let r be a prime ring with extended centroid c, h a generalized derivation of r and n ⩾ 1 a xed integer. in this paper we study the situations: (1) if (h(xy))n = (h(x))n(h(y))n for all x; y 2 r; (2) obtain some related result in case r is a noncommutative banach algebra and h is continuous or spectrally bounded.

an object $x$ of a category $mathbf{c}$ with finite limits is called exponentiable if the functor $-times x:mathbf{c}rightarrow mathbf{c}$ has a right adjoint. there are many characterizations of the exponentiable  spaces in the category $mathbf{top}$ of topological spaces. here, we study the exponentiable objects in the category $mathbf{stop}$ of soft topological spaces which is a generalizati...

a ring $r$ is a strongly clean ring if every element in $r$ is the sum of an idempotent and a unit that commutate. we construct some classes of strongly clean rings which have stable range one. it is shown that such cleanness of $2 imes 2$ matrices over commutative local rings is completely determined in terms of solvability of quadratic equations.

in this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring r such that, every regular matrix admits a diagonal power-reduction.

Here we present a next-generation experimental setup for high-resolution X-ray spectroscopy of solid and liquid samples in the soft X-ray region to elucidate the complex molecular structures of (bio)chemical systems. The setup consists of a main target chamber, a target holder for either solid samples or a liquid jet delivery system, and a high-resolution soft Xray grating spectrometer. This se...

Analysis of data from the IsoStar library shows that many hydrophobic groups exhibit strikingly strong directional preferences in their intermolecular interactions. Specific directional interactions may occur because of the large quadrupole moments of many aromatic ring systems, the residual electropositive charge on most carbon-bound H atoms and the effects of polarization on soft hetero-ring ...

We present a theory of magnetization reversal due to thermal fluctuations in thin submicron-scale rings composed of soft magnetic materials. The magnetization in such geometries is more stable against reversal than that in thin needles and other geometries, where sharp ends or edges can initiate nucleation of a reversed state. The two-dimensional ring geometry also allows us to evaluate the eff...