In this paper we establish a number of implications between various qualitative and quantitative versions of the global regularity problem for the Navier-Stokes equations, in the periodic, smooth finite energy, smooth H, Schwartz, or mild H categories, and with or without a forcing term. In particular, we show that if one has global well-posedness in H for the periodic Navier-Stokes problem wit...

[1] Global simulations of sea salt and mineral dust aerosols are integrated into a previously developed unified general circulation model (GCM), the Goddard Institute for Space Studies (GISS) GCM II0, that simulates coupled tropospheric ozone-NOxhydrocarbon chemistry and sulfate, nitrate, ammonium, black carbon, primary organic carbon, and secondary organic carbon aerosols. The fully coupled ga...

The focus of this paper is on spatial precoding in correlated multi-antenna channels, where the number of independent data-streams is adapted to trade-off the data-rate with the transmitter complexity. Towards the goal of a low-complexity implementation, a structured precoder is proposed, where the precoder matrix evolves fairly slowly at a rate comparable with the statistical evolution of the ...

For a connected graph G = (V,E), a set W ⊆ V is called a Steiner set of G if every vertex of G is contained in a Steiner W -tree of G. The Steiner number s(G) of G is the minimum cardinality of its Steiner sets and any Steiner set of cardinality s(G) is a minimum Steiner set of G. For a minimum Steiner set W of G, a subset T ⊆ W is called a forcing subset for W if W is the unique minimum Steine...

The zero forcing number of a graph G is the cardinality of the smallest subset of the vertices of G that forces the entire graph using a color change rule. This paper presents some basic properties of circulant graphs and later investigates zero forcing numbers of circulant graphs of the form C[n, {s, t}], while also giving attention to propagation time for specific zero forcing sets.