# Volume 14 (2013)

## Volume 14 (2013)

### Number 1 - 2013

1. A. Kontorovich, An Explicit Bound on the Transportation Cost Distance.Commun . Commun. Math. Anal. Vol. 14 (2013). no. 1, pp. 1 - 14
2. B. Ahmad, S. Al-Sulami, and S. K. Ntouyas, Existence Results for Fractional Differential Inclusions Involving Non-Convex Valued Maps with Four-Point Nonlocal Integral Boundary Conditions . Commun. Math. Anal. Vol. 14 (2013). no. 1, pp. 15 - 27
3. S. Yakubovich, On Some Rajchman Measures and Equivalent Salem's Problem . Commun. Math. Anal. Vol. 14 (2013). no. 1, pp. 28 - 41
4. S. S. Dragomir, Some Jensen Type Inequalities for Square-Convex Functions of Selfadjoint Operators in Hilbert Spaces . Commun. Math. Anal. Vol. 14 (2013). no. 1, pp. 42 - 58
5. J. P C. dos Santos, V. Vijayakumar, and R. Murugesu, Existence of Mild Solutions for Nonlocal Cauchy Problem for Fractional Neutral Integro-Differential Equation with Unbounded Delay . Commun. Math. Anal. Vol. 14 (2013). no. 1, pp. 59 - 71
6. M. Berbiche and A. Hakem, Finite Time Blow-Up of Solutions for Damped Wave Equation with Nonlinear Memory . Commun. Math. Anal. Vol. 14 (2013). no. 1, pp. 72 - 84
7. N. Das and R. P. Lal, Algebraic and Ergodicity Properties of the Berezin Transform . Commun. Math. Anal. Vol. 14 (2013). no. 1, pp. 85 - 103
8. S. Abbas and M. Benchohra, Nonlinear Fractional Order Riemman-Liouville Volterra-Stieltjes Partial Integral Equations on Unbounded Domains . Commun. Math. Anal. Vol. 14 (2013). no. 1, pp. 104 - 117
9. G. E. Karadzhov and Q. Mehmood, Optimal Regularity Properties of the Riesz Potential Operator . Commun. Math. Anal. Vol. 14 (2013). no. 1, pp. 118 - 132

### Number 2 - 2013

PREFACE

This issue of Communications in Mathematical Analysis is devoted to various aspects of Analysis, Operator Theory and their applications in problems of Mathematical Physics. In particular, in this volume there are studied relations between the properties of the radial Toeplitz operators on the unit ball and of the sequences of their eigenvalues, the structure of the poly-Bergman type spaces on the Siegel domain, and the properties of two families of discrete q-extensions of the classical Chebyshev polynomials.

The following problems of mathematical physics are investigated. The spreading rate estimates of soliton perturbations for relativistic nonlinear wave equations are obtained, the existence of transmission eigenvalues for non-regular cases of the scattering problem for the Helmholtz equation is proved, the convergence of Galerkin’s approximations for the regularized 3D periodic Navier-Stokes equations is established, the asymptotic behavior and stability of solutions to the barotropic vorticity equation on a sphere are studied.

Among of different topics of applications we refer to the formulation of the time-frequency integrals and the stationary phase method in problems of acoustic wave’s propagation, the numerical study of the behavior of the optical waves in quasi-periodic spherical structures, establishing a long time dynamics for nonlinear Hamilton system of a charged particle in the Klein-Gordon field, and others.

The existence of bang-bang controls with at most n-1 points of switching is established for a class of nonlinear n-dimensional control systems that can be mapped to linear ones by change of variables and an additive change of control. Finally, the asymptotics of European double-barrier option with compound Poisson component is studied.

These papers were presented in the International Workshop "Analysis, Operator Theory, and Mathematical Physics" which was held in Ixtapa (Mexico) in January 23--27, 2012. This workshop was organized by the Universidad Autonoma del Estado de Morelos (Cuernavaca, Mexico), Universidad Michoacana de San Nicolas de Hidalgo (Morelia, Mexico), Instituto Politecnico Nacional (Mexico, D.F.), and CINVESTAV (Mexico, D.F.) with assistance of scientific groups from Russia (Moscow) and Poland (Szczecin) that are joined by a scientific project of the so-called Red de Cuerpos Academicos" with support of the SEP-PROMEP (Mexico).

EDITORS

Prof. Gennadiy Burlak (Autonomous University of the State Morelos, Mexico)

Prof. Yuri Karlovich (Autonomous University of the State Morelos, Mexico)

Prof. Vladimir Rabinovich (National Polytechnic Institute of Mexico)

1. M. Atakishiyeva and N. Atakishiyev, On Discrete q-Extensions of Chebyshev Polynomials . Commun. Math. Anal. Vol. 14 (2013). no. 2, pp. 1 - 12
2. G. Burlak, V. Imaykin, and A. Merzon, Long-Time Decay for the Linearized System of a Charged Particle in the Klein-Gordon Field . Commun. Math. Anal. Vol. 14 (2013). no. 2, pp. 13 - 24
3. G. Burlak, V. Rabinovich, and J. R. Hernandez Juarez, Time-frequency Integrals and the Stationary Phase Method in Problems of Acoustic Waves Propagation from Moving Sources . Commun. Math. Anal. Vol. 14 (2013). no. 2, pp. 25 - 39
4. R. Carrada-Herrera, S. M. Grudsky, C. Palomino-Jimenez, and R. M. Porter, Asymptotics of European Double-Barrier Option with Compound Poisson Component . Commun. Math. Anal. Vol. 14 (2013). no. 2, pp. 40 - 66
5. A. Diaz-de-Anda, G. Burlak, and M. Najera-Villeda, Optical Fields in a Multilayer Microsphere with a Quasi-periodic Pascal Sequence . Commun. Math. Anal. Vol. 14 (2013). no. 2, pp. 67 - 76
6. S. M. Grudsky, E. A. Maximenko, and N. L. Vasilevski, Radial Toeplitz Operators on the Unit Ball and Slowly Oscillating Sequences . Commun. Math. Anal. Vol. 14 (2013). no. 2, pp. 77 - 94
7. E. A. Kopylova, Y. I. Karlovich, A. I. Komech, and A. E. Merzon, On the Spreading Rate of the Soliton Perturbation for Relativistic Nonlinear Wave Equations . Commun. Math. Anal. Vol. 14 (2013). no. 2, pp. 95 - 102
8. V. V. Kucherenko, On Convergence of Galerkin's Approximations for the Regularized 3D Periodic Navier-Stokes Equations . Commun. Math. Anal. Vol. 14 (2013). no. 2, pp. 103 - 112
9. J. R. Ortega, and A. S. Nungaray, Poly-Bergman Type Spaces on the Siegel Domain . Commun. Math. Anal. Vol. 14 (2013). no. 2, pp. 113 - 128
10. V. Serov, Transmission Eigenvalues for Non-regular Cases . Commun. Math. Anal. Vol. 14 (2013). no. 2, pp. 129 - 142
11. Y. N. Skiba, Asymptotic Behavior and Stability of Solutions to Barotropic Vorticity Equation on a Sphere . Commun. Math. Anal. Vol. 14 (2013). no. 2, pp. 143 - 162
12. K. V. Sklyar, G. M. Sklyar, and Y. I. Karlovich, On Bang-bang Controls for Some Nonlinear Systems . Commun. Math. Anal. Vol. 14 (2013). no. 2, pp. 163 - 178