Conditions of Invertibility for Functional Operators with Shift in Weighted Hölder Spaces

We consider functional operators with shift in weighted Hölder spaces. The main result of the work is the proof of the conditions of invertibility for these operators. We also indicate the forms of the inverse operators. As an application, we propose to use these results for the solution of equations with shift encountered in the study of cyclic models for natural systems with renewable resources.Розглядаються функціональні оператори із зсувом у просторах Гельдера з вагою. Основним результатом роботи є встановлення умов оборотності для цих операторів. Вказано види оберненого оператора. Як застосування запропоновано використовувати отримані результати для розв'язання рівнянь із зсувом, які виникають при дослідженні циклічних моделей природних систем з ресурсами, що відновлюються

Purity-bounded uncertainty relations in multidimensional space -- generalized purity

Uncertainty relations for mixed quantum states (precisely, purity-bounded position-momentum relations, developed by Bastiaans and then by Man'ko and Dodonov) are studied in general multi-dimensional case. An expression for family of mixed states at the lower bound of uncertainty relation is obtained. It is shown, that in case of entropy-bounded uncertainty relations, lower-bound state is thermal, and a transition from one-dimensional problem to multi-dimensional one is trivial. Results of numerical calculation of the relation lower bound for different types of generalized purity are presented. Analytical expressions for general purity-bounded relations for highly mixed states are obtained.Comment: 12 pages, 2 figures. draft version, to appear in J. Phys. A Partially based on a poster "Multidimensional uncertainty relations for states with given generalized purity" presented on X Intl. Conf. on Quantum Optics'2004 (Minsk, Belarus, May 30 -- June 3, 2004) More actual report is to be presented on ICSSUR-2005, Besan\c{c}on, France and on EQEC'05, Munich. V. 5: amended article after referees' remark

First steps to mapping of exoplanets: modeling secondary eclipses and search inhomogeneities in the infrared brightness profiles

С целью обнаружения неоднородностей собственного излучения экзопланеты HD209458b по наблюдениям космического телескопа Spitzer проведены обработка и моделирование кривых блеска вторичных транзитов (затмений). Работа является основой для последующего картирования распределения температуры на дневной стороне этой внесолнечной планеты. Неравномерность яркости вызвана звездно-планетными взаимодействиями, а также климатическими механизмами. Глубина затмения составила 0.101 ± 0.009% от общего блеска системы и согласуется с результатами других работ.To detect inhomogeneities in the thermal radiation of exoplanet HD209458b, based on observations of the Spitzer space telescope processing and modeling of the light curves of secondary transits (eclipses) were carried out. Current work is the basis for the mapping of the temperature distribution on the dayside of the exoplanet. Tidal and electromagnetic star-planet interactions, together with climate effects, lead to nonuniform heating of the surface. We obtained that the depth of the eclipse was 0.101±0.009% of the total flux of the system and is consistent with the results of other works

Revisiting the common envelope evolution in binary stars: a new semianalytic model for N -body and population synthesis codes

Stars and planetary system

Time dependence of the electron and positron components of the cosmic radiation measured by the PAMELA experiment between July 2006 and December 2015

Cosmic-ray electrons and positrons are a unique probe of the propagation of cosmic rays as well as of the nature and distribution of particle sources in our Galaxy. Recent measurements of these particles are challenging our basic understanding of the mechanisms of production, acceleration and propagation of cosmic rays. Particularly striking are the differences between the low energy results collected by the space-borne PAMELA and AMS-02 experiments and older measurements pointing to sign-charge dependence of the solar modulation of cosmic-ray spectra. The PAMELA experiment has been measuring the time variation of the positron and electron intensity at Earth from July 2006 to December 2015 covering the period for the minimum of solar cycle 23 (2006-2009) till the middle of the maximum of solar cycle 24, through the polarity reversal of the heliospheric magnetic field which took place between 2013 and 2014. The positron to electron ratio measured in this time period clearly shows a sign-charge dependence of the solar modulation introduced by particle drifts. These results provide the first clear and continuous observation of how drift effects on solar modulation have unfolded with time from solar minimum to solar maximum and their dependence on the particle rigidity and the cyclic polarity of the solar magnetic field.Comment: 11 pages, 2 figure

PAMELA Measurements of Cosmic-ray Proton and Helium Spectra

Protons and helium nuclei are the most abundant components of the cosmic radiation. Precise measurements of their fluxes are needed to understand the acceleration and subsequent propagation of cosmic rays in the Galaxy. We report precision measurements of the proton and helium spectra in the rigidity range 1 GV-1.2 TV performed by the satellite-borne experiment PAMELA. We find that the spectral shapes of these two species are different and cannot be well described by a single power law. These data challenge the current paradigm of cosmic-ray acceleration in supernova remnants followed by diffusive propagation in the Galaxy. More complex processes of acceleration and propagation of cosmic rays are required to explain the spectral structures observed in our data.Comment: 13 pages, 4 figures, link to SOM (with tables) in the references. This manuscript has been accepted for publication in Science. This version has not undergone final editing. Please refer to the complete version of record at http://www.sciencemag.org/ [www.sciencemag.org

PAMELA's measurements of geomagnetic cutoff variations during solar energetic particle events

Data from the PAMELA satellite experiment were used to measure the geomagnetic cutoff for high-energy ($\gtrsim$ 80 MeV) protons during the solar particle events on 2006 December 13 and 14. The variations of the cutoff latitude as a function of rigidity were studied on relatively short timescales, corresponding to single spacecraft orbits (about 94 minutes). Estimated cutoff values were cross-checked with those obtained by means of a trajectory tracing approach based on dynamical empirical modeling of the Earth's magnetosphere. We find significant variations in the cutoff latitude, with a maximum suppression of about 6 deg for $\sim$80 MeV protons during the main phase of the storm. The observed reduction in the geomagnetic shielding and its temporal evolution were compared with the changes in the magnetosphere configuration, investigating the role of IMF, solar wind and geomagnetic (Kp, Dst and Sym-H indexes) variables and their correlation with PAMELA cutoff results.Comment: Conference: The 34th International Cosmic Ray Conference (ICRC2015), 30 July - 6 August, 2015, The Hague, The Netherlands, Volume: PoS(ICRC2015)28