Abstract:
Atomic force microscopy (AFM) was used for the morphological characterization and precise height meas-urements of two-dimensional molecular layers of carbocyanine dye 3,3’-di(r-sulfopropyl)-4,4’,5,5’-dibenzo-9-ethylthiacarbocyanine betaine pyridinium salt. The AFM measurements reveal three morphological types of molecular aggregates: leaves, stripes and spots. The leaves are stripes have same monolayer height ~1.4 nm and different crystal shapes: the leaves are monoloyers with the lens shape and the stripes are bilay-ers with the shape of extended rectangles. The monolayer height ~1.4 nm was interpreted as indicating the symmetrical packing arrangement of dye molecules. In the symmetrical monolayer, the sulfopropyl groups of all-trans monomer units are located on both monolayer sides whereas the adjacent stacked dye molecules have a lateral slippage providing the J-aggregate optical properties. The lower height of spots ~1 nm was explained by the model of an asymmetric monolayer with sulfopropyl groups of all-trans monomers occupy-ing the same position with respect to the monolayer plane. The packing arrangement of all-trans monomers in the asymmetric monolayer corresponds to H-aggregate. The alternative models of the packing arrange-ment in monolayers with mono-cis1 monomer configuration are discussed.

Abstract:
The paper is concerned with spherically symmetric static problem of the Classical Gravitation Theory (CGT) and the General Relativity Theory (GRT). First, the Dark Stars, i.e. the objects that are invisible because of high gravitation preventing the propagation of light discovered in the 18th century by J. Michel and P. Laplace are discussed. Second, the Schwarzchild solution which was obtained in the beginning of the 20th century for the internal and external spaces of the perfect fluid sphere is analyzed. This solution results in singular metric coefficients and provides the basis of the Black Holes. Third, the general metric form in spherical coordinates is introduced and the solution of GRT problem is obtained under the assumption that gravitation does not affect the sphere mass. The critical sphere radius similar to the Black Hole horizon of events is found. In contrast to the Schwarzchild solution, the radial metric coefficient for the sphere with the critical radius referred to as the Dark Star is not singular. For the sphere with radius which is less than the critical value, the GRT solution becomes imaginary. The problem is discussed within the framework of the phenomenological theory which does not take into account the actual microstructure of the gravitating objects and, though the term “star” is used, the analysis is concerned with a model fluid sphere rather than with a real astrophysical object.

Abstract:
It is shown that in the model [3,4] of quantum mechanics besides probability amplitudes, the Planck constant and the Fock space, the cosmological constant also appear in the natural way. The Poisson brackets are generalized for the case of kinetics.

Abstract:
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic systems). The Planck constant and the Fock space appear after putting a dynamical system in a thermal bath. For harmonic oscillator in a thermal bath, the probability amplitudes can be identified with the complex valued phase functions $f(q+ip)$ describing small deviations from the equilibrium state, when the time of relaxation is large. A chain of such oscillators models both the one-dimensional space (or string), and one-dimensional quantum field theory.

Abstract:
The paper is concerned with the history of the spherically symmetric static problem solution of General Relativity found in 1916 by K. Schwarzschild [1] [2] which is interpreted in modern physics as the background of the objects referred to as Black Holes. First, the modern interpretation this solution which does not exactly coincide with original solution obtained by K. Schwarzschild is discussed. Second, the basic equations of the original Schwarzschild solution are presented in modern notations allowing us to compare existing and original solutions. Finally, a modification of the Schwarzschild approach is proposed allowing us to arrive at the exact solution of the Schwarzschild problem.

Abstract:
Frequency properties of intervalley electrons transfer in gallium nitride are considered. Estimations of the maximum low-frequency values of nitrides and their generation efficiency connections in a mode with restricted volume charge accumulation (MRVCA) are presented. Frequency dependences of diodes generation efficiency on the basis of GaN in MRVCA mode are defined by Monte-Carlo method taking account taken of all basic mechanisms of electron dispersion in a wide frequency range. The frequency limit of functioning of diodes on the basis of GaN in MRVCA mode is defined.

Abstract:
We study Nambu-Goto strings and branes. It is shown that they can be considered as continuous limits of ordered discrete sets of relativistic particles for which the tangential velocities are excluded from the action. The linear in unphysical momenta constraints are found. It allows to derive the evolution operators for the objects under consideration from the "first principles".

Abstract:
Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in details. The investigation can be of interest for string and brane theory, solid state physics (quantum wires) and quantum optics.

Abstract:
The aim of this paper is to clarify and generalize techniques of works alg-geom/9711024 (see also math.AG/9810097 and math.AG/9901004). Roughly speaking, we prove that for local Fano contractions the existence of complements can be reduced to the existence of complements for lower dimensional projective Fano varieties.

Abstract:
We prove the boundedness of complements modulo two conjectures: Borisov-Alexeev conjecture and effective adjunction for fibre spaces. We discuss the last conjecture and prove it in two particular cases.