Absolute Continuity Theorem for Random Dynamical Systems on RdR^d

In this article we provide a proof of the so called absolute continuity theorem for random dynamical systems on $R^d$ which have an invariant probability measure. First we present the construction of local stable manifolds in this case. Then the absolute continuity theorem basically states that for any two transversal manifolds to the family of local stable manifolds the induced Lebesgue measures on these transversal manifolds are absolutely continuous under the map that transports every point on the first manifold along the local stable manifold to the second manifold, the so-called Poincar\'e map or holonomy map. In contrast to known results, we have to deal with the non-compactness of the state space and the randomness of the random dynamical system.Comment: 46 page

Initiator tRNA genes template the 3\u27 CCA end at high frequencies in bacteria.

BACKGROUND: While the CCA sequence at the mature 3\u27 end of tRNAs is conserved and critical for translational function, a genetic template for this sequence is not always contained in tRNA genes. In eukaryotes and Archaea, the CCA ends of tRNAs are synthesized post-transcriptionally by CCA-adding enzymes. In Bacteria, tRNA genes template CCA sporadically. RESULTS: In order to understand the variation in how prokaryotic tRNA genes template CCA, we re-annotated tRNA genes in tRNAdb-CE database version 0.8. Among 132,129 prokaryotic tRNA genes, initiator tRNA genes template CCA at the highest average frequency (74.1%) over all functional classes except selenocysteine and pyrrolysine tRNA genes (88.1% and 100% respectively). Across bacterial phyla and a wide range of genome sizes, many lineages exist in which predominantly initiator tRNA genes template CCA. Convergent and parallel retention of CCA templating in initiator tRNA genes evolved in independent histories of reductive genome evolution in Bacteria. Also, in a majority of cyanobacterial and actinobacterial genera, predominantly initiator tRNA genes template CCA. We also found that a surprising fraction of archaeal tRNA genes template CCA. CONCLUSIONS: We suggest that cotranscriptional synthesis of initiator tRNA CCA 3\u27 ends can complement inefficient processing of initiator tRNA precursors, bootstrap rapid initiation of protein synthesis from a non-growing state, or contribute to an increase in cellular growth rates by reducing overheads of mass and energy to maintain nonfunctional tRNA precursor pools. More generally, CCA templating in structurally non-conforming tRNA genes can afford cells robustness and greater plasticity to respond rapidly to environmental changes and stimuli

Initiator tRNA genes template the 3' CCA end at high frequencies in bacteria.

BackgroundWhile the CCA sequence at the mature 3' end of tRNAs is conserved and critical for translational function, a genetic template for this sequence is not always contained in tRNA genes. In eukaryotes and Archaea, the CCA ends of tRNAs are synthesized post-transcriptionally by CCA-adding enzymes. In Bacteria, tRNA genes template CCA sporadically.ResultsIn order to understand the variation in how prokaryotic tRNA genes template CCA, we re-annotated tRNA genes in tRNAdb-CE database version 0.8. Among 132,129 prokaryotic tRNA genes, initiator tRNA genes template CCA at the highest average frequency (74.1%) over all functional classes except selenocysteine and pyrrolysine tRNA genes (88.1% and 100% respectively). Across bacterial phyla and a wide range of genome sizes, many lineages exist in which predominantly initiator tRNA genes template CCA. Convergent and parallel retention of CCA templating in initiator tRNA genes evolved in independent histories of reductive genome evolution in Bacteria. Also, in a majority of cyanobacterial and actinobacterial genera, predominantly initiator tRNA genes template CCA. We also found that a surprising fraction of archaeal tRNA genes template CCA.ConclusionsWe suggest that cotranscriptional synthesis of initiator tRNA CCA 3' ends can complement inefficient processing of initiator tRNA precursors, "bootstrap" rapid initiation of protein synthesis from a non-growing state, or contribute to an increase in cellular growth rates by reducing overheads of mass and energy to maintain nonfunctional tRNA precursor pools. More generally, CCA templating in structurally non-conforming tRNA genes can afford cells robustness and greater plasticity to respond rapidly to environmental changes and stimuli

d=4+1 gravitating nonabelian solutions with bi-azimuthal symmetry

We construct static, asymptotically flat solutions of SU(2) Einstein-Yang-Mills theory in 4+1 dimensions, subject to bi-azimuthal symmetry. Both particle-like and black hole solutions are considered for two different sets of boundary conditions in the Yang--Mills sector, corresponding to multisolitons and soliton-antisoliton pairs. For gravitating multi-soliton solutions, we find that their mass per unit charge is lower than the mass of the corresponding unit charge, spherically symmetric soliton.Comment: 13 pages, 5 figures; v2: typos corrected, published versio

Standing gravitational waves from domain walls

We construct a plane symmetric, standing gravitational wave for a domain wall plus a massless scalar field. The scalar field can be associated with a fluid which has the properties of `stiff' matter, i.e. matter in which the speed of sound equals the speed of light. Although domain walls are observationally ruled out in the present era the solution has interesting features which might shed light on the character of exact non-linear wave solutions to Einstein's equations. Additionally this solution may act as a template for higher dimensional 'brane-world' model standing waves.Comment: 4 pages two-column format, no figures, added discussion of physical meaning of solution, added refernces, to be published PR

A Poincar\'e section for the general heavy rigid body

A general recipe is developed for the study of rigid body dynamics in terms of Poincar\'e surfaces of section. A section condition is chosen which captures every trajectory on a given energy surface. The possible topological types of the corresponding surfaces of section are determined, and their 1:1 projection to a conveniently defined torus is proposed for graphical rendering.Comment: 25 pages, 10 figure

Sub-additive ergodic theorems for countable amenable groups

In this paper we generalize Kingman's sub-additive ergodic theorem to a large class of infinite countable discrete amenable group actions.Comment: Journal of Functional Analysi

How particle collisions increase the rate of accretion from the cosmological background onto primordial black holes in braneworld cosmology

It is shown that, contrary to the widespread opinion, particle collisions considerably increase accretion rate from the cosmological background onto 5D primordial black holes formed during the high-energy phase of the Randall-Sundrum Type II braneworld scenario. Increase of accretion rate leads to much tighter constraints on initial primordial black hole mass fraction imposed by the critical density limit and measurements of high-energy diffuse photon background and antiproton excess.Comment: 5 pages, 4 figure

On the photoionization of the outer electrons in noble gas endohedral atoms

We demonstrate the prominent modification of the outer shell photoionization cross-section in noble gas (NG) endohedral atoms NG@F under the action of the fullerene F electron shell. This shell leads to two important effects, namely to strong enhancement of the cross-section due to fullerenes shell polarization under the action of the incoming electromagnetic wave and to prominent oscillation of this cross-section due to the reflection of the photoelectron from NG by the F shell. All but He noble gas atoms are considered. The polarization of the fullerene shell is expressed via the total photoabsorption cross-section of F. The reflection of the photoelectron is taken into account in the frame of the so-called bubble potential that is a spherical zero --thickness potential. It is assumed in the derivations that NG is centrally located in the fullerene. It is assumed also, in accord with the existing experimental data, that the fullerenes radius R is much bigger than the atomic radius and the thickness of the fullerenes shell . These assumptions permit, as it was demonstrated recently, to present the NG@F photoionization cross-section as a product of the NG cross-section and two well defined calculated factors.Comment: 19 pages, 9 figure