We analyze the problem facing the team that wins the toss at the deciding fifth set of a volleyball match. The team’s decision to serve or to receive the service can make a difference to the eventual outcome of the match. We characterize the conditions under which it is better to serve or to receive the service at that set. These conditions are obtained by first expressing the exact probability...

In this paper, an effective technique is proposed to determine thenumerical solution of nonlinear Volterra-Fredholm integralequations (VFIEs) which is based on interpolation by the hybrid ofradial basis functions (RBFs) including both inverse multiquadrics(IMQs), hyperbolic secant (Sechs) and strictly positive definitefunctions. Zeros of the shifted Legendre polynomial are used asthe collocatio...

The analyzing power of pp → ppπ 0 reaction has been measured at the beam energy of 390 MeV. The missing mass technique of final protons has been applied to identify the π 0 production event. The dependences of the analyzing power on the pion emission-angle and the relative momentum of the protons have been obtained. The angular dependence could be decomposed by the Legendre polynomial and the r...

Newman polynomials are those with all coefficients in {0, 1}. We consider here the problem of finding Newman polynomials P such that all the coefficients of P 2 are so small as possible for deg P and P (1) given. A set A ⊂ [1, N ] is called a B2[g] sequence if every integer n has at most g distinct representations as n = a1 + a2 with a1, a2 ∈ A and a1 ≤ a2. Gang Yu [4] introduced a new idea to ...

Brightness temperature difference (BTD) values are calculated for selected Geostationary Operational Environmental Satellite (GOES-6) channels (3.9, 12.7 pm) and Advanced Very High Resolution Radiometer channels (3.7, 12.0 pm). Daytime and nighttime discrimination of particle size information is possible given the infrared cloud extinction optical depth and the BTD value. BTD values are present...

Many interesting properties of polynomials are closely related to the geometry of their Newton polytopes. We analyze the coercivity on R of multivariate polynomials f ∈ R[x] in terms of their Newton polytopes. In fact, we introduce the broad class of so-called gem regular polynomials and characterize their coercivity via conditions imposed on the vertex set of their Newton polytopes. These cond...

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 ...