The stochastic compressible Navier-Stokes system on the whole space and some singular limits

Firstly, we show the existence of at least one non-trivial solution to the stochastically forced compressible Navier–Stokes system defined on the whole Euclidean space. This solution is deterministically weak in the usual sense of distributions but also weak in the sense of probability, the latter meaning that the underlying probability space, as well as the stochastic driving force, are also unknowns. Secondly, we study various asymptotic results for the above mentioned system when the microscopic time and space variables are rescaled appropriately. Different rescaling leads to various singular versions of this system with coefficients which either blow up or dissipate when they are made small. Subsequently, we are able to show that any family of the solutions constructed above parametrised by the singular coefficients converges to solutions of other fluid dynamic models like the incompressible Navier–Stokes system and the compressible Euler system with corresponding stochastic forcing terms. Crucially, we also consider the case when rotation in the fluid is taken into account

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

NASA thesaurus. Volume 1: Hierarchical Listing

There are over 17,000 postable terms and nearly 4,000 nonpostable terms approved for use in the NASA scientific and technical information system in the Hierarchical Listing of the NASA Thesaurus. The generic structure is presented for many terms. The broader term and narrower term relationships are shown in an indented fashion that illustrates the generic structure better than the more widely used BT and NT listings. Related terms are generously applied, thus enhancing the usefulness of the Hierarchical Listing. Greater access to the Hierarchical Listing may be achieved with the collateral use of Volume 2 - Access Vocabulary and Volume 3 - Definitions

NASA thesaurus. Volume 2: Access vocabulary

The Access Vocabulary, which is essentially a permuted index, provides access to any word or number in authorized postable and nonpostable terms. Additional entries include postable and nonpostable terms, other word entries, and pseudo-multiword terms that are permutations of words that contain words within words. The Access Vocabulary contains 40,738 entries that give increased access to the hierarchies in Volume 1 - Hierarchical Listing

NASA thesaurus. Volume 2: Access vocabulary

The access vocabulary, which is essentially a permuted index, provides access to any word or number in authorized postable and nonpostable terms. Additional entries include postable and nonpostable terms, other word entries and pseudo-multiword terms that are permutations of words that contain words within words. The access vocabulary contains almost 42,000 entries that give increased access to the hierarchies in Volume 1 - Hierarchical Listing