Abstract:
In the
framework of the theory of the gravitational field, which distinguishes between
particles and antiparticles, it is shown that even in the Early Universe its
disintegration occurred into areas consisting of baryons (worlds), and areas
consisting of antibaryons (antiworlds). It is hypothesized that astronomers
have observed worlds and antiworlds for fifteen years. They are, according to
the authors, objects that can be seen as relatively bright spots against the
almost uniform background of cosmic microwave radiation, having a
characteristic angular size of quarter degree.

Abstract:
In the
present article, we give a variant of the theory of gravity, which
distinguishes between particles and antiparticles. In this theory that called
two-signed gravity, in contrast to Einstein’s gravity, contributions from
particles and antiparticles in the tensor, which are the source of the gravitational
field are taken with different signs. In two-sign gravity, antiattraction exists
between particles and antiparticles. In the framework of two-signed gravitation,
it is naturally assume that Universe is not only electroneutral, but also
gravitationally neutral too. In present paper, we suggest model of homogeneous,
isotropic, uniformly expanding Universe. It is shown, what within framework of
that model, which does not contain any free parameters, well explained observed
dynamics of the Universe.

Abstract:
In the paper we give an introduction to Anosov diffeomorphisms, ways to represent their chaotic properties and some historical remarks on this subject. A complete classification of hyperbolic linear automorphisms of 2-torus is presented. We introduce a notion of pre-Markov partition for such automorphisms and give their classification and an algorithm for their construction.

Abstract:
We study the dynamics of homogeneous isotropic three-dimensional worlds filled with radiation (3R-worlds). It is shown that the dynamics of these worlds with the additional fourth large-scale spatial dimension leads to an important effect. At 3R-worlds the forces of repulsion appear. The source of these forces is the thermal energy of the radiation that fills these worlds. In the four-dimensional space, these forces are centrifugal. They operate in an external for 3R-world spatial dimension and stretch it. In the three-dimensional comoving coordinate system the centrifugal forces shows themselves as forces of repulsion. Standard Einstein's equations do not describe these forces. Written generalized Einstein's equation describing the dynamics of a homogeneous isotropic universe, taking into consideration the centrifugal forces of repulsion. We propose a cosmological model of the universe, based on these equations. This model apply to explain the observation data.

Abstract:
It is shown that there are seven types of solutions described in the framework of general relativity theory (GRT), the dynamics of empty homogeneous isotropic three-dimensional spaces. Solution of the equations of GRT, which describes the dynamics of a homogeneous isotropic universe, in the limiting case of vanishingly small effect of matter on the metric properties of space must go to one of them.

Abstract:
It seems likely that the generalized Einstein equations are not complete and only partly account for the effect on the Universe dynamics of that part of the energy of the space environment the change of which is purely geometric. There are offered the generalized Einstein's equations, describing not only the gravity forces, but also the cosmological forces of repulsion, which are geometric in their nature. The generalized Einstein equations are used to derive the cosmological Friedman's equations describing the dynamics of a homogeneous isotropic universe with the influence of cosmological repulsion forces. We propose a cosmological model of the universe based on these equations. Application of the model for explanation of the observations is considered here.

Abstract:
A number of studies showed association of mental status with heart rate variability. This work discovered a feature of frequency structure of heart rate variability that is associated with mental readiness. In three independent groups of 64, 39, and 19 volunteers by the factor analysis of heart rate periodograms, it has been discovered that there are at least two other heart rate oscillation phenomena apart from the well known low frequency oscillations and respiratory arrhythmia. They have periods of 3 and 4 heart beats. Association of amplitude of 3-beats oscillation with level of mental readiness was shown due to further observation in two independent groups of 12 and 7. Moreover, possibility of assessment of mental readiness by the mathematical model based on heart rate periodogram was suggested.

Abstract:
Cesaro convergence of spherical averages is proven for measure-preserving actions of Markov semigroups and groups. Convergence in the mean is established for functions in $L^p$, $1\le p<\infty$, and pointwise convergence for functions in $L^\infty$. In particular, for measure-preserving actions of word hyperbolic groups (in the sense of Gromov) we obtain Cesaro convergence of spherical averages with respect to any symmetric set of generators.

Abstract:
In the presented work the results of numerical modeling of the UT-variation of the equatorial electrojet, executed on the basis of the model GSM TIP are presented, taking into account the dynamo electric fields generated by thermospheric winds in a current-carrying layer of the ionosphere at heights 80–175 km above a surface of the Earth. To the Global Self-consistent Model of the Thermosphere, Ionosphere and Protonosphere (GSM TIP), developed in WD IZMIRAN, a new block for the calculation of electric fields in the ionosphere has been added. In this block the solution of the three-dimensional equation describing the conservation law of the full current in the Earth's ionosphere is reduced to the solution of the two-dimensional equation by integration along geomagnetic field lines. Calculations of parameters of the near-Earth space plasmas have been executed for quiet equinoctial conditions on 22 March 1987 during the minimum of solar activity. It has been shown, that there is a distinct semidiurnal harmonic in the diurnal behavior of the linear density of the equatorial electrojet with maxima at 23:00 UT and 15:00 UT, as well as with minima at 06:00 UT and 20:00 UT. The greatest and smallest values of the peak intensity of the equatorial electrojet with respect to the diurnal behavior can differ by a factor of two. The longitudinal extent of the area of the equatorial electrojet does hardly show any UT-variation, but the greatest longitudinal extent is at 06 UT. With the growth of the peak intensity of the equatorial electrojet its latitudinal extent also increases (on ~5–10°) a little. At the same time the equatorial electrojet in the maxima of intensity has approximately an identical width, whereas in the minima the electrojet is narrow in the morning and wide in the afternoon. As for the surface density of the equatorial electrojet, its UT-variation is much weaker and equals ~1–3 A/km2 and the peak intensity is equal ~15–20 A/km2. The latitudinal extent of the surface density of the equatorial electrojet is maximal at 23:00 UT and 15:00 UT and minimal at 06:00 UT and 20:00 UT.