Automorphisms and forms of simple infinite-dimensional linearly compact Lie superalgebras

We describe the group of continuous automorphisms of all simple infinite-dimensional linearly compact Lie superalgebras and use it in order to classify F-forms of these superalgebras over any field F of characteristic zero.Comment: 24 page

Photochemical reactions of cyanoacetylene and dicyanoacetylene: Possible processes in Titan's atmosphere

Titan has an atmosphere which is subject to dramatic chemical evolution due mainly to the dramatic effect of the UV flux from the Sun. The energetic solar photons and other particles are converting the methane-nitrogen atmosphere into the unsaturated carbon compounds observed by the Voyager probes. These same solar photons are also converting some of these unsaturated reaction products into the aerosols observed in the atmosphere which obscure the view of the surface of Titan. In particular, the photochemical reactions of cyanoacetylene, dicyanoacetylene, acetylene and ethylene may result in the formation of the higher hydrocarbons and polymers which result in the aerosols observed in Titan's atmosphere. Polymers are the principal reaction products formed by irradiation of cyanoacetylene and dicyanoacetylene. Irradiation of cyanoacetylene with 185 nm of light also yields 1,3,5-tricyanobenzene while irradiation at 254 nm yields 1,2,4-tricyanobenzene and tetracyano cyclooctatetraenes. Photolyses of mixtures of cyanoacetylene and acetylene yields mono- and di- cyanobenzenes. The 1-Cyanocyclobutene is formed from the photochemical addition of cyanoacetylene with ethylene. The photolysis of dicyanoacetylene with acetylene yields 2,3-dicyano-1,3-butadiene and 1,2-dicyanobenzene. Tetracyano cyclooctatetraene products were also observed in the photolysis of mixtures of dicyanoacetylene and acetylene with 254 nm light. The 1,2-Dicyano cyclobutene is obtained from the photolysis dicyanoacetylene and ethylene. Reaction mechanisms will be proposed to explain the observed photoproducts

Cohomology of GKM Fiber Bundles

The equivariant cohomology ring of a GKM manifold is isomorphic to the cohomology ring of its GKM graph. In this paper we explore the implications of this fact for equivariant fiber bundles for which the total space and the base space are both GKM and derive a graph theoretical version of the Leray-Hirsch theorem. Then we apply this result to the equivariant cohomology theory of flag varieties.Comment: The paper has been accepted by the Journal of Algebraic Combinatorics. The final publication is available at springerlink.co

On the stability of Hamiltonian relative equilibria with non-trivial isotropy

We consider Hamiltonian systems with symmetry, and relative equilibria with isotropy subgroup of positive dimension. The stability of such relative equilibria has been studied by Ortega and Ratiu and by Lerman and Singer. In both papers the authors give sufficient conditions for stability which require first determining a splitting of a subspace of the Lie algebra of the symmetry group, with different splittings giving different criteria. In this note we remove this splitting construction and so provide a more general and more easily computed criterion for stability. The result is also extended to apply to systems whose momentum map is not coadjoint equivariant

QSOs and Absorption Line Systems Surrounding the Hubble Deep Field

We have imaged a 45x45 sq. arcmin. area centered on the Hubble Deep Field (HDF) in UBVRI passbands, down to respective limiting magnitudes of approximately 21.5, 22.5, 22.2, 22.2, and 21.2. The principal goals of the survey are to identify QSOs and to map structure traced by luminous galaxies and QSO absorption line systems in a wide volume containing the HDF. We have selected QSO candidates from color space, and identified 4 QSOs and 2 narrow emission-line galaxies (NELGs) which have not previously been discovered, bringing the total number of known QSOs in the area to 19. The bright z=1.305 QSO only 12 arcmin. away from the HDF raises the northern HDF to nearly the same status as the HDF-S, which was selected to be proximate to a bright QSO. About half of the QSO candidates remain for spectroscopic verification. Absorption line spectroscopy has been obtained for 3 bright QSOs in the field, using the Keck 10m, ARC 3.5m, and MDM 2.4m telescopes. Five heavy-element absorption line systems have been identified, 4 of which overlap the well-explored redshift range covered by deep galaxy redshift surveys towards the HDF. The two absorbers at z=0.5565 and z=0.5621 occur at the same redshift as the second most populated redshift peak in the galaxy distribution, but each is more than 7Mpc/h (comoving, Omega_M=1, Omega_L=0) away from the HDF line of sight in the transverse dimension. This supports more indirect evidence that the galaxy redshift peaks are contained within large sheet-like structures which traverse the HDF, and may be precursors to large-scale ``pancake'' structures seen in the present-day galaxy distribution.Comment: 36 pages, including 9 figures and 8 tables. Accepted for publication in the Astronomical Journa

On Krein-like theorems for noncanonical Hamiltonian systems with continuous spectra: application to Vlasov-Poisson

The notions of spectral stability and the spectrum for the Vlasov-Poisson system linearized about homogeneous equilibria, f_0(v), are reviewed. Structural stability is reviewed and applied to perturbations of the linearized Vlasov operator through perturbations of f_0. We prove that for each f_0 there is an arbitrarily small delta f_0' in W^{1,1}(R) such that f_0+delta f_0$is unstable. When$f_0$ is perturbed by an area preserving rearrangement, f_0 will always be stable if the continuous spectrum is only of positive signature, where the signature of the continuous spectrum is defined as in previous work. If there is a signature change, then there is a rearrangement of f_0 that is unstable and arbitrarily close to f_0 with f_0' in W^{1,1}. This result is analogous to Krein's theorem for the continuous spectrum. We prove that if a discrete mode embedded in the continuous spectrum is surrounded by the opposite signature there is an infinitesimal perturbation in C^n norm that makes f_0 unstable. If f_0 is stable we prove that the signature of every discrete mode is the opposite of the continuum surrounding it.Comment: Submitted to the journal Transport Theory and Statistical Physics. 36 pages, 12 figure

Noncommutative geometry and lower dimensional volumes in Riemannian geometry

In this paper we explain how to define "lower dimensional'' volumes of any compact Riemannian manifold as the integrals of local Riemannian invariants. For instance we give sense to the area and the length of such a manifold in any dimension. Our reasoning is motivated by an idea of Connes and involves in an essential way noncommutative geometry and the analysis of Dirac operators on spin manifolds. However, the ultimate definitions of the lower dimensional volumes don't involve noncommutative geometry or spin structures at all.Comment: 12 page

On the Connection Between Metal Absorbers and Quasar Nebulae

We establish a simple model for the distribution of cold gas around L* galaxies using a large set of observational constraints on the properties of strong MgII absorber systems. Our analysis suggests that the halos of L* galaxies are filled with cool gaseous clouds having sizes of order 1kpc and densities of ~10^{-2} cm^{-3}. We then investigate the physical effects of cloud irradiation by a quasar and study the resulting spectral signatures. We show that quasar activity gives rise to (i) extended narrow-line emission on ~100kpc scales and (ii) an anisotropy in the properties of the absorbing gas arising from the geometry of the quasar radiation field. Provided that quasars reside in halos several times more massive than those of L* galaxies, our model predictions appear to be in agreement with observations of narrow emission-line nebulae around quasars and the recent detections of ~100kpc cold gaseous envelopes around those objects, suggesting a common origin for these phenomena. We discuss the implications of our results for understanding absorption systems, probing quasar environments at high redshifts, and testing the quasar unification scheme.Comment: 15 pages, 13 figures (ApJ submitted