Tori embedded in S³ with dense asymptotic lines

In this paper are given examples of tori T² embedded in S³ with all their asymptotic lines dense.

Tori embedded in R(3) with dense principal lines

In this paper are given examples of tori T(2) embedded in R(3) with all their principal lines dense. These examples are obtained by stereographic projection of deformations of the Clifford torus in S(3). (C) 2008 Elsevier Masson SAS. All rights reserved.

Minimal surfaces in S(3) with constant contact angle

We provide a characterization of the Clifford Torus in S(3) via moving frames and contact structure equations. More precisely, we prove that minimal surfaces in S(3) with constant contact angle must be the Clifford Torus. Some applications of this result are then given, and some examples are discussed.

Determination of the minimum value of the safety factor from geodesic Alfven eigenmodes in Joint European Torus

An analysis of the experimental conditions under which low-frequency (70-150 kHz) Alfven eigertmodes (AE) are excited during the monster sawtooth in Joint European Torus [F Romanelli et al, Proceedings of the 22nd IAEA Fusion Energy Conference, Geneva, Switzerland, 2008] is presented for the specific case of a discharge with ion cyclotron heating (5 MW) Using a simplified AE model for modes excited at the Alfven wave continuum maximum with geodesic corrections taken into account, the temporal evolution of the value of the safety factor q(0) at the magnetic axis is determined We describe a new scheme to determine the time variation of q(0) that works under conditions in which other standard diagnostics, such as the motional Stark effect do not give reliable results such as during a monster sawtooth [doi 10 1063/1 3494212]

THE COMPTON-THICK SEYFERT 2 NUCLEUS OF NGC 3281: TORUS CONSTRAINTS FROM THE 9.7 mu m SILICATE ABSORPTION

We present mid-infrared (mid-IR) spectra of the Compton-thick Seyfert 2 galaxy NGC 3281, obtained with the Thermal-Region Camera Spectrograph at the Gemini-South telescope. The spectra present a very deep silicate absorption at 9.7 mu m, and [S IV] 10.5 mu m and [Ne II] 12.7 mu m ionic lines, but no evidence of polycyclic aromatic hydrocarbon emission. We find that the nuclear optical extinction is in the range 24 mag <= A(V) <= 83 mag. A temperature T = 300 K was found for the blackbody dust continuum component of the unresolved 65 pc nucleus and the region at 130 pc SE, while the region at 130 pc NW reveals a colder temperature (200 K). We describe the nuclear spectrum of NGC 3281 using a clumpy torus model that suggests that the nucleus of this galaxy hosts a dusty toroidal structure. According to this model, the ratio between the inner and outer radius of the torus in NGC 3281 is R(0)/R(d) = 20, with 14 clouds in the equatorial radius with optical depth of tau(V) = 40 mag. We would be looking in the direction of the torus equatorial radius (i = 60 degrees), which has outer radius of R(0) similar to 11 pc. The column density is N(H) approximate to 1.2 x 10(24) cm(-2) and the iron K alpha equivalent width (approximate to 0.5-1.2 keV) is used to check the torus geometry. Our findings indicate that the X-ray absorbing column density, which classifies NGC 3281 as a Compton-thick source, may also be responsible for the absorption at 9.7 mu m providing strong evidence that the silicate dust responsible for this absorption can be located in the active galactic nucleus torus.

Nonexistence of global solutions for a class of complex vector fields on two-torus

The goal of this paper is study the global solvability of a class of complex vector fields of the special form L = partial derivative/partial derivative t + (a + ib)(x)partial derivative/partial derivative x, a, b epsilon C(infinity) (S(1) ; R), defined on two-torus T(2) congruent to R(2)/2 pi Z(2). The kernel of transpose operator L is described and the solvability near the characteristic set is also studied. (c) 2008 Elsevier Inc. All rights reserved.

