A high-order quadrature algorithm is presented for computing integrals over curved surfaces and volumes whose geometry implicitly defined by the level sets of (one or more) multivariate polynomials. The recasts as graph an defined, multi-valued height function, applies a dimension reduction approach needing only one-dimensional quadrature. In particular, we explore use Gauss-Legendre tanh-sinh ...

The concept of Lucky k-polynomials and in particular Lucky χ-polynomials was recently introduced. This paper introduces Stirling number of the fourth kind and Lucky partitions of a finite set in order to determine either the Lucky k- or Lucky χ-polynomial of a graph. The integer partitions influence Stirling partitions of the second kind.

in order to estimate the genetic parameters and comparison legendre polynomials for production traits of iranian holstein dairy cattle test-day records of first lactation cows for milk yield, fat yield, protein yield, fat percentage and protein percentage traits were used. these records collected from 2006 to 2010, by the animal breeding center of iran. the genetic parameters were estimated usi...

A high order optimal control strategy is proposed in this work, based on the use of differential algebraic techniques. In the frame of orbital mechanics, differential algebra allows to represent, by high order Taylor polynomials, the dependency of the spacecraft state on initial conditions and environmental parameters. The resulting polynomials can be manipulated to obtain the high order expans...

Optimal feedback control is classically based on linear approximations, whose accuracy drops off rapidly in highly nonlinear dynamics. A high order optimal control strategy is proposed in this work, based on the use of differential algebraic techniques. In the frame of orbital mechanics, differential algebra allows the dependency of the spacecraft state on initial conditions and environmental p...

In this paper I propose to estimate densities with possibly restricted support semi-nonparametrically via semi-nonparametric (SNP) estimation of densities on the unit interval. The latter will be done similarly to the approach of Gallant and Nychka (1987), but instead of using Hermite polynomials I propose to use orthonormal Legendre polynomials on the unit interval. This approach will be appli...

the low earth orbiting (leo) satellites are widely used for geosciences applications. for most applications, precise orbital information of the satellites is required. a combination of the in suite observations and dynamic orbit yields the optimum solution. in order to obtain the combined optimal solution, one needs to analytically or numerically propagate the state vector epoch by an epoch bas...