The registration and the processing of signals of geomagnetic pulsations in the system of the geodynamic monitoring

Annotation: In this paper, methods of the implementing filtering are considered for recording of irregular disturbances of the geomagnetic field. The solution of problems of the processing of signals is considered for the system of the geodynamic control. They are based on the detection of the informative area of the registration in real time and the localization of the spatial location of the source of geomagnetic disturbances on the base of the regression analysis. It is noted that methods of simultaneous formation of borders of the bands of HPF and LPF necessary to use with the technical implementation of multi-band filtering. It allows to obtain the absolutely exact conjugation of frequency borders of neighboring subbands of filter, and also to reduce the number of tunable passive elements. Determined that in the technical implementation of the approach, obtaining an arbitrary phase-frequency characteristic that is not related to the amplitude-frequency response, and ensuring the stability of a multi-band filter of high order is important. Application of the regression analysis for selection and an assessment of parameters of distribution of geomagnetic pulsations at magnetotelluric sounding give the chance to consider features of use in system of monitoring of multirange filters and algorithms of spectral timing analysis.Keywords: geomagnetic field, disturbance, registration, processing, signal, geodynamic, monitoring, magnetotelluri

Monodromy transform and the integral equation method for solving the string gravity and supergravity equations in four and higher dimensions

The monodromy transform and corresponding integral equation method described here give rise to a general systematic approach for solving integrable reductions of field equations for gravity coupled bosonic dynamics in string gravity and supergravity in four and higher dimensions. For different types of fields in space-times of $D\ge 4$ dimensions with $d=D-2$ commuting isometries -- stationary fields with spatial symmetries, interacting waves or partially inhomogeneous cosmological models, the string gravity equations govern the dynamics of interacting gravitational, dilaton, antisymmetric tensor and any number $n\ge 0$ of Abelian vector gauge fields (all depending only on two coordinates). The equivalent spectral problem constructed earlier allows to parameterize the infinite-dimensional space of local solutions of these equations by two pairs of \cal{arbitrary} coordinate-independent holomorphic $d\times d$- and $d\times n$- matrix functions ${\mathbf{u}_\pm(w), \mathbf{v}_\pm(w)}$ of a spectral parameter $w$ which constitute a complete set of monodromy data for normalized fundamental solution of this spectral problem. The "direct" and "inverse" problems of such monodromy transform --- calculating the monodromy data for any local solution and constructing the field configurations for any chosen monodromy data always admit unique solutions. We construct the linear singular integral equations which solve the inverse problem. For any \emph{rational} and \emph{analytically matched} (i.e. $\mathbf{u}_+(w)\equiv\mathbf{u}_-(w)$ and $\mathbf{v}_+(w)\equiv\mathbf{v}_-(w)$) monodromy data the solution for string gravity equations can be found explicitly. Simple reductions of the space of monodromy data leads to the similar constructions for solving of other integrable symmetry reduced gravity models, e.g. 5D minimal supergravity or vacuum gravity in $D\ge 4$ dimensions.Comment: RevTex 7 pages, 1 figur

Water entry of a flat elastic plate at high horizontal speed

The two-dimensional problem of an elastic-plate impact onto an undisturbed surface of water of infinite depth is analysed. The plate is forced to move with a constant horizontal velocity component which is much larger than the vertical velocity component of penetration. The small angle of attack of the plate and its vertical velocity vary in time, and are determined as part of the solution, together with the elastic deflection of the plate and the hydrodynamic loads within the potential flow theory. The boundary conditions on the free surface and on the wetted part of the plate are linearized and imposed on the initial equilibrium position of the liquid surface. The wetted part of the plate depends on the plate motion and its elastic deflection. To determine the length of the wetted part we assume that the spray jet in front of the advancing plate is negligible. A smooth separation of the free-surface flow from the trailing edge is imposed. The wake behind the moving body is included in the model. The plate deflection is governed by Euler’s beam equation, subject to free–free boundary conditions. Four different regimes of plate motion are distinguished depending on the impact conditions: (a) the plate becomes fully wetted; (b) the leading edge of the plate touches the water surface and traps an air cavity; (c) the free surface at the forward contact point starts to separate from the plate; (d) the plate exits the water. We could not detect any impact conditions which lead to steady planing of the free plate after the impact. It is shown that a large part of the total energy in the fluid–plate interaction leaves the main bulk of the liquid with the spray jet. It is demonstrated that the flexibility of the plate may increase the hydrodynamic loads acting on it. The impact loads can cause large bending stresses, which may exceed the yield stress of the plate material. The elastic vibrations of the plate are shown to have a significant effect on the fluid flow in the wake

Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded interval

We consider polynomials p^w_n(x) that are orthogonal with respect to the oscillatory weight w(x)=exp(iwx) on [?1,1], where w>0 is a real parameter. A first analysis of p^?_n(x) for large values of w was carried out in connection with complex Gaussian quadrature rules with uniform good properties in w. In this contribution we study the existence, asymptotic behavior and asymptotic distribution of the roots of p^?_n(x) in the complex plane as n tends to infinity. The parameter w grows with n linearly. The tools used are logarithmic potential theory and the S-property, together with the Riemann--Hilbert formulation and the Deift-Zhou steepest descent method

Eigenvalue correlations on Hyperelliptic Riemann surfaces

In this note we compute the functional derivative of the induced charge density, on a thin conductor, consisting of the union of g+1 disjoint intervals, $J:=\cup_{j=1}^{g+1}(a_j,b_j),$ with respect to an external potential. In the context of random matrix theory this object gives the eigenvalue fluctuations of Hermitian random matrix ensembles where the eigenvalue density is supported on J.Comment: latex 2e, seven pages, one figure. To appear in Journal of Physics

Forecast accuracy of determining pseudo range in satellite navigation system through analysis of data from ionosphere monitoring

Annotation: The paper deals with the detection of wave arrival time errors in satellite navigation system by measurements conducted by stationary information system ionosphere monitoring. Develop a method of detecting the field increased ionization and the detection of the conditions for possible reduction of positioning accuracy in the presence of local ionospheric irregularities.The author examines in detail all mathematical aspects of the nature of the error; visual diagrams and graphs, as well as exhaustive mathematical calculations accompany the study. The article also discusses the process and results of computer modeling, an error that arises based on the data provided by the author, and allows one to verify the author's proposed method of detecting and predicting the occurrence of an error in determining the location. In the conclusion satity, the author speaks about the method of applying the developed method in the context of a specialized information system capable of preserving the positioning accuracy on the navigation radio signal.Keywords: radio navigation systems, pseudo range, monitoring, data analysi

Infinite hierarchies of exact solutions of the Einstein and Einstein-Maxwell equations for interacting waves and inhomogeneous cosmologies

For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational functions of an auxiliary complex parameter. They are constructed using the so called `monodromy transform' approach and our new method for the solution of the linear singular integral equation form of the reduced Einstein equations. The solutions presented, which describe inhomogeneous cosmological models or gravitational and electromagnetic waves and their interactions, include a number of important known solutions as particular cases.Comment: 7 pages, minor correction and reduction to conform with published versio

Development and research of the geoelectric model of the local zone of geodynamic control

The article deals with the question of constructing a geoelectrical model used in geotechnical control systems on the local areas of geodynamic observations. An equivalent scheme for replacing the geological medium at a local point of geodynamic control was develope

Multidimensional Inverse Scattering of Integrable Lattice Equations

We present a discrete inverse scattering transform for all ABS equations excluding Q4. The nonlinear partial difference equations presented in the ABS hierarchy represent a comprehensive class of scalar affine-linear lattice equations which possess the multidimensional consistency property. Due to this property it is natural to consider these equations living in an N-dimensional lattice, where the solutions depend on N distinct independent variables and associated parameters. The direct scattering procedure, which is one-dimensional, is carried out along a staircase within this multidimensional lattice. The solutions obtained are dependent on all N lattice variables and parameters. We further show that the soliton solutions derived from the Cauchy matrix approach are exactly the solutions obtained from reflectionless potentials, and we give a short discussion on inverse scattering solutions of some previously known lattice equations, such as the lattice KdV equation.Comment: 18 page

Discrete singular integrals in a half-space

We consider Calderon -- Zygmund singular integral in the discrete half-space $h{\bf Z}^m_{+}$, where ${\bf Z}^m$ is entire lattice ($h>0$) in ${\bf R}^m$, and prove that the discrete singular integral operator is invertible in $L_2(h{\bf Z}^m_{+}$) iff such is its continual analogue. The key point for this consideration takes solvability theory of so-called periodic Riemann boundary problem, which is constructed by authors.Comment: 9 pages, 1 figur