On the Fucik spectrum of the Laplacian on a torus

We study the Fucik spectrum of the Laplacian on a two-dimensional torus T(2). Exploiting the invariance properties of the domain T(2) with respect to translations we obtain a good description of large parts of the spectrum. In particular, for each eigenvalue of the Laplacian we will find an explicit global curve in the Fucik spectrum which passes through this eigenvalue; these curves are ordered, and we will show that their asymptotic limits are positive. On the other hand, using a topological index based on the mentioned group invariance, we will obtain a variational characterization of global curves in the Fucik spectrum; also these curves emanate from the eigenvalues of the Laplacian, and we will show that they tend asymptotically to zero. Thus, we infer that the variational and the explicit curves cannot coincide globally, and that in fact many curve crossings must occur. We will give a bifurcation result which partially explains these phenomena. (C) 2008 Elsevier Inc. All rights reserved.

A scenario for torus T(2) destruction via a global bifurcation

We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T(2) with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type-if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws. (C) 2007 Elsevier Ltd. All rights reserved.

Plasma confinement in tokamaks with robust torus

We present a non-linear symplectic map that describes the alterations of the magnetic field lines inside the tokamak plasma due to the presence of a robust torus (RT) at the plasma edge. This RT prevents the magnetic field lines from reaching the tokamak wall and reduces, in its vicinity, the islands and invariant curve destruction due to resonant perturbations. The map describes the equilibrium magnetic field lines perturbed by resonances created by ergodic magnetic limiters (EMLs). We present the results obtained for twist and non-twist mappings derived for monotonic and non-monotonic plasma current density radial profiles, respectively. Our results indicate that the RT implementation would decrease the field line transport at the tokamak plasma edge. (C) 2010 Elsevier B.V. All rights reserved.

Coincidence properties for maps from the torus to the Klein bottle

The authors study the coincidence theory for pairs of maps from the Torus to the Klein bottle. Reidemeister classes and the Nielsen number are computed, and it is shown that any given pair of maps satisfies the Wecken property. The 1-parameter Wecken property is studied and a partial negative answer is derived. That is for all pairs of coincidence free maps a countable family of pairs of maps in the homotopy class is constructed such that no two members may be joined by a coincidence free homotopy.

From Offshore to Onshore: Multiple Origins of Shallow-Water Corals from Deep-Sea Ancestors

Shallow-water tropical reefs and the deep sea represent the two most diverse marine environments. Understanding the origin and diversification of this biodiversity is a major quest in ecology and evolution. The most prominent and well-supported explanation, articulated since the first explorations of the deep sea, holds that benthic marine fauna originated in shallow, onshore environments, and diversified into deeper waters. In contrast, evidence that groups of marine organisms originated in the deep sea is limited, and the possibility that deep-water taxa have contributed to the formation of shallow-water communities remains untested with phylogenetic methods. Here we show that stylasterid corals (Cnidaria: Hydrozoa: Stylasteridae)-the second most diverse group of hard corals-originated and diversified extensively in the deep sea, and subsequently invaded shallow waters. Our phylogenetic results show that deep-water stylasterid corals have invaded the shallow-water tropics three times, with one additional invasion of the shallow-water temperate zone. Our results also show that anti-predatory innovations arose in the deep sea, but were not involved in the shallow-water invasions. These findings are the first robust evidence that an important group of tropical shallow-water marine animals evolved from deep-water ancestors.

DESCRIPTION OF ADULTS AND NYMPH, AND REDESCRIPTION OF THE LARVA, OF ORNITHODOROS MARINKELLEI (ACARI: ARGASIDAE), WITH DATA ON ITS PHYLOGENETIC POSITION

