Local assignability of Lyapunov exponents of linear discrete-time system

We consider sufficient and necessary conditions for the proportional local assignability of the Lyapunov spectrum of the system $$x(m+1)=\left(A(m)+B(m)U(m)\right)x(m), \quad m\in\mathbb Z,\quad x\in\mathbb R^n.$$ The properties of stability of the Lyapunov spectrum and integral separation of linear discrete-time systems are studied, description of the spectral set of a linear system in the case of the full spectrum stability is obtained, the property of uniform complete controllability of a linear system with discrete time is studied, and the properties of the Bebutov shell of a linear discrete-time control system are investigated.

CREATING OF A BANK OF SPACE IMAGES ON THE BASIS OF OPEN DATA SOURCES FOR MONITORING OF PROTECTED NATURAL TERRITORIES OF THE ALTAI REPUBLIC

The article deals with the role of satellite images bank creation for the Altai Republic region for the purpose of monitoring the results application of particularly protected natural territories. Absence of access to relevant spatial data, concerning the analysis of processes in the protected woodlands, reserves and natural parks makes it necessary to choose reliable information resources. The applications of open data sources is offered. The surveys of natural and technical parameters, that should be taken into account in choosing images on geoportals such as the spectral set of channels, availability of cloud and snow cover and seasonal aspects, are suggested. Some recommendations concerning the establishment of mosaic composites on the basis of multi-temporal images surveys result are offered in order to obtain the most uniform images results distribution with minimum noticeable stitching lines and distinction in brightness/contrast parameters of images in each spectral channel.

The ESO’s VLT type Ia supernova spectral set of the final two years of SNLS

Aims. We aim to present 70 spectra of 68 new high-redshift type Ia supernovae (SNe Ia) measured at ESO’s VLT during the final two years of operation (2006–2008) of the Supernova Legacy Survey (SNLS). This new sample complements the VLT three year spectral set. Altogether, these two data sets form the five year sample of SNLS SN Ia spectra measured at the VLT on which the final SNLS cosmological analysis will partly be based. In the redshift range considered, this sample is unique in terms of homogeneity and number of spectra. We use it to investigate the possibility of a spectral evolution of SNe Ia populations with redshift as well as SNe Ia spectral properties as a function of lightcurve fit parameters and the mass of the host-galaxy. Methods. Reduction and extraction are based on both IRAF standard tasks and our own reduction pipeline. Redshifts are estimated from host-galaxy lines whenever possible or alternatively from supernova features. We used the spectro-photometric SN Ia model SALT2 combined with a set of galaxy templates that model the host-galaxy contamination to assess the type Ia nature of the candidates. Results. We identify 68 new SNe Ia with redshift ranging from z = 0.207 to z = 0.98 for an average redshift of z = 0.62. Each spectrum is presented individually along with its best-fit SALT2 model. Adding this new sample to the three year VLT sample of SNLS, the final dataset contains 209 spectra corresponding to 192 SNe Ia identified at the VLT. We also publish the redshifts of other candidates (host galaxies or other transients) whose spectra were obtained at the same time as the spectra of live SNe Ia. This list provides a new redshift catalog useful for upcoming galaxy surveys. Using the full VLT SNe Ia sample, we build composite spectra around maximum light with cuts in color, the lightcurve shape parameter (“stretch”), host-galaxy mass and redshift. We find that high-z SNe Ia are bluer, brighter and have weaker intermediate mass element absorption lines than their low-z counterparts at a level consistent with what is expected from selection effects. We also find a flux excess in the range [3000–3400] Å for SNe Ia in low mass host-galaxies (M < 1010M⊙) or with locally blue U–V colors, and suggest that the UV flux (or local color) may be used in future cosmological studies as a third standardization parameter in addition to stretch and color.