Variace / covariance components of 227118 first lactaiom test-day milk yield records belonged to 31258 Iranian Holstein cows were estimated using nine random regression models. Afterwards, different measures of persistency based on estimation breeding value were evaluated. Three functions were used to adjust fixed lactation curve: Ali and Schaeffer (AS), quadratic (LE3) and cubic (LE4) order of...

We have studied the shadows of a Schwarzschild black hole under special polar gravitational perturbation, which is particular solution Einstein equations expanded up to first order. It shown that shadow changes periodically with time and change depends on Legendre polynomial order parameter l frequency {\sigma} wave. For odd polynomial, center oscillates along direction vertical equatorial plan...

A total of 20,065 weights recorded on 3016 Nelore animals were used to estimate covariance functions for growth from birth to 630 days of age, assuming a parametric correlation structure to model within-animal correlations. The model of analysis included fixed effects of contemporary groups and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orth...

We consider the problem of recovering a hidden monic polynomial f(X) of degree d ≥ 1 over a finite field Fp of p elements given a black box which, for any x ∈ Fp, evaluates the quadratic character of f(x). We design a classical algorithm of complexity O(d2pd+ε) and also show that the quantum query complexity of this problem is O(d). Some of our results extend those of Wim van Dam, Sean Hallgren...

We compare the convergence behavior of best polynomial approximations and Legendre Chebyshev projections derive optimal rates for analytic differentiable functions in maximum norm. For functions, we show that approximation degree n is better than projection same by a factor $$n^{1/2}$$ . such as piecewise fractional smoothness, however, only some constant factors. Our results provide new insig...

We determine the infinite sequences (ak) of integers that can be generated by polynomials with integral coefficients, in the sense that for each finite initial segment of length n there is an integral polynomial fn(x) of degree < n such that ak = fn(k) for k = 0, 1, . . . , n − 1. Let P be the set of such sequences and Π the additive group of all infinite sequences of integers. Then P is a subg...

Abstract We prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits DG approximation constructed from polynomial basis functions and integrals are approximated with high-order accurate Legendre–Gauss–Lobatto quadrature. theoretical discussion re-contextualizes stable results finite difference into setting. Numerical tests verify...

In this paper, we extend the operational matrix method to solve tempered fractional differential equation, via shifted Legendre polynomial. Although is widely used in solving various calculus problems, it yet apply equations defined derivatives. We first derive analytical expression for derivative x p</...

For a polynomial f(T ) ∈ Z[T ], the frequency with which the values f(n) are prime has been considered since at least the 18-th century. Euler observed, in a letter to Goldbach in 1752, that the sequence n + 1 has many prime values for 1 ≤ n ≤ 1500. Legendre assumed an arithmetic progression an+ b with (a, b) = 1 contains infinitely many primes in his work on the quadratic reciprocity law. Ther...