The argasid tick Ornithodoros marinkellei Kohls, Clifford, and Jones, 1969 was described 4 decades ago based on larval specimens collected from bats (Pteronotus spp.) in Colombia and Panama. Thereafter, larval O. marinkellei parasitizing bats were reported from Venezuela, Guyana, and Brazil. Herein, we describe the adults and nymph, and redescribe the larva of O. marinkellei based on specimens recently collected in the western Brazilian Amazon region. In contrast to all other known adult argasids, the idiosoma of both males and females of O. marinkellei is covered with sclerotized plaques. The idiosoma of the nymph of O. marinkellei is entirely micromamillated, and differs from the adults by the absence of plaques. The larva of O. marinkellei is morphologically similar to the larvae of the 2 other species belonging to the subgenus Subparmatus, i.e., Ornithodoros viguerasi Cooley and Kohls, 1941 and Ornithodoros mormoops Kohls, Clifford, and Jones, 1969. Because of the long and narrow dorsal plate, the larva of O. marinkellei is readily distinguished from O. viguerasi and O. mormoops. Comparison of our larvae from Brazil with O. marinkellei paratype specimens from Colombia confirmed their taxonomic identification. However, a few morphological differences, particularly in the size of the gnathosoma, were observed. Further studies are necessary to clarify whether O. marinkellei is a complex of different species, or a single species represented by morphologically polymorphic, and geographically distinct populations. Partial mitochondrial 16S rDNA gene sequences were generated for O. marinkellei specimens from Brazil, and compared with available homologous sequences in GenBank. Phylogenetic analyses revealed O. marinkellei to be distinct from the remaining argasid species available in GenBank, including other bat-associated tick species that are found in sympatry with O. marinkellei in the Neotropical region.

Skewness, splitting number and vertex deletion of some toroidal meshes

The skewness sk(G) of a graph G = (V, E) is the smallest integer sk(G) >= 0 such that a planar graph can be obtained from G by the removal of sk(C) edges. The splitting number sp(G) of C is the smallest integer sp(G) >= 0 such that a planar graph can be obtained from G by sp(G) vertex splitting operations. The vertex deletion vd(G) of G is the smallest integer vd(G) >= 0 such that a planar graph can be obtained from G by the removal of vd(G) vertices. Regular toroidal meshes are popular topologies for the connection networks of SIMD parallel machines. The best known of these meshes is the rectangular toroidal mesh C(m) x C(n) for which is known the skewness, the splitting number and the vertex deletion. In this work we consider two related families: a triangulation Tc(m) x c(n) of C(m) x C(n) in the torus, and an hexagonal mesh Hc(m) x c(n), the dual of Tc(m) x c(n) in the torus. It is established that sp(Tc(m) x c(n)) = vd(Tc(m) x c(n) = sk(Hc(m) x c(n)) = sp(Hc(m) x c(n)) = vd(Hc(m) x c(n)) = min{m, n} and that sk(Tc(m) x c(n)) = 2 min {m, n}.

LC-MSn analysis of the cis isomers of chlorogenic acids

The behaviour of cis isomers of selected mono- and di-acyl chlorogenic acids produced by UV-irradiation has been investigated by LC-MSn. cis Isomers fragment identically to the more common trans isomers. cis-5-Acyl chlorogenic acids are more hydrophobic and elute later than their mono- or di-trans counterparts whereas the reverse is true for cis-3-acyl and cis-4-acyl chlorogenic acids. The cis isomers of 1,3-dicaffeoylquinic acid, the only I-acyl chlorogenic acid investigated, are also more hydrophobic than the di-trans isomer. Coffee leaves had a proportionately greater content of cis isomers relative to trans isomers compared with coffee beans suggesting that UV-irradiation in vivo may also cause geometric isomerisation. (c) 2007 Elsevier Ltd. All rights reserved.

TOWARDS A BENJAMINIAN ANTHROPOLOGY: RETHINKING PARADIGMS OF DRAMATIC THEATRE

This essay is presented as a Benjaminian work site. The juxtaposition of apparently distant figures in brusque and surprising relations may well cause puzzlement. But the affinities are revealing. In the whirlpools of Michael Taussig`s studies, I search for a theoretical composition in counterpoint: on one side, Victor Turner and Clifford Geertz, whose writings possibly lead us to think of a kind of paradigm of the dramatic theatre in anthropology, and, on the other, two figures on the margins of anthropology and the dramatic theatre - Walter Benjamin and Bertolt Brecht. The essay`s gravitational force is located on these margins, especially the fragmented work of Benjamin. In short, this is an essay towards a Benjaminian anthropology, organized around three allegories: (1) magic mirror; (2) shattering; and (3) flashes of light. In some ways, the journey suggests the form of an unusual rite of passage: the passage towards a passing condition.