Cohomology of the minimal nilpotent orbit

We compute the integral cohomology of the minimal non-trivial nilpotent orbit in a complex simple (or quasi-simple) Lie algebra. We find by a uniform approach that the middle cohomology group is isomorphic to the fundamental group of the sub-root system generated by the long simple roots. The modulo $\ell$ reduction of the Springer correspondent representation involves the sign representation exactly when $\ell$ divides the order of this cohomology group. The primes dividing the torsion of the rest of the cohomology are bad primes.Comment: 29 pages, v2 : Leray-Serre spectral sequence replaced by Gysin sequence only, corrected typo

Black holes admitting a Freudenthal dual

The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding U-duality and whose U-invariant quartic norm Delta(x) determines the lowest order entropy. Here we introduce a Freudenthal duality x -> \tilde{x}, for which \tilde{\tilde{x}}=-x. Although distinct from U-duality it nevertheless leaves Delta(x) invariant. However, the requirement that \tilde{x} be integer restricts us to the subset of black holes for which Delta(x) is necessarily a perfect square. The issue of higher-order corrections remains open as some, but not all, of the discrete U-duality invariants are Freudenthal invariant. Similarly, the quantised charges A of five dimensional black holes and strings may be assigned to elements of an integral Jordan algebra, whose cubic norm N(A) determines the lowest order entropy. We introduce an analogous Jordan dual A*, with N(A) necessarily a perfect cube, for which A**=A and which leaves N(A) invariant. The two dualities are related by a 4D/5D lift.Comment: 32 pages revtex, 10 tables; minor corrections, references adde

A unified approach on Springer fibers in the hook, two-row and two-column cases

We consider the Springer fiber over a nilpotent endomorphism. Fix a Jordan basis and consider the standard torus relative to this. We deal with the problem to describe the flags fixed by the torus which belong to a given component of the Springer fiber. We solve the problem in the hook, two-row and two-column cases. We provide two main characterizations which are common to the three cases, and which involve dominance relations between Young diagrams and combinatorial algorithms. Then, for these three cases, we deduce topological properties of the components and their intersections.Comment: 42 page

Rapidly Destructive Staphylococcus epidermidis Endocarditis

Abstract : A 29-year-old man with rapidly destructive Staphylococcus epidermidis endocarditis after mitral valve reconstruction is presented. Resistance to rifampin and teicoplanin occurred during antibiotic treatment resulting in clinical failure and valve destruction. Subsequently, the patient was successfully treated, by combining valve replacement with antibiotic therapy including quinupristin/dalfopristin, levofloxacin, and vancomycin. In conclusion, S. epidermidis can cause rapid valve destruction with large vegetations, and combination of surgery and antibiotic therapy may be necessar

Research Progress Report: Fox-Pheasant Relationships in South Dakota, 1965

A 5-year cooperative study designed to obtain information regarding effects of foxes on pheasant populations in eastern South Dakota was initiated in 1964. Specific objectives were to determine (1) population fluctuations of foxes and pheasants, (2) fox food habits and reproductive characteristics and (3) effectiveness and cost of fox reduction to increase pheasant abundance. Studies were conducted on four pairs of 100-square-mile areas. Fox populations were reduced on one member of each pair beginning in January 1965, and individual foxes were removed on a complaint basis on the other. Each pair of areas is referred to as a unit. When summer pheasant data on the fox-reduction and check areas are considered, significant differences are noted in adult pheasants per mile, broods per mile, and brood size from 1964 to 1965. Changes in adult pheasants per mile in Unit 2 showed the decline in the fox-reduction area was significantly (0. 01) less than in the check area. However, in Units 1 and 4 the declines in the check areas were significantly (0. 01) less than those in the fox-reduction areas. The difference in decline in broods per mile in the fox-reduction compared to the check area from 1964 to 1965 was negligible in Unit 1. In Unit 2 the fox-reduction area showed a slight increase compared to a decrease in the check area. This difference is significant (0. 01). In Unit 4 a smaller decline occurred in the fox-reduction area than in the check area. The difference in Unit 4 is significant (0. 05). The proportion of hens with broods showed an increase from 1964 to 1965 in the fox-reduction areas of Units 1, 2, and 4 and a lesser increase or a decrease in the corresponding check areas. A significant (0. 01) increase in brood size occurred from 1964 to 1965 in the fox-reduction compared to the check area of Unit 1. A non-significant increase occurred in the check area compared to the fox-reduction area in Unit 2. The adult pheasant-per-mile averages during the spring of 1965 showed more birds in the fox-reduction area than in the check area of Unit 1, and the reverse in Unit 2. Neither difference is significant. Units 3 and 4 showed significantly (0. 01) more adults per mile in the fox reduction than in the check areas during this same period. Fox data revealed that counting tracks in snow along transects is the best of three methods for determining fox activity in an area. Such counts in reduction and check areas within each unit showed that fox activity was sufficiently comparable in each pair of areas prior to fox reduction. Methods used to reduce fox populations also reduced to some extent other predators, including nest robbers. Grasses, mice, pheasants, rabbits, and insects, in descending order, respectively, were the most frequently occurring items found in stomachs of foxes taken in the study areas from January to June 1965. Grasses were found in stomachs that also contained mice and insects. Pheasants were the item composing the greatest volume, followed by rabbits and mice. Prairie deer mice made up the majority of small mammal remains. (See more in Text

Glycotope structures and intramolecular affinity factors of plant lectins for Tn/T antigens

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Nonrelativistic Chern-Simons Vortices on the Torus

A classification of all periodic self-dual static vortex solutions of the Jackiw-Pi model is given. Physically acceptable solutions of the Liouville equation are related to a class of functions which we term Omega-quasi-elliptic. This class includes, in particular, the elliptic functions and also contains a function previously investigated by Olesen. Some examples of solutions are studied numerically and we point out a peculiar phenomenon of lost vortex charge in the limit where the period lengths tend to infinity, that is, in the planar limit.Comment: 25 pages, 2+3 figures; improved exposition, corrected typos, added one referenc