These notes give a summary of results that everyone who does work in functional analysis should know about the weak topology on locally convex topological vector spaces and the weak-* topology on their dual spaces. The most striking of the results we prove is Theorem 9, which shows that a subset of a locally convex space is bounded if and only if it is weakly bounded. It is straightforward to p...

We show that the energy transfer through an open quantum system with non-degenerate Hamiltonian weakly coupled two reservoirs in equilibrium is approximately proportional to difference of their temperatures unless both are small.

Abstract. In this paper, the authors defined a multifunction F : X → Y to be upper (resp. lower) weakly α-continuous if for each x ∈ X and each open set V of Y such that F (x) ⊂ V (resp. F (x) ∩ V 6= ∅), there exists an α-open set U of X containing x such that U ⊂ F(Cl(V )) (resp. U ⊂ F−(Cl(V ))). They give some characterizations and several properties concerning upper (lower) weakly α-continuo...

In order to make conditional alleles of the v-myb oncogene, we constructed and tested avian retroviruses which produce a number of different fusion proteins between v-Myb and the human estrogen receptor (ER). We found that the portion of the ER used in making these fusions profoundly affected their transcriptional activation. However, all the fusions tested were only weakly transforming in embr...