On the investigations of galaxy redshift periodicity

In this article we present a historical review of study of the redshift periodicity of galaxies, starting from the first works performed in the seventies of the twentieth century until the present day. We discuss the observational data and methods used, showing in which cases the discretization of redshifts was observed. We conclude that galaxy redshift periodisation is an effect which can really exist. We also discussed the redshift discretization in two different structures: the Local Group of galaxies and the Hercules Supercluster. Contrary to the previous studies we consider all galaxies which can be regarded as a structure member disregarding the accuracy of velocity measurements. We applied the power spectrum analysis using the Hann function for weighting, together with the jackknife error estimator. In both the structures we found weak effects of redshift periodisation.Comment: 10 pages, 4 figures, to be published in Part. and Nucl. Lett. 200

Fully differential cross sections for photo-double-ionization of D2

We report the first kinematically complete study of the four-body fragmentation of the D2 molecule following absorption of a single photon. For equal energy sharing of the two electrons and a photon energy of 75.5 eV, we observed the relaxation of one of the selection rules valid for He photo-double-ionization and a strong dependence of the electron angular distribution on the orientation of the molecular axis. This effect is reproduced by a model in which a pair of photoionization amplitudes is introduced for the light polarization parallel and perpendicular to the molecular axis

Field-free orientation of CO molecules by femtosecond two-color laser fields

We report the first experimental observation of non-adiabatic field-free orientation of a heteronuclear diatomic molecule (CO) induced by an intense two-color (800 and 400 nm) femtosecond laser field. We monitor orientation by measuring fragment ion angular distributions after Coulomb explosion with an 800 nm pulse. The orientation of the molecules is controlled by the relative phase of the two-color field. The results are compared to quantum mechanical rigid rotor calculations. The demonstrated method can be applied to study molecular frame dynamics under field-free conditions in conjunction with a variety of spectroscopy methods, such as high-harmonic generation, electron diffraction and molecular frame photoemission

Twenty Years of Galactic Observations in Searching for Bursts of Collapse Neutrinos with the Baksan Underground Scintillation Telescope

The results of twenty-year-long Galactic observations in neutrino radiation are summarized. Except for the recording of a neutrino signal from the supernova SN 1987A, no Galactic bursts of collapse neutrinos have been detected. An upper bound on the mean frequency of gravitational collapses in our Galaxy was obtained, $f_{collapse} (90$.Comment: latex, 7 pages, 2 eps figure

Particles and fields in fluid turbulence

The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a new quantitative theory of intermittency in turbulent transport. The first analytical description of anomalous scaling laws in turbulence has been obtained. The underlying physical mechanism reveals the role of statistical integrals of motion in non-equilibrium systems. For turbulent transport, the statistical conservation laws are hidden in the evolution of groups of fluid particles and arise from the competition between the expansion of a group and the change of its geometry. By breaking the scale-invariance symmetry, the statistically conserved quantities lead to the observed anomalous scaling of transported fields. Lagrangian methods also shed new light on some practical issues, such as mixing and turbulent magnetic dynamo.Comment: 165 pages, review article for Rev. Mod. Phy

A model of nonlinear evolution and saturation of the turbulent MHD dynamo

The growth and saturation of magnetic field in conducting turbulent media with large magnetic Prandtl numbers are investigated. This regime is very common in low-density hot astrophysical plasmas. During the early (kinematic) stage, weak magnetic fluctuations grow exponentially and concentrate at the resistive scale, which lies far below the hydrodynamic viscous scale. The evolution becomes nonlinear when the magnetic energy is comparable to the kinetic energy of the viscous-scale eddies. A physical picture of the ensuing nonlinear evolution of the MHD dynamo is proposed. Phenomenological considerations are supplemented with a simple Fokker--Planck model of the nonlinear evolution of the magnetic-energy spectrum. It is found that, while the shift of the bulk of the magnetic energy from the subviscous scales to the velocity scales may be possible, it occurs very slowly -- at the resistive, rather than dynamical, time scale (for galaxies, this means that generation of large-scale magnetic fields cannot be explained by this mechanism). The role of Alfvenic motions and the implications for the fully developed isotropic MHD turbulence are discussed.Comment: IOP latex, 19 pages, 6 figures; final published versio

Semantic Tagging of Mathematical Expressions

Semantic tagging of mathematical expressions (STME) gives semantic meanings to tokens in mathematical expressions. In this work, we propose a novel STME approach that relies on neither text along with expressions, nor labelled train-ing data. Instead, our method only requires a mathemati-cal grammar set. We point out that, besides the grammar of mathematics, the special property of variables and user habits of writing expressions help us understand the im-plicit intents of the user. We build a system that considers both restrictions from the grammar and variable properties, and then apply an unsupervised method to our probabilis-tic model to learn the user habits. To evaluate our system, we build large-scale training and test datasets automatically from a public math forum. The results demonstrate the significant improvement of our method, compared to the maximum-frequency baseline. We also create statistics to reveal the properties of mathematics language