Ergodicity criteria for non-expanding transformations of 2-adic spheres

In the paper, we obtain necessary and sufficient conditions for ergodicity (with respect to the normalized Haar measure) of discrete dynamical systems $$ on 2-adic spheres $\mathbf S_{2^{-r}}(a)$ of radius $2^{-r}$, $r\ge 1$, centered at some point $a$ from the ultrametric space of 2-adic integers $\mathbb Z_2$. The map $f\colon\mathbb Z_2\to\mathbb Z_2$ is assumed to be non-expanding and measure-preserving; that is, $f$ satisfies a Lipschitz condition with a constant 1 with respect to the 2-adic metric, and $f$ preserves a natural probability measure on $\mathbb Z_2$, the Haar measure $\mu_2$ on $\mathbb Z_2$ which is normalized so that $\mu_2(\mathbb Z_2)=1$

The Non-Archimedean Theory of Discrete Systems

In the paper, we study behavior of discrete dynamical systems (automata) w.r.t. transitivity; that is, speaking loosely, we consider how diverse may be behavior of the system w.r.t. variety of word transformations performed by the system: We call a system completely transitive if, given arbitrary pair $a,b$ of finite words that have equal lengths, the system $\mathfrak A$, while evolution during (discrete) time, at a certain moment transforms $a$ into $b$. To every system $\mathfrak A$, we put into a correspondence a family $\mathcal F_{\mathfrak A}$ of continuous maps of a suitable non-Archimedean metric space and show that the system is completely transitive if and only if the family $\mathcal F_{\mathfrak A}$ is ergodic w.r.t. the Haar measure; then we find easy-to-verify conditions the system must satisfy to be completely transitive. The theory can be applied to analyze behavior of straight-line computer programs (in particular, pseudo-random number generators that are used in cryptography and simulations) since basic CPU instructions (both numerical and logical) can be considered as continuous maps of a (non-Archimedean) metric space $\mathbb Z_2$ of 2-adic integers.Comment: The extended version of the talk given at MACIS-201

Production of (τ+τ−)b(\tau^+\tau^-)_b in electron positron collisions

$(\tau^+\tau^-)_b$ is an atom of simple hydrogenlike structure similar to positronium $(e^+e^-)_b$ and $(\mu^+\mu^-)_b$. In this paper energy levels and decay widths of different decay channels of $(\tau^+\tau^-)_b$ are given. Cross section of production of this atomic system in $e^+e^-$ annihilation taking into account radiative corrections is calculated. According to our estimates 886 $(\tau^+\tau^-)_b$ atoms may be produced at BEPCII and 29 $(\tau^+\tau^-)_b$ atoms are produced at VEPP-4M under the present experimental conditions.Comment: 5 pages, submitted to Int. Jour. Mod. Phys.

T-functions revisited: New criteria for bijectivity/transitivity

The paper presents new criteria for bijectivity/transitivity of T-functions and fast knapsack-like algorithm of evaluation of a T-function. Our approach is based on non-Archimedean ergodic theory: Both the criteria and algorithm use van der Put series to represent 1-Lipschitz $p$-adic functions and to study measure-preservation/ergodicity of these

The Bending Magnets for the Proton Transfer Line of CNGS

The project "CERN neutrinos to Gran Sasso (CNGS)", a collaboration between CERN and the INFN (Gran Sasso Laboratory) in Italy, will study neutrino oscillations in a long base-line experiment. High-energy protons will be extracted from the CERN SPS accelerator, transported through a 727 m long transfer line and focused onto a graphite target to produce a beam of pions and kaons and subsequently neutrinos. The transfer line requires a total of 78 dipole magnets. They were produced in the framework of an in-kind contribution of Germany via DESY to the CNGS project. The normal conducting dipoles, built from laminated steel cores and copper coils, have a core length of 6.3 m, a 37 mm gap height and a nominal field range of 1.38 T - 1.91 T at a maximum current of 4950 A. The magnet design was a collaboration between CERN and BINP. The half-core production was subcontracted to EFREMOV Institute; the coil fabrication, magnet assembly and the field measurements were concluded at BINP in June 2004. The main design issues and results of the acceptance tests, including mechanical, electrical and magnetic field measurements, are discussed

Measurement of J/psi to eta_c gamma at KEDR

We present a study of the inclusive photon spectra from 5.9 million J/psi decays collected with the KEDR detector at the VEPP-4M e+e- collider. We measure the branching fraction of radiative decay J/psi to eta_c gamma, eta_c width and mass. Our preliminary results are: M(eta_c) = 2979.4+-1.5+-1.9 MeV, G(eta_c) = 27.8+-5.1+-3.3 MeV, B(J/psi to eta_c gamma) = (2.34+-0.15+-0.40)%.Comment: To be published in Proceedings of the PhiPsi09, Oct. 13-16, 2009, Beijing, Chin

p-Adic Mathematical Physics

A brief review of some selected topics in p-adic mathematical physics is presented.Comment: 36 page

Experimental investigation of high-energy photon splitting in atomic fields

The new data analysis of the experiment, where the photon splitting in the atomic fields has been observed for the first time, is presented. This experiment was performed at the tagged photon beam of the ROKK-1M facility at the VEPP-4M collider. In the energy region of 120-450 MeV, the statistics of $1.6\cdot 10^9$ photons incident on the BGO target was collected. About 400 candidates to the photon splitting events were reconstructed. Within the attained experimental accuracy, the experimental results are consistent with the cross section calculated exactly in an atomic field. The predictions obtained in the Born approximation significantly differ from the experimental results.Comment: 11 pages, 6 figures, LaTe

Measurement of J/ψ→γηcJ/\psi\to\gamma\eta_{\rm c} decay rate and ηc\eta_{\rm c} parameters at KEDR

Using the inclusive photon spectrum based on a data sample collected at the $J/\psi$ peak with the KEDR detector at the VEPP-4M $e^+e^-$ collider, we measured the rate of the radiative decay $J/\psi\to\gamma\eta_{\rm c}$ as well as $\eta_{\rm c}$ mass and width. Taking into account an asymmetric photon lineshape we obtained $\Gamma^0_{\gamma\eta_{\rm c}}=2.98\pm0.18 \phantom{|}^{+0.15}_{-0.33}$ keV, $M_{\eta_{\rm c}} = 2983.5 \pm 1.4 \phantom{|}^{+1.6}_{-3.6}$ MeV/$c^2$, $\Gamma_{\eta_{\rm c}} = 27.2 \pm 3.1 \phantom{|}^{+5.4}_{-2.6}$ MeV.Comment: 6 pages, 3 figure