Article discusses how a Cantor series expansion for a real number x with respect to a basic sequence Q=(q), where qi≥2, is a generalization of the base b expansion to an infinite sequence of bases. The authors show that for any basic sequence the set of distribution normal numbers is Π03-complete, and if Q is 1-divergent then the sets of normal and ratio normal numbers are Π03-complete.

This article identifies that an rRNA released in hemolysis activates clotting in human and zebrafish plasma. Furthermore, it shows that fish Hgfac plays a role in rRNA-mediated activation of coagulation.

Data management plan for the grant, "Conference: Dynamical Systems and Fractal Geometry."

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.

Article on an abstract index theorem on non-compact Riemannian manifolds.

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.

Article on the essential uniqueness of the Connes-Morley theorem.

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.

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

Article discussing the Levi problem on mixed manifolds. This article gives a new proof that the problem of Levi, to mixed varieties have a solution in the sense that every pseudoconvex closely mixed variety, with enough real global morphisms, is a variety of Cartan.

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.

Article discussing Bär's conformal lower bound for the spectrum of generalized Dirac operators.

Article on Morley's miracle theorem. The authors use work by A. Connes to explore possible generalizations of Morley's trisector theorem to triangles in arbitrary value fields.

Article on the constructibility with ruler and compass of a minimum chord in a parabola. The author gives a constructive description of all the points inside a parabola admitting a minimum chord of fixed direction.

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.

This article discusses the first Vafa-Witten bound for two-dimensional tori.

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 paper, the authors adapt Axler and Ramey's method of constructing the harmonic part of a homogeneous polynomial to the Fischer decomposition associated to Dirac operators acting on polynomial spinors.