### SCENARIOS OF TRANSITION FROM HARMONIC NONLINEAR OSCILLATIONS IN CHAOTIC BEAMS TIMOSHENKO TYPE

In this paper we consider a single-layer beam under the influence of the local oscillating loads, taking into account the geometric nonlinearity. Constructed a mathematical model based on hypotheses SPTimoshenko. Transition from harmonic oscillations to chaos scenario occurs Ruelle-Takens-Newhouse.

Read More### REFLECTION OF ELECTROMAGNETIC WAVES FROM THE LAYERED STRUCTURE OF FERROELECTRIC FERROMAGNET

The paper studies the frequency dependence of the reflection coefficient of electromagnetic waves from a layered structure ferroelectric – ferromagnetic.

Read More### INFLUENCE OF NONLINEAR PLANETARY WAVES ON FOCUSED IN THE STENK WIDTH DIRECTION

The article consideres model of distribution of nonlinear planetary waves, and also their interaction on the wall focused in the width direction is mathematically realized. The received decisions allow to get the qualitative analysis of studied dynamic process, and also its numerical realization.

Read More### ON DIFFUSION IN LATTICE GAS FOR LARGE CONCENTRATION GRADIENTS

The article derives expressions for flows and diffusion coefficients in an imperfect lattice gas from equations of chemical kinetics convenient for study. Coefficients are linear operators depending on concentrations and their gradients. It is shown that the flow direction can build any angle with the direction of the gradient.

Read More### MATRIX CALCULATION IN LOGIC ALGEBRA

Using the modulo two addition operation, the fundamental concepts of matrix calculus are defined in the logic algebra, such as linearly dependent and independent sets of rows (columns) of a matrix, matrix rank, sum and product of matrices, matrix determinant, inverse matrix. The properties of the determinants of the logic algebra are given. Using inverse matrices of the logic algebra, systems of linear equations with modulo two sums are solved. Examples are given for calculating the rank of a matrix, determinants, inverse matrices and solving systems of linear equations with modulo two sums in the logic algebra.

Read More### GIANT RAMAN SCATTERING OF ORGANIC LUMINOPHORS ADSORBED ON QUARTZ SURFACE MODIFIED BY SILVER NANOPARTICLES

This work shows the results of studies on the development of a methodology for creating hydrosol-modified silver nanoparticles with a size of 44 nm quartz surfaces for sensory purposes. A method for the controlled synthesis of silver hydrosols by means of reducing sodium salt AgNO3 with sodium citrate is proposed. Media are proposed that enable the realization of the effect of giant Raman scattering by dye molecules of rhodamine 6G. It was shown that the order of amplification of the Raman signal by surface plasmons of silver nanoparticles for rhodamine 6G dye molecules can reach orders of magnitude 102 times. The efficiency of the practical use of hydrosols of silver nanoparticles of quartz surfaces to obtain the allowed spectra of the molecular structure of the rhodamine 6G dye is shown. In the future, the results of this work can be used to analyze chemical compounds in low concentrations and macroscopic biological objects.

Read More### COMPLEX OSCILLATION OF THE EULER-BERNOULLI BEAMS WITH REGARD GEOMETRICALLY AND PHYSICALLY NONLINEAR

In this paper, we consider the behavior of the inhomogeneous single-layer beam under alternating load (pressure), distributed uniformly over its entire surface. The research is conducted from the perspective of the qualitative theory of differential equations and nonlinear dynamics. Construct a theory of nonlinear dynamics beams taking into account physical geometric nonlinearity. Physical nonlinearity associated with taking into account the relationship between strain and stress, and geometric nonlinearity associated with the relationship between the deformation and displacement. It accepted the formula of Theodore von Karman. The theory is based on the Euler- Bernoulli hypothesis.

Read More### WORKING OUT AND RESEARCH OF SPECTRAL-TOMOGRAPHIC SYSTEM FOR DIAGNOSIS PARAMETERS OF A HYDROGEN PLASMA OF PLASMA ENGINES

In the article the authors developed methods and algorithms for tomographic diagnosis of few parameters of plasma thrusters. The description of few optical scanner designed for such research. Describes a method for solving the direct 3D-reconstruction within a few-optical tomography.

Read More### THE STUDY OF TECHNOLOGY VIA COMPARING WITH THE BIOLOGY EVOLUTION

One knows a set of general laws which are valid in all areas of human knowledge. Their comparing detects several useful recommendations. The most interesting is transforming some biological observations into technique and into describing of some social processes. Several useful recommendations were found on this way.

