Abstract:
We analyze the spectral distribution of localisation in a 1D diagonally disordered chain of fragments each of which consist of m coupled two-level systems. The calculations performed by means of developed perturbation theory for joint statistics of advanced and retarded Green’s functions. We show that this distribution is rather inhomogeneous and reveals spectral regions of weakly localized states with sharp peaks of the localization degree in the centers of these regions.

Abstract:
Non analytic behaviour of Hanle effect in InGaAs quantum dots is described in terms of a simple 4-level model. Despite simplicity the model makes it possible to explain the observed fracture of Hanle curve at zero magnetic field and obtain quantitative agreement with the experiment.

Abstract:
In this paper, we consider informative potentialities of the "active" optical noise spectroscopy, under which we understand, generally, spectroscopy of response of a multilevel quantum system to the resonant optical field with its intensity modulated by "white" noise. We show that calculations of such a response can be most conveniently performed, in the linear approximation, by introducing the notion of light-intensity susceptibility (LIS) whose spectrum is determined by Laplace transform of the response to a small step-wise change of the optical field intensity. The results of calculations for a simple four-level quantum system show that its LIS spectrum may provide information not only about the ground-state structure (like conventional Faraday-rotation-based spin noise spectroscopy), but also about properties of the optical transitions (including nutation frequencies in the applied optical field). From the experimental point of view, such a noise spectroscopy of the intensity-related susceptibility can be especially efficient in combination with the up-to-date spectrum analyzers providing extremely fast data processing.

Abstract:
The mechanisms of epidural-associated fever remain incompletely understood [1-3]. We propose that action of local anesthetic on TPRV1. The transient receptor potential cation channel subfamily V member 1 (TRPV1), also known as the capsaicin receptor and the vanilloid receptor can explain this effect and explain mechanism of burning sensation on local anesthetic injected subcutaneously or intramuscular. Role of TRPV1 receptor was not discussed previously in Obstetric Anesthesia literature. Based on available data, we propose that Local Anesthetics work as agonist/antagonist on TPRV1 receptors. Antagonist action may cause hyperthermia through modifying thermoregulation [4], agonist action may cause hyperthermia thru release of IL-6 and other mediators of inflammation [5-10]. Agonist action may explain burning sensation on injection of Local Anesthetics. Burning sensation can be diminished by increasing pH of Local Anesthetic solution, because vanillin receptors are stimulated by acidification through lower pH [11,12].

Abstract:
The basic morphological aspects of auditory cortex organization in different orders of eutherian mammals are considered in the present review. The modern data describing a partitioning of mammalian auditory cortex into subfields are presented. A detailed observation of the structural organization of primary auditory cortex is given, as well as a review of recent morphological data about secondary auditory areas. Another section describes the system of auditory cortical projections. The data are considered from the perspective of possible homologies existing between the auditory cortices in different mammalian species.

Abstract:
The nuclear spin fluctuations (NSF) as well as the dynamic nuclear polarization (DNP) and their effects on the electron spins in negatively charged (In,Ga)As/GaAs quantum dots have been studied by polarized pump-probe and photoluminescence spectroscopy techniques. The effective magnetic field of the NSF is about 30 mT at low excitation power. The NSF distribution becomes highly anisotropic at strong optical excitation by circularly polarized light with periodically alternating helicity. This phenomenon is attributed to a decrease of the nuclear spin entropy due to the hyperfine interaction with polarized electron spins. The DNP is limited to small values for intense, but short photoexcitation.

Abstract:
The intrinsic fluctuations of electron spins in semiconductors and atomic vapors generate a small, randomly-varying "spin noise" that can be detected by sensitive optical methods such as Faraday rotation. Recent studies have demonstrated that the frequency, linewidth, and lineshape of this spin noise directly reveals dynamical spin properties such as dephasing times, relaxation mechanisms and g-factors without perturbing the spins away from equilibrium. Here we demonstrate that spin noise measurements using wavelength-tunable probe light forms the basis of a powerful and novel spectroscopic tool to provide unique information that is fundamentally inaccessible via conventional linear optics. In particular, the wavelength dependence of the detected spin noise power can reveal homogeneous linewidths buried within inhomogeneously-broadened optical spectra, and can resolve overlapping optical transitions belonging to different spin systems. These new possibilities are explored both theoretically and via experiments on spin systems in opposite limits of inhomogeneous broadening (alkali atom vapors and semiconductor quantum dots).

Abstract:
For a generic (polynomial) one-parameter deformation of a complete intersection, there is defined its monodromy zeta-function. We provide explicit formulae for this zeta-function in terms of the corresponding Newton polyhedra in the case the deformation is non-degenerate with respect to its Newton polyhedra. Using this result we obtain the formula for the monodromy zeta-function at the origin of a polynomial on a complete intersection, which is an analog of the Libgober--Sperber theorem.

Abstract:
We construct a monomorphism from the differential algebra $k\{x\} / [x^m]$ to a Grassmann algebra endowed with a structure of differential algebra. Using this monomorphism we prove primality of $k\{x\} / [x^m]$ and its algebra of differential polynomials, solve one of Ritt's problems and give a new proof of integrality of the ideal $[x^m]$.

Abstract:
In this paper the local singularities of integrable Hamiltonian systems with two degrees of freedom are studied. The topological obstruction to the existence of focus-focus singularity with given complexity was found. It has been showed that only simple focus-focus singularities can appear in a typical mechanical system. The model examples of mechanical systems with complex focus-focus singularity are given.