On the Penrose Inequality for general horizons

For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the ADM mass and the area of an outermost apparent horizon, if the data are restricted suitably. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass under a smooth inverse mean curvature flow, for data with non-negative Ricci scalar. Unlike Geroch we need not confine ourselves to minimal surfaces as horizons. Modulo smoothness issues we also show that our restrictions on the data can locally be fulfilled by a suitable choice of the initial surface in a given spacetime.Comment: 4 pages, revtex, no figures. Some comments added. No essential changes. To be published in Phys. Rev. Let

Isometric Representations of Totally Ordered Semigroups

Let S be a subsemigroup of an abelian torsion-free group G. If S is a positive cone of G, then all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic. Proved by Murphy, this statement generalized the well-known theorems of Coburn and Douglas. In this note we prove the reverse. If all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic, then S is a positive cone of G. Also we consider G = Z\times Z and prove that if S induces total order on G, then there exist at least two unitarily not equivalent irreducible isometrical representation of S. And if the order is lexicographical-product order, then all such representations are unitarily equivalent.Comment: February 21, 2012. Kazan, Russi

Droop models of nutrient–plankton interaction with intratrophic predation

Droop models of nutrient–phytoplankton–zooplankton interaction with intratrophic predation of zooplankton are introduced and investigated. The models proposed in this study are open ecosystems which include both a constant and a periodic input nutrient models. A simple stochastic model mimics a randomly varying nutrient input is also presented. For the deterministic models it is shown analytically that intratrophic predation has no effect on the global asymptotic dynamics of the systems if either one of the populations has a negative growth rate. Numerical simulations are also used to investigate the effects of intratrophic predation. Unlike the deterministic models for which both populations can coexist with each other if populations’ net growth rates are positive, plankton populations can become extinct if the input nutrient concentration is varied randomly

B -> Xs l_i^+ l_j^+ Decays with R-parity Violation

We derive the upper bounds on certain products of R-parity- and lepton-flavor-violating couplings from B \ra X_s {l_i}^+ {l_j}^- decays. These modes of B-meson decays can constrain the product combinations of the couplings with one or more heavy generation indices which are comparable with or stronger than the present bounds. From the studies of the invariant dilepton mass spectrum and the forward backward asymmetry of the emitted leptons we note the possibility of detecting R-parity-violating signals even when the total decay rate due to R-parity violating couplings is comparable with that in the standard model and discriminating two types of R-parity-violating signals. The general expectation of the enhancement of the forward backward asymmetry of the emitted leptons in the minimal supersymmetric standard model with R-parity may be corrupted by R-parity violation.Comment: 10 pages, Revtex, 1 table and 2 figure

Permutation sampling in Path Integral Monte Carlo

A simple algorithm is described to sample permutations of identical particles in Path Integral Monte Carlo (PIMC) simulations of continuum many-body systems. The sampling strategy illustrated here is fairly general, and can be easily incorporated in any PIMC implementation based on the staging algorithm. Although it is similar in spirit to an existing prescription, it differs from it in some key aspects. It allows one to sample permutations efficiently, even if long paths (e.g., hundreds, or thousands of slices) are needed. We illustrate its effectiveness by presenting results of a PIMC calculation of thermodynamic properties of superfluid Helium-four, in which a very simple approximation for the high-temperature density matrix was utilized