In this paper, the authors present a modified convergent analytic algorithm for the solution of nonlinear boundary value problems by means of a variable parameter method and briefly, the method is called optimal variable parameter method. This method, based on the embedding of a parameter and an auxiliary operator, provides a computational advantage for the convergence of the approximate soluti...

The geometry of an accelerator cavity determines its eigenmodes and thereby its performance characteristics. Therefore, accelerating performance and wakefield characteristics may be improved by an intentional modification of the geometry. However, undesired geometry perturbations due to manufacturing tolerances and operational demands can likewise impair it. To analyze the effects of geometry v...

one of the main steps within the geoid computation methodology without applying the stokes formula is downward continuation of the harmonic residual observables from the surface of the earth down to the surface of the reference ellipsoid. this downward continuation is done via the abel-poisson integral and its derivatives. this integral in which the unknowns, i.e. harmonic residual potential va...

We discuss a two-parameter family of maps that generalize piecewise linear, expanding maps of the circle. One parameter measures the effect of a non-linearity which bends the branches of the linear map. The second parameter rotates points by a fixed angle. For small values of the nonlinearity parameter, we compute the invariant measure and show that it has a singular density to first order in t...