Toward the Jamming Threshold of Sphere Packings: Tunneled Crystals

We have discovered a new family of three-dimensional crystal sphere packings that are strictly jammed (i.e., mechanically stable) and yet possess an anomalously low density. This family constitutes an uncountably infinite number of crystal packings that are subpackings of the densest crystal packings and are characterized by a high concentration of self-avoiding "tunnels" (chains of vacancies) that permeate the structures. The fundamental geometric characteristics of these tunneled crystals command interest in their own right and are described here in some detail. These include the lattice vectors (that specify the packing configurations), coordination structure, Voronoi cells, and density fluctuations. The tunneled crystals are not only candidate structures for achieving the jamming threshold (lowest-density rigid packing), but may have substantially broader significance for condensed matter physics and materials science.Comment: 19 pages, 5 figure

Does the Supreme Court Follow the Economic Returns? A Response to A Macrotheory of the Court

Today, there is a widespread idea that parents need to learn how to carry out their roles as parents. Practices of parental learning operate throughout society. This article deals with one particular practice of parental learning, namely nanny TV, and the way in which ideal parents are constructed through such programmes. The point of departure is SOS family, a series broadcast on Swedish television in 2008. Proceeding from the theorising of governmentality developed in the wake of the work of Michel Foucault, we analyse the parental ideals conveyed in the series, as an example of the way parents are constituted as subjects in the ‘advanced liberal society’ of today. The ideal parent is a subject who, guided by the coach, is constantly endeavouring to achieve a makeover. The objective of this endeavour, however, is self-control, whereby the parents will in the end become their own coaches.

Vowel harmony in the Volga–Kama region: an areal phenomenon?

Vowel harmony is typical for the languages of the Volga–Kama area. As both Turkic and Uralic proto-languages exhibited vowel harmony, we could suggest that the existence of vowel harmony in the area follows from the historical heritage and is a mere coincidence. However, we know that at least some of the vowel harmonies do not originate from the proto-languages, but are new phenomena. In these cases, we cannot exclude that the development of these new harmonies was influenced by another language. Гармония гласных типичная для языков Волго-Камского ареала. Хотя гармония гласных и в тюрском, и в уральском праязыкам существовала, и по этому можно думать что существование этого явления языковые наследие и просто случайность, знаем, что по крайнем мере некоторые типы гармонии гласных не происходят из праязыков, а новые феномены. В последних случаях мы не можем исключять, что появление этих гармоний не произошло без влиянии других языков

Equidistribution of the Fekete points on the sphere

The Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of the Fekete points in the sphere. The way we proceed is by showing their connection with other array of points, the Marcinkiewicz-Zygmund arrays and the interpolating arrays, that have been studied recently

Symmetry induced by economy

AbstractVarious extremum problems are presented which lead to highly symmetric geometrical configurations

Equidistribution of the Fekete points on the sphere

The Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of the Fekete points in the sphere. The way we proceed is by showing their connection with other array of points, the Marcinkiewicz-Zygmund arrays and the interpolating arrays, that have been studied recently

Dense Packings of Congruent Circles in Rectangles with a Variable Aspect Ratio

We use computational experiments to find the rectangles of minimum area into which a given number n of non-overlapping congruent circles can be packed. No assumption is made on the shape of the rectangles. Most of the packings found have the usual regular square or hexagonal pattern. However, for 1495 values of n in the tested range n =< 5000, specifically, for n = 49, 61, 79, 97, 107,... 4999, we prove that the optimum cannot possibly be achieved by such regular arrangements. The evidence suggests that the limiting height-to-width ratio of rectangles containing an optimal hexagonal packing of circles tends to 2-sqrt(3) as n tends to infinity, if the limit exists.Comment: 21 pages, 13 figure

Gallstone Ileus, Bouveret's Syndrome and Choledocholithiasis in a Patient with Billroth II Gastrectomy – A Case Report of Combined Endoscopic and Surgical Therapy

Intestinal obstruction due to gallstone is a rare, but quite severe gastrointestinal disorder, which always requires a rapid and correct diagnosis to achieve optimal therapy. Digestive endoscopy is an important method to determine the level of the bowel obstruction and to plan an optimal therapeutic strategy. Our present case demonstrates that in a high-risk patient, a combined endoscopic and surgical therapy is the best choice to solve the obstruction of the colon, of the stomach and of the common bile duct caused by multiple gallstones

The strong thirteen spheres problem

The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag