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For an oscillatory matrix A (that is, a totally positive matrix one of whose powers is strictly totally positive), we give an exact formula for the ratio of two successive eigenvalues of A, similar to the classical formula for the spectral radius, <img height="22" border="0" style="vertical-align:bottom" width="181" alt="" title="" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-0024379594003033-si1.gif">. Related formulae are derived for strictly sign-regular matrices.
Most protection and control equipment is usually tested in the open-loop mode. However, closed-loop testing is often the only cost-effective approach. This paper highlights the areas where closed-loop testing of protective relays and control equipment is preferable. Test setups with a real-time digital simulator for closed-loop testing of protective relays, power system stabilizers, Nike Free Haven 3.0 Shield and controllers for controlled closing of individual poles of a shunt capacitor breaker are described.
Light reflection from a dielectric slab, composed of identical atoms subject to thermal motion, is studied theoretically under the Born approximation. When the atomic motion is assumed to have a fixed magnitude, it is found that, although light is still reflected into the same incident plane, it is actually along two directions, all different from the direction specified by Snell’s law. It is also found that along these two *Free Run 5.0* reflection directions the light has different frequencies.