On a Generalized Oscillator: Invariance Algebra and Interbasis Expansions

This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian and cylindrical bases as well as the cylindrical and spherical bases for D=3. These interbasis expansion coefficients are found to be analytic continuations to real values of their arguments of the Clebsch-Gordan coefficients for the group SU(2). For D=2, the superintegrable character for the generalized oscillator system is investigated from the points of view of a quadratic invariance algebra.Comment: 13 pages, Latex file. Submitted for publication to Yadernaya Fizik

The Cosmic Microwave Background and Inflation Parameters

We review the currrent cosmic parameter determinations of relevance to inflation using the WMAP-1year, Boomerang, CBI, Acbar and other CMB data. The basic steps in the pipelines which determine the bandpowers from the raw data from which these estimations are made are summarized. We forecast how the precision is likely to improve with more years of WMAP in combination with future ground-based experiments and with Planck. We address whether the current data indicates strong breaking from uniform acceleration through the relatively small region of the inflaton potential that the CMB probes, manifest in the much-discussed running spectral index or in even more radical braking/breaking scenarios. Although some weak ``anomalies'' appear in the current data, the statistical case is not there. However increased precision, at the high multipole end and with polarization measurements, will significantly curtail current freedom.Comment: 24 pages, 10 figures, 2 tables, Int. J. Theor. Phys. 2004, ed. E. Verdaguer, "Peyresq Physics 8", "The Early Universe: Confronting theory with observations" (June 21-27, 2003

Coulomb-oscillator duality in spaces of constant curvature

In this paper we construct generalizations to spheres of the well known Levi-Civita, Kustaanheimo-Steifel and Hurwitz regularizing transformations in Euclidean spaces of dimensions 2, 3 and 5. The corresponding classical and quantum mechanical analogues of the Kepler-Coulomb problem on these spheres are discussed.Comment: 33 pages, LaTeX fil

Non Gaussian extrema counts for CMB maps

In the context of the geometrical analysis of weakly non Gaussian CMB maps, the 2D differential extrema counts as functions of the excursion set threshold is derived from the full moments expansion of the joint probability distribution of an isotropic random field, its gradient and invariants of the Hessian. Analytic expressions for these counts are given to second order in the non Gaussian correction, while a Monte Carlo method to compute them to arbitrary order is presented. Matching count statistics to these estimators is illustrated on fiducial non-Gaussian "Planck" data.Comment: 4 pages, 1 figur

ФАКТОРЫ, ВЛИЯЮЩИЕ НА РАСПРОСТРАНЕНИЕ И ПРИНЯТИЕ ИННОВАЦИЙ В СФЕРЕ ПЛАТЕЖНЫХ ТЕХНОЛОГИЙ

Non-cash payments provide a small part of total payment volume, but the usage of innovative products in named area is growing quite rapidly. The present study attempts to identify the factors determining consumers’ acceptance of payment innovation with the aim of developing a conceptual model of payment services acceptance. A research model that reflects economic, technological and socio-demographic factors are all important determinants for payment services adoption and use. Besides, there are specific correlation between them. To simulate the behavior of the consumer it was due to use parameters that reflect the actual level of awareness of innovation, the intention to use and real use of innovation. The result was the conceptual model developed in this research that focuses on factors determining consumers’ acceptance of payment services and their statement.Безналичные платежные инструменты обеспечивают пока незначительную часть платежей, но использование инновационных продуктов в этой сфере растет довольно высокими темпами. Проанализированы факторы, влияющие на распространение и принятие инноваций в платежной сфере, в целях разработки концептуальной модели процесса принятия данного вида инноваций. В результате были выявлены экономико-технологические и социально-демографические факторы, оказывающие наибольшее влияние на рассматриваемый процесс, а также специфические зависимости между ними. Для моделирования поведения потребителя было предложено использовать параметры, отражающие фактический уровень информированности об инновации, намерения использовать инновацию и использования инновации. В результате была построена концептуальная модель, учитывающая факторы, определяющие принятие инноваций в платежной сфере и состояние агента

Velocity Modification of Power Spectrum from Absorbing Medium

Quantitative description of the statistics of intensity fluctuations within spectral line data cubes introduced in our earlier work is extended to the absorbing media. A possibility of extracting 3D velocity and density statistics from both integrated line intensity as well as from the individual channel maps is analyzed. We find that absorption enables the velocity effects to be seen even if the spectral line is integrated over frequencies. This regime that is frequently employed in observations is characterized by a non-trivial relation between the spectral index of velocities and the spectral index of intensity fluctuations. For instance when density is dominated by fluctuations at large scales, i.e. when correlations scale as r^{-\gamma}, \gamma<0, the intensity fluctuations exhibit a universal spectrum of fluctuations ~K^{-3} over a range of scales. When small scale fluctuations of density contain most of the energy, i.e. when correlations scale as r^{-\gamma}, \gamma>0, the resulting spectrum of the integrated lines depends on the scaling of the underlying density and scales as K^{-3+\gamma}. We show that if we take the spectral line slices that are sufficiently thin we recover our earlier results for thin slice data without absorption. As the result we extend the Velocity Channel Analysis (VCA) technique to optically thick lines enabling studies of turbulence in molecular clouds. In addition, the developed mathematical machinery enables a quantitative approach to solving other problems that involved statistical description of turbulence within emitting and absorbing gas.Comment: 51 page, 3 figures. Accepted to Astrophysical Journa

Quantum Systems with Hidden Symmetry. Interbasis Expansions

This monograph is the English version of the book "Quantum systems with hidden symmetry. Interbasis expansions" published in 2006 by the publishing house FIZMATLIT (Moscow) in Russian. When compiling this version of the book, typos and inaccuracies noted since the release of the Russian edition have been corrected