Invariant decomposition of the retarded electromagnetic field.

The integral representation of the electromagnetic two-form, defined on Minkowski space-time, is studied from a new point of view. The aim of the paper is to obtain an invariant criteria in order to define the radiative field. This criteria generalizes the well-known structureless charge case. We begin with the curvature two-form, because its field equations incorporate the motion of the sources. The gauge theory methods (connection one-forms) are not suited because their field equations do not incorporate the motion of the sources. We obtain an integral solution of the Maxwell equations in the case of a flow of charges in irrotational motion. This solution induces us to propose a new method of solving the problem of the nature of the retarded radiative field. This method is based on a projection tensor operator which, being local, is suited to being implemented on general relativity. We propose the field equations for the pair {electromagnetic field, projection tensor J. These field equations are an algebraic differential first-order system of oneforms, which verifies automatically the integrability conditions.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

Massless minimally coupled fields in de Sitter space: O(4)-symmetric states versus de Sitter invariant vacuum

The issue of de Sitter invariance for a massless minimally coupled scalar field is examined. Formally, it is possible to construct a de Sitterinvariant state for this case provided that the zero mode of the field is quantized properly. Here we take the point of view that this state is physically acceptable, in the sense that physical observables can be computed and have a reasonable interpretation. In particular, we use this vacuum to derive a new result: that the squared difference between the field at two points along a geodesic observers spacetime path grows linearly with the observers proper time for a quantum state that does not break de Sitter invariance. Also, we use the Hadamard formalism to compute the renormalized expectation value of the energy-momentum tensor, both in the O(4)-invariant states introduced by Allen and Follaci, and in the de Sitterinvariant vacuum. We find that the vacuum energy density in the O(4)-invariant case is larger than in the de Sitterinvariant case.

Linear relations between writhe and minimal crossing number in Conway families of ideal knots and links

We showed earlier how to predict the writhe of any rational knot or link in its ideal geometric configuration, or equivalently the average of the 3D writhe over statistical ensembles of random configurations of a given knot or link (Cerf and Stasiak 2000 Proc. Natl Acad. Sci. USA 97 3795). There is no general relation between the minimal crossing number of a knot and the writhe of its ideal geometric configuration. However, within individual families of knots linear relations between minimal crossing number and writhe were observed (Katritch et al 1996 Nature 384 142). Here we present a method that allows us to express the writhe as a linear function of the minimal crossing number within Conway families of knots and links in their ideal configuration. The slope of the lines and the shift between any two lines with the same

Os links e os estudos webométricos

Neste artigo são abordados os estudos quantitativos aplicados à Internet e à Web. É dada especial atenção ao conceito de webometria, à sua abrangência, aplicações e possíveis denominações. São assinaladas as suas diferenças com a cibermetria e estabelecidas as relações que estes dois métodos mantêm com os tradicionais campos da bibliometria, cientometria e informetria. É enfocado também um recurso que vem despertando grande interesse entre os investigadores, não só por facilitar a navegabilidade entre sítios dentro da Web, mas também por constituir um dos indicadores mais relevantes dentro dos estudos webométricos: os weblinks. Na parte final, é feita breve revisão das pesquisas que têm sido realizadas sobre a estrutura, as funções e as motivações para a criação de links no espaço Web.

Spatial pattern and process at the plant neighbourhood scale: insights from communities dominated by the clonal grass Elymus repens (L.) Gould.

Question: How do clonal traits of a locally dominant grass (Elymus repens (L.) Gould.) respond to soil heterogeneity and shape spatial patterns of its tillers? How do tiller spatial patterns constrain seedling recruitment within the community?Locations: Artificial banks of the River Rhone, France.Material and Methods: We examined 45 vegetation patches dominated by Elymus repens. During a first phase we tested relationships between soil variables and three clonal traits (spacer length, number of clumping tillers and branching rate), and between the same clonal traits and spatial patterns (i.e. density and degree of spatial aggregation) of tillers at a very fine scale. During a second phase, we performed a sowing experiment to investigate effects of density and spatial patterns of E. repens on recruitment of eight species selected from the regional species pool.Results: Clonal traits had clear effects - especially spacer length - on densification and aggregation of E. repens tillers and, at the same time, a clear response of these same clonal traits as soil granulometry changed. The density and degree of aggregation of E. repens tillers was positively correlated to total seedling cover and diversity at the finest spatial scales.Conclusions: Spatial patterning of a dominant perennial grass responds to soil heterogeneity through modifications of its clonal morphology as a trade-off between phalanx and guerrilla forms. In turn, spatial patterns have strong effects on abundance and diversity of seedlings. Spatial patterns of tillers most probably led to formation of endogenous gaps in which the recruitment of new plant individuals was enhanced. Interestingly, we also observed more idiosyncratic effects of tiller spatial patterns on seedling cover and diversity when focusing on different growth forms of the sown species.

