The given angular electron distributions and the initial par

The given angular zvad fmk distributions and the initial parameters of the problem are listed in Table 1.
Conclusion Analysis of time delays of hard X-ray radiation during solar flares from the data of the BATSE X-ray spectrometer allowed to systematize the obtained energy spectra of the chosen flares and to identify three species of spectra in the data array: the increasing, the decreasing and the U-shaped ones with an increase in quantum energy Е. Apparently, the integral HXR delay spectra of the majority of the examined 82 flares did not obey either the Е1/2 law (free electron scattering), nor Е3/2 (trap model with precipitation). So we also examined an alternative model of electron beam kinetics in magnetic loop plasma with the acceleration regions separated high in the corona, in the current sheet and subsequent injection along the lines of force into a closed loop structure of the magnetic field. At the time of injection the electrons with the energy of 20 keV were delayed for tens of milliseconds compared to electrons of higher energies. Further dynamics of electrons in the magnetic loop was defined by the parameters of the beam, the plasma, and the magnetic field. It turned out that the distribution of hard X-ray radiation was inhomogeneous along the loop, and, therefore, radiation time delays and their spectra are different from different parts of the loop. Consequently, the integral HXR delay spectrum over the whole loop may belong to any of the three species. The proposed concept is confirmed by the fact that the 82 flares are distributed about evenly over all species of delay spectra.
Introduction It is well known that this singularity of the classical planetary model is resolved by quantum theory. Currently quantum theory seems equally promising in settling the problem of cosmological singularity. Although there is as yet no complete definition of the quantum version of GR, i.e. quantum cosmology, convincing scenarios for the evolution of the early Universe have been proposed. A number of theories discuss a quantum epoch in the emergence of the Universe from ‘nothing’, e.g., in the form of Vilenkin quantum tunneling [1], or of a similarly-defined Hartle–Hawking no-boundary wave function of the Universe [2]. In the latter, the quantum epoch exists as a limitation on the semi-classical approximation of the no-boundary wave function in its continuation backward in time [3,4]. However, both theories predict a probability of initial values for a cosmic scalar field ϕ which “operates” the following expansion of the Universe. For a scalar field with a potential V(ϕ) the probability predicted, for instance, by the Vilenkin tunneling mechanism [5] is equal to where G is the Newton gravitational constant. The radius of the Universe “upon tunnel exit” equals
The following stage of evolution is an exponential expansion of the Universe with the scalar field slow-rolling to its minimal value . This expansion is described by different inflation scenarios (see, for example, Linde [6]), where the initial radius of the Universe is taken to equal not its “tunneling” value (2) but the Planck radius . Still, the initial size of the Universe is not particularly important for its final state after its exponential expansion. There is, however, a practical interest in calculating the quantum fluctuations of the inflaton scalar field which are assumed to be responsible for the inhomogeneities observed in the large-scale structure of the Universe. In any case, a quantum formulation of the inflationary phase of the evolution of the Universe seems necessary, especially at its early stage, when the inflaton scalar field ϕ is large and the radius of the Universe is small. Here we are faced with the fundamental problem of quantum cosmology, the absence of a time parameter and the impossibility of altogether formulating the quantum dynamics of the Universe [7]. The term “frozen dynamics” has been proposed to describe this specific case [8]. To “re-freeze” the dynamics, either a modification of quantum GR, or any physically motivated approximation that introduces a cosmic time parameter, is necessary.