On applications of Maupertuis-Jacobi correspondence for Hamiltonians $F(x,|p|)$ in some 2-D stationary semiclassical problems

We make use of the Maupertuis -- Jacobi correspondence, well known in Classical Mechanics, to simplify 2-D asymptotic formulas based on Maslovs canonical operator, when constructing Lagrangian manifolds invariant with respect to phase flows for Hamiltonians of the form $F(x,|p|)$. As examples we consider Hamiltonians coming from the Schrodinger equation, the 2-D Dirac equation for graphene and linear water wave theory.

Differences in the effects of turns and constrictions on the resistive response in current-biased superconducting wire after single photon absorption

We study how turns and constrictions affect the resistive response of the superconducting wire after instant in time and local in space heating, which models the absorption of the single photon by the wire. We find that the presence of constriction favors detection of photons of various energies but the presence of turn increases only ability to detect relatively low energy photons. The main reason is that in case of constriction the current density is increased over whole length and width of the constriction while in case of the turn the current density is enhanced only near the inner corner of the turn. It results in inhomogeneous Joule heating near the turn and worsens the conditions for appearance of the normal domain at relatively small currents when the high energy photons already could create normal domain in straight part of the wire. We also find that the amplitude of the voltage pulse depends on the place where the photon is absorbed. It is the smallest one when photon is absorbed near the turn and it is the largest one when photon is absorbed near the constriction. This effect comes from the difference in resistance of constriction and the turn in the normal state from the resistance of the rest of the wire.

Marriage of Electromagnetism and Gravity in Extended Space Model and Astrophysical Phenomena

The generalization of Einsteins special theory of relativity (SRT) is proposed. In this model the possibility of unification of scalar gravity and electromagnetism into a single united field is considered. Formally, the generalization of the SRT is that instead of (1+3)-dimensional Minkowski space the (1+4)-dimensional extension G is considered. As a fifth additional coordinate the interval S is used. This value is saved under the usual Lorentz transformations in Minkowski space M, but it changes when the transformations in the extended space G are used. We call this model the extended space model (ESM). From a physical point of view our expansion means that processes in which the rest mass of the particles changes are acceptable now. If the rest mass of a particle does not change and the physical quantities do not depend on an additional variable S, then the electromagnetic and gravitational fields exist independently of each other. But if the rest mass is variable and there is a dependence on S, then these two fields are combined into a single united field. In the extended space model a photon can have a nonzero mass and this mass can be either positive or negative. The gravitational effects such as the speed of escape, gravitational red shift and deflection of light can be analyzed in the frame of the extended space model. In this model all these gravitational effects can be found algebraically by the rotations in the (1+4) dimensional space. Now it becomes possible to predict some future results of visible size of super massive objects in our Universe due to new stage of experimental astronomy development in the Radio Astron Project and analyze phenomena of the star V838 Monocerotis explosion as possible Local Big Bang (LBB).

Matrix genetics, part 1: permutations of positions in triplets and symmetries of genetic matrices

The Kronecker family of the genetic matrices is investigated, which is based on the genetic matrix [C T; A G], where C, T, A, G are the letters of the genetic alphabet. The matrix [C T; A G] in the second Kronecker power is the (4*4)-matrix of 16 duplets. The matrix [C T; A G] in the third Kronecker power is the (8*8)-matrix of 64 triplets. It is significant that peculiarities of the degeneracy of the genetic code are reflected in the symmetrical black-and-white mosaic of these genetic matrices. The article represents interesting mathematical properties of these mosaic matrices, which are connected with positional permutations inside duplets and triplets; with projector operators; with unitary matrices and cyclic groups, etc. Fractal genetic nets are proposed as a new effective tool to study long nucleotide sequences. Some results about revealing new symmetry principles of long nucleotide sequences are described.

Synchronous Evolution of Galaxies in Groups: NGC 524 Group

By means of panoramic spectroscopy at the SAO RAS BTA telescope, we investigated the properties of stellar populations in the central regions of five early-type galaxies -- the NGC 524 group members. The evolution of the central regions of galaxies looks synchronized: the average age of stars in the bulges of all the five galaxies lies in the range of 3--6 Gyr. Four of the five galaxies revealed synchronized bursts of star formation in the nuclei 1--2 Gyr ago. The only galaxy, in which the ages of stellar population in the nucleus and in the bulge coincide (i.e. the nuclear burst of star formation did not take place) is NGC 502, the farthest from the center of the group of all the galaxies studied.

