In this paper, we consider the extrapolation method for second order elliptic problems on general meshes and derive a type of finite element expansion which is dependent of the triangulation. It allows to prove the effectiveness of the extrapolation on general meshes and also validates the extrapolation method can be applied on the automatically produced meshes of the general computing domains....

Given a truncated portion of a band-limited image with known x and y bandwidths, the extrapolation problem is to determine the signal over all x and y. An iterative extrapolation algorithm, recently proposed by Gerchberg, requires only the repeated operations of Fourier transformation and truncation. A coherent optical processor is presented that implements Gerchberg's iterative extrapolation a...

Introduction: The ability of quadratic dose protocol to maintain a good quality image for an overweight and obese patient is well reported. However, a practical approach to the implementation of this protocol in whole-body imaging in Malaysia is currently lacking. Hence, the aim of this study is to derive the quadratic dose formula that suits our PET system. Metho...

In this paper, we study the problem of minimizing the ratio of two quadratic functions subject to a quadratic constraint. First we introduce a parametric equivalent of the problem. Then a bisection and a generalized Newton-based method algorithms are presented to solve it. In order to solve the quadratically constrained quadratic minimization problem within both algorithms, a semidefinite optim...

We discuss the interpolation strategies related to Richardson extrapolation and repeated Richardson extrapolation. We emphasize that, in most computations, the interest is in obtaining accurate solution on the current computational grid, not that on the coarse level grids on which the extrapolated solutions reside. We tackle the interpolation issue that has largely been overlooked in Richardson...

Riemannian wavefield extrapolation is a technique for one-way extrapolation of acoustic waves. Riemannian wavefield extrapolation generalizes wavefield extrapolation by downward continuation by considering coordinate systems different from conventional Cartesian ones. Coordinate systems can conform with the extrapolated wavefield, with the velocity model or with the acquisition geometry. When c...

CONTEXT An estimated correlation between 2 variables is valid only within the range of observed data. Extrapolation is risky and should be performed with caution. METHODS To assess the prevalence of problems with data extrapolation in the medical literature, all articles published from January through June 2000 in BMJ, JAMA, The Lancet, and The New England Journal of Medicine (NEJM) were revi...

an alumina supported co/ni catalyst was prepared by sol-gel procedure to study the catalytic behavior during fischer-tropsch synthesis in a fixed-bed reactor. the effect of co conversion (10-50%) on hydrocarbon product distribution (ch4, c5+ and c2-c4 olefin selectivities) was studied. selectivity for ch4 decreased, while those of c5+ and olefin selectivities increased with increasing co conver...

In this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-Archimedean number with $alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $alpha$-functional equation (0.1) in non-Archimedean Banach spaces.

We construct a class of codes of length such that the minimum distance outside of a certain subcode is, up to a constant factor, bounded below by the square root of , a well-known property of quadratic residue codes. The construction, using the group algebra of an Abelian group and a special partition or splitting of the group, yields quadratic residue codes, duadic codes, and their generalizat...