For {φ_n(x)}, x ε [0,1] an orthonormalsystem of uniformly bounded functions, ||φ_n||_{∞}≤ M

We reconsider some families of orthogonal polynomials, within the framework of the so called monomiality principle. We show that the associated operational formalism allows the framing of the polynomial orthogonality using an algebraic point of view. Within such a framework, we introduce families of pseudo-orthogonal polynomials, namely polynomials, not orthogonal under the ordinary definition,...

To investigate the material removal characteristic of paste polishing, experimental investigations based on Taguchi method have been carried out. In the experiments, the dwell time was fixed 300 seconds and the bonnet position was 4. The four variable factors (precess angles, head speed, head pressure and tool offset) with 3 levels were chosen to design the orthogonal array. With the designed o...

Abstract Let H be a graph on n vertices and G a collection of n subgraphs of H, one for each vertex. Then G is an orthogonal double cover (ODC) of H if every edge of H occurs in exactly two members of G and any two members of G share exactly an edge whenever the corresponding vertices are adjacent in H. If all subgraphs in G are isomorphic to a given spanning subgraph G, then G is said to be an...

In this paper we calibrate the stationary Gaussian Musiela model to time series of market data using the Karhunen-Loeve expansion in order to get an ortonormal basis (classically known as EOF, empirical orthonormal functions) in a separable Hilbert space. The basis found is optimal for representing the covariance of the invariant measure of the forward rates’ process.

Non-orthogonal wavelet expansions associated with a class of mother wavelets is considered. This class of wavelets comprises mother wavelets that are not necessarily integrable over the whole real line, such as Shannon’s wavelet. The pointwise convergence of these wavelet expansions is investigated. It is shown that, unlike other wavelet expansions, the ones under consideration do not necessari...

This Article is brought to you for free and open access by the Center for Coastal Physical Oceanography at ODU Digital Commons. It has been accepted for inclusion in CCPO Publications by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. Repository Citation Oey, Lie-Yauw; Ezer, Tal; and Sturges, Wilton, "Modeled and Observed Empirica...

In this paper, we develop the theory of the wavelet transform over Galois elds. To avoid the limitations inherent in the number theoretic Fourier transform over nite elds, our wavelet transform relies on a basis decomposition in the time domain rather than in the frequency domain. First, we characterize the in nite dimensional vector spaces for which an orthonormal basis expansion of any sequen...

In this study wavelet based high-order Taylor Galerkin methods is introduced. Additional time layers are used to obtain high-order temporal accuracy unattainable within a two-step strategy. Two explicit model schemes are constructed and asymptotic stability of schemes are verified. The compactly supported orthogonal wavelet bases developed by Daubechies are used in Galerkin scheme. The behavior...

The Chebyshev orthogonal collocation is a powerful and accurate numerical technique, which is also relatively easy to implement using modern mathematical software (e.g., MATHEMATICA and MATLAB). This technique allows the elucidation of engineering problems involving partial differentials equations or boundary value problems. Six chemical engineering problems concerning the transfer of momentum,...