Read More### THE THEORETICAL DESCRIPTION OF FILLING “DOMES – SEPARATOR”

Due to the reduction of hydrocarbonic stocks development of offshore fields is the actual direction in preservation of stable levels of production of oil and gas. It is thus important to minimize the environmental risks connected with leakage of hydrocarbons from wells at an ocean floor. In this work theoretical basics of modeling of “dome separator” which can be used for prevention of consequences of accidents on oil fields in a shelf zone are covered [1]. The mathematical model describing process of filling of a dome by hydrocarbonic raw materials and its pumping in the conditions of an ocean floor is constructed. Dynamics of change of pressure of gas and as some elements of installation are offered is described.

Read More### REDUCTION ENUMERATION OF BIPARTITE GRAPHS

В статье рассмотрен способ элиминации перебора неизоморфных бирегулярных графов, порожденных на небольших множествах вершин.

Read More### ABOUT A VARIATIONAL PROBLEM FOR NURBS SURFACE

Suppose we want to deform a base surface of a face in order to achieve some continuity condition (e.g., G continuity) with the given neighbors at common edges. We formulate a problem for preserving G continuity and present equations for a deformation that changes the surface geometry as little as possible.

Read More### ANALYSIS OF LANDSCAPE OF OPTIMIZABLE FUNCTIONS WHEN MAKING DECISIONS RELATED TO DATA MANAGEMENT

The article states the principle of searching for the most efficient data management solutions by metaheuristic algorithms. Metaheuristics is an iterative procedure that uses randomization and self-learning elements, intensification and diversification of searches, adaptive control mechanisms, constructive heuristics,, and local search methods. It is a very promising approach to solving many optimization problems. A pseudo-code program that illustrates the search for solutions by metaheuristic algorithms is proposed. General landscape model of the optimized function is considered. The distance between the solutions is determined. Various measures are used to analyze the landscape: Changing the average distance between the set of uniformly distributed solutions and the set of locally optimal solutions; entropy; amplitude; correlation.

Read More### COMBINATORIAL MEANING OF EULER’S NUMBER

In this paper, we consider a new limit for the number e and give its rigorous proof using the apparatus of mathematical analysis. With the help of this limit, a combinatorial interpretation is given for Euler’s number. It means that Euler’s number is the ratio of the number of permutations (or combinations) of 04-09-2019 10-48-27 by n to the number of permutations (or combinations) of 04-09-2019 10-48-35 by n with an infinitely large number of elements n.

Read More### MAIN PROPERTIES OF A GAS-LIQUID MIXTURE IN PIPES

Recently carried out experimental and theoretical studies with gas-containing liquids have shown that rheological and relaxation properties of gas-liquid systems under pre-transition conditions (i.e., in pressures exceeding the saturation pressure, but close to it) are largely determined by the presence of “micro germs” – the smallest gas bubbles, the cooperative action of which manifests itself when approaching the saturation pressure [1]. When solving many practical problems, it becomes necessary to study the wave propagation with regard to the influence of the interaction between the liquid and the wall of the deformable pipe. In this case, the system consisting of a deformed body, liquid, and gas is obtained; therefore, the study should be carried out with regard to the interaction forces between the deformed body, liquid and gas.

Read More### OPTIMIZATION OF PROCESSING INPUT INFORMATION IN THE INDUSTRIAL FISHERIES MONITORING SYSTEM

The article is devoted to the estimation of the effectiveness of the distributed input data processing model in sectorial fisheries monitoring system (SMS) and the justification of the processing algorithm based on simulation modeling with regard to the performance of the SMS software. Modeling the processing of the input data flow of the SMS enabled the comparison of different processing models in several system operation modes. The results of numerical experiments allowed selecting and implementing the most appropriate scheme based on parallel processing. In general, due to the developed flexible data processing system, SMS has shown its efficiency, resilience to failures, and reliability in providing the users of the system with analytical information.

Read More### MODELING OF IMAGES OF NON-COHERENT OBJECTS IN TURBU-LENT ATMOSPHERE

The application of the pre-ray-tracing method for solving the radiation transfer equation for the numerical simulation of images of incoherent objects in a turbulent atmosphere is dis-cussed. The accuracy of this method is estimated under various conditions of radiation propaga-tion as well as its effectiveness.

Read More### IMPULSE RESPONSE FUNCTION OF THE ACTION POTENTIAL IN NERVE FIBER

Behavior of the impulse signal was analyzed during the propagation process in the nerve fiber. An infinitesimal duration signal which is used as an axon input value has a view of asymmetrical impulse in space and time cross section. The maximum of pulse decreases and width of signal increases when coordinate and time increase.

Read More### ROLE AND CHARGED SURFACES dEBYE TEMPERATURE IN TRIBOLOGY

It is shown that the charged metal surfaces influence on friction coefficient and chemical processes. The adhesive component of friction, the surface parameters of the metal layers are closely related to the Debye temperature of the metal element.

Read More### NONLINEAR OSCILLATOR WITH HYSTERESIS PROPERTIES

The article describes a mathematical model of a nonlinear oscillator with hysteresis properties. We got the qualitative aspects of irregular oscillations in nonlinear dynamical system.

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