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This paper presents data on the simultaneous and complementary observations of the gamma-ray burst (GRB) GRB 161017A for optical, X-ray, and gamma wavelengths obtained by the Russian multi-messenger Lomonosov space observatory and supplemented by additional data from the Swift satellite as well as the ground-based MASTER Global Robotic Net and the 10 m Gran Telescopio Canarias. Multifrequency spectra of this very powerful explosion indicate that it originated at a distance of 10 billion light years from Earth. Here, we present the results of the prompt, early, and afterglow optical observations. The light curves and spectra suggest that the prompt optical and high-energy emissions occur in the same region near the GRB source.

The article deals with the global demographic transition and phenomenological models of demographic dynamics by Sergey Kapitsa and Boris Dolgonosov developed on the basis of the principles of demographic and informational imperatives. The technological imperative is analyzed, which is intermediate between the first two. The authors propose a new mathematical model for forecasting demographic dynamics in the era of widespread use of intelligent machines. The model has been developed on the basis of the demographic model of Sergey Kapitza and equations for the production of useful information in human society, based on the assumption of Sergey Kuznets about technological progress. Calculations made using this model show that the population of the Earth, having reached a maximum value c. 8.7 billion in 2060, will then begin to decline steadily and by 2100 will not exceed 8.3 billion.

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In this paper we develop the Conditional Density Matrix formalism for adequate description of division and unification of quantum systems.Applications of this approach to the descriptions of parapositronium, quantum teleportation and others examples are discussed. INTRODUCTIONRecent progress in quantum communications has caused the great interest to the problems connected with divisions of quantum systems into subsystems and reunifications of subsystems into a joint system. Although general theory of such processes was proposed in 1927 [von Neumann 1927], so far, a division of a quantum system into subsystems is usually described in a fictitious manner. As an example, here we quote the classical paper on the photon teleportation . Describing the photon teleportation experiment they write: Nevertheless Einstein was quite right in his non-acceptance of such point of view. In this paper we develope the correct approach to describe the phenomena completely adequate to the physical problem. The basic notion of our approach is Conditional Density Matrix. 1 CONDITIONAL DENSITY MATRIXConsider two systems S 1 and S 2 . The joint system is denoted as S 12 . The principal question that we want to answer here is how the states of the subsystems are related to the state of the joint system, and vice versa.Let ρ 1 and ρ 2 be the density matrices of the systems S 1 and S 2 . If at least one of the states ρ 1 or ρ 2 is pure (i.e. ρ i 2 = ρ i ) then these states determine the state of the compound system S 12 uniquely:If the state of the system S 12 is ρ 12 then the state of the system S 1 is determined by the following equation:Now we can define the conditional density matrix. If the state of the system S 12 is ρ 12 then the state of the system S 1 upon the condition that the system S 2 is in the pure state ρ 2 , ρ 2 2 = ρ 2 is Example: ParapositroniumAs an example we consider parapositronium -the system consisting of an electron and a positron. The total spin of the system is equal to zero. In this case the nonrelativistic approximation is valid and the state vector of the system is represented in the form of the product Ψ( r e , σ e ; r p , σ p ) = Φ( r e , r p )χ(σ e , σ p ).The spin wave function is equal toHere χ n (σ) and χ (− n) (σ) are the eigenvectors of the operator that projects spin onto the vector n:The spin density matrix of the system is determined by the operator with the kernelThe spin density matrix of the electron isIn this state the electron is completely unpolarized.If an electron passes through polarization filter then the pass probability is independent of the filter orientation. The same fact is valid for the positron if its spin state is measured independently of the electron. Now let us consider quite different experiment. Namely, the positron passes through the polarization filter and the electron polarization is simultaneously measured. The operator that projects the positron spin onto the vector m (determined by the filter) is given by the kernelNow the conditional density matrix of the electron eq...

A new quantum mechanical notion -Conditional Density Matrix -proposed by the authors [5], [6], is discussed and is applied to describe some physical processes. This notion is a natural generalization of von Neumann density matrix for such processes as divisions of quantum systems into subsystems and reunifications of subsystems into new joint systems. Conditional Density Matrix assigns a quantum state to a subsystem of a composite system under condition that another part of the composite system is in some pure state.