In this paper we prove that for a type II1 factor N with a Cartan maximal abelian subalgebra (masa), the Hochschild cohomology groups Hn(N, N)=0, for all n ≥ 1. This generalizes the result of Sinclair and Smith, who proved this for all N having separable predual.

We show that in the one-dimensional case the weighted Hardy–Littlewood maximal operator Mμ is bounded on BMO(μ) for arbitrary Radon measure μ, and that this is not the case in higher dimensions.

In this paper we consider Q the class of solvable Lie algebras L with the following property: if A is a subalgebra of L, then Φ(A) ⊆ Φ(L) (where Φ(L) denotes the Frattini subalgebra of L;that is Φ(L) is the intersection of all maximal subalgebras of L). The class Q is shown to contain all solvable Lie algebras whose derived algebra is nilpotent. Necessary conditions are found such that an ideal...

one of the fundamental issues in the ethics of medical researches is cost-benefit assessment which consists a main part of related codes. this article is aimed to propose a model for ethical assessment of researches with judgment about their costs and benefits. after reviewing related materials and our experiences and discussions with experts, we proposed a model for ethical assessment of costs...

We present a unified approach to Doob’s Lp maximal inequalities for 1 ≤ p < ∞. The novelty of our method is that these martingale inequalities are obtained as consequences of elementary deterministic counterparts. The latter have a natural interpretation in terms of robust hedging. Moreover our deterministic inequalities lead to new versions of Doob’s maximal inequalities. These are best possib...