On the Areas of Cyclic and Semicyclic Polygons

We investigate the ``generalized Heron polynomial'' that relates the squared area of an n-gon inscribed in a circle to the squares of its side lengths. For a (2m+1)-gon or (2m+2)-gon, we express it as the defining polynomial of a certain variety derived from the variety of binary (2m-1)-forms having m-1 double roots. Thus we obtain explicit formulas for the areas of cyclic heptagons and octagons, and illuminate some mysterious features of Robbins' formulas for the areas of cyclic pentagons and hexagons. We also introduce a companion family of polynomials that relate the squared area of an n-gon inscribed in a circle, one of whose sides is a diameter, to the squared lengths of the other sides. By similar algebraic techniques we obtain explicit formulas for these polynomials for all n <= 7.Comment: 22 page

Вибір способу управлінських дій за вузькофункціональним вартісним критерієм в управлінні економічною безпекою підприємства

Метою дослідження є розробка логічної схеми вибору способу управлінських дій в управлінні економічною безпекою підприємства на основі поєднання ідеології ризик-менеджменту та вузькофункціонального підходу в управлінні економічною безпекою підприємства

Contamination of spacecraft by recontact of dumped liquids

Liquids partially freeze when dumped from spacecraft producing particles which are released into free space at various velocities. Recontact of these particles with the spacecraft is possible for specific particle sizes and velocities and, therefore, can become contamination for experiments within the spacecraft or released experiments as a result of waste and potable water dumped from Space Shuttle. An examination of dump characteristics was conducted on STS-29 using both on-board video records and ground based measurements. A preliminary analysis of data from this flight indicates particle velocities are in the range of 30 to 75 ft/sec and recontact is possible for limited particle sizes

Inferring Species Trees Directly from Biallelic Genetic Markers: Bypassing Gene Trees in a Full Coalescent Analysis

The multi-species coalescent provides an elegant theoretical framework for estimating species trees and species demographics from genetic markers. Practical applications of the multi-species coalescent model are, however, limited by the need to integrate or sample over all gene trees possible for each genetic marker. Here we describe a polynomial-time algorithm that computes the likelihood of a species tree directly from the markers under a finite-sites model of mutation, effectively integrating over all possible gene trees. The method applies to independent (unlinked) biallelic markers such as well-spaced single nucleotide polymorphisms (SNPs), and we have implemented it in SNAPP, a Markov chain Monte-Carlo sampler for inferring species trees, divergence dates, and population sizes. We report results from simulation experiments and from an analysis of 1997 amplified fragment length polymorphism (AFLP) loci in 69 individuals sampled from six species of {\em Ourisia} (New Zealand native foxglove)

The late Holocene palaeoenvironment in the lake Njupi area, west Cameroon : implications regarding the history of lake Nyos

Le lac Njupi, au sein de la ligne volcanique du Cameroun, s'est constitué par barrage d'une dépression à 1 km à l'est du lac Nyos. Les deux sondages du lac Nyos analysés ont traversé les sédiments déposés au marges du lac. Les dépôts les plus anciens sont datés à 3400 BP, cet âge est proposé comme un minimum pour l'apparition du lac Njupi. Des études sédimentologiques, palynologiques et géochimiques d'une coupe de 2 m permettent de reconstituer l'histoire fini-holocène de cet environnement. Il s'agit d'un dépôt tourbeux (plus de 30% de carbone organique) avec une importante fraction de spicules silicieux de Spongiaires. La sédimentation a été relativement régulière, entrecoupée seulement durant les 800 ans du dépôt, de cinq lamines plus grossières caractérisées par des grains de quartz et de gros débris ligneux. Ces flux sont soulignés par des concentrations de carbohydrates ou parfois par des composés phénoliques bien conservés. Cette étude confirme et précise l'existence d'une phase aride qui s'intensifie ici entre 2500 et 2000 ans BP. Cette crise climatique qui a débuté vers 3000 ans BP est, en fait, très générale dans l'Afrique centrale Atlantique (sud Cameroun). Le lac Njupi, situé aujourd'hui dans un paysage essentiellement composé de savanes d'où sa dénomination de "Grass Fields", permet d'observer avant 2500 ans BP un paysage mixte de forêts et savane en mosaïque, puis son évolution vers une savane avec quelques îlots forestiers, couvert défini alors par 75% à 85% de pollens herbacés. La végétation montagnarde, caractérisée par #Podocarpus et #Olea capensis, régresse vers 2300 ans BP, au moment où #Elaeis guineensis$ (le Palmier à Huile) initie son expansion, d'abord comme un arbre pionnier, offrant ainsi ultérieurement à l'Homme l'opportunité de sa culture. (Résumé d'auteur

Angular dependent vortex pinning mechanisms in YBCO coated conductors and thin films

We present a comparative study of the angular dependent critical current density in YBa2Cu3O7 films deposited on IBAD MgO and on single crystal MgO and SrTiO3 substrates. We identify three angular regimes where pinning is dominated by different types of correlated and uncorrelated defects. We show that those regimes are present in all cases, indicating that the pinning mechanisms are the same, but their extension and characteristics are sample dependent, reflecting the quantitative differences in texture and defect density. In particular, the more defective nature of the films on IBAD turns into an advantage as it results in stronger vortex pinning, demonstrating that the critical current density of the films on single crystals is not an upper limit for the performance of the IBAD coated conductors.Comment: 14 pages, 3 figures. Submitted to AP