Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators

We derive a spectral representation for the oblate spheroidal wave operator which is holomorphic in the aspherical parameter $\Omega$ in a neighborhood of the real line. For real $\Omega$, estimates are derived for all eigenvalue gaps uniformly in $\Omega$. The proof of the gap estimates is based on detailed estimates for complex solutions of the Riccati equation. The spectral representation for complex $\Omega$ is derived using the theory of slightly non-selfadjoint perturbations.Comment: 33 pages, LaTeX, 3 figures, typo in Lemma 4.1 corrected (published version

Spatial Patterns of Soil Development, Methane Oxidation, and Methanotrophic Diversity along a Receding Glacier Forefield, Southeast Greenland

Increasing global annual temperature leads to massive loss of ice cover worldwide. Consequently, glaciers retreat and ice-covered areas become exposed. We report on a study from the Mittivakkat Gletscher forefield in Southeast Greenland with special focus on methanotrophy in relation to exposure time to the atmosphere. The Mittivakkat Gletscher has receded since the end of the Little Ice Age (LIA; about AD 1850) and has left behind a series of deposits of decreasing age concurrently with its recession. Soil samples from this chronosequence were examined in order to elucidate main soil variables, as well as the activity and community structure of methanotrophs, a group of microorganisms involved in regulation of atmospheric methane. Soil variables revealed poor soil development, and incubation experiments showed methane consumption rates of 2.14 nmol CH4 day−1 gsoil −1 at 22 °C and 1.24 nmol CH4 day−1 gsoil −1 at 10 °C in the LIA terminal moraine. Methane consumption was not detected in younger samples, despite the presence of high-affinity methanotrophs in all samples. This was indicated by successful amplification of partial pmoA genes, which code for a subunit of a key enzyme involved in methane oxidation. In addition, the results of the diversity study show that the diversity of the methanotrophic community at the younger, recently deglaciated site P5 is poorer than the diversity of the community retrieved from the LIA moraine. We put forward the hypothesis that aerobic methanotrophs were at very low abundance and diversity during glaciation probably due to anoxia at the ice-sediment interface and that colonization after deglaciation is not completed yet. More detailed studies are required to explain the causes of discrepancy between activity and presence of high-affinity methanotrophs and its relation to the transit from ice-covered probably anoxic to ice-free oxi

Complete genome sequence of Desulfocapsa sulfexigens, a marine deltaproteobacterium specialized in disproportionating inorganic sulfur compounds

Desulfocapsa sulfexigens SB164P1 (DSM 10523) belongs to the deltaproteobacterial family Desulfobulbaceae and is one of two validly described members of its genus. This strain was selected for genome sequencing, because it is the first marine bacterium reported to thrive on the disproportionation of elemental sulfur, a process with a unresolved enzymatic pathway in which elemental sulfur serves both as electron donor and electron acceptor. Furthermore, in contrast to its phylogenetically closest relatives, which are dissimilatory sulfate-reducers, D. sulfexigens is unable to grow by sulfate reduction and appears metabolically specialized in growing by disproportionating elemental sulfur, sulfite or thiosulfate with CO2 as the sole carbon source. The genome of D. sulfexigens contains the set of genes that is required for nitrogen fixation. In an acetylene assay it could be shown that the strain reduces acetylene to ethylene, which is indicative for N-fixation. The circular chromosome of D. sulfexigens SB164P1 comprises 3,986,761 bp and harbors 3,551 protein-coding genes of which 78% have a predicted function based on auto-annotation. The chromosome furthermore encodes 46 tRNA genes and 3 rRNA operons

Resolvent estimates for normally hyperbolic trapped sets

We give pole free strips and estimates for resolvents of semiclassical operators which, on the level of the classical flow, have normally hyperbolic smooth trapped sets of codimension two in phase space. Such trapped sets are structurally stable and our motivation comes partly from considering the wave equation for Kerr black holes and their perturbations, whose trapped sets have precisely this structure. We give applications including local smoothing effects with epsilon derivative loss for the Schr\"odinger propagator as well as local energy decay results for the wave equation.Comment: Further changes to erratum correcting small problems with Section 3.5 and Lemma 4.1; this now also corrects hypotheses, explicitly requiring trapped set to be symplectic. Erratum follows references in this versio

Stability Analysis and Area Spectrum of 3-Dimensional Lifshitz Black Holes

In this work, we probe the stability of a $z=3$ three-dimensional Lifshitz black hole by using scalar and spinorial perturbations. We found an analytical expression for the quasinormal frequencies of the scalar probe field, which perfectly agree with the behavior of the quasinormal modes obtained numerically. The results for the numerical analysis of the spinorial perturbations reinforce the conclusion of the scalar analysis, i.e., the model is stable under scalar and spinor perturbations. As an application we found the area spectrum of the Lifshitz black hole, which turns out to be equally spaced.Comment: 23 pages, 6 figures. References added. Version to appear in Phys. Rev.

Singularity-free model of electric charge in physical vacuum: Non-zero spatial extent and mass generation

We propose a model of a spinless electrical charge as a self-consistent field configuration of the electromagnetic (EM) field interacting with a physical vacuum effectively described by the logarithmic quantum Bose liquid. We show that, in contrast to the EM field propagating in a trivial vacuum, a regular solution does exist, and both its mass and spatial extent emerge naturally from dynamics. It is demonstrated that the charge and energy density distribution acquire Gaussian-like form. The solution in the logarithmic model is stable and energetically favourable, unlike that obtained in a model with a quartic (Higgs-like) potential.Comment: 10 pages, 9 figures, final/published versio

Investigating biological activity spectrum for novel styrylquinazoline analogues

In this study, series of ring-substituted 2-styrylquinazolin-4(3H)-one and 4-chloro-2-styrylquinazoline derivatives were prepared. The syntheses of the discussed compounds are presented. The compounds were analyzed by RP-HPLC to determine lipophilicity. They were tested for their inhibitory activity on photosynthetic electron transport (PET) in spinach (Spinacia oleracea L.) chloroplasts. Primary in vitro screening of the synthesized compounds was also performed against four mycobacterial strains and against eight fungal strains. Several compounds showed biological activity comparable with or higher than that of the standard isoniazid. It was found that the electronic properties of the R substituent, and not the total lipophilicity of the compound, were decisive for the photosynthesis-inhibiting activity of tested compounds

Возникновение и развитие еврейской прессы Крыма

В статье выделяются основные этапы процесса возникновения и развития еврейской прессы Крыма, вводится в научный оборот ряд еврейских изданий.У статті виділяються основні етапи процесу виникнення і розвитку єврейської преси Криму, вводиться в науковий обіг ряд єврейських видань.The article researches the Jewish Crimean mass-media

On the bound states of the Dirac equation in the extreme Kerr metric

We study the eigenvalues of the angular equation arising after the separation of the Dirac equation in the extreme Kerr metric. To this purpose a self-adjoint holomorphic operator family associated to this eigenvalue problem is considered. We show that the eigenvalues satisfy a first order nonlinear differential equation with respect to the black hole mass and we solve it. Finally, we prove that there exist no bound states for the Dirac equation in the aforementioned metric.Comment: 13 page

Fundamental Solutions for the Klein-Gordon Equation in de Sitter Spacetime

In this article we construct the fundamental solutions for the Klein-Gordon equation in de Sitter spacetime. We use these fundamental solutions to represent solutions of the Cauchy problem and to prove $L^p-L^q$ estimates for the solutions of the equation with and without a source term