[en] We prove a number of new results related to Gram's law in the theory of the Riemann zeta-function that reflect irregularity in the distribution of the ordinates of the complex zeros of that function. Results are obtained on the distribution of pairs, triples, quadruples, ... of adjacent ordinates of such zeros that simultaneously do not obey Gram's law

[en] The parity violating W ^± single spin asymmetry, in longitudinally polarized p + p collisions, can give us a clean way to access the $\mathrm{\Delta <!--\; ??\; -->}\stackrel{¯<!--\; ??\; -->}{u}$ and $\mathrm{\Delta <!--\; ??\; -->}\stackrel{¯<!--\; ??\; -->}{d}$ polarized parton distribution functions. The current status of the analysis of the 2011 data set and future prospects will be presented.

[en] We present an overview of the status of ongoing work on physics models describing beam matching and halo control for particle accelerators, particularly high power ion linacs. We consider moments and various new variables that more naturally describe beam halo evolution. We compute matched beams and ''mode invariants'' (analogs of moment invariants) using primarily symbolic techniques

[en] For certain predominantly one-dimensional distribution functions, an analytic inversion has been found which yields the velocity distribution of superthermal electrons given their Bremsstrahlung radiation. 5 refs

[en] The principle of maximum entropy, a powerful and general method for inferring the distribution function given a set of constraints, is applied to deduce the overall distribution of 3D plasmoids (flux ropes/tubes) for systems where resistive MHD is applicable and large numbers of plasmoids are produced. The analysis is undertaken for the 3D case, with mass, total flux, and velocity serving as the variables of interest, on account of their physical and observational relevance. The distribution functions for the mass, width, total flux, and helicity exhibit a power-law behavior with exponents of -4/3, -2, -3, and -2, respectively, for small values, whilst all of them display an exponential falloff for large values. In contrast, the velocity distribution, as a function of v=|v|, is shown to be flat for v→0, and becomes a power law with an exponent of -7/3 for v→∞. Most of these results are nearly independent of the free parameters involved in this specific problem. In conclusion, a preliminary comparison of our results with the observational evidence is presented, and some of the ensuing space and astrophysical implications are briefly discussed.

No abstract available

[en] Three definitions of entropy for a nonequilibrium system of particles, driven homogeneously by external forces and thermostatted homogeneously by a feedback mechanism, are discussed. The first is proposed to be S(t) = -k< lnf/sub xi/>, i.e., the nonequilibrium ensemble average of the logarithm of the thermostatted equilibrium distribution function f/sub xi/. We show here, for a specific example, namely, the Nose-Hoover thermostat, that the entropy so defined reduces properly to the equilibrium result when the external forces are turned off, that this entropy behaves correctly when the thermostat is turned off, and that the thermostatted steady state is achievable. A reasonable alternative definition from information theory, namely replacing f/sub xi/ by the nonequilibrium distribution function f, is shown to give incorrect results. If, however, the distribution function f is coarse grained in time to give f-bar, then the resulting coarse-grained information-theory entropy, like the first definition, satisfies the requirements of the nonequilibrium entropy, with the added advantage of being easier to interpret in terms of the number of accessible states. Additional implications are discussed

No abstract available

[en] The lectures on structure and dynamics of galaxies includes a description of a ''normal'' galaxy and the analytical form of the distribution function. (U.S.)

[en] The Lick observatory counts of galaxies are considered. The distribution of number of galaxies in elementary regions (ER) of 1 degx1 deg is investigated. Each field of 6 degx6 deg was treated separately At b>40 deg the probab+lity to observe of n galaxies in ER is an exponential decreasing function of n, if unequality n>< n> were fulfilled. The mean apparent multiplicity of a galaxy (2.8+-0.9) was derived. The galaxy number distribution was simple model for the number of various systems of galaxies. The supperclustering of galaxies was not introduced. Based on that model the approximate expression for galaxy number distribution was considered and was compared with observed distributions. The agreement between these distributions become better with reducing of the interstellar absorption of light