Rotating solenoidal perfect fluids of Petrov type D

We prove that aligned Petrov type D perfect fluids for which the vorticity vector is not orthogonal to the plane of repeated principal null directions and for which the magnetic part of the Weyl tensor with respect to the fluid velocity has vanishing divergence, are necessarily purely electric or locally rotationally symmetric. The LRS metrics are presented explicitly.Comment: 6 pages, no figure

Zeroth Poisson homology of symmetric powers of isolated quasihomogeneous surface singularities

Let X be a surface with an isolated singularity at the origin, given by the equation Q(x,y,z)=0, where Q is a weighted-homogeneous polynomial. In particular, this includes the Kleinian surfaces X = C^2/G for G < SL(2,C) finite. Let Y be the n-th symmetric power of X. We compute the zeroth Poisson homology of Y, as a graded vector space with respect to the weight grading. In the Kleinian case, this confirms a conjecture of Alev, that the zeroth Poisson homology of the n-th symmetric power of C^2/G is isomorphic to the zeroth Hochschild homology of the n-th symmetric power of the algebra of G-invariant differential operators on C. That is, the Brylinski spectral sequence degenerates in this case. In the elliptic case, this yields the zeroth Hochschild homology of symmetric powers of the elliptic algebras with three generators modulo their center, for the parameter equal to all but countably many points of the elliptic curve.Comment: 17 page

Competing recombinant technologies for environmental innovation

This article presents a model of sequential decisions about investments in environmentally dirty and clean technologies, which extends the path-dependence framework of Arthur (1989). This allows us to evaluate if and how an economy locked into a dirty technology can be unlocked and move towards the clean technology. The main extension involves the inclusion of the effect of recombinant innovation of the two technologies. A mechanism of endogenous competition is described involving a positive externality of increasing returns to investment which are counterbalanced by recombinant innovation. We determine conditions under which lock-in can be avoided or escaped. A second extension is symmetry breaking of the the system due to the introduction of an environmental policy that charges a price for polluting. A final extension adds a cost of environmental policy in the form of lower returns on investment implemented through a growth-depressing factor. We compare cumulative pollution under different scenarios, so that we can evaluate the combination of environmental regulation and recombinant innovation

Some Musings on Galaxy Morphology

Careful inspection of large-scale photographs of Shapley-Ames galaxies seems to show a smooth transition between the morphological characteristics of galaxies located on the narrow red, and on the broad blue, sequences in the galaxian color-magnitude diagram. In other words there does not appear to be a dichotomy between blue and red galaxies. Both the colors and the morphologies of galaxies are found to correlate strongly with their environments. Red and early-type Shapley-Ames galaxies are dominant in clusters, whereas blue late-type star forming objects dominate the general field. Interestingly the colors and morphologies of galaxies in small groups resemble the field and differ from those in clusters. As noted by Baade the presence of dust and star formation are very closely correlated, except in a few galaxies that probably had unusual evolutionary histories. Over the entire range from S0 to Sc there is no significant difference between the integrated colors of normal and barred objects suggesting that the formation of a bar does not significantly affect the stellar evolutionary history of a galaxy.Comment: 13 figures; Astronomical Journal in pres

Globular Clusters and Dwarf Spheroidal Galaxies

Traditionally globular clusters and dwarf spheroidal galaxies have been distinguished by using one or more of the following criteria: (1) mass, (2) luminosity, (3) size, (4) mass-to-light ratio and (5) spread in metallicity. However, a few recently discovered objects show some overlap between the domains in parameter space that are occupied by galaxies and clusters. In the present note it is shown that ellipticity can, in some cases, be used to help distinguish between globular clusters and dwarf spheroidal galaxies.Comment: MNRAS (Letters), in pres

Jet triggered Type Ia supernovae in radio-galaxies?

We report the serendipitous discovery of a supernova (SN) in the nearby radio-galaxy 3C 78. Observations obtained with the STIS spectrograph on board the Hubble Space Telescope show, at a distance of 0.54 arcsec (300 pc) from the galaxy nucleus, a second bright source, not present in previous images. As this source was fortuitously covered by the spectrograph slit its spectrum was obtained and it is characteristic of a Type Ia SN. This SN is closely aligned with the radio-jet of 3C 78. Analysis of historical records shows that such a close association between jet and supernova occurred in 6 of the 14 reported SNe in radio-galaxies. The probability that this results from a random distribution of SN in the host galaxy is less than 0.05%. We then argue that jets might trigger supernova explosions.Comment: 9 pages, 3 figures, 1 table, to appear in ApJL, 20 Jul 200