Algorithms for optimal area triangulations of a convex polygon

Given a convex polygon with n vertices in the plane, we are interested in triangulations of its interior, i.e., maximal sets of non-intersecting diagonals that subdivide the interior of the polygon into triangles. The MaxMin area triangulation is the triangulation of the polygon that maximizes the area of the smallest triangle in the triangulation. Similarly, the MinMax area triangulation is the triangulation that minimizes the area of the largest area triangle in the triangulation. We present algorithms that construct MaxMin and MinMax area triangulations of a convex polygon in O(n²logn) time and O(n²) space. The algorithms use dynamic programming and a number of geometric properties that are established within the paper.     

φ meson production in NA60

NA60 is a fixed-target experiment at the CERN SPS which measured dimuon production in nucleus–nucleus and proton–nucleus collisions. The experiment collected muon pair samples of unprecedented quality in heavy-ion experiments. This paper presents a high quality measurement of the p_T distribution of the φ meson, covering a broad p_T window. The data were collected in 2003 in In-In collisions at 158 GeV per nucleon. The results, presented as a function of centrality, were studied against several possible sources of systematic effects and proved to be fairly stable. We show that the inverse m_T slope measured in In-In collisions, in the φ→μμ decay channel, depends significantly on the range used to perform the fit. When the fit is performed at low transverse momentum, the effective inverse slope increases from peripheral to central collisions, as measured by other experiments. We finally show that our measurement for In-In is compatible with the overall systematics of T slope versus mass, measured in different collision systems by the NA49 experiment PACS 25.75.Nq; 25.75.-q; 25.75.Dw; 14.40.Cs; 12.38.Mh     

Understanding the loading dependence of self-diffusion in carbon nanotubes

The influence of flexible walls on the self-diffusion of CH4 in an isolated single walled carbon nanotube, as an example, is studied by molecular dynamics simulations. By simulating the carbon nanotube as a flexible framework we demonstrate that the flexibility has a crucial influence on self-diffusion at low loadings. We show how this influence can be incorporated in a simulation of a rigid nanotube by using a Lowe-Andersen thermostat which works on interface-fluid collisions. The reproduction of the results of a flexible carbon nanotube by a rigid nanotube simulation is excellent.     

Dichlorocarbene Addition to

In contrast to the terminal phosphinidene complex PhPW(CO)(5) (2), which adds to [5]metacyclophane (1) in a 1,4-fashion, dichlorocarbene preferentially adds in a 1,2-fashion to the formal "anti-Bredt" type double bond of the aromatic ring of 1 to afford the norcaradiene 11b, which immediately rearranges to the bridged cycloheptatriene 12b and further by a [1,5] sigmatropic chlorine migration to the isomeric 13b as the first observable product. More slowly, the latter isomerizes via a dissociative mechanism to give 15b. A computational study supports the notion that the [1,5] chlorine migration in the rearrangement 12b --> 13b, for which an activation barrier of 70.2 kJ mol(-)(1) was calculated, is essentially concerted with minor charge separation. In contrast, the analogous [1,5] chlorine migration in the flat model compound 7,7-dichlorocycloheptatriene (12a) displays features of a dissociative pathway.     

On the evaluation of elasto-plastic strains measured with strain gages

The analysis of plane-stress conditions using strain gages is feasible even when the deformations of the materials are in the elasto-plastic range. The calculation of stresses from the measured strain values is based on an analysis which requires knowledge of the stress-strain curve of the material as obtained from a uniaxial tensile test. In this paper, the practical procedure of such an analysis is described together with the application of a nomograph to allow a simplified evaluation to be made of the results of measurements. A numerical example is also given.     

Selektive spektralphotometrische Uranbestimmung

A simple, versatile spectrophotometric uranium determination was developed, which is not disturbed by over 60 cations and about 20 anions investigated. A separation with triphenylarsinoxide is first performed. The uranium extracted is then transferred by a simple method to the 8-hydroxyquinoline-complex and measured spectrophotometrically. Larger quantities of uranium can be directly measured in the extract. Further experiments with other reagents as a substitute for 8-hydroxyquinoline are described.