Classifying Four-Body Convex Central Configurations

We classify the full set of convex central configurations in the Newtonian four-body problem. Particular attention is given to configurations possessing some type of symmetry or defining geometric property. Special cases considered include kite, trapezoidal, co-circular, equidiagonal, orthodiagonal, and bisecting-diagonal configurations. Good coordinates for describing the set are established. We use them to prove that the set of four-body convex central configurations with positive masses is three-dimensional, a graph over a domain $D$ that is the union of elementary regions in $\mathbb{R}^{+^3}$.Comment: 28 pages, 14 figure

Double-Antiprism Central Configurations of the 3n-Body Problem

Abstract In this paper we study numerically a new type of central configurations of the 3n-body problem with equal masses which consist of three n-gons contained in three planes z = 0 and z = ±β = 0. The n-gon on z = 0 is scaled by a factor α and it is rotated by an angle of π/n with respect to the ones on z = ±β. In this kind of configurations, the masses on the planes z = 0 and z = β are at the vertices of an antiprism with bases of different size. The same occurs with the masses on z = 0 and z = −β. We call this kind of central configurations double-antiprism central configurations. We will show the existence of central configurations of this type

Symmetry, bifurcation and stacking of the central configurations of the planar 1+4 body problem

In this work we are interested in the central configurations of the planar 1+4 body problem where the satellites have different infinitesimal masses and two of them are diametrically opposite in a circle. We can think this problem as a stacked central configuration too. We show that the configuration are necessarily symmetric and the other sattelites has the same mass. Moreover we proved that the number of central configuration in this case is in general one, two or three and in the special case where the satellites diametrically opposite have the same mass we proved that the number of central configuration is one or two saying the exact value of the ratio of the masses that provides this bifurcation.Comment: 9 pages, 2 figures. arXiv admin note: text overlap with arXiv:1103.627

WAIS-III and WMS-III performance in chronic Lyme disease

There is controversy regarding the nature and degree of intellectual and memory deficits in chronic Lyme disease. In this study, 81 participants with rigorously diagnosed chronic Lyme disease were administered the newest revisions of the Wechsler Adult Intelligence Scale (WAIS-III) and Wechsler Memory Scale (WMS-III), and compared to 39 nonpatients. On the WAIS-III, Lyme disease participants had poorer Full Scale and Performance IQ's. At the subtest level, differences were restricted to Information and the Processing Speed subtests. On the WMS-III, Lyme disease participants performed more poorly on Auditory Immediate, Immediate, Auditory Delayed, Auditory Recognition Delayed, and General Memory indices. Among WMS-III subtests, however, differences were restricted to Logical Memory (immediate and delayed) and Family Pictures (delayed only), a Visual Memory subtest. Discriminant analyses suggest deficits in chronic Lyme are best characterized as a combination of memory difficulty and diminished processing speed. Deficits were modest, between one-third and two-thirds of a standard deviation, consistent with earlier studies. Depression severity had a weak relationship to processing speed, but little other association to test performance. Deficits in chronic Lyme disease are consistent with a subtle neuropathological process affecting multiple performance tasks, although further work is needed to definitively rule out nonspecific illness effects

Composition and distribution of the peracarid crustacean fauna along a latitudinal transect off Victoria Land (Ross Sea, Antarctica) with special emphasis on the Cumacea

The following study was the first to describe composition and structure of the peracarid fauna systematically along a latitudinal transect off Victoria Land (Ross Sea, Antarctica). During the 19th Antarctic expedition of the Italian research vessel “Italica” in February 2004, macrobenthic samples were collected by means of a Rauschert dredge with a mesh size of 500 m at depths between 85 and 515 m. The composition of peracarid crustaceans, especially Cumacea was investigated. Peracarida contributed 63% to the total abundance of the fauna. The peracarid samples were dominated by amphipods (66%), whereas cumaceans were represented with 7%. Previously, only 13 cumacean species were known, now the number of species recorded from the Ross Sea increased to 34. Thus, the cumacean fauna of the Ross Sea, which was regarded as the poorest in terms of species richness, has to be considered as equivalent to that of other high Antarctic areas. Most important cumacean families concerning abundance and species richness were Leuconidae, Nannastacidae, and Diastylidae. Cumacean diversity was lowest at the northernmost area (Cape Adare). At the area off Coulman Island, which is characterized by muddy sediment, diversity was highest. Diversity and species number were higher at the deeper stations and abundance increased with latitude. A review of the bathymetric distribution of the Cumacea from the Ross Sea reveals that most species distribute across the Antarctic continental shelf and slope. So far, only few deep-sea records justify the assumption of a shallow-water–deep-sea relationship in some species of Ross Sea Cumacea, which is discussed from an evolutionary point of view

(±)-Polysiphenol and other Analogues via Symmetrical Intermolecular Dimerizations: a Synthetic, Spectroscopic, Structural and Computational Study

We report an improved total synthesis of 4,5-dibromo-9,10-dihydrophenanthrene-2,3,6,7-tetraol, (±)-polysiphenol, via intermolecular McMurray dimerization of 5-bromovanillin and subsequent intramolecular oxidative coupling as the key steps. The synthetic route is applicable to 4,5-dichloro- and 4,5-difluoro-halologues (as well as a 4,5-dialkyl-analogue). Distinctive AA′BB′ multiplets in their 1H NMR spectra for the dimethylene bridges of the dibromo and dichloro compounds reveal them to be room-temperature stable atropisomers, while for the difluoro compound they present as a singlet. X-ray crystal structure determinations of their tetramethylated synthetic precursors show atropisomeric twist angles of 48°, 46°, and 32°, respectively, with the former representing the largest yet observed in any 4,5-disubstituted-9,10-dihydrophenanthrene. DFT computational studies reveal an unprecedented two-stage atropisomeric interconversion process involving time-independent asynchronous rotations of the dimethylene bridge and the biaryl axis for halologues containing chlorine or bromine, but a more synchronous rotation for the difluoro analogue