Perturbation of spectra and spectral subspaces

We consider the problem of variation of spectral subspaces for linear self-adjoint operators under off-diagonal perturbations. We prove a number of new optimal results on the shift of the spectrum and obtain (sharp) estimates on the norm of the difference of two spectral projections

Application software GeoniCS when designing the olympic ski runs

GeoniCS implementation for Olympic mountain skiing routes designing is considered an international standard. This program allows optimizing plan and profiling development. Besides, the author adapted the program for lines engineering protection with special metal mesh

On a Subspace Perturbation Problem

We discuss the problem of perturbation of spectral subspaces for linear self-adjoint operators on a separable Hilbert space. Let $A$ and $V$ be bounded self-adjoint operators. Assume that the spectrum of $A$ consists of two disjoint parts $\sigma$ and $\Sigma$ such that $d=\text{dist}(\sigma, \Sigma)>0$. We show that the norm of the difference of the spectral projections \EE_A(\sigma) and \EE_{A+V}\big (\{\lambda | \dist(\lambda, \sigma) $<d/2\}\big)$ for $A$ and $A+V$ is less then one whenever either (i) $\|V\|<\frac{2}{2+\pi}d$ or (ii) $\|V\|<{1/2}d$ and certain assumptions on the mutual disposition of the sets $\sigma$ and $\Sigma$ are satisfied

Astrometric jitter of the sun as a star

The daily variation of the solar photocenter over some 11 years is derived from the Mount Wilson data reprocessed by Ulrich et al. 2010 to closely match the surface distribution of solar irradiance. The standard deviations of astrometric jitter are 0.52 $\mu$AU and 0.39 $\mu$AU in the equatorial and the axial dimensions, respectively. The overall dispersion is strongly correlated with the solar cycle, reaching $0.91 \mu$AU at the maximum activity in 2000. The largest short-term deviations from the running average (up to 2.6 $\mu$AU) occur when a group of large spots happen to lie on one side with respect to the center of the disk. The amplitude spectrum of the photocenter variations never exceeds 0.033 $\mu$AU for the range of periods 0.6--1.4 yr, corresponding to the orbital periods of planets in the habitable zone. Astrometric detection of Earth-like planets around stars as quiet as the Sun is not affected by star spot noise, but the prospects for more active stars may be limited to giant planets.Comment: Accepted in Ap

HI properties of nearby galaxies from a volume-limited sample

We consider global HI and optical properties of about three hundred nearby galaxies with V$_0 < 500$ km/s. The majority of them have individual photometric distance estimates. The galaxy sample parameters, e.g. their linear diameters, their HI mass-to-luminosity ratio, their total mass-to-luminosity ratio, their mean optical surface brightness show some known and some new correlations implying a meaningful dynamic explanation. For the LV galaxies their HI mass and angular momentum follow a nearly linear relation expected for rotating gaseous disks being near the threashold of gravitational instability, favourable for active star formation.Comment: 5 pages, 9 figures, uses laa.sty accepted by A&A Suppl. Serie