clean rings: A survey

Combination of general antithetic transformations and control variables

Constructions from empty polygons

{$C\sp *$}-algebras associated with topological relations

Distinct distances in the plane

Dividing polynomials when you only know their values

Effects of Foot Orthoses on the Musculoskeletal System of Recreational Runners: A Functional Data Analsysis Approach

Endomorphisms of type {I} von {N}eumann algebras with discrete center

"Ergodic theory and its application to the analysis of nucleic acid sequences" Proceedings of the South Dakota Academy of Sciences 83: 55-63

EWMA Charts for Monitoring the Mean Censored Weibull Lifetimes

Grauert- and Lax-Halmos-type theorems and extension of matrices with entries in H^\infty

HIV/AIDS Modeling:A Case for Universal Medicaid in America

Infinitely Many Quadratic Diophantine Equations Solvable Everywhere Locally but Not Solvable Globally

Inverse Modeling of Aerosol Dynamics: Condensational Growth

Large transversals to small families of unit disks

Millennial-scale Relationships of Diatom Species Richness and Production in Two Prairie Lakes

Modern algebra with applications

Monodromy in the resonant swing spring

On {B}ohl-{P}erron type theorems for linear difference equations

On impulsive {B}everton-{H}olt difference equations and their applications

On seven points in the boundary of a plane convex body in large relative distances

By the relative distance of points $p$ and $q$ of a convex body $C$ we mean the ratio of the Euclidean length of the segment $pq$ to the half of the Euclidean length of a longest chord of C parallel to $pq$. We show that in the boundary of every plane convex body there exist seven points in pairwise relative distances at least $2 \over 3$. We also give an estimate in case of three points.

Ordering optimal proportions in the asset allocation problem with dependent default risks

Pricing Options and Variance Swaps in Markov-Modulated Brownian and Fractional Brownian Markets

Projections in the space H^\infty and the corona theorem for subdomains of coverings of finite bordered Riemann surfaces

Radical classes of polynomial rings

Rational methods for recognizing generalized homogeneous functors

Remote Preparation and Distribution of Bipartite Entangled States

Rings with the dual of the isomorphism theorem

Simple curves on surfaces and an analog of a theorem of Magnus for surface groups

Testing regression models: a strong martingale approach

The arithmetic of certain cubic function fields

In this paper, we discuss the properties of curves of the form $y^3=f(x)$ over a given field K of characteristic different from 3. If $f(x)$ satisfies certain properties, then the Jacobian of such a curve is isomorphic to the ideal class group of the maximal order in the corresponding function field. We seek to make this connection concrete and then use it to develop an explicit arithmetic for the Jacobian of such curves. From a purely mathematical perspective, this provides explicit and efficient techniques for performing arithmetic in certain ideal class groups which are of fundamental interest in algebraic number theory. At the same time, it provides another source of groups which are suitable for Diffie-Hellman type protocols in cryptographic applications.

The Kneser-Poulsen Conjecture for Spherical Polytopes

If a finite set of balls of radius pgr/2 (hemispheres) in the unit sphere Sn is rearranged so that the distance between each pair of centers does not decrease, then the (spherical) volume of the intersection does not increase, and the (spherical) volume of the union does not decrease. This result is a spherical analog to a conjecture by Kneser (1954) and Poulsen (1955) in the case when the radii are all equal to pgr/2.

The {R}eissner-{S}agoci type problem for a non-homogeneous elastic cylinder embedded in an elastic non-homogeneous half-space

Winning ways for your mathematical plays. {V}ol. 4