Phosphorus and carbon burial during cretaceous oceanic anoxic events, links with climatic changes

According to Jenkyns (2010), oceanic anoxic events (OAE) record profound changes in the climatic and paleoceanographic state of the planet and represent major disturbances in the global carbon cycle. One of the most studied OAEs on a worldwide scale is the Cenomanian-Turonian OAE 2, which is characterized by a pronounced positive excursion in carbon-isotope records and the important accumulation of organic-rich sediments. The section at Gongzha (Tibet) and the sections at Barranca and Axaxacualco (Mexico) are located in remote parts of the Tethys, and show δ13C records, which are well correlated with those of classical Tethyan sections. Both sections, however, do not exhibit the presence of organic-rich sediments. Phosphorus Mass Accumulation Rates (PMAR) in Tibet show a pattern similar to that observed in the Tethys by Mort et al. (2007), which suggests enhanced Ρ regeneration during the OAE 2 time interval, though there is no evidence for anoxic conditions in Tibet. Ρ appears here to have been mainly driven by detrital influx and sea-level fluctuations. The sections at Barranca and Axaxacualco show that the Mexican carbonate platform persisted during this anoxic event, which allowed the evolution of platform fauna otherwise not present in Tethyan sections. The persistence of this carbonate platform close to the Caribbean Igneous Plateau, which is thought to have released bio-limiting metals, is explained by local uplift which delayed the drowning of the platform and a specific oceanic circulation that permitted the preservation of oligotrophic conditions in the area. The Coniacian-Santonian OAE (OAE3) appears to have been more dependent on local conditions than OAE2. The presence of black shales associated with OAE3 appear to have been restricted to shallow-water settings and epicontinental seas in areas located around the Atlantic Ocean. The sections at Olazagutia (Spain), and Ten Mile - Arbor Park (USA), two potential Global Boundary Stratotype Sections and Points (GSSP) sites, are devoid of organic-rich sediments and lack a δ13C positive excursion around the C-S boundary. The Gabal Ekma section (Sinai, Egypt) exhibits accumulations of organic-rich sediments, in addition to phosphorite bone beds layers, which may have been linked to an epicontinental upwelling zone and/or storm inputs. Our data suggest that OAE 3 is rarely expressed by truly anoxic conditions and seems to have been linked to local conditions rather than global paleoenvironmental change. The evidence for detrital-P being the likely cause of Ρ fluctuations during the OAEs studied here does not negate the idea that anoxia was the principal driver of these fluctuations in the western Tethys. However, an explanation is required as to why the Ρ accumulation signatures are mirrored in both oxic and anoxic sedimentary successions. 'Eustatic/climatic' and 'productivity/anoxic' models may have both operated simultaneously in different parts of the world depending on local conditions, both producing similar trends in Ρ accumulation. - Selon Jenkyns (2010), les événements anoxiques océaniques enregistrent de profonds changements dans le climat et la paléoceanographie de la planète et représente des perturbations majeures du cycle du carbone. L'un des plus étudiés à l'échelle mondiale est l'ΟΑΕ2 du Cénomanien-Turonien, qui est caractérisé par une très forte excursion positive des isotopes du carbone et une importante accumulation de sédiments riche en matière organique. La section de Gongzha (Tibet) et les sections de Barranca et Axaxcualco (Mexique) sont situées aux confins de la Téthys, et enregistrent une courbe isotopique en δ13C parfaitement corrélable avec les sections téthysiennes, mais ne montre pas d'accumulation de black shales. Le taux de phosphore en accumulation de masses (PMAR) au Tibet montre un pattern similaire observé également par Mort et al. (2007) dans la Téthys, suggérant un model de régénération du Ρ durant l'anoxie, cependant aucune conditions anoxiques régnent dans la région du Tibet. Ρ apparaît donc principalement guidé par le détritisme et les fluctuations du niveau marin. Les sections de Barranca et d'Axaxacualco montrent que la plateforme carbonatée mexicaine persiste durant cet événement anoxique, et permet le développement d'une faune de plateforme qui n'est pas présente dans les sections téthysiennes. La persistance de cette plateforme carbonatée si proche du plateau Caribéen, qui est connu pour le relâchement de métaux bio-limitant, peut être expliqué par un soulèvement tectonique local qui inhibe l'ennoiement de la plateforme et une circulation océanique spécifique qui permet la préservation de conditions oligotrophiques dans cette région. L'événement anoxique océanique du Coniacien-Santonien apparaît plus dépendant des conditions locales que pour l'ΟΑΕ2. Les black shales associés à POAE3 sont restreints aux zones situées autour de l'océan Atlantique et plus particulièrement aux eaux peu profondes et épicontinentales. Les sections d'Olazagutia (Espagne), Ten Mile Creek et Arbor Park (USA), qui sont deux potentielles sections GSSP (Sections de stratotype de limite globaux et de points), ne montre pas d'accumulation de black shales et pas de forte excursion positive en δ13C autour de la limite C-S. La section de Gabal Ekma (Sinai, Egypte) montre des accumulations de black shales, en plus des couches de phosphorites et d'accumulation d'os (« bone beds »), vraisemblablement lié à des zones active d'upwelling épicontinentale et/ou d'apport de tempêtes. Nos données suggèrent que l'OAE 3 est rarement exprimé par de vraies conditions anoxiques et semble être plus lié à des conditions plus locales que des changements paléo-environnementaux globaux, comme observés pour le Cénomanien- Turonien. Les arguments pour un modèle lié au phosphore détritique qui serait la cause des fluctuations du phosphore total durant les OAEs, n'écartent pas l'idée que l'anoxie est la principale cause de ces fluctuations dans les sections riches en matière organique de l'Ouest téthysien. Cependant une explication est nécessaire pour comprendre pourquoi la signature de l'accumulation du phosphore est semblable dans les successions sédimentaires déposées dans des conditions oxygénées et anoxiques. Les modèles « Eustatisme/Climat » et « Productivité/anoxie » ont simultanément opéré dans les différentes parties du monde dépendant de conditions locales, et ont produit des tendances similaires en accumulation de phosphore.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

