In this paper, we develop the theory of so-called nonstandard Gaussian quadrature formulae based on operator values for a general family of linear operators, acting of the space of algebraic polynomials, such that the degrees of polynomials are preserved. Also, we propose a stable numerical algorithm for constructing such quadrature formulae. In particular, for some special classes of linear op...

We propose a concatenated code structure combined with high-order modulations suitable for implementation with iterative decoders operating at gigabit-persecond (Gbps) data rates. The examples considered in this article are serial/parallel concatenations of Hamming and accumulator codes. Performance results are given for binary phase-shift keyed (BPSK) modulation, quadrature phase-shift keyed (...

A 'differential measure' is used to cast our calculus for the group SU (3) into a form similar to Schwinger's boson operator calculus for the group SU (2). It is then applied to compute (i) the inner product between the basis states and (ii) an algebraic formula for the Clebsch-Gordan coefficients. These were obtained earlier by us using Gaussian integration techniques.

Continuing the work started in [Å-I] and [Å-II], we prove the relationship between the Århus integral and the invariant Ω (henceforth called LMO) defined by T.Q.T. Le, J. Murakami and T. Ohtsuki in [LMO]. The basic reason for the relationship is that both constructions afford an interpretation as “integrated holonomies”. In the case of the Århus integral, this interpretation was the basis for e...

We consider polynomials pn(x) that are orthogonal with respect to the oscillatory weight w(x) = e on [−1, 1], where ω > 0 is a real parameter. A first analysis of pn(x) for large values of ω was carried out in [5], in connection with complex Gaussian quadrature rules with uniform good properties in ω. In this contribution we study the existence, asymptotic behavior and asymptotic distribution o...

This paper presents an extension ofWeissinger’s method and its use in analyzingmorphing wings. This method is shown to be ideal for preliminary analyses of these wings due to its speed and adaptability to many disparate wing geometries. It extends Prandtl’s lifting-line theory to planform wings of arbitrary curvature and chord distribution and nonideal airfoil cross sections. The problem formul...

A form of Gauss-Quadrature rule over [0,1] has been investigated that involves the derivative of the integrand at the pre-assigned left or right end node. This situation arises when the underlying polynomials are orthogonal with respect to the weight function (): 1 x x ω = − over [0,1]. Along the lines of Golub's work, the nodes and weights of the quadrature rule are computed from a Jacobi-type...

This paper derives semi-analytical pricing formulae for geometric average options (GAO) within a stochastic volatility framework. Assuming a general mean reverting process for the underlying asset and a square-root process for the volatility, the cross-moment generating function is derived and the cumulative probabilities are recovered using the Gauss-Laguerre quadrature rule. Fixed and floatin...

In analogy to the subject of Gaussian integration formulas we present an overview of some Gaussian summation formulas. The derivation involve polynomials that are orthogonal under discrete inner products and the resulting formulas are useful as a numerical device for summing fairly general series. Several illuminating examples are provided in order to present various aspects of this not very we...

The modified two-stream approximation is derived from the radiative transfer equation using a two-point gaussian quadrature and neglecting terms of order 2 > 3 in the Legendre expansion of the phase function. The results are compared with the Eddington approximation and with exact results for the special cases of perfect absorption, perfect scattering, and a semi-infinite layer with isotropic s...