On the Lebesgue and Sobolev spaces on a time-scale

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

On The Sobolev-type Inequality for Lebesgue Spaces with a Variable Exponent

A Simple Characterization of Chaos for Weighted Composition C0-semigroups on Lebesgue and Sobolev Spaces

The purpose of this article is to give a simple characterization of chaos for certain weighted composition C0-semigroups on Lebesgue spaces and Sobolev spaces over open intervals. Recall that a C0-semigroup T on a separable Banach space X is called chaotic if T is hypercyclic, i.e. there is x ∈ X such that {T (t)x; t ≥ 0} is dense in X , and if the set of periodic points, i.e. {x ∈ X ; ∃t > 0 :...

Spanning and Sampling in Lebesgue and Sobolev Spaces

We establish conditions on ψ under which the small-scale affine system {ψ(ajx− k) : j ≥ J, k ∈ Zd} spans the Lebesgue space L(R) and the Sobolev space W(R), for 1 ≤ p < ∞ and J ∈ Z. The dilation matrices aj are expanding (meaning limj→∞ ‖a−1 j ‖ = 0) but they need not be diagonal. For spanning L our result assumes ∫ Rd ψ dx 6= 0 and, when p > 1, that the periodization of |ψ| or of 1{ψ 6=0} is b...

the effects of multiple intelligences (focus on musical, visual, and linguistic) and direct instruction on learning grammar: a case on iranian efl students at elementary level

1.0 overview it seems that grammar plays a crucial role in the area of second and foreign language learning and widely has been acknowledged in grammar research. in other words, teaching grammar is an issue which has attracted much attention to itself, and a lot of teachers argue about the existence of grammar in language teaching and learning. this issue will remind us a famous sentence f...