Algebraic description of jacobians isogeneous to certain prym varieties with polarization (1,2)

For a class of non-hyperelliptic genus 3 curves C which are twofold coverings of elliptic curves E, we give an explicit algebraic description of all birationally nonequivalent genus 2 curves whose Jacobians are degree 2 isogeneous to the Prym varieties associated with such coverings. Our description is based on previous studies of Prym varieties with polarization (1,2) in connection with separation of variables in a series of classical and new algebraic integrable systems linearized on such varieties. We also consider some special cases of the covering C ¿ E, in particular, when the corresponding Prym varieties contain pairs of elliptic curves and the Jacobian of C is isogeneous (but not isomorphic) to the product of three different elliptic curves. Our description is accompanied with explicit algorithms of calculation of periods of the Prym varieties and of absolute invariants of genus 2 curves. They are followed by numerical examples, which experimentally confirm main results of the articlPeer ReviewedPostprint (published version

Dynamics on strata of trigonal Jacobians and some integrable problems of rigid body motion

We present an algebraic geometrical and analytical description of the Goryachev case of rigid body motion. It belongs to a family of systems sharing the same properties: although completely integrable, they are not algebraically integrable, their solution is not meromorphic in the complex time and involves dynamics on the strata of the Jacobian varieties of trigonal curves. Although the strata of hyperelliptic Jacobians have already appeared in the literature in the context of some dynamical systems, the Goryachev case is the first example of an integrable system whose solution involves a more general curve. Several new features (and formulae) are encountered in the solution given in terms of sigma-functions of such a curve.Comment: 22 pages, 1 figur

INTERACTION OF CLEAVAGE CRACKS WITH SLIPBANDS IN ALKALI-HALIDE CRYSTALS

Authors have shown that when the cleavage crack crosses the border of the artificially introduced and aged slipband at {110}, the spreading rate of the crack in LiF crystals changes in comparison with the same value at crossing the fresh slipband. The cleaved surface relief in the first and the second cases is also different. Reasons of the change of speed of the crack and differences in the cleaved surface relief are determined. 

Rehabilitation of patients with post-traumatic stress disorder by complementary methods

Introduction. The article analyzes the relationship between stress, post-traumatic stress syndrome (PTSD) and changes in the functioning of the neuroendocrine system. Aim. Development of a hypothesis and practical evaluation of its effectiveness based on the proposed rehabilitation protocols for patients with post-traumatic stress disorder resulting from psychoemotional stress, based on a multi-level multifactorial approach with the use of transcranial stimulation by pulse currents at the frequency of rhythms of the cerebral cortex, stimulation by light pulses at the frequencies of alpha, beta and theta rhythms of the cerebral cortex in combination with neuroacoustic correction of the neuroendocrine system. Materials and methods. The study involved 36 men, combatants, aged 28-54 full years, who gave their written consent to participate in the study. In the course of the research at the first stage, a hypothesis was formed about possible options for multifactorial multilevel effects on the central nervous system in order to rehabilitate patients with PTSD. Results. The implementation of the proposed solution is to increase the efficiency and reduce the time of rehabilitation of PTSD due to a multi-level multifactorial approach: Conclusion. The results of the study revealed positive dynamics of clinical manifestations in both groups of patients. After analyzing the data obtained (assessment of the quality of life according to the SF-36 questionnaire), it was found that the protocol of rehabilitation of patients with post-traumatic stress disorder is based on the use of a multi-level approach that allows correction

An ontological model for planning urban areas with a given level of economic efficiency

The paper presents an ontological model for planning urban areas with a given level of economic efficiency, the use of which can provide optimal configurations of future neighbourhoods for all participants in their construction and operation. The implementation of intelligent systems based on the algorithms of the proposed model can provide optimal configurations of future neighborhoods for all parties involved in their construction and operatio

Rehabilitation of patients with post-traumatic stress disorder by complementary methods

Introduction. The article analyzes the relationship between stress, post-traumatic stress syndrome (PTSD) and changes in the functioning of the neuroendocrine system. Aim. Development of a hypothesis and practical evaluation of its effectiveness based on the proposed rehabilitation protocols for patients with post-traumatic stress disorder resulting from psychoemotional stress, based on a multi-level multifactorial approach with the use of transcranial stimulation by pulse currents at the frequency of rhythms of the cerebral cortex, stimulation by light pulses at the frequencies of alpha, beta and theta rhythms of the cerebral cortex in combination with neuroacoustic correction of the neuroendocrine system. Materials and methods. The study involved 36 men, combatants, aged 28-54 full years, who gave their written consent to participate in the study. In the course of the research at the first stage, a hypothesis was formed about possible options for multifactorial multilevel effects on the central nervous system in order to rehabilitate patients with PTSD. Results. The implementation of the proposed solution is to increase the efficiency and reduce the time of rehabilitation of PTSD due to a multi-level multifactorial approach: Conclusion. The results of the study revealed positive dynamics of clinical manifestations in both groups of patients. After analyzing the data obtained (assessment of the quality of life according to the SF-36 questionnaire), it was found that the protocol of rehabilitation of patients with post-traumatic stress disorder is based on the use of a multi-level approach that allows correction

Highly Exfoliated Graphite Fluoride as a Precursor for Graphene Fluoride Dispersions and Films

We synthesized highly exfoliated graphite fluoride of approximate composition C2F by treating highly exfoliated graphite with ClF3. The formed material was found to be dispersible in solvents giving 1 to 5 layered fluorinated graphene. Dispersions successfully formed in polar organic solvents capable of establishing hydrogen bonds. The highest stability is achieved in branched alcohols such as tert-butanol. The dispersions may be further processed into thin films by vacuum filtration technique. Also, composite multilayered films of graphene fluoride and graphene may be prepared. (doi: 10.5562/cca1972