Growth rates of amenable groups

Let Fm be a free group with m generators and let R be a normal subgroup such that Fm /R projects onto ℤ. We give a lower bound for the growth rate of the group Fm / R′(where R′ is the derived subgroup of R) in terms of the length ρ= ρ(R) of the shortest non-trivial relation in R. It follows that the growth rate of Fm / R′ approaches 2m-1 as ρ approaches infinity. This implies that the growth rate of an m-generated amenable group can be arbitrarily close to the maximum value 2m- 1. This answers an open question of P. de la Harpe. We prove that such groups can be found in the class of abelian-by-nilpotent groups as well as in the class of virtually metabelian group

Scattering defect in large diameter titanium-doped sapphire crystals grown by the Kyropoulos technique

International audienceThe Kyropoulos technique allows growing large diameter Ti doped sapphire for Chirped pulse amplification laser. A scattering defect peculiar to Kyropoulos grown crystals is presented. This defect is characterized by different techniques: luminescence, absorption measurement, X-ray rocking curve. The impact of this defect to the potential application in chirped pulse amplification CPA laser is evaluated. The nature of this defect is discussed. Modified convexity of the interface is proposed to avoid the formation of this defect and increase the quality of the Ti sapphire crystal

Decaying shock studies of phase transitions in MgOSiO2 systems: implications for the Super-Earths interiors

We report an experimental study of the phase diagrams of periclase (MgO), enstatite (MgSiO3) and forsterite (Mg2SiO4) at high pressures. We investigated with laser driven decaying shocks the pressure/temperature curves of MgO, MgSiO3 and Mg2SiO4 between 0.2-1.2 TPa, 0.12-0.5 TPa and 0.2-0.85 TPa respectively. A melting signature has been observed in MgO at 0.47 TPa and 9860 K, while no phase changes were observed neither in MgSiO3 nor in Mg2SiO4. An increasing of reflectivity of MgO, MgSiO3 and Mg2SiO4 liquids have been detected at 0.55 TPa -12 760 K, 0.15 TPa - 7540 K, 0.2 TPa - 5800 K, respectively. In contrast to SiO2, melting and metallization of these compounds do not coincide implying the presence of poor electrically conducting liquids close to the melting lines. This has important implications for the generation of dynamos in Super-earths mantles

The effects of using P and G purifier of water during the treatment of severe acute malnutrition

Facilitated in Bandundu, D.R.C over a span of 4 months, this study evaluated the efficacy of P&G Purifier of Water, a point-of-use water treatment product produced and provided by Procter & Gamble. The evaluation was conducted by comparing the efficiency of using Ready-to-use-Food (RUTF) and treating domestic water with P&G Purifier of Water versus RUTF alone in the nutrition treatment of severe acute malnutrition (SAM) children under the age of 5 years without medical complications. Two hypotheses were tested: 1.) SAM cases without medical complication benefiting from RUTF + P&G Purifier of Water have a lower prevalence of waterborne diseases during the course of their treatment 2.) SAM children benefiting from RUTF + P&G Purifier of Water have better outcomes in terms of treatment time (shorter) and weight gain (higher). Ultimately, the study determined the importance of promoting P&G Purifier of Water as part of the standard nutrition treatment of SAM children without medical complications, in areas with difficult or no access to clean drinking water

Variable range hopping conduction in semiconductor nanocrystal solids

The temperature and electrical field dependent conductivity of n-type CdSe nanocrystal thin films is investigated. In the low electrical field regime, the conductivity follows G ~ exp(-(T*/T)^0.5) in the temperature range 10K<T<120K. At high electrical field, the conductivity is strongly field dependent. At 4K, the conductance increases by eight orders of magnitude over one decade of bias. At very high field, conductivity is temperature-independent with G ~ exp(-(E*/E)^0.5). The complete behavior is very well described by variable range hopping with Coulomb gap.Comment: Submitted to Physical Review Letters on Dec. 22, 200

Cosmological Perturbations with Multiple Fluids and Fields

We consider the evolution of perturbed cosmological spacetime with multiple fluids and fields in Einstein gravity. Equations are presented in gauge-ready forms, and are presented in various forms using the curvature (\Phi or \phi_\chi) and isocurvature (S_{(ij)} or \delta \phi_{(ij)}) perturbation variables in the general background with K and \Lambda. We clarify the conditions for conserved curvature and isocurvature perturbations in the large-scale limit. Evolutions of curvature perturbations in many different gauge conditions are analysed extensively. In the multi-field system we present a general solution to the linear order in slow-roll parameters.Comment: 19 pages, 6 figures, revised thoroughly; published version in Class. Quant. Gra

Expanding the scope of leaf symbiosis: Caballeronia endophytes in Empogona and Tricalysia (Coffeeae, Rubiaceae)

Leaf symbiosis is a remarkable phenomenon observed in Rubiaceae host plants, where they interact with bacterial endophytes residing within their leaves. Although approximately 650 species from 8 genera across 4 tribes exhibit this symbiosis, its fiill extent within Rubiaceae remains unknown. Our primary objective is to investígate the potential presence of leaf endophytes in the African plant genera Empogona and Tricalysia and, if confirmed, determine their identity. To accomplish this, we extracted total DNA from the leaves of four Coffeeae tribe species {Empogona congesta, Tricalysia hensii, T. lasiodelphys, and T. semidecidua) and sequenced it. Subsequently, we filtered out bacterial reads. Through phylogenetic analysis o f the endophytes, we were able to ascertain their identity and establish their relationship with known symbiotic organisms. Notably, all four species harboured non-nodulated leaf endophytes, specifically identified as Caballeronia. Although these endophytes are distinct from one another, they are related to other nodulated and non-nodulated endophytes. Interestingly, we did not observe any discemible phylogenetic or geographic pattems among the endophytes or their host plants. Our findings demónstrate the presence of Caballeronia endophytes in the leaves o f Empogona and Tricalysia, two genera previously not associated with leaf symbiosis. This interaction is likely to have a broader distribution, and further discoveries are inevitable in the future