where the kernel K(x, y) is strictly cyclic variation diminishing, and related problems including periodic generalized perfect splines. For various approximation problems of this type, we show the uniqueness of the best approximation and characterize the best approximation by extremal properties of the error function. The results are proved by using a characterization of best approximants from ...

A dire need for additional dental educators is emerging. This article reflects on the heavily skewed age groups of our current dental educators and the lack of sufficient new faculty to undertake the tasks of faculty members. A literature review is presented of previous studies monitoring the current demographics of dental faculty, projected trends, and factors that influence an individual's ca...

The lower average correlations among mental tests in groups of individuals of above-average IQ than is found in groups of individuals of below-average IQ implies a smaller general factor, or g, in the higherIQ group, a phenomenon Spearman called the ‘Law of Diminishing Returns’. This phenomenon was confirmed in six independent data sets based on three different test batteries. It implies that p...

In this paper we further explore a class of high order TVD (total variation diminishing) Runge-Kutta time discretization initialized in a paper by Shu and Osher, suitable for solving hyperbolic conservation laws with stable spatial discretizations. We illustrate with numerical examples that non-TVD but linearly stable Runge-Kutta time discretization can generate oscillations even for TVD (total...

We investigate the task switching problem of a robot maximizing its long-term average rate of return on work performed. We propose an online method to maximize the average gain rate based on only past experience. For that we alter the formulation from optimal foraging theory and recursively include estimates of global task qualities. We demonstrate and analyze our method on a puck-foraging exam...

For the high order numerical approximation of hyperbolic systems of conservation laws, we propose to use as a building principle an entropy diminishing criterion instead of the familiar total variation diminishing criterion introduced by Harten for scalar equations. Based on this new criterion, we derive entropy diminishing projections that ensure, both, the second order of accuracy and all of ...