Functional education of invariant NKT cells by dendritic cell tuning of SHP-1.

Invariant NKT (iNKT) cells play key roles in host defense by recognizing lipid Ags presented by CD1d. iNKT cells are activated by bacterial-derived lipids and are also strongly autoreactive toward self-lipids. iNKT cell responsiveness must be regulated to maintain effective host defense while preventing uncontrolled stimulation and potential autoimmunity. CD1d-expressing thymocytes support iNKT cell development, but thymocyte-restricted expression of CD1d gives rise to Ag hyperresponsive iNKT cells. We hypothesized that iNKT cells require functional education by CD1d(+) cells other than thymocytes to set their correct responsiveness. In mice that expressed CD1d only on thymocytes, hyperresponsive iNKT cells in the periphery expressed significantly reduced levels of tyrosine phosphatase SHP-1, a negative regulator of TCR signaling. Accordingly, heterozygous SHP-1 mutant mice displaying reduced SHP-1 expression developed a comparable population of Ag hyperresponsive iNKT cells. Restoring nonthymocyte CD1d expression in transgenic mice normalized SHP-1 expression and iNKT cell reactivity. Radiation chimeras revealed that CD1d(+) dendritic cells supported iNKT cell upregulation of SHP-1 and decreased responsiveness after thymic emigration. Hence, dendritic cells functionally educate iNKT cells by tuning SHP-1 expression to limit reactivity.