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

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

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

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

Production and optical properties of liquid scintillator for the JSNS2^{2} experiment

The JSNS$^{2}$ (J-PARC Sterile Neutrino Search at J-PARC Spallation Neutron Source) experiment will search for neutrino oscillations over a 24 m short baseline at J-PARC. The JSNS$^{2}$ inner detector will be filled with 17 tons of gadolinium-loaded liquid scintillator (LS) with an additional 31 tons of unloaded LS in the intermediate $\gamma$-catcher and outer veto volumes. JSNS$^{2}$ has chosen Linear Alkyl Benzene (LAB) as an organic solvent because of its chemical properties. The unloaded LS was produced at a refurbished facility, originally used for scintillator production by the RENO experiment. JSNS$^{2}$ plans to use ISO tanks for the storage and transportation of the LS. In this paper, we describe the LS production, and present measurements of its optical properties and long term stability. Our measurements show that storing the LS in ISO tanks does not result in degradation of its optical properties.Comment: 7 pages, 4 figures

Mechanical Properties Transformation on Zr54Al17Co29 Bulk Metallic Glass by Partial Crystallization

Study on biomaterials is recently essential for rapid development of medical application and Zr54Al17Co29 BMGbecomes promising candidate due to the lack of toxic elements. Partial crystallization by isothermal annealing at SCL region was used to variate the crystallinities of BMG. The structural and thermal properties of as cast and partially crystallized samples were confirmed by XRD and DSC test, while microvickers and compression test were further utilized to investigate their mechanical properties. By the higher crystallinity, the hardness could be slightly increased in range 540 ± 5 to 575 ± 5 Hv. As-cast sample shows the yield strength and plastic strain of 2130 ± 75 MPa and 2.2 ± 1.6%. The yield strength is increased by the presence of 10% nanocrystal, afterwards, fall and raise phenomena are obtained with further crystallinity. However, with higher crystallinity, the plasticity is significantly degraded and no more plastic strain observed at sample with 50% of crystallinity. Both the presence of nanocrystalline phase and free volume annihilation are the reason of mechanical properties change on the Zr-based BMG