Abstract We show that the determinant of a Hankel matrix of odd dimension n whose entries are the enumerators of the Jacobi symbols which depend on the row and the column indices vanishes iff n is composite. If the dimension is a prime p, then the determinant evaluates to a polynomial of degree p−1 which is the product of a power of p and the generating polynomial of the partial sums of Legendr...

Finite energy QCD sum rules with Legendre polynomial integration kernels are used to determine the heavy meson decay constant fBc , and revisit fB and fBs . Results exhibit excellent stability in a wide range of values of the integration radius in the complex squared energy plane, and of the order of the Legendre polynomial. Results are fBc = 528 ± 19 MeV, fB = 186 ± 14 MeV, and fBs = 222± 12 M...

In this project we discuss Least Square MonteCarlo methods for valuing American options on bonds. We investigate when we use different base functions, vary the number of base functions and sample paths, how the option price vary. From experiments, we know that we have better choose simple base functions, like Shifted Legendre polynomial; for the balance between time and accuracy issue, we sugge...

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...

We give the explicit time description of four the following problems: dynamics and optimal dynamics for some important electromechanical system, Galerkin approximation for beam equation, computations of Melnikov function for perturbed Hamiltonian systems. All these problems are reduced to the problem of the solving of the systems of diierential equations with polynomial nonlinearities and with ...

The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or' an highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct an uniform exponen...

The aim of this research is an improvement of plant seedling recognition by two new approaches of shape feature generation based on plant silhouettes. Experiments show that the proposed feature sets possess value in plant recognition when compared with other feature sets. Both methods approximate a distance distribution of an object, either by resampling or by approximation of the distribution ...

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...

We continue to investigate binary sequence (fu) over {0, 1} defined by (−1)fu = ( (u−u)/p p ) for integers u ≥ 0, where ( · p ) is the Legendre symbol and we restrict ( 0 p ) = 1. In an earlier work, the linear complexity of (fu) was determined for w = p − 1 under the assumption of 2p−1 6≡ 1 (mod p2). In this work, we give possible values on the linear complexity of (fu) for all 1 ≤ w < p− 1 un...

An efficient Spectral Collocation method based on the shifted Legendre polynomials was applied to get solution of heat transfer of a micropolar fluid through a porous medium with radiation. A similarity transformation is applied to convert the governing equations to a system of nonlinear ordinary differential equations. Then, the shifted Legendre polynomials and their operational matrix of deri...