One-dimensional quasi-relativistic particle in the box

Two-term Weyl-type asymptotic law for the eigenvalues of one-dimensional quasi-relativistic Hamiltonian (-h^2 c^2 d^2/dx^2 + m^2 c^4)^(1/2) + V_well(x) (the Klein-Gordon square-root operator with electrostatic potential) with the infinite square well potential V_well(x) is given: the n-th eigenvalue is equal to (n pi/2 - pi/8) h c/a + O(1/n), where 2a is the width of the potential well. Simplicity of eigenvalues is proved. Some L^2 and L^infinity properties of eigenfunctions are also studied. Eigenvalues represent energies of a `massive particle in the box' quasi-relativistic model.Comment: 40 pages, 4 figures; minor correction

VIRGO sensitivity to binary coalescences and the Population III black hole binaries

We analyze the properties of VIRGO detector with the aim of studying its ability to search for coalescing black hole binaries. We focus on the remnants of the Population III stars, which currently should be massive black holes ($\sim 100-1000 M_\odot$), some of them bound in binary systems. The coalescence of such binaries due to emission of gravitational waves may be currently observable. We use a binary population synthesis to model the evolution of Population III binaries. We calculate the signal to noise ratios of gravitational waves emitted by the system in each of the coalescence phase: inspiral, merger and ringdown, and provide simple formulae for the signal to noise ratio as a function of masses of the binaries. We estimate the detection rates for the VIRGO interferometer and also compare them with the estimates for the current LIGO. We show that these expected rates are similar to, or larger than the expected rates from coalescences of Population I and II compact object binaries.Comment: sumbitted to A&

Influence of timing on CSF tests value for Creutzfeldt-Jakob disease diagnosis

Background: The analysis of markers in the cerebrospinal fluid (CSF) is useful in the diagnosis of sporadic Creutzfeldt-Jakob disease (sCJD). However, the time at which the study of these markers is most sensitive remains controversal. Objective: To assess the influence of time of sampling on the value of CSF tests in the diagnosis of sCJD. Method: In the framework of a multinational European study, we studied the results of 14-3-3, S100b, neurone specific enolase (NSE) and tau protein in 833 CSF samples from sCJD patients at different stages of disease and in 66 sequentially repeated lumbar punctures (LP). Results: 14-3-3 and tau protein tended to increase in sensitivity from onset (88%, 81%) to the advanced stage (91%, 90%). This was significant only in the methionine-valine (MV) heterozygous group of patients at codon 129. The absolute levels of S100b (p < 0.05), NSE and tau protein increased in the last stage of disease. High levels of tau protein, NSE and S100b were associated with shorter survival times (p < 0.01). Sixty-six sCJD patients underwent repeated LP. These sCJD patients were younger, had longer disease durations and were more frequently MV at codon 129 (p < 0.001) than the whole group. 14-3-3 sensitivity increased from 64% to 82% in the second LP (p = 0.025) and 88% sCJD patients had at least one positive result. Conclusions: Sensitivity and absolute levels of CJD markers increased with disease progression and were modulated by the codon 129 genotype. Early negative results should be inter-preted with caution, especially in young patients or those who are MV at codon 129

Kinetics of biodegradation of diethylketone by Arthrobacter viscosus

The performance of an Arthrobacter viscosus culture to remove diethylketone from aqueous solutions was evaluated. The effect of initial concentration of diethylketone on the growth of the bacteria was evaluated for the range of concentration between 0 and 4.8 g/l, aiming to evaluate a possible toxicological effect. The maximum specific growth rate achieved is 0.221 h-1 at 1.6 g/l of initial diethylketone concentration, suggesting that for higher concentrations an inhibitory effect on the growth occurs. The removal percentages obtained were approximately 88%, for all the initial concentrations tested. The kinetic parameters were estimated using four growth kinetic models for biodegradation of organic compounds available in the literature. The experimental data found is well fitted by the Haldane model (R2 = 1) as compared to Monod model (R2 = 0.99), Powell (R2 = 0.82) and Loung model (R2 = 0.95). The biodegradation of diethylketone using concentrated biomass was studied for an initial diethylketone concentration ranging from 0.8–3.9 g/l in a batch with recirculation mode of operation. The biodegradation rate found followed the pseudo-second order kinetics and the resulting kinetic parameters are reported. The removal percentages obtained were approximately 100%, for all the initial concentrations tested, suggesting that the increment on the biomass concentration allows better results in terms of removal of diethylketone. This study showed that these bacteria are very effective for the removal of diethylketone from aqueous solutions.The authors would like to gratefully acknowledge the financial support of this project by the Fundacao para a Ciencia e Tecnologia (FCT), Ministerio da Ciencia e Tecnologia, Portugal and Fundo Social Europeu (FSE). Cristina Quintelas thanks FCT for a Post-Doc grant

Isolation and purification of Cu-free methanobactin from Methylosinus trichosporium OB3b

<p>Abstract</p> <p>Background</p> <p>The isolation of highly pure copper-free methanobactin is a prerequisite for the investigation of the biogeochemical functions of this chalkophore molecule produced by methane oxidizing bacteria. Here, we report a purification method for methanobactin from <it>Methylosinus trichosporium </it>OB3b cultures based on reversed-phase HPLC fractionation used in combination with a previously reported resin extraction. HPLC eluent fractions of the resin extracted product were collected and characterized with UV-vis, FT-IR, and C-1s NEXAFS spectroscopy, as well as with elemental analysis and ESI-MS.</p> <p>Results</p> <p>The results showed that numerous compounds other than methanobactin were present in the isolate obtained with resin extraction. Molar C/N ratios, mass spectrometry measurements, and UV-vis spectra indicated that methanobactin was only present in one of the HPLC fractions. On a mass basis, methanobactin carbon contributed only 32% to the total organic carbon isolated with resin extraction. Our spectroscopic results implied that besides methanobactin, the organic compounds in the resin extract comprised breakdown products of methanobactin as well as polysaccharide-like substances.</p> <p>Conclusion</p> <p>Our results demonstrate that a purification step is indispensable in addition to resin extraction in order to obtain pure methanobactin. The proposed HPLC purification procedure is suitable for semi-preparative work and provides copper-free methanobactin.</p

Symmetric Jump Processes and their Heat Kernel Estimates

We survey the recent development of the DeGiorgi-Nash-Moser-Aronson type theory for a class of symmetric jump processes(or equivalently, a class of symmetric integro-differential operators). We focus on the sharp two-sided estimates for the transition density functions (or heat kernels) of the processes, a priori Holder estimate and parabolic Harnack inequalities for their parabolic functions. In contrast to the second order elliptic differential operator case, the methods to establish these properties for symmetric integro-differential operators are mainly probabilistic.Comment: To appear in Science in China Series A: Mathematic