A function f ∈ C(Ω) is holomorphic on Ω, if it satisfies the CauchyRiemann equations: ∂̄f = ∑n k=1 ∂f ∂z̄k dz̄k = 0 in Ω. Denote the set of holomorphic functions on Ω by H(Ω). The Bergman projection, B0, is the orthogonal projection of square-integrable functions onto H(Ω)∩L2(Ω). Since the Cauchy-Riemann operator, ∂̄ above, extends naturally to act on higher order forms, we can as well define Bergm...

The traditional theory of chaotic intermittency developed for return maps hypothesizes a uniform density reinjected points from the zone to laminar one. In past few years, we have described how reinjection probability function (RPD) can be generalized as power law function. Here, introduce broad and general analytical approach determine RPD other statistical variables, such characteristic relat...

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebys...

On the basis of the half-Cauchy distribution, we propose the called beta-half-Cauchy distribution for modeling lifetime data. Various explicit expressions for its moments, generating and quantile functions, mean deviations, and density function of the order statistics and their moments are provided. The parameters of the new model are estimated by maximum likelihood, and the observed informatio...