Quantum Kinetic Evolution of Marginal Observables

We develop a rigorous formalism for the description of the evolution of observables of quantum systems of particles in the mean-field scaling limit. The corresponding asymptotics of a solution of the initial-value problem of the dual quantum BBGKY hierarchy is constructed. Moreover, links of the evolution of marginal observables and the evolution of quantum states described in terms of a one-particle marginal density operator are established. Such approach gives the alternative description of the kinetic evolution of quantum many-particle systems to generally accepted approach on basis of kinetic equations.Comment: 18 page

The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems

The Cauchy problem for the von Neumann hierarchy of nonlinear equations is investigated. One describes the evolution of all possible states of quantum many-particle systems by the correlation operators. A solution of such nonlinear equations is constructed in the form of an expansion over particle clusters whose evolution is described by the corresponding order cumulant (semi-invariant) of evolution operators for the von Neumann equations. For the initial data from the space of sequences of trace class operators the existence of a strong and a weak solution of the Cauchy problem is proved. We discuss the relationships of this solution both with the $s$-particle statistical operators, which are solutions of the BBGKY hierarchy, and with the $s$-particle correlation operators of quantum systems.Comment: 26 page

Towards Rigorous Derivation of Quantum Kinetic Equations

We develop a rigorous formalism for the description of the evolution of states of quantum many-particle systems in terms of a one-particle density operator. For initial states which are specified in terms of a one-particle density operator the equivalence of the description of the evolution of quantum many-particle states by the Cauchy problem of the quantum BBGKY hierarchy and by the Cauchy problem of the generalized quantum kinetic equation together with a sequence of explicitly defined functionals of a solution of stated kinetic equation is established in the space of trace class operators. The links of the specific quantum kinetic equations with the generalized quantum kinetic equation are discussed.Comment: 25 page

Epidural Stimulation Induced Modulation of Spinal Locomotor Networks in Adult Spinal Rats

The importance of the in vivo dynamic nature of the circuitries within the spinal cord that generate locomotion is becoming increasingly evident. We examined the characteristics of hindlimb EMG activity evoked in response to epidural stimulation at the S1 spinal cord segment in complete midthoracic spinal cord-transected rats at different stages of postlesion recovery. A progressive and phase-dependent modulation of monosynaptic (middle) and long-latency (late) stimulation-evoked EMG responses was observed throughout the step cycle. During the first 3 weeks after injury, the amplitude of the middle response was potentiated during the EMG bursts, whereas after 4 weeks, both the middle and late responses were phase-dependently modulated. The middle- and late-response magnitudes were closely linked to the amplitude and duration of the EMG bursts during locomotion facilitated by epidural stimulation. The optimum stimulation frequency that maintained consistent activity of the long-latency responses ranged from 40 to 60 Hz, whereas the short-latency responses were consistent from 5 to 130 Hz. These data demonstrate that both middle and late evoked potentials within a motor pool are strictly gated during in vivo bipedal stepping as a function of the general excitability of the motor pool and, thus, as a function of the phase of the step cycle. These data demonstrate that spinal cord epidural stimulation can facilitate locomotion in a time-dependent manner after lesion. The long-latency responses to epidural stimulation are correlated with the recovery of weight-bearing bipedal locomotion and may reflect activation of interneuronal central pattern-generating circuits

On Rigorous Derivation of the Enskog Kinetic Equation

We develop a rigorous formalism for the description of the kinetic evolution of infinitely many hard spheres. On the basis of the kinetic cluster expansions of cumulants of groups of operators of finitely many hard spheres the nonlinear kinetic Enskog equation and its generalizations are justified. It is established that for initial states which are specified in terms of one-particle distribution functions the description of the evolution by the Cauchy problem of the BBGKY hierarchy and by the Cauchy problem of the generalized Enskog kinetic equation together with a sequence of explicitly defined functionals of a solution of stated kinetic equation is an equivalent. For the initial-value problem of the generalized Enskog equation the existence theorem is proved in the space of integrable functions.Comment: 28 page

NAADP mobilizes Ca2+ from a thapsigargin-sensitive store in the nuclear envelope by activating ryanodine receptors

Ca2+ release from the envelope of isolated pancreatic acinar nuclei could be activated by nicotinic acid adenine dinucleotide phosphate (NAADP) as well as by inositol 1,4,5-trisphosphate (IP3) and cyclic ADP-ribose (cADPR). Each of these agents reduced the Ca2+ concentration inside the nuclear envelope, and this was associated with a transient rise in the nucleoplasmic Ca2+ concentration. NAADP released Ca2+ from the same thapsigargin-sensitive pool as IP3. The NAADP action was specific because, for example, nicotineamide adenine dinucleotide phosphate was ineffective. The Ca2+ release was unaffected by procedures interfering with acidic organelles (bafilomycin, brefeldin, and nigericin). Ryanodine blocked the Ca2+-releasing effects of NAADP, cADPR, and caffeine, but not IP3. Ruthenium red also blocked the NAADP-elicited Ca2+ release. IP3 receptor blockade did not inhibit the Ca2+ release elicited by NAADP or cADPR. The nuclear envelope contains ryanodine and IP3 receptors that can be activated separately and independently; the ryanodine receptors by either NAADP or cADPR, and the IP3 receptors by IP3

Correction of school disadaptation of teenagers by art therapy methods

© 2016 Gerasimenko.Relevance of research is caused by growth of number of pupils with school disadaptation that is expressed in problems of development of the school program, socialization problems, and the general trouble. In this regard, this article is directed to identification or disclosure of opportunities of assistance to teenagers with this problem, to take them in a difficult educational situation, to help to overcome vital difficulties. The leading method in research of this problem is the art therapy method. It allows pupils to create the atmosphere of emotional wellbeing in the course of mobilization of creative potential, to find experience of new kinds of activity, to develop creative abilities, to promote internal self-control of feelings and behavior. On the basis of the provision of the humanistic focused art therapy about self-expression and self-realization in creativity products, opportunities art and therapeutic the technician in work with the teenagers in the diagnostic, correctional, therapeutic and developing purposes are shown in article. Results of correctional work speak about positive changes in the emotional and personal relation to the doctrine, teachers, peers, and about increase of the general school progress. Materials of article show practical value for specialists of the educational organizations in the solution of problems of school disadaptation of teenagers

On the spectrum of a bent chain graph

We study Schr\"odinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by $\delta$-couplings with a parameter $\alpha\in\R$. If the graph is "straight", i.e. periodic with respect to ring shifts, its Hamiltonian has a band spectrum with all the gaps open whenever $\alpha\ne 0$. We consider a "bending" deformation of the chain consisting of changing one position at a single ring and show that it gives rise to eigenvalues in the open spectral gaps. We analyze dependence of these eigenvalues on the coupling $\alpha$ and the "bending angle" as well as resonances of the system coming from the bending. We also discuss the behaviour of the eigenvalues and resonances at the edges of the spectral bands.Comment: LaTeX, 23 pages with 7 figures; minor changes, references added; to appear in J. Phys. A: Math. Theo