Relations between stochastic and partial differential equations in hilbert spaces

The aim of the paper is to introduce a generalization of the Feynman-Kac theorem in Hilbert spaces. Connection between solutions to the abstract stochastic differential equation d X (t) = A X (t) d t + B d W (t) and solutions to the deterministic partial differential (with derivatives in Hilbert spaces) equation for the probability characteristic t, x h (X (T)) is proved. Interpretation of objects in the equations is given. © 2012 I. V. Melnikova and V. S. Parfenenkova

Generalized solutions of differential-operator equations with singular white noise

In various distribution spaces, we study the Cauchy problem for the equation u′(t) = Au(t)+BW(t), t ≥ 0, with a singular white noise W and an operator A generating various regularized semigroups in a Hilbert space. Depending on the properties of the operator A, we construct solutions generalized separately and jointly with respect to the time, random, and "space" variables. © 2013 Pleiades Publishing, Ltd

The generalized well-posedness of the Cauchy problem for an abstract stochastic equation with multiplicative noise

We study the existence, uniqueness, and stability of a solution to the Cauchy problem for a stochastic differential equation with multiplicative noise in the spaces of generalized random variables with values in a Hilbert space. © 2013 Pleiades Publishing, Ltd

New spectral functions of the near-ground albedo derived from aircraft diffraction spectrometer observations

The airborne spectral observations of the upward and downward irradiances are revisited to investigate the dependence of the near-ground albedo as a function of wavelength in the entire solar spectrum for different surfaces (sand, water, snow) and under different conditions (clear or cloudy sky). The radiative upward and downward fluxes were determined by a diffraction spectrometer flown on a research aircraft that was performing multiple flight paths near the ground. The results obtained show that the near-ground albedo does not generally increase with increasing wavelengths for all kinds of surfaces as is widely believed today. Particularly, in the case of water surfaces it was found that the albedo in the ultraviolet region is more or less independent of the wavelength on a long-term basis. Interestingly, in the visible and near-infrared spectra the water albedo obeys an almost constant power-law relationship with wavelength. In the case of sand surfaces it was found that the sand albedo is a quadratic function of wavelength, which becomes more accurate if the ultraviolet wavelengths are neglected. Finally, it was found that the spectral dependence of snow albedo behaves similarly to that of water, i.e. both decrease from the ultraviolet to the near-infrared wavelengths by 20–50%, despite the fact that their values differ by one order of magnitude (water albedo being lower). In addition, the snow albedo vs. ultraviolet wavelength is almost constant, while in the visible near-infrared spectrum the best simulation is achieved by a second-order polynomial, as in the case of sand, but with opposite slopes

Determining rhenium in crude ore by the method of X-ray fluorescence analysis

Optimal conditions of sorption concentration of perrhenate-ions with activated carbon have been considered. The possibility of rhenium determination with accompanying element is show

Use of albumin in the composition of wood pellets in order to improve their quality

Chemical treatment of wood albumin in the technology of pellets is considered from the point of view of the possible directions of chemical reactions in the interactiontion of its reactivity with components of wood – lignin and polysaccharides (cellulose and hemicellulose). It has b een shown that at high temperature and pressure parameters for the compression step – primary to obtain pellets technology, car-bonyl, carboxyl, amine and amide functional groups of albumin may enter into an esterification reaction involving the hydroxyl groups of the reactive lignin and also a reaction of formation of new hydrogen bonds between two electronegative atoms which, together as oxygen and nitrogen acts. Using albumin as a glue with its variation rate of from 0.1 to 0.5% to a. d. a wood composite pellets composed of different kinds of wood resulting in improved performance pellets complex values characterizing their mechanical strength. Pellets obtained with the introduction of albumin in their composi-tion, meet all the requirements for the materials of the fuel use