Abstract:
For {the} Fourier image $widehat{D}'_Gamma$ of {the} algebra $D'_Gamma$ of the distributions with supports on {a}cone $Gamma$ the functional calculus for generators of$n$--parametric $(C_o)$--semigroups of operators is determined. {For this purpose, we consider construction of the dual pair} $langlewidehat{D}'_Gamma,,widehat{D}_Gamma angle$, {and provide some examples with respect to the formula of operator calculus.}

Abstract:
The article is devoted to the problem of Hilbert-Schmidt type analytic extensions in Hardy spaces over the infinite-dimensional unitary matrix group endowed with an invariant probability measure. An orthogonal basis of Hilbert-Schmidt polynomials, reproducing kernels, integral formulas and boundary values are investigated.

Abstract:
The performed experimental studies of X-ray excited and photoluminescence, optical absorption and Raman scattering of CdS1-xSex nanocrystals, embedded in borosilicate glass matrix, have enabled the nanocrystal parameters (chemical composition, average radius, acceptor levels energy depth, electron-hole Coulomb interaction energy) is to be determined.

Abstract:
A series of samples with quaternary CdS1？？SeTe nanocrystals with cations of three types distributed over nanocrystal lattice sites were grown in a borosilicate glass matrix by the diffusion-limited growth technique. Their Raman spectra confirm the three-mode compositional behaviour of CdS1？？SeTe phonon spectra. The compositional dependence of the LO phonon frequencies is analysed experimentally for a series of samples containing nanocrystals with ≈.

Abstract:
Development of the orbital-free (OF) approach of the density functional theory (DFT) may result
in a power instrument for modeling of complicated nanosystems with a huge number of atoms. A
key problem on this way is calculation of the kinetic energy. We demonstrate how it is possible to
create the OF kinetic energy functionals using results of Kohn-Sham calculations for single atoms.
Calculations provided with these functionals for dimers of sp-elements of the C, Si, and Ge periodic
table rows show a good accordance with the Kohn-Sham DFT results.

Abstract:
Radioactivity of nuclei in a centrifugal force field of an ultracentrifuge is considered for heavy radioactive nuclei, i.e., for the same nuclei, but with a significant virtual mass thousands of times larger than the actual mass and is characterized by an angular momentum. As the nucleus leaves the centrifugal force field, the virtual mass disappears, but the spin number appears and/or changes. The role of centrifugal and gravitational forces in radioactive decay of nuclei is studied. According to the terminology of western researchers, such a virtual mass state is called the dynamic gravitation which is more adequate. The oscillator and possible changes in the nucleus state are considered under conditions of dynamic gravitation and taking into account features of atomic nucleus physics. To a first approximation, the drop model of the nucleus was used, in which shape fluctuations have much in common with geophysical and astrophysical analogues. Shape fluctuations of analogues strongly depend on the gravitational force g defined by their mass (or nucleus mass). Experiments were performed by radiometric measurements of transbaikalian uranium ore (1.5 g) with known composition in a centrifuge at various rotation rates or gravitational forces g. The existence of characteristic times or the effect of rotation frequencies (i.e., g) on atomic nuclei, which, along with the nucleus type itself, controls the nucleus response to perturbation (stability increase or decay), is found statistically significant.

The study of natural radioactivity of objects which are able to change their temporal timing feature is presented. It is of interest to compare the latest data on the activity of the Sun and the periodicity of solar neutrinos and the temporal characteristics of the radioactive source. That is, to conduct a search for the possible influence of external sources for radioactivity. There are cycles 5 min, 18 min and 53 min found in solar physics. The cycle of 27 days corresponds to the activity of the Sun. During of the solar activeity these temporal pulsations are lost in a strong variation of solar wind (Neugebauer, NASA). The Stanford University scientists (P. Starrek, G. Valter and M. Vitlend) have found the cycle of 28.4 days as pulsations of the solar neutrinos. Neutrinos come from the depths of the Sun and they tell about the frequency of oscillations of solar bowels. It is also seen online: Kostyantynivska L. V. Solar activity. Search experiment is better to have a known but modified experiment. Experiments on monitoring natural radioactivity and the possible influence from the Sun were previously carried out by measuring the variations of the gamma-ray sample of ore from the TransBaikal uranium deposit; the characteristics of the sample are known. The spectrum of temporal variations in the activity of the sample Zabaikalskaya radioactive ore contains peaks which coincide with the period of natural oscillations of the Sun. The capture cross section of the radioactive heavy deformed nucleus in time decay increases in many orders and is able to interact with the stream of solar neutrinos which are modulated by own oscillations of the Sun. The picks of spectrum of long-period oscillations of the Earth exceed its own contain peaks that match the value with an accuracy of 1% 3% with peaks of its own oscillations of the Sun. The mechanism of excitation of these oscillations is similar to the nature of variations in the activity of a radioactive sample of ore. These effects are included in the mechanisms of interaction of the Earth—the Sun systems and impact on seismicity; search problem of existing natural nuclear reactor inside Earth core.

In the paper, we report about the possibilities to apply the photon sieve principle to binary diffractive lens in millimeter wave band. The FDTD simulation showing the idea of the photon sieve application to millimeter wave optics does not allow increasing the resolution power. The reason is the small number of holes in the FZP aperture. But such simulation results may be used as computational experiments of simple scale in millimeter wave allowing obtaining insight into physical systems which are characterized by nanometric objects, because the D/f and D/λ are almost the same.

Abstract:
In today’s digital era, developing digital circuits is bounded by the research towards investigating various nano devices. This paper provides the design of compact Baugh-Wooley multiplier using reversible logic. Even though various researches have been done for designing reversible multiplier, this work is the first in the literature to use Baugh-Wooley algorithm using reversible logic. In this work, a new 5 × 5 reversible multiplier cell is proposed which will be useful in designing Baugh-Wooley multiplier. The proposed single multiplier cell is able to perform addition of a 1 × 1 product with the sum and carry from the previous cell. This reversible multiplier cell is useful in building up regularity in the array multipliers. The Toffoli gate synthesis of the proposed reversible multiplier cell is also given.

Abstract:
We analyze the periodic orbits of “f” family (simply symmetric retrograde periodic orbits) and the regions of quasi-periodic motion around Saturn in the photo gravitational Sun-Saturn system in the framework of planar circular restricted three-body problem with oblateness. The location, nature and size of these orbits are studied using the numerical technique of Poincare surface of sections (PSS). In this paper we analyze these orbits for different solar radiation pressure (q) and actual oblateness coefficient of Sun Saturn system. It is observed that as Jacobi constant (C) increases, the number of islands in the PSS and consequently the number of periodic and quasi-periodic orbits increase. The periodic orbits around Saturn move towards the Sun with decrease in solar radiation pressure for given value of “C”. It is observed that as the perturbation due to solar radiation pressure decreases, the two separatrices come closer to each other and also come closer to Saturn. It is found that the eccentricity and semi major axis of periodic orbits at both separatrices are increased by perturbation due to solar radiation pressure.