We introduce a new class of fuzzy open sets called fuzzy $bigwedge_e$ sets which includes the class of fuzzy $e$-open sets. We also define a weaker form of fuzzy $bigwedge_e$ sets termed as fuzzy locally $bigwedge_e$ sets. By means of these new sets, we present the notions of fuzzy $bigwedge_e$ continuity and fuzzy locally $bigwedge_e$ continuity which are weaker than fuzzy $e$-continuity and f...

The strong interaction limit of the discrete-time weakly self-avoiding walk (or Domb–Joyce model) is trivially seen to be the usual strictly self-avoiding walk. For the continuous-time weakly self-avoiding walk, the situation is more delicate, and is clarified in this paper. The strong interaction limit in the continuous-time setting depends on how the fugacity is scaled, and in one extreme lea...

Aweak completeness phenomenon is investigated in the complexity class E = DTIME(2linear). According to standard terminology, a language H is m-hard for E if the set Pm(H), consisting of all languages A m H , contains the entire class E. A language C is P m-complete for E if it is m-hard for E and is also an element of E. Generalizing this, a language H is weakly m-hard for E if the set Pm(H) do...

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.