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.

the concepts of fuzzy semi-ideals of r with respect to h≤r and generalized fuzzy quotient rings are introduced. some properties of fuzzy semiideals are discussed. finally, several isomorphism theorems for generalized fuzzy quotient rings are established.

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

The importance of unsymmetrical N-heterocyclic carbenes (uNHCs) as ligands in metal-catalyzed reactions is undeniable. While uNHCs show similar properties as compared with symmetrical NHCs, dissymmetrization allows for further fine-tuning. The introduction of chelatization, hemilability, bifunctionality, shielding effects, and chirality-transfer influences the catalyst's stability, reactivity, ...

Alkoxide-functionalized N-heterocyclic carbenes (NHCs) stabilise the potassium-imidazole-2-ylidene fragment against 1,2 alkyl rearrangement reactions; this allows the first structural characterisation of a potassium NHC complex, which reveals distorted and unusual bonding interactions between the imidazole ring and the potassium cation.

The Balbiani ring (BR) genes in the midge Chironomus, a genus belonging to Diptera, code for large secretory proteins, used to construct the larval tube. The 15-23-kb long core block in each gene consists of an array of tandemly arranged approximately 200-bp long repeat units, where a single repeat unit is composed of a constant and a subrepeat region. In order to investigate the evolutionary f...

Observation and tracking of fluorescently labeled molecules and particles in living cells reveals detailed information about intracellular processes on the molecular level. Whereas light microscopic particle observation is usually limited to two-dimensional projections of short trajectory segments, we report here image-based real-time three-dimensional single particle tracking in an active feed...

To evaluate the acute effect of lovastatin on diabetic endothelial dysfunction, we examined this effect on the aortic rings of streptozotocin-diabetic rats. The endothelial function was assessed in aortic rings isolated from diabetic rats, 12 weeks after treatment with streptozotocin (45 mg/kg, i.p.). The concentration-response curve to acetylcholine (Ach) in the aortic rings precontracted with...

in this note we introduce the notion of weak mccoy rings as a generalization of mccoy rings, and investigate their properties. also we show that, if is a semi-commutative ring, then is weak mccoy if and only if is weak mccoy.