We prove that there are at most finitely many complex λ = 0, 1 such that two points on the Legendre elliptic curve Y2 = X(X − 1)(X − λ) with coordinates X = 2, 3 both have finite order. This is a very special case of some conjectures on unlikely intersections in semiabelian schemes.

Random regression test-day models using Legendre polynomials are commonly used for the estimation of genetic parameters and genetic evaluation for test-day milk production traits. However, some researchers have reported that these models present some undesirable properties such as the overestimation of variances at the edges of lactation. Describing genetic variation of saturated fatty acids ex...

This study generalizes the cross product defined in 3-dimensional almost contact metric manifolds and describes a new generalized for n=1 (2n+s)-dimensional framed manifolds. Moreover, it studies some of proposed product’s basic properties. It also performs characterizations curvature Legendre curve on an S-manifold calculates curve. Furthermore, shows that curves are biharmonic curves. Next, t...

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...

Everybody knows from school how to solve a quadratic equation of the form $x^2-px+q=0$ graphically. But this method can become tedious if several equations ought be solved, as for each pair $(p,q)$ new parabola has drawn. Stunningly, there is one single curve that used every via drawing tangent lines through given point curve. In article we derive in an elementary way and generalize it $x^n-p...

The celebrated Expected Shortfall (ES) optimization formula implies that ES at a fixed probability level is the minimum of linear real function plus scaled mean excess function. We establish reverse formula, which says any threshold maximum an curve minus Despite being simple result, this reveals elegant symmetries between and curve, as well their optimizers. closely related to Fenchel-Legendre...

The objective was to evaluate 6 different lactation curve models for daily water and dry matter intake. Data originated from the Futterkamp dairy research farm of the Chamber of Agriculture of Schleswig-Holstein in Germany. A data set of about 23,000 observations from 193 Holstein cows was used. Average daily water and dry matter intake were 82.3 and 19.8 kg, respectively. The basic linear mixe...

Variance components of the covariance function coefficients in a random regression test-day model were estimated by Legendre polynomials up to a fifth order for first-parity records of Dutch dairy cows using Gibbs sampling. Two Legendre polynomials of equal order were used to model the random part of the lactation curve, one for the genetic component and one for permanent environment. Test-day ...

In this study test-day records of milk (kg), fat (g), and protein (g) yields, somatic cell score (SCS, cells/ML) collected by Animal Breeding Center of Iran during 2007 and 2009 were used to estimate genetic parameters using random regression model. Models with different order of Legendre polynomials were compared using Bayesian information criterion (BIC).For milk, fat yield and SCS genetic an...