The general form of the Euler--Poisson--Darboux equation and application of transmutation method

In the paper we find solution representations in the compact integral form to the Cauchy problem for a general form of the Euler--Poisson--Darboux equation with Bessel operators via generalized translation and spherical mean operators for all values of the parameter $k$, including also not studying before exceptional odd negative values. We use a Hankel transform method to prove results in a unified way. Under additional conditions we prove that a distributional solution is a classical one too. A transmutation property for connected generalized spherical mean is proved and importance of applying transmutation methods for differential equations with Bessel operators is emphasized. The paper also contains a short historical introduction on differential equations with Bessel operators and a rather detailed reference list of monographs and papers on mathematical theory and applications of this class of differential equations.Comment: Electronic Journal of Differential Equations, 201

On fractional powers of the Bessel operator on a semiaxis

In this paper we study fractional powers of the Bessel differential operator defined on a semiaxis. Some important properties of such fractional powers of the Bessel differential operator are proved. They include connections with Legendre functions for kernel representations, fractional integral operators of Liouville and Saigo, Mellin transform and index laws. Possible applications are indicated to differential equations with fractional powers of the Bessel differential operator.Comment: English version (pp. 1--8) and Russian version (pp. 9--18

Periodic Pattern in the Residual-Velocity Field of OB Associations

An analysis of the residual-velocity field of OB associations within 3 kpc of the Sun has revealed periodic variations in the radial residual velocities along the Galactic radius vector with a typical scale length of lambda=2.0(+/-0.2) kpc and a mean amplitude of fR=7(+/-1) km/s. The fact that the radial residual velocities of almost all OB-associations in rich stellar-gas complexes are directed toward the Galactic center suggests that the solar neighborhood under consideration is within the corotation radius. The azimuthal-velocity field exhibits a distinct periodic pattern in the region 0<l<180 degrees, where the mean azimuthal-velocity amplitude is ft=6(+/-2) km/s. There is no periodic pattern of the azimuthal-velocity field in the region 180<l<360 degrees. The locations of the Cygnus arm, as well as the Perseus arm, inferred from an analysis of the radial- and azimuthal-velocity fields coincide. The periodic patterns of the residual-velocity fields of Cepheids and OB associations share many common features.Comment: 21 page

Kinematics of the outer pseudorings and the spiral structure of the Galaxy

The kinematics of the outer rings and pseudorings is determined by two processes: the resonance tuning and the gas outflow. The resonance kinematics is clearly observed in the pure rings, while the kinematics of the gas outflow is manifested itself in the pseudorings. The direction of systematical motions in the pure rings depends on the position angle of a point with respect to the bar major axis and on the class of the outer ring. The direction of the radial and azimuthal components of the residual velocities of young stars in the Perseus, Carina, and Sagittarius regions can be explained by the presence of the outer pseudoring of class R1R2' in the Galaxy. We present models, which reproduce the directions and values of the residual velocities of OB-associations in the Perseus and Sagittarius regions, and also model reproducing the directions of the residual velocities in the Perseus, Sagittarius, and Carina regions. The kinematics of the Sagittarius region accurately defines the solar position angle with respect to the bar elongation, theta_b=45 (+/-5) deg.Comment: 16 pages, 10 figures, accepted for publication in Astronomy Letter

Measurement of GEp/GMp in ep -> ep to Q2 = 5.6 GeV2

The ratio of the electric and magnetic form factors of the proton, GEp/GMp, was measured at the Thomas Jefferson National Accelerator Facility (JLab) using the recoil polarization technique. The ratio of the form factors is directly proportional to the ratio of the transverse to longitudinal components of the polarization of the recoil proton in the elastic $\vec ep \to e\vec p$ reaction. The new data presented in this article span the range 3.5 < Q2 < 5.6 GeV2 and are well described by a linear Q2 fit. Also, the ratio QF2p/F1p reaches a constant value above Q2=2 GeV2.Comment: 6 pages, 4 figures Added two names to the main author lis

Leading Wave as a Component of the Spiral Pattern of the Galaxy

The spiral pattern of the Galaxy identified by analyzing the kinematics of young stars within 3 kpc of the Sun is Fourier decomposed into spiral harmonics. The spiral pattern of the Galaxy is shown to be representable as a superposition of trailing and leading waves with interarm distances of 1.8(+/-0.4) kpc and 4(+/-2) kpc, respectively. Shock waves are probably present only in the portions of the trailing spiral pattern where it crosses the crest of the leading wave. The small interarm distance of the trailing spiral wave (1.8 kpc) can be explained by its evolution - by the decrease in the interarm distance as the wave is displaced toward the inner Lindblad resonance. The Carina arm may be part of this resonance ring.Comment: 17 pages, 4 figures, to be published in Astronomy Letters, 200

Upper limits for a narrow resonance in the reaction p + p -> K^+ + (Lambda p)

The reaction pp -> K^+ + (Lambda p) has been measured at T_p = 1.953 GeV and \Theta = 0 deg with a high missing mass resolution in order to study the Lambda p final state interaction. Narrow S = -1 resonances predicted by bag model calculations are not visible in the missing mass spectrum. Small structures observed in a previous experiment are not confirmed. Upper limits for the production cross section of a narrow resonance are deduced for missing masses between 2058 and 2105 MeV/c^2.Comment: 8 pages, 5 figure