We derive the generalized Hermite interpolation by using the contour integral and extend the generalized Hermite interpolation to obtain the sampling expansion involving derivatives for band-limited functions f , that is, f is an entire function satisfying the following growth condition |f(z)| ≤ A exp(σ|y|) for some A, σ > 0 and any z = x + iy ∈ C.

Spectral indices from models of inflation which incorporate a Generalized Einstein Theory (GET) gravity sector are calculated to first order in a slow-roll expansion. By quantizing a suitably-generalized measure of the intrinsic curvature perturbation, the spectral indices as calculated in the Jordan frame now match those as calculated following a conformal transformation, in the Einstein frame...

given a mapping $f:xto x$ we naturally associate to it a monotonic map $gg_f:exp xto exp x$ from the power set of $x$ into itself, thus inducing a generalized topology on $x$. in this paper we investigate some properties of generalized topologies which are defined by such a procedure.

The Bethe approximation, or loopy belief propagation algorithm, is a successful method for approximating partition functions of probabilistic models associated with graphs. Chertkov and Chernyak derived an interesting formula called “Loop Series Expansion”, which is an expansion of the partition function. The main term of the series is the Bethe approximation while the other terms are labeled b...

The small slope approximation (SSA) of Voronovich [Soy. Phys. JETP 62, 65-70 (1985)] is a promising method for application to scattering from many natural surfaces. The theory gives a systematic expansion that can be interpreted as a series in generalized surface slope. The SSA series for the T matrix satisfies the appropriate reciprocity condition at each order and reduces to the standard pert...

A least-squares identification method is studied that estimates a finite number of expansion coefficients in the series expansion of a transfer function, where the expansion is in terms of recently introduced generalized basis functions. The basis functions are orthogonal in 8$, and generalize the pulse, Laguerre and Kautz bases. One of their important properties is that, when chosen properly, ...

We consider the asymptotic analysis of penalized likelihood type estimators for generalized non-parametric regression problems in which the target parameter is a vector valued function defined in terms of the conditional distribution of a response given a set of covariates, A variety of examples including ones related to generalized linear models and robust smoothing are covered by the theory. ...

The Advection-Diffusion Equation (ADE) is solved for a constant pollutant emission from a point-like source placed inside an unstable Atmospheric Boundary Layer (ABL). The solution is obtained adopting the novel analytical approach named Generalized Integral Laplace Transform Technique (GILTT). The concentration solution of the equation is expressed through an infinite series expansion. After s...

We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in C∗-algebras is consider...