The multimode dynamics of vertical-cavity surfaceemitting lasers with different active-region diameters was measured under subnanosecond electrical excitation (800-ps pulse duration, 100-ps risetime). The dynamics is characterized by the delayed onset of higher order modes which have a turn-on delay that is dependent on the active-region diameter and the excitation parameters. A simple model th...

We introduce the delayed sine/cosine-type matrix function and use Laplace transform method to obtain a closed form solution IVP for second-order time-delayed linear system with noncommutative matrices A ?. also delay Gramian examine relative controllability linear/semi-linear time system. have obtained necessary sufficient condition of In addition, we conditions semi-linear time-delay Finally, ...

‎‎For a finite group $G$ and a subgroup $H$ of $G$‎, ‎the relative commutativity degree of $H$ in $G$‎, ‎denoted by $d(H,G)$‎, ‎is the probability that an element of $H$ commutes with an element of $G$‎. ‎Let $mathcal{D}(G)={d(H,G):Hleq G}$ be the set of all relative commutativity degrees of subgroups of $G$‎. ‎It is shown that a finite group $G$ admits three relative commutativity degrees if a...