Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space-times

We prove upper bounds on angular momentum and centre of mass in terms of the Hamiltonian mass and cosmological constant for non-singular asymptotically anti-de Sitter initial data sets satisfying the dominant energy condition. We work in all space-dimensions larger than or equal to three, and allow a large class of asymptotic backgrounds, with spherical and non-spherical conformal infinities; in the latter case, a spin-structure compatibility condition is imposed. We give a large class of non-trivial examples saturating the inequality. We analyse exhaustively the borderline case in space-time dimension four: for spherical cross-sections of Scri, equality together with completeness occurs only in anti-de Sitter space-time. On the other hand, in the toroidal case, regular non-trivial initial data sets saturating the bound exist.Comment: improvements in the presentation; some statements correcte

Implant strategies for finishing calves

Two hundred-sixteen Angus and Angus-cross steer calves (690 lb) were used in a 129- day finishing study to evaluate different implant strategies, including an experimental new implant for feedlot cattle that contains 28 mg of estradiol benzoate and 200 mg of trenbolone acetate (EBTBA). Treatments were 1) nonimplanted control, 2) implanted and reimplanted with Synovex-Sfi, 3) single initial implant with EBTBA, 4) single initial implant with Revalor-Sfi, 5) implanted with Synovex-S and reimplanted with EBTBA, and 6) implanted and reimplanted with EBTBA. Initial implants and reimplants were administered on day 0 and 63, respectively. All implant treatments increased feed intake, slaughter and carcass weights, and rate and efficiency of gain. Compared with other implant treatments, the use of EBTBA as a reimplant treatment (trts 5 and 6) resulted in improved (P<.08) rate and efficiency of gain and heavier carcass weights (P<.07). However, only 58.3% of cattle in trts 5 and 6 graded Choice vs. 86.1% for controls and 80.6% for steers implanted twice with Synovex-S (P<.07). Carcasses were more masculine (P<.07) for steers in trts 5 and 6 than for nonimplanted controls, steers implanted with Revalor-S, and steers implanted twice with Synovex-S. Performance of steers implanted once with EBTBA did not differ from that of steers implanted once with Revalor-S or twice with Synovex-S, but carcasses were more masculine (P<.07) for EBTBA vs. Revalor-S steers. Implant treatment did not affect meat tenderness, as measured by Warner-Bratzler shear force determinations. Single EBTBA or Revalor-S implants resulted in performance and carcass traits similar to those resulting from implanting twice with Synovex-S

A specialist toxicity database (TRACE) is more effective than its larger, commercially available counterparts

A comparison of the retrieval precision and recall of a specialist bibliographic toxicity database (TRACE) with that of a wide range of commercial on-line databases indicated that the larger size and resources of the commercial databases did not, for a series of test queries, assure superior retrieval of relevant papers. The specialist database, in which document selection and indexing is undertaken by the same (in this case) expert toxicologists who subsequently use the database in their day-to-day work, achieved markedly better retrieval, using simpler search strategies, than the commercial databases. Small specialist databases may offer a valuable alternative to existing commercial databases

An explicit height bound for the classical modular polynomial

For a prime m, let Phi_m be the classical modular polynomial, and let h(Phi_m) denote its logarithmic height. By specializing a theorem of Cohen, we prove that h(Phi_m) <= 6 m log m + 16 m + 14 sqrt m log m. As a corollary, we find that h(Phi_m) <= 6 m log m + 18 m also holds. A table of h(Phi_m) values is provided for m <= 3607.Comment: Minor correction to the constants in Theorem 1 and Corollary 9. To appear in the Ramanujan Journal. 17 pages

Excavation at Aguas Buenas, Robinson Crusoe Island, Chile, of a gunpowder magazine and the supposed campsite of Alexander Selkirk, together with an account of early navigational dividers

Excavations were undertaken of a ruined building at Aguas Buenas, identified as an 18th-century Spanish gunpowder magazine. Evidence was also found for the campsite of an early European occupant of the island. A case is made that this was Alexander Selkirk, a castaway here from 1704 to 1709. Selkirk was the model for Defoe’s Robinson Crusoe. A detailed discussion is given of a fragment of copper alloy identifi ed as being from a pair of navigational dividers

Ground state properties of the 2D disordered Hubbard model

We study the ground state of the two-dimensional (2D) disordered Hubbard model by means of the projector quantum Monte Carlo (PQMC) method. This approach allows us to investigate the ground state properties of this model for lattice sizes up to $10 \times 10$, at quarter filling, for a broad range of interaction and disorder strengths. Our results show that the ground state of this system of spin-1/2 fermions remains localised in the presence of the short-ranged Hubbard interaction.Comment: 7 pages, 9 figure

Static black holes with a negative cosmological constant: Deformed horizon and anti-de Sitter boundaries

Using perturbative techniques, we investigate the existence and properties of a new static solution for the Einstein equation with a negative cosmological constant, which we call the deformed black hole. We derive a solution for a static and axisymmetric perturbation of the Schwarzschild-anti-de Sitter black hole that is regular in the range from the horizon to spacelike infinity. The key result is that this perturbation simultaneously deforms the two boundary surfaces--i.e., both the horizon and spacelike two-surface at infinity. Then we discuss the Abbott-Deser mass and the Ashtekar-Magnon one for the deformed black hole, and according to the Ashtekar-Magnon definition, we construct the thermodynamic first law of the deformed black hole. The first law has a correction term which can be interpreted as the work term that is necessary for the deformation of the boundary surfaces. Because the work term is negative, the horizon area of the deformed black hole becomes larger than that of the Schwarzschild-anti-de Sitter black hole, if compared under the same mass, indicating that the quasistatic deformation of the Schwarzschild-anti-de Sitter black hole may be compatible with the thermodynamic second law (i.e., the area theorem).Comment: 31 pages, 5 figures, one reference added, to be published in PR

Solving variational inequalities defined on a domain with infinitely many linear constraints

We study a variational inequality problem whose domain is defined by infinitely many linear inequalities. A discretization method and an analytic center based inexact cutting plane method are proposed. Under proper assumptions, the convergence results for both methods are given. We also provide numerical examples to illustrate the proposed method

Schwinger-Keldysh Approach to Disordered and Interacting Electron Systems: Derivation of Finkelstein's Renormalization Group Equations

We develop a dynamical approach based on the Schwinger-Keldysh formalism to derive a field-theoretic description of disordered and interacting electron systems. We calculate within this formalism the perturbative RG equations for interacting electrons expanded around a diffusive Fermi liquid fixed point, as obtained originally by Finkelstein using replicas. The major simplifying feature of this approach, as compared to Finkelstein's is that instead of $N \to 0$ replicas, we only need to consider N=2 species. We compare the dynamical Schwinger-Keldysh approach and the replica methods, and we present a simple and pedagogical RG procedure to obtain Finkelstein's RG equations.Comment: 22 pages, 14 figure