Transport Equations from Liouville Equations for Fractional Systems

We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the fractional systems are non-Hamiltonian. Generalized transport equation is derived from Liouville and Bogoliubov equations for fractional systems. Fractional generalization of average values and reduced distribution functions are defined. Hydrodynamic equations for fractional systems are derived from the generalized transport equation.Comment: 11 pages, LaTe

Fractional Systems and Fractional Bogoliubov Hierarchy Equations

We consider the fractional generalizations of the phase volume, volume element and Poisson brackets. These generalizations lead us to the fractional analog of the phase space. We consider systems on this fractional phase space and fractional analogs of the Hamilton equations. The fractional generalization of the average value is suggested. The fractional analogs of the Bogoliubov hierarchy equations are derived from the fractional Liouville equation. We define the fractional reduced distribution functions. The fractional analog of the Vlasov equation and the Debye radius are considered.Comment: 12 page

Fractional Liouville and BBGKI Equations

We consider the fractional generalizations of Liouville equation. The normalization condition, phase volume, and average values are generalized for fractional case.The interpretation of fractional analog of phase space as a space with fractal dimension and as a space with fractional measure are discussed. The fractional analogs of the Hamiltonian systems are considered as a special class of non-Hamiltonian systems. The fractional generalization of the reduced distribution functions are suggested. The fractional analogs of the BBGKI equations are derived from the fractional Liouville equation.Comment: 20 page

ProMoVer: Modular Verification of Temporal Safety Properties

This paper describes ProMoVer, a tool for fully automated procedure–modular verification of Java programs equipped with method–local and global assertions that specify safety properties of sequences of method invocations. Modularity at the procedure–level is a natural instantiation of the modular verification paradigm, where correctness of global properties is relativized on the local properties of the methods rather than on their implementations, and is based here on the construction of maximal models for a program model that abstracts away from program data. This approach allows global properties to be verified in the presence of code evolution, multiple method implementations (as arising from software product lines), or even unknown method implementations (as in mobile code for open platforms). ProMoVer automates a typical verification scenario for a previously developed tool set for compositional verification of control flow safety properties, and provides appropriate pre– and post–processing. Modularity is exploited by a mechanism for proof reuse that detects and minimizes the verification tasks resulting from changes in the code and the specifications. The verification task is relatively light–weight due to support for abstraction from private methods and automatic extraction of candidate specifications from method implementations. We evaluate the tool on a number of applications from the smart card domain

The Large Enriched Germanium Experiment for Neutrinoless Double Beta Decay (LEGEND)

The observation of neutrinoless double-beta decay (0${\nu}{\beta}{\beta}$) would show that lepton number is violated, reveal that neutrinos are Majorana particles, and provide information on neutrino mass. A discovery-capable experiment covering the inverted ordering region, with effective Majorana neutrino masses of 15 - 50 meV, will require a tonne-scale experiment with excellent energy resolution and extremely low backgrounds, at the level of $\sim$0.1 count /(FWHM$\cdot$t$\cdot$yr) in the region of the signal. The current generation $^{76}$Ge experiments GERDA and the MAJORANA DEMONSTRATOR utilizing high purity Germanium detectors with an intrinsic energy resolution of 0.12%, have achieved the lowest backgrounds by over an order of magnitude in the 0${\nu}{\beta}{\beta}$ signal region of all 0${\nu}{\beta}{\beta}$ experiments. Building on this success, the LEGEND collaboration has been formed to pursue a tonne-scale $^{76}$Ge experiment. The collaboration aims to develop a phased 0${\nu}{\beta}{\beta}$ experimental program with discovery potential at a half-life approaching or at $10^{28}$ years, using existing resources as appropriate to expedite physics results.Comment: Proceedings of the MEDEX'17 meeting (Prague, May 29 - June 2, 2017

ANTIBODIES TO BENZO[A]PYRENE IN SERUM OF PATIENTS WITH NON-SMALL CELL LUNG CANCER

The features of immune response to chemical carcinogen benzo[a]pyrene (Bp) at the patients with non-small cell lung cancer (NSCLC) are investigated. The isotypical distinctions in formation of antibodies (Ab) to Bp at the men with NSCLC in comparison with healthy are revealed. There were more often observed the high levels of IgG Ab-Bp at the men with NSCLC. Thus risk of occurrence NSCLC grows almost in 2 times at high levels of Ab-Bp of a class G

LEGEND-1000 Preconceptual Design Report

We propose the construction of LEGEND-1000, the ton-scale Large Enriched Germanium Experiment for Neutrinoless $\beta \beta$ Decay. This international experiment is designed to answer one of the highest priority questions in fundamental physics. It consists of 1000 kg of Ge detectors enriched to more than 90% in the $^{76}$Ge isotope operated in a liquid argon active shield at a deep underground laboratory. By combining the lowest background levels with the best energy resolution in the field, LEGEND-1000 will perform a quasi-background-free search and can make an unambiguous discovery of neutrinoless double-beta decay with just a handful of counts at the decay $Q$ value. The experiment is designed to probe this decay with a 99.7%-CL discovery sensitivity in the $^{76}$Ge half-life of $1.3\times10^{28}$ years, corresponding to an effective Majorana mass upper limit in the range of 9-21 meV, to cover the inverted-ordering neutrino mass scale with 10 yr of live time