Linear bound for the dyadic paraproduct on weighted Lebesgue space L2(w)L_2(w)

The dyadic paraproduct is bounded in weighted Lebesgue spaces $L_p(w)$ if and only if the weight $w$ belongs to the Muckenhoupt class $A_p^d$. However, the sharp bounds on the norm of the dyadic paraproduct are not known even in the simplest $L_2(w)$ case. In this paper we prove the linear bound on the norm of the dyadic paraproduct in the weighted Lebesgue space $L_2(w)$ using Bellman function techniques and extrapolate this result to the $L_p(w)$ case.Comment: 13 page

Calculating nuclear accident probabilities from empirical frequencies

International audienceSince there is no authoritative, comprehensive and public historical record of nuclear power plant accidents, we reconstructed a nuclear accident data set from peer-reviewed and other literature. We found that, in a sample of five random years, the worldwide historical frequency of a nuclear major accident, defined as an INES level 7 event, is 14 %. The probability of at least one nuclear accident rated at level ≥4 on the INES scale is 67 %. These numbers are subject to uncertainties because of the fuzziness of the definition of a nuclear accident. © 2014 Springer Science+Business Media New York

Ruelle-Perron-Frobenius spectrum for Anosov maps

We extend a number of results from one dimensional dynamics based on spectral properties of the Ruelle-Perron-Frobenius transfer operator to Anosov diffeomorphisms on compact manifolds. This allows to develop a direct operator approach to study ergodic properties of these maps. In particular, we show that it is possible to define Banach spaces on which the transfer operator is quasicompact. (Information on the existence of an SRB measure, its smoothness properties and statistical properties readily follow from such a result.) In dimension $d=2$ we show that the transfer operator associated to smooth random perturbations of the map is close, in a proper sense, to the unperturbed transfer operator. This allows to obtain easily very strong spectral stability results, which in turn imply spectral stability results for smooth deterministic perturbations as well. Finally, we are able to implement an Ulam type finite rank approximation scheme thus reducing the study of the spectral properties of the transfer operator to a finite dimensional problem.Comment: 58 pages, LaTe

Concerning the Wave equation on Asymptotically Euclidean Manifolds

We obtain KSS, Strichartz and certain weighted Strichartz estimate for the wave equation on $(\R^d, \mathfrak{g})$, $d \geq 3$, when metric $\mathfrak{g}$ is non-trapping and approaches the Euclidean metric like $x ^{- \rho}$ with $\rho>0$. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for $\rho> 1$ and $d=3$. Also, we establish the Strauss conjecture when the metric is radial with $\rho>0$ for $d= 3$.Comment: Final version. To appear in Journal d'Analyse Mathematiqu

Stable directions for small nonlinear Dirac standing waves

We prove that for a Dirac operator with no resonance at thresholds nor eigenvalue at thresholds the propagator satisfies propagation and dispersive estimates. When this linear operator has only two simple eigenvalues close enough, we study an associated class of nonlinear Dirac equations which have stationary solutions. As an application of our decay estimates, we show that these solutions have stable directions which are tangent to the subspaces associated with the continuous spectrum of the Dirac operator. This result is the analogue, in the Dirac case, of a theorem by Tsai and Yau about the Schr\"{o}dinger equation. To our knowledge, the present work is the first mathematical study of the stability problem for a nonlinear Dirac equation.Comment: 62 page

Алгоритм сжатия на основе вычисления скорости изменения ультразвукового сигнала

The intermittency structure of multihadronic e+e- annihilation is analyzed by evaluating the factorial moments F2-F5 in three-dimensional Lorentz invariant phase space as a function of the resolution scale. We interpret our data in the language of fractal objects. It turns out that the fractal dimension depends on the resolution scale in a way that can be attributed to geometrical resolution effects and dynamical effects, such as the pi-O Dalitz decay. The LUND 7.2 hadronization model provides an excellent description of the data. There is no indication of unexplained multiplicity fluctuations in small phase space regions

A three-step numerical approximant based on block hybrid backward differentiation formula for stiff system of ordinary differential equation

We present results of an analysis of the reaction $γγ→ωϱ$ in the two-photon process $e^+e^−→ϵ^+e^−2π^+2π^−π^0$ in the untagged mode. The cross section is largely compatible with previous determinations; however, we do not confirm the enhancement claimed at 1.9 GeV. All observed ω's are accompanied by ϱ's in the recoiling ππ spectrum. An angular correlation analysis shows that the data is not dominated by a single spin-parity state, thus establishing severe constraints on $qqqq$ models which predict $JP= 2^+$

Разработка модульного стенда физического подобия для изучения гидротехнических систем

В рамках данной работы проведен обзор и анализ образовательных стендов, сформулирована концепция модульного стенда физического подобия, разработаны функциональные схемы двух модулей, в соответствии с которыми подобраны основные элементы. Для первого модуля предоставлены принципиальная схема и демонстрационный алгоритм работы.In this work, a review and analysis of educational booths, formulated the concept of modular stand physical similarity, developed functional diagrams of the two modules, in accordance with which the selected basic elements. For the first module, a schematic diagram and a demonstration algorithm are provided

Накопление газообразных продуктов деления и соединений в микрокапсулированном топливе в сверхдлинных кампаниях

The production of b and c quarks in $e^+e^−$ annihilation has been studied with the CELLO detector in the range from 35 GeV up to the highest PETRA energies. The heavy quarks have been tagged by their semileptonic decays. The charge asymmetries for b quarks at 35 and 43 GeV have been found to be $A^b=−(22.2±8.1)$, respectively, using a method incorporating jet variables and their correlations for the separation of the heavy quarks from the back ground of the lighter quarks. For c quarks we obtain $A^c=−(12.9±8.8)$ and $A^c=+(7.7±14.0)$, respectively. The axial vector coupling constants of the heavy quarks c and b are found to be $a^c=+(0.29±0.46)$ and $a^b=−(1.15±0.41)$ taking $B^0 \bar(B^0) B^0\bar(B^0)$ mixing into account. The results are in agreement with the expectations from the standard model