There is a wide body of research to support the view that children with low levels of phonemic awareness on entering school are more likely to be poorer readers and spellers than those with high levels (Adams, 1990; Bradley & Bryant, 1983, 1985; Frith, 1985; Mann, 1993; Snow, Burns & Griffin, 1998). Because academic success is largely dependent upon reading, teachers need a quick and accurate w...

In this note we give an upper bound for λ(n), the maximum number of edges in a strongly multiplicative graph of order n, which is sharper than the upper bounds given by Beineke and Hegde [3] and Adiga, Ramaswamy and Somashekara [2], for n ≥ 28.

a University of Virginia, United States b University of Toronto, Canada c University of California, Davis, United States d Pennsylvania State University, Abington, United States e The University of Southern Mississippi, United States f Ashland University, United States g Virginia Commonwealth University, United States h Bradley University, United States i Ithaca College, United States j Center ...

We define the decomposable extensions of difference fields and study the irreducibility of q-Painlevé equation of type A 7 ′ . Every strongly normal extension or Liouville-Franke extension, the latter of which is a difference analogue of the Liouvillian extension, satisfies that its appropriate algebraic closure is a decomposable extension.

Consider the energy critical focusing wave equation on the Euclidian space. A blow-up type II solution of this equation is a solution which has finite time of existence but stays bounded in the energy space. The aim of this work is to exhibit universal properties of such solutions. Let W be the unique radial positive stationary solution of the equation. Our main result is that in dimension 3, u...

Let A be a Banach algebra with the second dual A∗∗. If A has a bounded approximate identity (= BAI), then A∗∗ is unital if and only if A∗∗ has a weak∗ bounded approximate identity(= W ∗BAI). If A is Arens regular and A has a BAI, then A∗ factors on both sides. In this paper we introduce new concepts LW ∗W and RW ∗W property and we show that under certain conditions if A has LW ∗W and RW ∗W prop...

We consider the optimization problem of minimizing R Ω G(|∇u|) + λχ{u>0} dx in the class of functions W (Ω) with u − φ0 ∈ W 1,G 0 (Ω), for a given φ0 ≥ 0 and bounded. W (Ω) is the class of weakly differentiable functions with R Ω G(|∇u|) dx < ∞. The conditions on the function G allow for a different behavior at 0 and at ∞. We prove that every solution u is locally Lipschitz continuous, that it ...

It is an observation due to J.J. Kohn that for a smooth bounded pseudoconvex domain Ω in C there exists s > 0 such that the ∂-Neumann operator on Ω maps W s (0,1)(Ω) (the space of (0, 1)-forms with coefficient functions in L -Sobolev space of order s) into itself continuously. We show that this conclusion does not hold without the smoothness assumption by constructing a bounded pseudoconvex dom...