For a graph G we denote by dG(u, v) the distance between vertices u and v in G, by dG(u) the degree of vertex u. The Hosoya polynomial of G is H(G) = ∑ {u,v}⊆V (G) x dG (u,v). For any positive numbers m and n, the partial Hosoya polynomials of G are Hm(G) = ∑ {u, v} ⊆ V (G) dG (u) = dG (v) = m xdG (u,v), Hmn(G) = ∑ {u, v} ⊆ V (G) dG (u) = m, dG (v) = n xdG (u,v). It has been shown that H(G1) − ...

In this article, we discuss a parallel implementation of efficient algorithms for computation of Legendre polynomial transforms and other orthogonal polynomial transforms. We develop an approach to the Driscoll–Healy algorithm using polynomial arithmetic and present experimental results on the accuracy, efficiency, and scalability of our implementation. The algorithms were implemented in ANSI C...

X iv :1 00 8. 50 35 v1 [ m at h. N T ] 3 0 A ug 2 01 0 RECOVERING FOURIER COEFFICIENTS OF MODULAR FORMS AND FACTORING OF INTEGERS Sergei N. Preobrazhenskĭi It is shown that if a function defined on the segment [−1, 1] has sufficiently good approximation by partial sums of the Legendre polynomial expansion, then, given the function’s Fourier coefficients cn for some subset of n ∈ [n1, n2], one c...

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 ...

This paper discusses about the solution of fuzzy Volterra integral equation of first-kind (F-VIE1) using spectral method. The parametric form of fuzzy driving term is applied for F-VIE1, then three classifications for (F-VIE1) are searched to solve them. These classifications are considered based on the interval sign of the kernel. The Gauss-Legendre points and Legendre weights for arithmetics ...

We analyzed 75,555 test-day milk flow records from 2175 primiparous Holstein cows that calved between 1997 and 2005. Milk flow was obtained by dividing the mean milk yield (kg) of the 3 daily milking by the total milking time (min) and was expressed as kg/min. Milk flow was grouped into 43 weekly classes. The analyses were performed using a single-trait Random Regression Models that included di...

Random regression models (RRM) have become common for the analysis of longitudinal data or repeated records on individual over time. The goal of this paper was to explore the use of random regression models with orthogonal / Legendre polynomials (RRL) to analyze new repeated measures called clutch size (CS) as a meristic trait for Iranian native fowl. Legendre polynomial functions of increasing...

Graphical inspection of multimodality is demonstrated using unsupervised lateral-inhibition neural networks. Three projection pursuit indices are compared on low dimensional simulated and real-world data: principal components 22], Legendre polynomial 6] and projection pursuit network 16].

urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. the main objective of this paper is to solve the urysohn type fredholm integral equation. to do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known legendre polynomials instead of the known function. after discretization of the problem o...