Novel mobile electronic-nose (e-nose) devices and algorithms capable of real-time detection of industrial and municipal pollutants, released from point-sources, recently have been developed by scientists worldwide that are useful for monitoring specific environmental-pollutant levels for enforcement and implementation of effective pollution-abatement programs. E-nose devices are ideal instrumen...

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.