Uniform approximation of Poisson integrals of functions from the class H_omega by de la Vallee Poussin sums

We obtain asymptotic equalities for least upper bounds of deviations in the uniform metric of de la Vall\'{e}e Poussin sums on the sets C^{q}_{\beta}H_\omega of Poisson integrals of functions from the class H_\omega generated by convex upwards moduli of continuity \omega(t) which satisfy the condition \omega(t)/t\to\infty as t\to 0. As an implication, a solution of the Kolmogorov-Nikol'skii problem for de la Vall\'{e}e Poussin sums on the sets of Poisson integrals of functions belonging to Lipschitz classes H^\alpha, 0<\alpha <1, is obtaine

Multiwavelength studies of MHD waves in the solar chromosphere: An overview of recent results

The chromosphere is a thin layer of the solar atmosphere that bridges the relatively cool photosphere and the intensely heated transition region and corona. Compressible and incompressible waves propagating through the chromosphere can supply significant amounts of energy to the interface region and corona. In recent years an abundance of high-resolution observations from state-of-the-art facilities have provided new and exciting ways of disentangling the characteristics of oscillatory phenomena propagating through the dynamic chromosphere. Coupled with rapid advancements in magnetohydrodynamic wave theory, we are now in an ideal position to thoroughly investigate the role waves play in supplying energy to sustain chromospheric and coronal heating. Here, we review the recent progress made in characterising, categorising and interpreting oscillations manifesting in the solar chromosphere, with an impetus placed on their intrinsic energetics.Comment: 48 pages, 25 figures, accepted into Space Science Review

Right invertible multiplication operators and stable rational matrix solutions to an associate Bezout equation, I. the least squares solution.

In this paper a state space formula is derived for the least squares solution X of the corona type Bezout equation G(z)X(z) =

Limb Spicules from the Ground and from Space

We amassed statistics for quiet-sun chromosphere spicules at the limb using ground-based observations from the Swedish 1-m Solar Telescope on La Palma and simultaneously from NASA's Transition Region and Coronal Explorer (TRACE) spacecraft. The observations were obtained in July 2006. With the 0.2 arcsecond resolution obtained after maximizing the ground-based resolution with the Multi-Object Multi-Frame Blind Deconvolution (MOMFBD) program, we obtained specific statistics for sizes and motions of over two dozen individual spicules, based on movies compiled at 50-second cadence for the series of five wavelengths observed in a very narrow band at H-alpha, on-band and in the red and blue wings at 0.035 nm and 0.070 nm (10 s at each wavelength) using the SOUP filter, and had simultaneous observations in the 160 nm EUV continuum from TRACE. The MOMFBD restoration also automatically aligned the images, facilitating the making of Dopplergrams at each off-band pair. We studied 40 H-alpha spicules, and 14 EUV spicules that overlapped H-alpha spicules; we found that their dynamical and morphological properties fit into the framework of several previous studies. From a preliminary comparison with spicule theories, our observations are consistent with a reconnection mechanism for spicule generation, and with UV spicules being a sheath region surrounding the H-alpha spicules