‎in a recent paper c‎. ‎miguel proved that the diameter of the commuting graph of the matrix ring $mathrm{m}_n(mathbb{r})$ is equal to $4$ if either $n=3$ or $ngeq5$‎. ‎but the case $n=4$ remained open‎, ‎since the diameter could be $4$ or $5$‎. ‎in this work we close the problem showing that also in this case the diameter is $4$.

Progress in the synthesis of semiconductor nanowires (NWs) has prompted intensive inquiry into understanding the science of their growth mechanisms and ultimately the technological applications they promise. We present new results for the size-dependent growth kinetics of Ge NWs and correlate the results with a direct experimental measurement of the Gibbs-Thomson effect, a measured increase in ...

We report the demonstration of high-photoresponsivity Ge-dot photoMOSFETs in a standard MOS configuration for the detection of 850-1550 nm illumination. Each device has a self-organized, gate-stacking heterostructure of SiO2/Ge-dot/SiO2/SiGe-channel which is simultaneously fabricated in a single oxidation step. Superior control of the geometrical size and chemical composition for our Ge nanodot...

We demonstrate the formation of hollow nickel germanide nanostructures of Ni-Ge core-shell nanoparticles by solid state reactions. The structural evolutions of nickel germanide hollow nanostructures have been investigated in real-time ultrahigh vacuum transmission electron microscopy (UHV-TEM). Annealed above 450 °C, the nonequilibrium interdiffusion of core and shell species occurred at the in...