Using assistive reading software may be a cost-effective way to increase the opportunity for independent learning in students with learning disabilities. However, the effectiveness and perception of assistive reading software has seldom been explored in English-as-a-second language students with learning disabilities. This research was designed to explore the perception and effect of using assi...

In this paper, we survey recent progress on the constructive theory of the Feynman operator calculus. We first develop an operator version of the Henstock-Kurzweil integral, and a new Hilbert space that allows us to construct the elementary path integral in the manner originally envisioned by Feynman. After developing our time-ordered operator theory we extend a few of the important theorems of...

The dual space of the class of Henstock-Kurzweil integrable functions is well known in the one-dimensional case and corresponds to the space of multipliers which, in turn, coincides with the class of functions of bounded essential variation. Comparable results in higher dimensions have been elusive. For cases in which the partitions defining the Henstock-Kurzweil integrals are defined on n-cell...

When a real-valued function of one variable is approximated by its n th degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue p-norms in cases where f (n) or f (n+1) are Henstock–Kurzweil integrable. When the only assumption is that f (n) is Henstock–Kurzweil integrable then a modified form of the n th degree Taylor polynomial is used. When the only assumption i...

We give a sufficient and necessary condition such that for almost all s ∈ R ‖nθ − s‖ < ψ(n) for infinitely many n ∈ N, where θ is fixed and ψ(n) is a positive, non-increasing sequence. This improves upon an old result of Kurzweil and contains several previous results as special cases: two theorems of Kurzweil, a theorem of Tseng and a recent result of the second author. Moreover, we also discus...

The constructive definition usually begins with a function f, then by the process of using Riemann sums and limits, we arrive the definition of the integral of f, ∫ b a f. On the other hand, a descriptive definition starts with a primitive F satisfying certain condition(s) such as F ′ = f and F is absolutely continuous if f is Lebesgue integrable, and F is generalized absolutely continuous if f...