The dynamical bifurcations of a laser with a saturable absorber were calculated, with the 3-2 level model, as function of the gain parameter. The average power of the laser is shown to have specific behavior at bifurcations. The succession of periodic-chaotic windows, known to occur in the homoclinic chaos, was studied numerically. A critical exponent of 1/2 is found on the tangent bifurcations...

The linear operator c + (??)?/2, where > 0 and (??)?/2 is the fractional Laplacian on periodic domain, arises in existence of travelling waves Korteweg-de Vries equation. We establish a relation Green function this with Mittag-Leffler function, which was previously used context Riemann-Liouville Caputo derivatives. By using relation, we prove that strictly positive single-lobe (monotonically de...

background: normokalemic periodic paralysis is an autosomal dominant disorder involving the abnormal function of skeletal muscle’s voltage-gated alpha-subunits. it is characterized by paralysis attack of varying severity with concomitant normal serum potassium concentration. although normokalemic periodic paralysis is well established in the literature, but its cardiac manifestations are very r...

7. The Case of Periodic Data.-In a recent paper5 I introduced the method of trigonometric spline interpolation. The discussion of sections 4 and 5 carries over to the periodic case and need not be elaborated. The analogue of Problem 1 is as follows: assuming 2m + 2 < n, e > 0, we are seeking the function f(x), of period 2 r, having a square integrable (2m + 1)st derivative and which solves the ...