Explicit relations for harmonic potentials are obtained when the density of the potentials is specified on two segments of parallel straight lines. These results may be used for testing numerical algorithms for calculating the harmonic potentials in boundary value problems outside open arcs in a plane. Moreover, explicit solutions to two systems of singular integral equations are obtained, and these solutions may be used for testing numerical methods for solving singular integral equations. Futhermore, explicit solutions to Neumann problem for Laplace equation are obtained for specific functions in the boudary conditions.
Show AbstractGhost imaging allows to extract information about an object from the spatial correlation function of photons that interacted with the object and photons in reference arm(s). Reference beam does not interact with the object, but it is measured by a CCD matrix. The mathematical method of measurement reduction allows to use both presence of mutual correlations of multiplexed ghost images and researcher's prior information about how the research object's image can look like in order to improve reconstructed image quality. The information about the object is sparsity of its transparency distribution under a given transform. Computer modeling of image reconstruction using multiplexed ghost images formed by four-mode entangled quantum light states confirms efficiency of the proposed algorithm even with a small numer of photons.
Show AbstractThe evolution function of the differential operator $ -(-\Delta)^\nu$ in $d$ -dimensional Euclidean space is calculated. Its analytic expression is obtained through the Fox-Wright psi-functions, which is well-defined for both integer and noninteger values of $\nu$ and $d$. Possible applications of the obtained functions in quantum field theory and the connection with fractional calculus are discussed.
Show AbstractIn this paper we present the results of studies of the process of association production of a Higgs boson and a heavy fermion pair in arbitrarily polarized electron-positron collisions. Analytical expressions for differential cross sections of processes are obtained, features of the behavior of cross sections, angular and spin asymmetries are investigated as a function of the energies and emission angles of the particles.
Show AbstractWe suggest utilization of samples with pre-formed ordered surface nanorelief to reveal the mechanisms of surface topography evolution under ion beam irradiation. The suggested approach is used to study the case of silicon surface bombardment with cluster ion beam. The sampled with patterned surface were manufactured with electron beam lithography, their surface was examined with SEM and AFM. It is shown that the relief after cluster ion irradiation is formed as the result of competition between sputtering and migration processes; their effectiveness is determines by the local angle of incident and surface curvature. The possibility of obtaining a predetermined asymmetrical pattern by adjusting the ion beam incidence angle, the dosage of irradiation and the initial surface relief.
Show AbstractTwo samples of S – band BAC multiple-beam klystrons BT258 were developed, fabricated and tested at VDBT with support of CERN. Maximum efficiency of 66% was obtained at an output level of 6,6 MW. The efficiency in the vicinity of 60% for one of multiple beam klystrons was successively confirmed in tests at CERN. BAC – method of electron grouping is discussed and comparison of output parameters of multuple-beam klystron with the existing classical klystrons is given in the article. Possibility of increasing output power by BAC – method of electron grouping of S – band multiple-beam klystron at output power level of 10, 20 MW is discussed.
Show AbstractThis paper is concerned with investigating of the possibilities of low-frequency ultrasound tomography in medicine. The main application is the development of tomographic methods for differential diagnosis of breast cancer. To solve the inverse problem, a mathematical model is used that describes both the phenomena of diffraction and refraction and the absorption of ultrasound in an inhomogeneous medium. The algorithms developed for reconstructing the velocity structure were evaluated using the test bench for experimental studies. Broadband ultrasonic sources in the 50 – 600 kHz range were used for sounding. Teledyne Reson TC4038 hydrophone with a sensitivity of approximately 4 μV/Pa and a frequency range of 10-800 kHz was used as a receiver. Teledyne Reson VP1000 preamplifier was used to amplify the signals. The studies were carried out on phantoms with acoustic parameters close to the properties of human soft tissues. A layerwise model was used to reconstruct the 3D velocity structure. The sound speed cross-sections reconstructed from the experimental data have a resolution of approximately 2 mm, while the central wavelength is approximately 4 mm. An important result of the work is an experimental confirmation of the adequacy of the model to physical processes.
Show AbstractThe possibilities and prospects of laser generation in active media cooled down to cryogenic temperatures based on organic dyes are considered in the article. The obtained results demonstrate the possibility of creating highly effective active laser media (based on the analogue of the Shpol'sky matrix) on the basis of cooled carbon-containing matrices.
Show AbstractA new analogue of Heisenberg principle has been introduced for complex biological systems – complexity within the frame of new theory of chaos self-organization. This requirement results from the absence of stationary regimes of biosystems (dx/dt≠0 continuously) vector of state x(t) and uninterrupted chaotic change of distribution function f(x) and other characteristics. Now this identified as type 2 uncertainty. At the same time type 1 uncertainty has been introduced when f(x) do not change but quasi-attractor’s parameters vary. Neuron network simulator reveals the difference between samples whereas absence of statistical significance.
Show AbstractIn the work with the help of mathematical modeling, the dependences between the evolution velocity of the spring thermal bar (TB) in the reservoir and morphometric parameters of its bottom were obtained. The characteristic intervals of rates of TB movement in reservoirs differing in depth and bottom inclination have been revealed. It is shown that the main factor affecting the lifetime of the TB is the reservoir depth. The influence of the relative humidity of the air and the flux of solar radiation on the rate of spring TB movement was estimated. Using the simulation results and quantitative characteristics of the underwater relief of the Ladoga lake, isolines of the space-time variability of the TB location on the water area of the reservoir was constructed. A satisfactory agreement between the modeling data and field observations was obtained.
Show AbstractA study of the effect of the Coriolis force and wind stress on the hydrodynamic processes in Kamloops Lake during the evolution of the autumnal thermal bar was undertaken by means of numerical modeling using meteorological data from 01.12.2017 to 30.12.2017. It was determined that the Coriolis force in combination with strong winds, generating the large-scale circulation flows of water masses, has a significant impact on the alongshore flow velocity. Analysis of the spatial distributions of physical parameters showed that the strong westerly winds that directed opposite to the horizontal movement of the thermal front lead to a displacement of the cyclonic circulation induced by the Coriolis force into the lower layers of water column.
Show AbstractThe interaction of a short cylindrical vortex, elongated along a transverse coordinate, with a flow with a velocity shift near a solid surface is considered. It is shown how a cylindrical vortex, whose ends are lowered to the bottom of the channel, turns into a circular vortex. The obtained qualitative model is verified in the experiment.
Show AbstractAn analysis of the possibilities and limitations of the determination of the skeewness and kurtosis excess according to the radiosonde data at the incidence angles, where the backscattered signal is determined by the mechanism of quasi-mirror reflection is completed. It is shown that direct recovery of skewness and kurtosis based on the dependence of the normalized backscattering cross section on the incidence angles leads to significant errors. The determination of these parameters by minimizing the discrepancy between the empirical probability density function and the given a priory truncated Gram-Charlier series essentially depends on the choice of this model.
Show AbstractThis article introduces the results of measurements of the distributions of current velocity, temperature, suspended sediments and chlorofill-a by presence of the drift and density flows, jet and internal waves in the Onego Lake. The interpretation of the mechanisms of the formation of currents is given. There are introduced theoretical distributions of current velocity and chlorofill-a obtained and verified in this paper.
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