Singularities of equidistants and global centre symmetry sets of Lagrangian submanifolds

We define the Global Centre Symmetry set (GCS) of a smooth closed m-dimensional submanifold M of R^n, $n \leq 2m$, which is an affinely invariant generalization of the centre of a k-sphere in R^{k+1}. The GCS includes both the centre symmetry set defined by Janeczko and the Wigner caustic defined by Berry. We develop a new method for studying generic singularities of the GCS which is suited to the case when M is lagrangian in R^{2m} with canonical symplectic form. The definition of the GCS, which slightly generalizes one by Giblin and Zakalyukin, is based on the notion of affine equidistants, so, we first study singularities of affine equidistants of Lagrangian submanifolds, classifying all the stable ones. Then, we classify the affine-Lagrangian stable singularities of the GCS of Lagrangian submanifolds and show that, already for smooth closed convex curves in R^2, many singularities of the GCS which are affine stable are not affine-Lagrangian stable.Comment: 26 pages, 2 figure

Species of Bursaphelenchus Fuchs, 1937 (Nematoda: Parasitaphelenchidae) and other nematode genera associated with insects from Pinus pinaster in Portugal

Insects associated with maritime pine, Pinus pinaster, in Portugal were collected and screened for the presence of Bursaphelenchus species. Nematodes were identified using Internal Transcribed Spacers-Restriction Fragment Length Polymorphism (ITS-RFLP) analysis of dauer juveniles and morphological identification of adults that developed from dauer juveniles on fungal cultures or on cultures in pine wood segments at 26 C. Several associations are described: Bursaphelenchus teratospicularis and Bursaphelenchus sexdentati are associated with Orthotomicus erosus; Bursaphelenchus tusciae, B. sexdentati and/or Bursaphelenchus pinophilus with Hylurgus ligniperda and Bursaphelenchus hellenicus with Tomicus piniperda, Ips sexdentatus and H. ligniperda. An unidentified Bursaphelenchus species is vectored by Hylobius sp. The previously reported association of Bursaphelenchus xylophilus with Monochamus galloprovincialis was confirmed. The association of Bursaphelenchus leoni with Pityogenes sp. is not definitively established and needs further studies for clarification. Other nematode genera besides Bursaphelenchus were found to be associated with the insects sampled, including two different species of Ektaphelenchus, Parasitorhabditis sp., Parasitaphelenchus sp., Contortylenchus sp. and other unidentified nematodes. The Ektaphelenchus species found in O. erosus is morphologically similar to B. teratospicularis found in the same insect; adults of both the species are found in cocoon-like structures under the elytra of the insects. Introduction Approximately one third of the nematodes belonging to the order Aphelenchida Siddiqi, 1980 are associated with insects (Poinar, 1983). These nematodes establish a variety of associations with the insects, which may be described as commensalism, e.g. phoresy (to the benefit of the nematode but not affecting the insect), mutualism (both the organisms benefit) or parasitism (nematodes benefit at the expense of the insect) (Giblin-Davis, 2004). Most Bursaphelenchus Fuchs, 1937 species are mycetophagous, feeding on fungi in the galleries of bark beetles and thu

Gamma-Ray Burst Pulse Correlations as Redshift Indicators

Correlations among pulse properties in the prompt emission of long GRBs can potentially be used as cosmological distance indicators to estimate redshifts of GRBs to which these pulses belong. We demonstrate application of this technique to a sample of GRBs for which redshifts are not known. We also study the scatter of predicted redshifts of pulses found within individual bursts. We explore the characteristics of this scatter in hopes of identifying systematic corrections and/or pulse subsets that can be used to increase the technique's reliability.Comment: 3 pages and 6 figures, to appear in the proceedings of the Sixth Huntsville Gamma-Ray Burst Symposium, edited by C.A. Meegan, N. Gehrels, and C. Kouvelioto

Level sets of functions and symmetry sets of smooth surface sections

We prove that the level sets of a real C^s function of two variables near a non-degenerate critical point are of class C^[s/2] and apply this to the study of planar sections of surfaces close to the singular section by the tangent plane at hyperbolic points or elliptic points, and in particular at umbilic points. We also analyse the cases coming from degenerate critical points, corresponding to elliptic cusps of Gauss on a surface, where the differentiability is now reduced to C^[s/4]. However in all our applications to symmetry sets of families of plane curves, we assume the C^infty smoothness.Comment: 15 pages, Latex, 6 grouped figures. The final version will appear in Mathematics of Surfaces. Lecture Notes in Computer Science (2005

The International Space Station: A National Laboratory

After more than a decade of assembly missions and the end of the space shuttle program, the International Space Station (ISS) has reached assembly completion. With other visiting spacecraft now docking with the ISS on a regular basis, the orbiting outpost now serves as a National Laboratory to scientists back on Earth. The ISS has the ability to strengthen relationships between NASA, other Federal entities, higher educational institutions, and the private sector in the pursuit of national priorities for the advancement of science, technology, engineering, and mathematics. The ISS National Laboratory also opens new paths for the exploration and economic development of space. In this presentation we will explore the operation of the ISS and the realm of scientific research onboard that includes: (1) Human Research, (2) Biology & Biotechnology, (3) Physical & Material Sciences, (4) Technology, and (5) Earth & Space Science

The International Space Station: A National Science Laboratory

After more than a decade of assembly missions and on the heels of the final voyage of Space Shuttle Discovery, the International Space Station (ISS) has reached assembly completion. With visiting spacecraft now docking with the ISS on a regular basis, the Station now serves as a National Laboratory to scientists back on Earth. ISS strengthens relationships among NASA, other Federal entities, higher educational institutions, and the private sector in the pursuit of national priorities for the advancement of science, technology, engineering, and mathematics. In this lecture we will explore the various areas of research onboard ISS to promote this advancement: (1) Human Research, (2) Biology & Biotechnology, (3) Physical & Material Sciences, (4) Technology, and (5) Earth & Space Science. The ISS National Laboratory will also open new paths for the exploration and economic development of space