It is shown that there exists an α-rigid transformation with α less or equal to 1 2 whose spectrum has Lebesgue component. This answers the question raised by Klemes and Reinhold in [30]. Moreover, we introduce a new criterium to identify a large class of α-rigid transformations with singular spectrum.

In this paper we present a new approach to Grothendieck duality over commutative rings. Our approach is based on the idea of rigid dualizing complexes, which was introduced by Van den Bergh in the context of noncommutative algebraic geometry. We obtain many of the important local features of Grothendieck duality, yet manage to avoid lengthy and difficult compatibility verifications. Our results...

A conjugated diosma-octacyclic complex, with aromatic osmapentalene termini and the rigid naphthalene bridge linked by non-aromatic osmafuran rings, forms a singly reduced valence-trapped species characterised at low temperature.

Let R be a prime ring with center Z, I nonzero ideal of and D: × → symmetric bi–(α, α)-derivation d the trace D. In present paper, we have considered following conditions: i) [d(x), x]α,α = 0, ii)[d(x), ⊆ Cα,α, iii)(d(x), x)α,α iv)D1(d2(x), x) v)d1(d2(x)) f(x), for all x, y ∈ I, where D1 D2 are two bi-(α, α)-derivations, d1, d2 traces D1, respectively, B: is bi-additive mapping, f B.

We prove a version of faithfully flat descent in rigid analytic geometry, for almost perfect complexes and without finiteness assumptions on the rings involved. This extends results Drinfeld vector bundles.

In this paper, we introduce (α, α)-symmetric derivations and establish some interesting results and also extend an important result of J. Vukman by using (α, α)-derivation.

The aim of this research is to investigate the vasorelaxing effects and mechanisms involved in the phytoestrogen α-zearalanol (α-ZAL) in rat thoracic aortas rings. Intact or endothelium denuded rat thoracic aortas rings were put in individual organ chamber to observe the endothelium-dependent or independent vasorelaxing effects of α-ZAL (10-10-10-5 M). The thoracic aortas rings were pre-contrac...