Abstract:
For the Riemann zeta-function on the critical line the terminal estimate have been proved, which had been conjectured by Lindel\"of at the beginning of this Centure. The proof is based on the authors relations which connect the bilinear forms of the eigenvalues of the Hecke operators with sums of the Kloosterman sums. By the way, it is proved that for the Hecke series (which are associated with the eigenfunctions of the automorphic Laplacian) the natural analogue of the Lindel\"of conjecture is true also. \noindent Bibl. 14.

Abstract:
Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered.

The effects of the constituents of mineral matter in brown coals from different deposits of Kansk-Achinsk, Lenaand from Yallourn Basins on the structural parameters and steam gasification reactivities of respective coal chars at moderate temperature and at low and high pressure were studied in this paper. The data on how the preliminary decationization with diluted hydrochloric, acetic and sulphuric acids affect char gasification reactivities are presented. The importance of surface area and crystallinity of chars and the presence of naturally occurring metals on gasification reactivity is considered. Quantitative correlations between the calcium contents and the extents of gasification are revealed. The gasification results obtained in a flow reactor with steam stream and in an autoclave reactor at high pressure of gaseous products are compared. The catalytic effect of dispersed calcium oxide-carbonate particles produced from the naturally occurring calcium containing carboxylates was shown to be a key factor for char gasification reactivity, the effect in the flow reactor being much larger as compared to that in the autoclave reactor. This was mainly related to different forms of catalytically active calcium species and to the composition of the gaseous reaction mixture.

Abstract:
In recent years, small modular reactors (SMRs) have been attracting considerable attention around the world. SMR designs incorporate innovative approaches to achieve simplicity, modularity and speed of build, passive safety features, proliferation resistance, and reduced financial risk. The incremental capacity expansion associated with SMR deployment could provide a better match (than the large-scale reactors) to the limited grid capacity of many developing countries. Because of their lower capital requirements, SMRs could also effectively address the energy needs of small developing countries with limited financial resources. Although SMRs can have substantially higher specific capital costs as compared to large-scale reactors, they may nevertheless enjoy significant economic benefits due to shorter build times, accelerated learning effects and co-siting economies, temporal and sizing flexibility of deployment, and design simplification.

Abstract:
Based on the renormalization group approach developed by Kuznetsov and Pikovsky (Phys. Lett., A140, 1989, 166) several types of scaling are discussed, which can be observed in a neighborhood of Feigenbaum’s critical point at small amplitudes of the driving. The type of scaling behavior depends on a structure of binary representation of the frequency parameter: F-scaling (Feigenbaum’s) for finite binary fractions, P- and Q-scaling (periodic and quasiperiodic) for periodic binary fractions, and S-scaling (statistical) for non-periodic binary fractions. All types of scaling are illustrated by parameter-plane diagrams for the rescaled Lyapunov exponent.

Abstract:
The fermion spin-flip conversion f_L -> f_R + gamma is considered, caused by the difference of the additional energies of the electroweak origin, acquired by left- and right-handed fermions (neutrino, electron) in medium. An accurate taking account of the fermion and photon dispersion in medium is performed. It is shown that the threshold arises in the process, caused by the photon (plasmon) effective mass. This threshold leaves no room for the so-called ``spin light of neutrino'' and ``spin light of electron'' in the real astrophysical situations.

Abstract:
The fermion spin-flip conversion $f_L \to f_R + \gamma$ is considered, caused by the difference of the additional energies of the electroweak origin, acquired by left- and right-handed fermions (neutrino, electron) in medium. An accurate taking account of the fermion and photon dispersion in medium is shown to be important.

Abstract:
The neutrino chirality-flip process under the conditions of the supernova core is investigated in detail with the plasma polarization effects in the photon propagator taken into account in a more complete form than in earlier publications. It is shown in part that the contribution of the proton fraction of plasma is essential. New upper bounds on the neutrino magnetic moment are obtained: mu_nu < (0.5 - 1.1) 10^{-12} mu_B from the limit on the supernova core luminosity for nu_R emission, and mu_nu < (0.4 - 0.6) 10^{-12} mu_B from the limit on the averaged time of the left-handed neutrino washing out. The best upper bound on the neutrino magnetic moment from SN1987A is improved by the factor of 3 to 7.

Abstract:
Problem statement. Modern informational technologies make it possible to solve various complexproblems of aerodynamics including problems of ventilation at different dynamic characteristicsof flows. The article deals with the problem of ventilation with the use of low-velocity irrotationalair flows. Known numerical methods of calculation of electric current related to the solutionof large systems of partial differential equations and are faulty with respect to reliability and calculationprecision. The use of the method of conformal mappings to determine velocity fields in ventilationproblems is substantiated.Results and conclusions. The method for calculation of velocity fields and electric current lines inventilated premises has been developed based on the method of conformal mappings and assumptionof irrotational type of air flow motion. Application of this method allows one to calculate requiredfields using simpler algorithms without multiple computer calculations.

This study is focused on investigation of
biofilms formed in an anaerobic laboratory-scale bioreactor fed with medium for
anammox bacteria oxidizing ammonia with nitrite. The mixed culture of anammox
bacteria was enriched from the microbial community that sampled from the
activated sludge of a denitrifying reactor at a wastewater treatment station located
in the Sochi region, Russia. This community forms biofilms on the surface of
the flexible polymer brush carriers, which are used for biomass immobilization
in both laboratory and full-scale bioreactors. Anammox bacteria were
discovered in the activated sludge community. The anammox community was
enriched by incubation in an up-flow laboratory-scale anaerobic bioreactor with
a flexible brush carrier. In the course of ~3 years, the loading rate of
nitrogen substrates (ammonium and nitrite) increased from 100 to 5000 mg N L-1 day-1. The concentration of the substrates in the upper part of the
reactor was 40 times less than in the influent. The pH values were 7.5 at the
bottom and up to 9 in the upper part up of the reactor. Biofilms of two types
developed in the reactor. Bunches of irregular spherical granules formed on the
carrier filaments, while films of irregular thickness containing submerged
spherical granules were formed on the walls of reactor. The anammox population
was found to consist of at least three active species: a new strain of Candidatus “Jettenia asiatica” named “strain ecos” and two species of the genus Candidatus“