This article considers an analogous problem in which the observed random variables are the steps of a symmetric random walk. Assuming continuously distributed step sizes, it describes the optimal stopping rules for the cases n = 2 and n = 3 in two versions of the problem: a "full information" version in which the actual steps of the random walk are disclosed to the decision maker; and a "partial information" version in which only the relative ranks of the positions taken by the random walk are observed. When n = 3, the optimal rule and expected rank depend on the distribution of the step sizes. The authors give sharp bounds for the optimal expected rank in the partial information version, and fairly sharp bounds in the full information version.

Presentation for the 2011 University Scholars Day at the University of North Texas discussing research on continued fractions as an alternative to decimal expansions.

This article establishes uses a Gauss-like relationship to examine how the curvature bundle morphisms relate.

This article focuses on the nontrivial determinant identities which typically underlie the complex analytic proofs of all the results in the plane geometry of lines and circles.

In this article, the author presents an elementary proof of a result due to Dickson characterizing those integers n admitting non-abelian groups of order n.

This article identifies the principal features in Foias’ original proof and streamlines them into a general result. The result gives further evidence to the observation that the connection between the sequence with initial seed the Foias constant and the Prime Number Theorem must be fortuitous.

The '5 lei coin' problem of Titeica is generalized to circles of arbitrary radii.

In this article, the author investigates a computational proof of the Cayley-Hamilton theroem, based on induction.

Article discussing studies of the relationship between the Stieltjes sums and the elementary symmetric sums.

This article identifies a class of magnetic Schrödinger operators on Kähler manifolds which exhibit pure point spectrum.

In this article, the author presents a generalization of a certain Putnam problem.

Article on a class of Stieltjes-Van Vleck polynomials.

This article discusses a family of iterated integrals and generalizing an iterated integral identity proposed at a Putnam competition in 1941.

This article examines how in view of the fundamental theorem of algebra and basic Galois theory solving nonlinear systems of polynomial equations exactly means in general reducing them to one single equation in one variable.

Article on polynomial harmonic decompositions. For real polynomials in two indeterminates a classical polynomial harmonic decomposition is extended from square-norm divisors to conic ones.

In this article, the author investigates the real 2 x 2 matrices which admit real square roots.

Article on the analogy between the description of the real square roots of 3x3 matrices and the zeros of the (depressed) real quartic polynomial, using the Cayley-Hamilton theorem.

This article is concerned with optimality conditions and duality results for nondifferentiable multi-objective fractional programming problems.

Article on interpreting genomic data via entropic dissection.

Presentation for the 2011 University Scholars Day at the University of North Texas discussing a mathematical game using the tiling of a plane.

Presentation for the 2011 University Scholars Day at the University of North Texas discussing research on predictable patterns in continued fractions and decimal expansions.

This article investigates Poincaré series, particularly the study of Siegel–Poincaré series of degree 2 attached to products of terms of Fourier series of harmonic Siegel–Maass forms and holomorphic Siegel modular forms

This paper discusses autonomous robot localization using WiFi fingerprinting.

This article discusses a comprehensive analysis of the Medicago truncatula genome and transcriptome that entailed search for novel Auxin Response Factor genes and the co-expression networks.