The positivity and accuracy properties of the widely used ENO and WENO methods are considered by undertaking an analysis based upon data-bounded polynomial methods. The positivity preserving approach of Berzins based upon data-bounded polynomial interpolants is generalized to arbitrary meshes. This makes it possible to prove positivity conditions for ENO Methods by using a derivation based on s...

The positivity-preserving property is an important and challenging issue for the numerical solution of radiative transfer equations. In the past few decades, different numerical techniques have been proposed to guarantee positivity of the radiative intensity in several schemes, however it is difficult to maintain both high order accuracy and positivity. The discontinuous Galerkin (DG) finite el...

As people get older, they tend to remember more positive than negative information. This age-by-valence interaction has been called "positivity effect." The current study addressed the hypotheses that baseline functional connectivity at rest is predictive of older adults' brain activity when learning emotional information and their positivity effect in memory. Using fMRI, we examined the relati...

It is commonplace to use a 3 3 linear transform to map device RGBs to XYZs. Two particular types of transforms have been developed based on the assumptions that we either maximally ignorant or maximally prescient about the world. Under the maximum ignorance assumption, it is assumed that nothing is known about the spectral statistics of the world and so the best correction transform is the one ...

Over the last million years, human language has emerged and evolved as a fundamental instrument of social communication and semiotic representation. People use language in part to convey emotional information, leading to the central and contingent questions: (1) What is the emotional spectrum of natural language? and (2) Are natural languages neutrally, positively, or negatively biased? Here, w...

Let B be a Borel subset of R and let p(t, x, y) be the transition densities of Brownian motion killed on leaving B. Fix x and y in B. If p(t, x, y) is positive for one t, it is positive for every value of t. Some related results are given. 1. Statement of results. Let d ≥ 2, let B be a Borel subset of R, and let p(t, x, y) denote the transition density of d-dimensional Brownian motion killed on...

In recent years, there has been considerable interest in showing that certain conditions on skew shapes A and B are sufficient for the difference sA − sB of their skew Schur functions to be Schur-positive. We determine necessary conditions for the difference to be Schur-positive. Our conditions are motivated by those of Reiner, Shaw and van Willigenburg that are necessary for sA = sB , and we d...