On Convergence to Equilibrium Distribution, I. The Klein - Gordon Equation with Mixing

Consider the Klein-Gordon equation (KGE) in $\R^n$, $n\ge 2$, with constant or variable coefficients. We study the distribution $\mu_t$ of the random solution at time $t\in\R$. We assume that the initial probability measure $\mu_0$ has zero mean, a translation-invariant covariance, and a finite mean energy density. We also asume that $\mu_0$ satisfies a Rosenblatt- or Ibragimov-Linnik-type mixing condition. The main result is the convergence of $\mu_t$ to a Gaussian probability measure as $t\to\infty$ which gives a Central Limit Theorem for the KGE. The proof for the case of constant coefficients is based on an analysis of long time asymptotics of the solution in the Fourier representation and Bernstein's `room-corridor' argument. The case of variable coefficients is treated by using an `averaged' version of the scattering theory for infinite energy solutions, based on Vainberg's results on local energy decay.Comment: 30 page

Peculiar Motions in the Region of the Ursa Major Supercluster of Galaxies

We have investigated the peculiar motions of clusters of galaxies in the Ursa Major (UMa) supercluster and its neighborhood. Based on SDSS (Sloan Digital Sky Survey) data, we have compiled a sample of early-type galaxies and used their fundamental plane to determine the cluster distances and peculiar velocities. The samples of early-type galaxies in the central regions (within R_200) of 12 UMa clusters of galaxies, in three main subsystems of the supercluster -- the filamentary structures connecting the clusters, and in nine clusters from the nearest UMa neighborhood have similar parameters. The fairly high overdensity (3 by the galaxy number and 15 by the cluster number) suggests that the supercluster as a whole is gravitationally bound, while no significant peculiar motions have been found: the peculiar velocities do not exceed the measurement errors by more than a factor of 1.5-2. The mean random peculiar velocities of clusters and the systematic deviations from the overall Hubble expansion in the supercluster are consistent with theoretical estimates. For the possible approach of the three UMa subsystems to be confirmed, the measurement accuracy must be increased by a factor of 2-3.Comment: 21 pages, 4 tables, 7 figure

Spectral and electroluminescent properties of coordination compounds of terbium (III) with ibuprofen (in solid form, chloroform solutions, and polyvinylcarbazole films)

Spectral properties of terbium (III) complexes with composition of TbL3DL, where L is an anion of d,l-2-(4-isobutylphenyl)propanoic acid (ibuprofen) and DL is 2,2′-dipyridyl (Dipy), 1,10-phenanthroline (Phen), or triphenylphosphine oxide (TPPO), have been studied in a solid form, chloroform solutions, and polyvinylcarbazole (PVC) films. It has been demonstrated that, in PVC films, occupation of the emitting level of terbium (III) involves the participation of polymer. The emission decay lifetimes of terbium in the chloroform solutions and PVC films have been measured. The possibility of the appearance of electroluminescence of complexes in PVC films has been studied

The Structure of Clusters with Bimodal Distributions of Galaxy Radial Velocities. I. A1035

The structure of the A1035 cluster of galaxies (10h32m +40d13', cz ~ 22000 km/s), which exhibits a bimodal distribution of galaxy radial velocities (\Delta V\approx 3000 km/s), is analyzed using three methods of determining the relative distances to clusters from early-type galaxies: the Kormendy relation corrected for the dependence of residuals on galaxy magnitude, the photometric plane, and the fundamental plane. We use the data obtained with the 1-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences and SDSS (DR5) data to show that A1035 consists of two gravitationally unbound independent clusters. These clusters with the velocity dispersions of 566 km/s and 610 km/s and masses within R_200 equal to 2.7 10^14 and 3.5 10^14 M_sun, respectively, obey the Hubble law.Comment: 13 pages, 3 tables, 6 figure

СОСТОЯНИЕ ДИАГНОСТИКИ ТУБЕРКУЛЕЗА ЦЕНТРАЛЬНОЙ НЕРВНОЙ СИСТЕМЫ

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Detailed Study of the Ursa Major Supercluster of Galaxies Using the 2MASS and SDSS Catalogs

We study the infrared (K_s band) properties of clusters of galaxies in the Ursa Major supercluster using data from 2MASS (Two-Micron All-Sky Survey) and SDSS (Sloan Digital Sky Survey). We identified three large filaments with mean redshifts of z = 0.051, 0.060, and 0.071. All clusters of the supercluster are located in these filaments. We determined the total K_s-band luminosities and masses for 11 clusters of galaxies within comparable physical regions (within a radius R_200 close to the virial radius) using a homogeneous method. We constructed a combined luminosity function for the supercluster in this region, which can be described by the Schechter function with the following parameters: M*_K = -24^m.50 and \alpha = -0.98. The infrared luminosities of the clusters of galaxies correlate with their masses; the M/L_K ratios of the systems increase with their masses (luminosities), with most of the Ursa Major clusters of galaxies (particularly the richer ones) closely following the relations derived previously for a large sample of clusters and groups of galaxies. The total mass-to-infrared-luminosity ratio is 52 M_{\odot}/L_{\odot} for six Abell clusters and 49 M_{\odot}/L_{\odot} for all of the clusters, except Anon2.Comment: 16 pages, 5 figure

ЭФФЕКТИВНОСТЬ СТАЦИОНАРНОГО ЭТАПА ЛЕЧЕНИЯ БОЛЬНЫХ ТУБЕРКУЛЕЗОМ С ЛЕКАРСТВЕННОЙ УСТОЙЧИВОСТЬЮ МИКОБАКТЕРИЙ

The composition and effectiveness of the treatment of patients 159 drug-resistant TB of Mycobacterium tuberculosis. Dominated by common processes (87%), massive bacterioexcretion (74.2%) and multidrug-resistant TB. Full clinical effect achieved in 54.8% (n = 68), including 28.8% (37) by surgical methods. Изучен состав и эффективность лечения 159 больных туберкулезом с лекарственной устойчиво-стью (ЛУ) микобактерий туберкулеза, преимущественно множественной. Преобладали распро-страненные процессы (в 87%) с массивным бактериовыделением (74,2%) и с ЛУ ко всем препара-там основного ряда. Полный клинический эффект достигнут в 54,8% (у 68 больных), в том числе в 28,8% (у 37) хирургическими методами

НАНОЧАСТИЦЫ ГИДРОКСОКАРБОНАТА ЦЕРИЯ, ИНКРУСТИРОВАННЫЕ ПАЛЛАДИЕМ. СИНТЕЗ И ИССЛЕДОВАНИЕ

Cerium(III) nitrate and urea solution mixture were treated by hydrothermal and microwavehydrothermal methods, as a result cerium(III) carbonate hydroxide nanoparticles (22-37 nm) were obtained. Cerium(III) carbonate hydroxide nanoparticles, encrusted by palladium were obtained using palladium reduction process from cerium(III) carbonate hydroxide solution. It is shown, that palladium occurrence disturbs hard hydrogen bond system, leading to carbonate hydroxide nanoparticles structure disorder and also increases efficiency of catalytic reactivity process.Из смеси растворов нитрата церия(III) и мочевины с использованием различных методов и приемов выделены наночастицы (22-37 нм) гидроксокарбоната церия(III). Путем восстановления палладия в растворах в присутствии гидроксокарбоната церия(III) получены образцы наночастиц гидроксокарбоната церия(III) с поверхностью, инкрустированной палладием. Показано, что присутствие Pd нарушает жесткую систему водородных связей матрицы и приводит к разупорядочению строения наночастиц гидроксокарбоната. Подчеркивается перспективность использования указанных композитов в катализе