We obtain constraints on the slope of a universal stellar initial mass function (IMF) over a range of cosmic star-formation histories (SFH) using z ≈ 0.1 luminosity densities in the range from 0.2μm to 2.2μm. The age-IMF degeneracy of integrated spectra of stellar populations can be broken for the Universe as a whole by using direct measurements of (relative) cosmic SFH from high-redshift obser...

While it was noted by R. Hardy and proved in a famous paper by C. A. Micchelli that radial basis function interpolants s(x) = ∑ λjφ(‖x − xj‖) exist uniquely for the multiquadric radial function φ(r) = √ r2 + c2 as soon as the (at least two) centres are pairwise distinct, the error bounds for this interpolation problem always demanded an added constant to s. By using Pontryagin native spaces, we...

A treecode algorithm is presented for the fast evaluation of multiquadric radial basis function (RBF) approximations. The method is a dual approach to one presented by Krasny and Wang, which applies far-field expansions to clusters of RBF centers (source points). The new approach clusters evaluation points instead and is therefore easily able to cope with basis functions that have different mul...

In the 1990’s exponential-type error bounds appeared in the theory of radial basis functions. For multiquadric interpolation it is O(λ 1 d ) as d → 0, where λ is a constant satisfying 0 < λ < 1. For Gaussian interpolation it is O(C d) c′ d as d → 0 where C ′ and c are constants. In both cases the parameter d, called fill distance, measures the spacing of the points where interpolation occurs. T...

In this paper, coupled nonlinear Burgers’ equations are solved through a variety of meshless methods known as multiquadric quasi-interpolation scheme. In this scheme, the extension of univariate quasi-interpolation method is used to approximate the unknown functions and their spatial derivatives and the Taylor series expansion is used to discretize the temporal derivatives. The multiquadric qua...

A previous paper by the authors [FH93] noted that there was a strong tendency to obtain near-repeated knots in their algorithm for least squares approximation of scattered data by multiquadric functions. In this paper we observe that this leads naturally to the inclusion of derivatives of the multiquadric basis function in the approximation, and give an algorithm for accomplishing this. A compa...

We use the results of a new, multi-epoch, multi-wavelength, near-infrared census of the Trapezium Cluster in Orion to construct and to analyze the structure of its infrared (K band) luminosity function. Specifically, we employ an improved set of model luminosity functions to derive this cluster’s underlying Initial Mass Function (IMF) across the entire range of mass from OB stars to sub-stellar...

We derive the expectation value for the maximum stellar mass (mmax) in an ensemble of N stars, as a function of the IMF upper-mass cutoff (mup) and N . We statistically demonstrate that the upper IMF of the local massive star census observed thus far in the Milky Way and Magellanic Clouds clearly exhibits a universal upper mass cutoff around 120− 200 M⊙ for a Salpeter IMF, although the result i...