Radial basis function interpolation has attracted a lot of interest in recent years. For popular choices, for example thin plate splines, this problem has a variational formulation, i.e. the interpolant minimizes a semi-norm on a certain space of radial functions. This gives rise to a function space, called the native space. Every function in this space has the property that the semi-norm of an...

This article is a sequel to [M.Z.Z.1] aimed at completing the characterization of the pathwise local structure of solutions of semi-linear stochastic evolution equations (see’s) and stochastic partial differential equations (spde’s) near stationary solutions. The characterization is expressed in terms of the almost sure long-time behavior of trajectories of the equation in relation to the stati...

In Part I of this work we derived a duality theorem for partially finite convex programs, problems for which the standard Slater condition fails almost invariably. Our result depended on a constraint qualification involving the notion of quasi relative interior. The derivation of the primal solution from a dual solution depended on the differentiability of the dual objective function: the diffe...

A Chebyshev or Fourier series may be evaluated on the standard collocation grid by the fast Fourier transform (FFT). Unfortunately, the FFT does not apply when one needs to sum a spectral series at N points which are spaced irregularly. The cost becomes O(N’) operations instead of the FFTs O(N log N). This sort of “off-grid” interpolation is needed by codes which dynamically readjust the grid e...

Model order reduction techniques are known to work reliably for finite-element-type simulations of MEMS devices. These techniques can tremendously shorten computational times for transient and harmonic analysis. However, standard model reduction techniques cannot be applied if the equation system incorporates time-varying matrices or parameters that are to be preserved for the reduced model. Ho...

Specific antibodies to human fetal hemoglobin were prepared and, after conjugation with a fluorescent dye, were used to determine the distribution of Hb F-containing cells in blood smears from normal adults and individuals with hereditary and acquired conditions associated with abnormal levels of Hb F. The mean proportion of F-cells in normal persons was 2.7% +/- 1.4%, with a range of 0.5%-7.0%...

In this paper fuzzy piecewise cubic interpolation is constructed for fuzzy data based on B-spline basis functions. We add two new additional conditions which guarantee uniqueness of fuzzy B-spline interpolation.Other conditions are imposed on the interpolation data to guarantee that the interpolation function to be a well-defined fuzzy function. Finally some examples are given to illustrate the...