On the cohomological spectrum and support varieties for infinitesimal unipotent supergroup schemes

We show that if $G$ is an infinitesimal elementary supergroup scheme of height $\leq r$, then the cohomological spectrum $|G|$ of $G$ is naturally homeomorphic to the variety $\mathcal{N}_r(G)$ of supergroup homomorphisms $\rho: \mathbb{M}_r \rightarrow G$ from a certain (non-algebraic) affine supergroup scheme $\mathbb{M}_r$ into $G$. In the case $r=1$, we further identify the cohomological support variety of a finite-dimensional $G$-supermodule $M$ as a subset of $\mathcal{N}_1(G)$. We then discuss how our methods, when combined with recently-announced results by Benson, Iyengar, Krause, and Pevtsova, can be applied to extend the homeomorphism $\mathcal{N}_r(G) \cong |G|$ to arbitrary infinitesimal unipotent supergroup schemes.Comment: Fixed some algebra misidentifications, primarily in Sections 1.3 and 3.3. Simplified the proof of Proposition 3.3.

Mercury orbiter transport study

A data base and comparative performance analyses of alternative flight mode options for delivering a range of payload masses to Mercury orbit are provided. Launch opportunities over the period 1980-2000 are considered. Extensive data trades are developed for the ballistic flight mode option utilizing one or more swingbys of Venus. Advanced transport options studied include solar electric propulsion and solar sailing. Results show the significant performance tradeoffs among such key parameters as trip time, payload mass, propulsion system mass, orbit size, launch year sensitivity and relative cost-effectiveness. Handbook-type presentation formats, particularly in the case of ballistic mode data, provide planetary program planners with an easily used source of reference information essential in the preliminary steps of mission selection and planning

Habitat connectivity in reef fish communities and marine reserve design in Old Providence-Santa Catalina, Colombia

On the insular platform of Old Providence/Santa Catalina, Colombia, we compared nearshore lagoonal patch reefs to those on the northern bank distant from the islands to determine the importance of habitat connectivity to fish community structure. Nearshore patch reefs had greater proximity to mangrove, seagrass and rocky shore habitats, and they had significantly more individuals. Nearshore reefs also tended to have a greater total biomass, more species, a higher proportion of predators of mobile invertebrates and small fishes, and a lower proportion of herbivores. Biomass of snappers and grunts at nearshore sites was four times greater compared to bank sites, and was correlated with the amount of seagrass and sand/rubble habitat within 500 m of each patch reef. We also compared length-frequency distributions and abundances of grunts and snappers among all sites (deep and shallow forereefs, patch reefs and deep and shallow leeside slopes). The results were consistent with ontogenetic migrations from shallow sites, primarily seagrass and mangrove habitats, to deeper sites and to those further out on the bank. The evidence suggests that species differed in both distance and direction of dispersal, which may be affected by the abundance and distribution of preferred habitats. Marine reserves near the islands should target nearshore nursery areas and patch reefs harboring species of limited dispersal capability. Reserves on the northern bank would protect spawners of those species showing the greatest dispersal capability

Linear instability criteria for ideal fluid flows subject to two subclasses of perturbations

In this paper we examine the linear stability of equilibrium solutions to incompressible Euler's equation in 2- and 3-dimensions. The space of perturbations is split into two classes - those that preserve the topology of vortex lines and those in the corresponding factor space. This classification of perturbations arises naturally from the geometric structure of hydrodynamics; our first class of perturbations is the tangent space to the co-adjoint orbit. Instability criteria for equilibrium solutions are established in the form of lower bounds for the essential spectral radius of the linear evolution operator restricted to each class of perturbation.Comment: 29 page

Reflection on Terrorist Havens

Any group of extremists, however justifiable some of their grievances may be, can thus, through hijacking of aircraft or kidnapping of foreign diplomats, receive international attention, remain unpunished, involve innocent people, and sow the seeds of international anarchy