In this paper, we derive explicit bounds for the Kolmogorov distance in the CLT and we prove the almost sure CLT for the quadratic variation of the sub-fractional Brownian motion. We use recent results on the Stein method combined with the Malliavin calculus and an almost sure CLT for multiple integrals.
Stable, dual-wavelength operation of a diode-pumped, passively mode-locked, ytterbium-erbium “figure-of-eight” (F8L) fibre laser has been achieved by including tunable filters and/or fibre gratings in the Nike Roshe Run Toronto
laser cavity. The centre wavelengths of the two channels were independently tunable when gain compensation was provided in the cavity. Bandwidth-limited solitons could be generated.
By making use of a special Lyapunov-type function and applying the comparison method Cheap Nike Free Run due to Conti, we prove global existence of solutions for a general class of nonlinear second-order differential equations that includes, in particular, van der Pol, Rayleigh, and Liénard equations, widely encountered in applications. Relevant examples are discussed.
In this note we consider linear maps on the complex n × n matrix algebra MnMn preserving products of either two positive matrices, a positive matrix and a Hermitian matrix, or two Hermitian matrices. We give characterizations of all those injections.