The classical Weyl groups appear as special cases: for r = s = 1 we have the symmetric group G1,1,n = Sn, for r = 2s = 2 we have the hyperoctahedral group G2,1,n = Bn, and for r = s = 2 we have the group of even-signed permutations G2,2,n = Dn. We say that a permutation π ∈ Gr,s,n is an involution if π 2 = 1. More generally, we define G r,s,n = {σ ∈ Gr,s,n|σ m = 1}. Recently, Bagno, Garber and ...

By transforming an exact stability condition, a new Nyquist-like plot is proposed to predict occurrences of three typical instabilities in DC-DC converters. The three instabilities are saddle-node bifurcation (coexistence of multiple solutions), period-doubling bifurcation (subharmonic oscillation), and Neimark bifurcation (quasi-periodic oscillation). In a single plot, it accurately predicts w...

We present a simple yet highly sensitive single-beam experimental technique for the determination of both the sign and magnitude of n(2). The sample is moved along the z direction of a focused Gaussian beam while the repetitively pulsed laser energy is held fixed. The resultant plot of transmittance through an aperture in the far field yields a dispersion-shaped curve from which n(2) is easily ...