Physics, mathematics, and technology

This is the eighth paper of a series of papers that will give a survey on several topics on formal languages and automata by using semirings, formal power series, matrices and xed point theory. The seventh paper of this series deals with tree (series) automata and systems of equations over tree . The main topics of the paper are the following. 1. Pushdown tree automata, whose behaviors are tree series over a semiring, and algebraic tree systems are equivalent; moreover, the class of algebraic tree series is characterized by algebraic tree series expressions (a Kleene result). 2. The class of recognizable tree series is closed under nondeterðministic simple recognizable tree series transductions.3. The families of recognizable tree series and of algebraic tree series are full abstract families of tree series (full AFTs). 4. The macro power series, a generalization of the indexed languages, and the algebraic power series are exactly the yields of algebraic tree series and of recognizable tree series, respectively; there is a Kleene result for macro power series; the yield of a full AFT is a full abstract family of power series.

A mathematical model of filtration of moisture in heavy soils. The transfer of a film of moisture on the surface took into account.

Mathematical model of interaction between low density thermal plasma with charged simple shape space probe was considered. Molecular dynamics simulation method was used. Modeling result shows a positive cloud of protons before the satellite and ion shadow behind it.

Sensitivity of large-scale numerical model of climate of the World Ocean (a five degree latitude-longitudinal grid and 24 levels in the vertical) from initial data on temperature and salinity is investigated in numerical global ocean climate model.

Differences methods of the approximate solution of the two-dimensional equation of ions diffusion with the mixed derivatives and the first derivatives of a divergent look are considered. Test calculations on a modeling task with the known analytical decision are carried out. Operability of algorithm is shown and the estimation of speed of its convergence is given.

Compact presentations for solution of the generalized Padè problem are presented, that have been known only for the Padè problem (so called compact Nutall presentation). Using them determinant presentations for the approximants [M – 1 / M], [M / M] и [M / M – 1] were obtained.

An algorithm of numerical solving the inverse boundary value problem for the dynamical Lame system on the base of linearized presentations of kinetic and  potential energies is proposed. Results of numerical testing in 3D are presented.

The hybrid algorithm of the decision of problems of a design of elements of digital techniques is presented. Statement of a considered optimizing problem is formulated. The description developed heuristics, operators and search strategy is resulted. The generalized schemes of search of optimum decisions are given. The basic results of computing experiments are resulted

Concept of mobile automotive object control system, based on skills extraction
and fuzzy logic is described. Virtual model of vehicle, created in specialized simulation environment is described. Parking phase and achieved results are considered.

The method of automatic analysis of images made with microscope for detection and classification of blood cells is proposed. The algorithm of cell detection on the image is described. Deep neural network with logistic regression layer as an output layer is used to classify images of blood cells.

The results numeral analysis structure of flat vertical lager that is formed triangle prism are presented. Complex analyses had unequivocally revealed presence of quasiperiodic structure in distribution particle. Is being offered a hypothesis about the nature of this reveal.

A multiple RuO2-chip thermometer based on commercial Vishay RCW575 chips for applications in 0,02—30 K range is proposed. Possible design and packaging of the sensor are suggested. Thermometer saturation and thermal resistance of our sensor are measured and compared with a single-chip configuration and commercial Lakeshore ROX-102A thermometer.

Results of computer simulation of power supply and control subsystem of solar electrically powered propulsion system and creating simulation models using the elektroanalogy method are represented.

The experimental study of the influence of the effect size of the crystallites in the powders on the form and the width of the 35Cl NQR lines in the potassium chlorate, as well as the spin-spin and spin-lattice relaxation is described. It is established that the width of the NQR lines in the direct method of detection is increased, and the relaxation times are reduced with a decrease in the average crystallite size, which is due, mainly, due the process of spin-spin diffusion. To obtain the distribution of relaxation times used a multi-exponential inversion of the recessions of the longitudinal and transverse components of the nuclear magnetization.

The algorithm of definition of the attitude a signal/noise for a mix of a signal and narrow-band noise is offered at various noise levels that can be used at various ways of processing of signals.

Mission and proof of existence theorem for hyperband m n SH  A which carrier conjugated system (; * ) of planar elements are examined: the tangent subbundle of (; * ) -planes (-subbundle) and the tangent subbundle of lines (* -subbundle). Internal beams of normalizations of hyperband m SH and its tangent subbundles in the second-order differential neighborhood are constructed.

It is proved that mean value of almost periodic function with values in Banach space is an internal point of a solid cone.

Various visualization methods for classical mathematic models, including statistical graphics, 2D and 3D animation are reviewed, and possible means of realization for such animations are suggested.

The features of the method implementation Persistent Scatterers Interferometry in MATLAB environment on a high performance computer cluster are considered. The process and results of interferometric processing of multi-time measurements made by radar ALOS/PALSAR in 2007—2011 is described. For processing software package developed used high-precision evaluation of the displacement of man-made objects. The technology publication of displacement velocity of terrestrial surface on the basis of GeoServer and Google Maps services is offered.

A numerical algorithm for solving inverse dynamical problem recovering an absorption by the boundary control method is developed. The absorption coefficient is determined independently of a speed of sound, which can be an arbitrary smooth positive function. The results of numerical experiments are represented.

Formal approaches to creation of algorithms implemented in automated tests generation system are considered. Structure of a software system of programming tests generation is presented. Problem statements and mathematical models for some modules of the system are described.