On the Anomalous Diffusion in Nonisothermal plasma

In nonisothermal plasma at temperature T_e>> T_i diffusion plays decisive role at conditions of smooth inhomogeneity when the inhomogeneity size is larger than the Debye radius by more than {T_e/T_i}^1/2 times. When the inhomogeneity is rather abrupt and the condition is violated, then during the spreading process the Maxwellian relaxation of ion charges becomes significant. Here, we consider these two phenomena together and refer to the anomalous character of diffusion, i.e. anomalous diffusion.

Dynamics of non-harmonic internal gravity wave packets in stratified media

In the paper taking the assumption of the slowness of the change of the parameters of the vertically stratified medium in the horizontal direction and in time, the evolution of the non-harmonic wave packages of the internal gravity waves has been analyzed. The concrete form of the wave packages can be expressed through some model functions and is defined by the local behavior of the dispersive curves of the separate modes near to the corresponding special points. The solution of this problem is possible with the help of the modified variant of the special-time ray method offered by the authors (the method of geometrical optics), the basic difference of which consists that the asymptotic representation of the solution may be found in the form the series of the non-integer degrees of some small parameter. At that the exponent depends on the concrete form of representation of this package. The obvious kind of the representation is determined from the principle of the localness and the asymptotic behavior of the solution in the stationary and the horizontally-homogeneous case. The phases of the wave packages are determined from the corresponding equations of the eikonal, which can be solved numerically on the characteristics (rays). Amplitudes of the wave packages are determined from the laws of conservation of the some invariants along the characteristics (rays).

On reverberation and cross-correlation estimates of the size of the broad-line region in active galactic nuclei

It is known that the dependence of the emission-line luminosity of a typical cloud in the active galactic nuclei broad-line regions (BLRs) upon the incident flux of ionizing continuum can be nonlinear. We study how this nonlinearity can be taken into account in estimating the size of the BLR by means of the reverberation methods. We show that the BLR size estimates obtained by cross-correlation of emission-line and continuum light curves can be much (up to an order of magnitude) less than the values obtained by reverberation modelling. This is demonstrated by means of numerical cross-correlation and reverberation experiments with model continuum flares and emission-line transfer functions and by means of practical reverberation modelling of the observed optical spectral variability of NGC 4151. The time behaviour of NGC 4151 in the H_alpha and H_beta lines is modelled on the basis of the observational data by Kaspi et al. (1996, ApJ, 470, 336) and the theoretical BLR model by Shevchenko (1984, Sov. Astron. Lett., 10, 377; 1985, Sov. Astron. Lett., 11, 35). The values of the BLR parameters are estimated that allow to judge on the size and physical characteristics of the BLR. The small size of the BLR, as determined by the cross-correlation method from the data of Kaspi et al. (1996, ApJ, 470, 336), is shown to be an artifact of this method. So, the hypothesis that the BLR size varies in time is not necessitated by the observational data.

Matrix genetics, part 2: the degeneracy of the genetic code and the octave algebra with two quasi-real units (the genetic octave Yin-Yang-algebra)

Algebraic properties of the genetic code are analyzed. The investigations of the genetic code on the basis of matrix approaches (matrix genetics) are described. The degeneracy of the vertebrate mitochondria genetic code is reflected in the black-and-white mosaic of the (8*8)-matrix of 64 triplets, 20 amino acids and stop-signals. This mosaic genetic matrix is connected with the matrix form of presentation of the special 8-dimensional Yin-Yang-algebra and of its particular 4-dimensional case. The special algorithm, which is based on features of genetic molecules, exists to transform the mosaic genomatrix into the matrices of these algebras. Two new numeric systems are defined by these 8-dimensional and 4-dimensional algebras: genetic Yin-Yang-octaves and genetic tetrions. Their comparison with quaternions by Hamilton is presented. Elements of new genovector calculation and ideas of genetic mechanics are discussed. These algebras are considered as models of the genetic code and as its possible pre-code basis. They are related with binary oppositions of the Yin-Yang type and they give new opportunities to investigate evolution of the genetic code. The revealed fact of the relation between the genetic code and these genetic algebras is discussed in connection with the idea by Pythagoras: All things are numbers. Simultaneously these genetic algebras can be utilized as the algebras of genetic operators in biological organisms. The described results are related with the problem of algebraization of bioinformatics. They take attention to the question: what is life from the viewpoint of algebra?