We consider tomograms and quasidistributions, such as the Wigner functions, the Glauber–Sudarshan Pfunctions, and the Husimi Q-functions, that violate the standard normalization condition for probability distribution fucntions. We introduce special conditions for the Wigner function to determine the tomogram with the Radon transform and study three different examples of states like the de Broglie plane wave, the Moschinsky shutter problem, and the stationary state of a charged particle in a uniform constant electric field. We show that their tomograms and quasidistribution functions expressed in terms of the Dirac delta function, the Airy function, and Fresnel integrals violate the standard normalization condition and the density matrix of the state therefore cannot always be reconstructed. We propose a method that allows circumventing this problem using a special tomogram in the limit form.

In this paper, we study the efficiency of egoistic and altruistic strategies within the model of social dynamics determined by voting in a stochastic environment (the ViSE model) using two criteria: maximizing the average capital increment and minimizing the number of bankrupt participants. The proposals are generated stochastically; three families of the corresponding distributions are considered: normal distributions, symmetrized Pareto distributions, and Student's t-distributions. It is found that the "pit of losses" paradox described earlier does not occur in the case of heavy-tailed distributions. The egoistic strategy better protects agents from extinction in aggressive environments than the altruistic ones, however, the efficiency of altruism is higher in more favorable environments. A comparison of altruistic strategies with each other shows that in aggressive environments, everyone should be supported to minimize extinction, while under more favorable conditions, it is more efficient to support the weakest participants. Studying the dynamics of participants' capitals we identify situations where the two considered criteria contradict each other. At the next stage of the study, combined voting strategies and societies involving participants with selfish and altruistic strategies will be explored.

Studying of stress field in the Martian interior is of importance for the seismic exploration of Mars. It’s assumed to place a seismometer on Mars at the end of November 2018 (mission InSight of NASA) to determine the present level of tectonic activity and get information on its deep interior. We perform the stress field analysis in the lithosphere of Mars in order to reveal the areas of maximum shear and extensional stresses as potential marsquakes’ sources.

Regions of maximum shear and tension-compression stresses in the Martian interior have been revealed using the three-level compensation model. Nonequilibrium relief, density anomalies at the crust−mantle boundary, and density anomalies at the base of the lithosphere are the sources of the anomalous gravitational field. The thickness of elastic lithosphere positioned on a weak layer that has partially lost its elastic properties varies from 150 to 500 km. The weakening of the layer under the lithosphere is simulated by a tenfold lower value of the shear modulus down to the core boundary. In general, the stresses for the threelevel compensation model differ from the values obtained for the two-level model (nonequilibrium relief and density anomalies at the crust−mantle boundary are the sources of the anomalous gravitational field) by 5−10%. Considerable differences between the models of two-level and three-level compensation are revealed beneath Hellas and Argyre regions.

In this paper the energy optimal control of harmonic oscillator is found. The solution is compared to the solution of the time optimal nulling of harmonic oscillator’s energy. The results of the modeling of the oscillator’s phase coordinates and full energy for given control time are shown.