Задача фiльтрацiї для перiодично корельованих випадкових послiдовностей iз пропущенними значеннями

The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a periodically correlated stochastic sequence from observations of the sequence with missings is considered. Formulas for calculation the mean-square error and the spectral characteristic of the optimal estimate of the functionals are proposed in the case where spectral densities of the sequences are exactly known. Formulas that determine the least favorable spectral densities and the minimax spectral characteristics are proposed in the case of spectral uncertainty, when spectral densities of sequences are not exactly known but the class of admissible spectral densities is given. Pages of the article in the issue: 30 - 43 Language of the article: EnglishДослiджується задача оптимального оцiнювання лiнiйних функцiоналiв вiд невiдомих значень перiодично корельованої стохастичної послiдовностi за спостереженнями послiдовностi iз пропущеними значеннями. Знайдено формули для обчислення значень середньокваратичних похибок та спектральних характеристик оптимальних оцiнок функцiоналiв у випадку, коли спектральнi щiльностi послiдовностей точно вiдомi. Отримано формули для визначення найменш сприятливих спектральних щiльностей та мiнiмаксних спектральних характеристик оптимальних лiнiйних оцiнок функцiоналiв у випадку спектральної невизначеностi, коли спектральнi щiльностi послiдовностей точно не вiдомi, але задано множини допустимих спектральних щiльностей

On estimation problem for continuous time stationary processes from observations in special sets of points

The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a stochastic stationary process from observations of the process with missings is considered. Formulas for calculating the mean-square error and the spectral characteristic of the optimal linear estimate of the functionals are derived under the condition of spectral certainty, where the spectral density of the process is exactly known. The minimax (robust) method of estimation is applied in the case where the spectral density of the process is not known exactly while some sets of admissible spectral densities are given. Formulas that determine the least favourable spectral densities and the minimax spectral characteristics are derived for some special sets of admissible densities. Pages of the article in the issue: 20 - 33 Language of the article: Englis

Track D Social Science, Human Rights and Political Science

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138414/1/jia218442.pd

Optical Characterization of SERS Substrates Based on Porous Au Films Prepared by Pulsed Laser Deposition

The SERS (surface enhanced Raman spectroscopy) substrates based on nanocomposite porous films with gold nanoparticles (Au NPs) arrays were formed using the method of the pulsed laser deposition from the back low-energy flux of erosion torch particles on the glass substrate fixed at the target plain. The dependencies of porosity, and morphology of the surface of the film regions located near and far from the torch axis on the laser ablation regime, laser pulses energy density, their number, and argon pressure in the vacuum chamber, were ascertained. The Au NPs arrays with the controllable extinction spectra caused by the local surface plasmon resonance were prepared. The possibility of the formation of SERS substrates for the detection of the Rhodamine 6G molecules with the concentration 10−10 Mol/L with the enhancement factor 4·107 was shown