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

Attributes Preferred and Premiums Offered for Naturally Produced Beef Cattle

A growing number of beef cattle producers in the US are using limited information to determine whether or not it would be economical for them to grow naturally produced cattle. The objective was to discover the attributes that marketing companies prefer for the naturally produced cattle they purchase, and to elicit the price premiums being offered for cattle that possess these attributes. Results of a phone survey of companies that purchase natural cattle show that 27 out of 32 companies report their willingness to pay a premium of $5.95/cwt for cattle that have never received antibiotics, ionophores, hormones or animal by-products.Key words: attributes, beef, cattle, naturally produced, premiums, Agribusiness, Food Consumption/Nutrition/Food Safety, Livestock Production/Industries, Marketing,

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

Shear sum rules at finite chemical potential

We derive sum rules which constrain the spectral density corresponding to the retarded propagator of the T_{xy} component of the stress tensor for three gravitational duals. The shear sum rule is obtained for the gravitational dual of the N=4 Yang-Mills, theory of the M2-branes and M5-branes all at finite chemical potential. We show that at finite chemical potential there are additional terms in the sum rule which involve the chemical potential. These modifications are shown to be due to the presence of scalars in the operator product expansion of the stress tensor which have non-trivial vacuum expectation values at finite chemical potential.Comment: The proof for the absence of branch cuts is corrected.Results unchange

Sum rules and three point functions

Sum rules constraining the R-current spectral densities are derived holographically for the case of D3-branes, M2-branes and M5-branes all at finite chemical potentials. In each of the cases the sum rule relates a certain integral of the spectral density over the frequency to terms which depend both on long distance physics, hydrodynamics and short distance physics of the theory. The terms which which depend on the short distance physics result from the presence of certain chiral primaries in the OPE of two R-currents which are turned on at finite chemical potential. Since these sum rules contain information of the OPE they provide an alternate method to obtain the structure constants of the two R-currents and the chiral primary. As a consistency check we show that the 3 point function derived from the sum rule precisely matches with that obtained using Witten diagrams.Comment: 41 page

Economic Potential of Substituting Legumes for Synthetic Nitrogen in Warm Season Perennial Grasses used for Stocker Cattle Grazing

Stocker cattle grazing warm season perennial grasses is an important economic activity in the southern Great Plains. Substantial increases in the price of nitrogen fertilizer is negatively affecting forage producers’ profitability. Two alternative nitrogen management systems that use annual and perennial legumes have been developed for bermudagrass pastures. The goal of the study is to determine if the legumes systems are more profitable than the conventional practice of applying synthetic sources of nitrogen. Results of the two-year grazing study show that the legume systems could not compete economically with the common practice.economics, grazing, legumes, bermudagrass, nitrogen fertilizer, stocker cattle, Crop Production/Industries, Farm Management, Production Economics,

First-Year Vitality of Reforestation Plantings in Response to Herbivore Exclusion on Reclaimed Appalachian Surface-Mined Land

Conventional Appalachian surface-mine reclamation techniques repress natural forest regeneration, and tree plantings are often necessary for reforestation. Reclaimed Appalachian surface mines harbor a suite of mammal herbivores that forage on recently planted seedlings. Anecdotal reports across Appalachia have implicated herbivory in the hindrance and failure of reforestation efforts, yet empirical evaluation of herbivory impacts on planted seedling vitality in this region remains relatively uninitiated. First growing-season survival, height growth, and mammal herbivory damage of black locust (Robinia pseudoacacia L.), shortleaf pine (Pinus echinata Mill.), and white oak (Quercus alba L.) are presented in response to varying intensities of herbivore exclusion. Seedling survival was generally high, and height growth was positive for all species. The highest herbivory incidence of all tree species was observed in treatments offering no herbivore exclusion. While seedling protectors lowered herbivory incidence compared with no exclusion, full exclusion treatments resulted in the greatest reduction of herbivore damage. Although herbivory from rabbits, small mammals, and domestic animals was observed, cervids (deer and elk) were responsible for 95.8% of all damaged seedlings. This study indicates that cervids forage heavily on planted seedlings during the first growing-season, but exclusion is effective at reducing herbivory

Lyashko-Looijenga morphisms and submaximal factorisations of a Coxeter element

When W is a finite reflection group, the noncrossing partition lattice NCP_W of type W is a rich combinatorial object, extending the notion of noncrossing partitions of an n-gon. A formula (for which the only known proofs are case-by-case) expresses the number of multichains of a given length in NCP_W as a generalised Fuss-Catalan number, depending on the invariant degrees of W. We describe how to understand some specifications of this formula in a case-free way, using an interpretation of the chains of NCP_W as fibers of a Lyashko-Looijenga covering (LL), constructed from the geometry of the discriminant hypersurface of W. We study algebraically the map LL, describing the factorisations of its discriminant and its Jacobian. As byproducts, we generalise a formula stated by K. Saito for real reflection groups, and we deduce new enumeration formulas for certain factorisations of a Coxeter element of W.Comment: 18 pages. Version 2 : corrected typos and improved presentation. Version 3 : corrected typos, added illustrated example. To appear in Journal of Algebraic Combinatoric