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[en] In this article the mathematical evaluation level of the process of pollution of an atmosphere by radioactive and carcinogenic substances is considered. With knowledge of results of meteorological forecasts and primary intensity of carcinogenic and radioactive substances leading to pollution, the given model will help to calculate the distribution of the given impurities in atmosphere. According to the model a relative error in calculations reaches 40 percent.
[en] In this paper we consider an evolution of ideas in vacuum photodetector developments. Diverse approaches in developments of vacuum photodetectors (classical photomultipliers and hybrid phototubes) for the last half of century are covered. A particular emphasis is made on large area vacuum photodetectors developments. Some other issues concerning WLS and light guide techniques for increasing photodetectors sensitivity are highlighted as well.
[en] In this communication, we show that there is general construction to produce non-evolutionary integrable equations from a given integrable evolutionary equation. To support the main theorem, a few examples are explicitly given. (fast track communication)
[en] Classical and nonclassical symmetries are considered to reduce evolution equations with initial conditions in two independent variables. First of all, we rearrange the classical infinitesimal operators such that they leave the initial value problems invariant. Secondly, we give a sufficient condition for the nonclassical symmetry reductions of initial value problems. The generalized Kuramoto-Sivashinsky equation with dispersive effects is considered to examine the algorithms.
[en] In this work, we extend the bottom-up reconstruction framework of gravity to other modified gravities, and in particular for and mimetic gravities. We investigate which are the important conditions in order for the method to work, and we study several viable cosmological evolutions, focusing on the inflationary era. Particularly, for the theory case, we specify the functional form of the Hubble rate and of the scalar-to-tensor ratio as a function of the e-foldings number and accordingly, the rest of the physical quantities and also the slow-roll and the corresponding observational indices can be calculated. The same method is applied in the mimetic gravity case, and in both cases we thoroughly analyze the resulting free parameter space, in order to show that the viability of the models presented is guaranteed and secondly that there is a wide range of values of the free parameters for which the viability of the models occurs. In addition, the reconstruction method is also studied in the context of mimetic gravity. As we demonstrate, the resulting theory is viable, and also in this case, only the scalar-to-tensor ratio needs to be specified, since the rest follow from this condition. Finally, we discuss in brief how the reconstruction method could function for other modified gravities.
[en] A new formula of entanglement fidelity has been introduced, which can serve as a measure of the preservation of entanglement between two initially entangled subsystems exposed to local noisy environments. For a simple model we derive analytic expressions of concurrence and entanglement fidelity and draw the relationship between them. We find that such entanglement fidelity exhibits the behavior similar to that of the concurrence in quantum evolutions. (general)
[en] Leighton's well-known conjecture about singular points of a meromorphic function defined by its expansion in a general C-fraction is discussed. A theorem proved in the paper yields, in particular, this conjecture for an arbitrary non-decreasing sequence of exponents αk→∞.