The main focus of this paper is on efficiency analysis of two kinds of approximating functions (characteristic orthogonal polynomials and characteristic beam functions) that have been applied in the Rayleigh-Ritz method to determine the non-dimensional buckling and frequency parameters of an angle ply symmetric laminated composite plate with fully elastic boundaries. It has been observed that o...

in this study, the problem of determining an optimal trajectory of a nonlinear injection into orbit problem with minimum time was investigated. the method was based on orthogonal polynomial approximation. this method consists of reducing the optimal control problem to a system of algebraic equations by expanding the state and control vector as chebyshev or legendre polynomials with undetermined...

In the last decade, Daubechies’ wavelets have been successfully used in many signal processing paradigms. The construction of these wavelets via two channel perfect reconstruction filter bank requires the identification of necessary conditions that the coefficients of the filters and the roots of binomial polynomials associated with them should exhibit. In this paper, orthogonal and Biorthogona...

In this paper, a new method is presented to estimate the 3D pose of facial image based on statistical Gaussian error models. The basic idea is that the pose angle can be computed by the orthogonal projection computation if the specific 3D shape vector of the given person is known. In our algorithm, Gaussian probability density function is used to model the distributions of the 3D shape vector a...

In this paper we propose a method for conducting stochastic collocation on arbitrary sets of nodes. To accomplish this, we present the framework of least orthogonal interpolation, which allows one to construct interpolation polynomials based on arbitrarily located grids in arbitrary dimensions. These interpolation polynomials are constructed as a subspace of the family of orthogonal polynomials...

Abstract: This paper carries out an investigation of the orthogonal-polynomial approach to reshaping symmetric distributions to fit in with data requirements so as to cover the multivariate case. With this objective in mind, reference is made to the class of spherical distributions, given that they provide a natural multivariate generalization of univariate even densities. After showing how to ...

In this paper we study the asymptotic behavior of a family of polynomials which are orthogonal with respect to an exponential weight on certain contours of the complex plane. The zeros of these polynomials are the nodes for complex Gaussian quadrature of an oscillatory integral on the real axis with a high order stationary point, and their limit distribution is also analyzed. We show that the z...

Orthogonal arrays are found on plasma membranes of glial cells, in the central nervous system, on muscle plasma membranes at neuromuscular junctions, and on a variety of epithelial cells. These structures have been correlated with ion flux. With the aid of freeze fracture technique, orthogonal particle arrays were found on plasma membranes on airway epithelial cells of rats and hamsters. They h...

The Gaussian mixture modeling (GMM) techniques are increasingly being used for both speaker identification and verification. Most of these models assume diagonal covariance matrices. Although empirically any distribution can be approximated with a diagonal GMM, a large number of mixture components are usually needed to obtain a good approximation. A consequence of using a large GMM is that its ...

Analogous to time signals that can be composed of multiple frequency functions, we use uniquely structured orthogonal spatial modes to create different beam shapes. We tailor the spatial structure by judiciously choosing a weighted combination of multiple modal states within an orthogonal orbital angular momentum (OAM) basis set, creating desired beam intensity "shapes." The weights of the OAM ...