This paper presents a measure of Internet “connectivity” (number of connected companies per capita) normalized by the economic “size ” of areas in the United States. We use cross sectional variation in connectivity to test some hypotheses about technology adoption. We find that areas in the South and Midwest have below average connectivity. Connectivity is also related to the living “attractive...

We investigate the sufficient condition under which each positive b-weakly compact operator is Dunford-Pettis. We also investigate the necessary condition on which each positive b-weakly compact operator is Dunford-Pettis. Necessary condition on which each positive b-weakly compact operator is weakly compact is also considered. We give the operator that is semi-compact, but it is not bweakly. W...

A closed horocycle $$\mathcal {U}$$ on $$SL_N(\mathbb {Z}) \backslash SL_N(\mathbb {R})/SO_N({\mathbb {R}})$$ has many lifts to the universal cover . Under some conditions horocycle, we give a precise asymptotic count of its bounded distance away from given base point in cover. This partially generalizes previous work Mohammadi–Golsefidy.

Abstract We consider the MHD system in a bounded domain Ω ⊂ ℝ N , = 2; 3, with Dirichlet boundary conditions. Using Dan Henry’s semigroup approach and Giga–Miyakawa estimates we construct global time, unique solutions to fractional approximations of base space ( L 2 (Ω )) × . Solutions are obtained next as limits that approximations.

In this paper we prove necessary and sufficient conditions for the validity of the classical chain rule in the Sobolev space W 1,1 loc ( R ;R ) and in the space of functions of bounded variation BVloc ( R ;R ) .