### APPROXIMATION OF PERIODIC FUNCTIONS BY COMPOSITE TWO-POINT HERMITE POLYNOMIALS

This paper deals with polynomial approximating a periodic functions by composite two-point Hermite polynomials. The final formulas of these polynomials, using the function values and its derivatives at a given point, are constructed. The relation of Taylor’s polynomial and two-point polynomials with respect to representation of periodic function is specified. The estimation of proximity, expressed through the evaluation of the derivative of the corresponding order is given. A sufficient condition for the convergence of a sequence of two-point polynomials to a given periodic function is established. Examples are given in which periodic function is approximated by a sequence of two-point Hermite polynomials with data on an errors and its evaluation.

Read More### INVESTMENT PORTFOLIO FORMATION AND ANALYSIS ON EXAMPLE OF TWO SECURITIES

The paper considers the econometric models of stock prices of large domestic companies based on modeling a portfolio of securities and predicting its behavior using mathematical modeling with the elements of probability theory and mathematical statistics. Based on the obtained results, companies and entrepreneurs can build a strategy for investing and buying shares, knowing the likely income from a portfolio of certain types of securities.

Read More### NUMERICAL RESEARCH OF INFLUENCE UNEVEN DISTRIBUTION OF CONCENTRATION OF ONE FROM FRACTIONS OF DISPERSED COMPONENT PER PROCESS PROPAGATION OF SHOCK WAVE FROM HOMOGENEOUS GAS TO TWO-FRACTIONAL GAS-SUSPENSION

The effect of the non-uniform concentration of one of the fractions of a two-fraction gas suspension on the parameters of a shock wave moving from pure gas to a gas suspension is numerically studied. The motion of a direct shock wave in a two-fraction gas suspension was simulated. The finely dispersed fraction of the gas suspension had a uniform initial mass content, while larger particles had an uneven initial mass content along the transverse coordinate. The mathematical model took into account the viscosity of the carrier medium, as well as interphase force and thermal interaction. The equations of the mathematical model were integrated by an explicit finite-difference method.

Read More### ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ПРОЦЕССОВ ТЕПЛОМАССООБМЕНА СЖИЖЕННОГО ПРИРОДНОГО ГАЗА В ГОФРИРОВАННОМ КРИОБАКЕ

В статье рассматривается перспективная модель топливного СПГ-бака, позволяющая увеличить время бездренажного хранения за счет обеспечения постоянной степени заполнения изотермического сосуда жидкой фазой топлива. Выполнено технологическое описания способа поддержания неизменяемой объемной доли криогенного топлива в сжиженном состоянии путем использования гофрированной конструкции сосуда по типу сильфонного осевого компенсатора. Осуществлена постановка задачи программного расчета с использованием метода конечных объемов, позволяющего описать распределение физических параметров двухфазной системы «жидкость-газ» с учетом наличия теплопритока к стенкам рассматриваемого гофрированного сосуда. Приведены результаты численного эксперимента бездренажного хранения криожидкости без стравливания продукта в систему питания двигателя внутреннего сгорания, выявлены недостатки аналитического исследования процессов тепломассопереноса и гидродинамики СПГ в криогенной изотермической емкости.

Read More### FINITE ELEMENT MESH AUTOMATIC GENERATION USING TRIANGULAR SUBDIVISION SCHEMES

We suggest here a new algorithm for triangular finite element mesh generation for NURBS surface represented as a set of control points. We use a modern approach – subdivision techniques, which has many advantages. Two different subdivision schemes are presented here: Modified Butterfly and Loop ones.

Read More### TEACHING MS EXCEL FINANCIAL COMPUTATIONS IN ENGLISH

This article is based on 6 years experience of teaching IT disciplines (in particular, financial computations in MS Excel) in English at International Finance Faculty of the Financial University under the Government of the Russian Federation.

Read More### RESONANCE CONDITION IN MICROHETEROGENEOUS MOLECULAR COMPLEX WITH HYDROGEN BOND

The article considered hydrogen bonds intermolecular resonance in microheterogeneous structures, influence of external electric field on the ferroelectric crystals molecular dynamics and its manifestation in the croconic acid IR-spectra, cooperativity phenomenon of various structures molecular associates.

Read More### PREDICTION OF ENERGY CONSUMPTION BASED ON HOLT-WINTERS MODEL

In the article described one of the most popular adaptive models — Holt-Winters model. It includes a review of strengths and weaknesses of this model, the results of forecasting energy consumption based on the Holt-Winters model, and how forecasting error depends on the choice of the model parameters.

Read More### DEVELOPMENT OF A UNIVERSAL MODULAR AUTOMATED COMPLEX REMOTE PRESENCE

In modern industry, high requirements for the control of technological processes by automated methods. One of the main areas is the remote process control methods. This paper discusses the developed methods and algorithms for control a robotic platform, implemented by server technologies, and the creation of management software platform through wireless data transfer Bluetooth. / These technologies can be used to build complex robotic systems remote process monitoring.

Read More### MODELS OF FATIGUE AND AVALANCHE DESTRUCTION OF ROCKS

The article presents a model of fatigue and avalanche of rock failure with loss of deformations and spatial stability rock of the collector.

Read More### SUBSTANTIATION OF THE PARAMETERS OF ROCKS (HETEROGENEITY ENVIRONMENTS) WHEN MODELING

The article considers the initial analytical scheme for estimation of statistical quantities weak local areas and areas of rock fracture.

Read More### THE FORMATION AND PROPAGATION OF SHOCK WAVES IN SATURATED POROUS MEDIA

The aim is to determine the relation of the physical properties of the porous medium and the fluid saturating the pore space, the characteristics of the transmitted and reflected weak shock waves. For the experiment used a setup like “shock tube”.

To solve the problem of shock tube equipped with a section of bulk media. For pressure detecting used piezoelectric sensor and L-card board consisting of a charge amplifier and ADC.

Read More### ALGEBRA OF LOGIC IN THEORY OF EVENTS

The article introduces the concept of the binary (Boolean) event. We consider event E defined by Boolean functions E=F(E1, E2,…,En), in which E1, E2,…,En are Boolean events. A theorem on the probability of an event provided by such a formula is proved, and the application of the theorem is shown on the problems. A theorem on the structure of the truth table of the Boolean function E=F(E 1, E 2,…,En) is given, in which E 1, E 2,…,En are Boolean events that form exhaustive events. For the events under consideration, the form of the formula for the full probability is obtained, as well as the calculated formulas for the conditional probabilities and the Bayes’ formula. The problems on the application of the obtained formulas are given.

Read More### ALGORITHMS TO DETERMINE SOLVABILITY OF LINEAR INTEGRO-DIFFERENTIAL EQUATIONS WITH ANALYTIC FUNCTIONS

Applying the method of power series to linear integro-differential equations yields vast infinite systems of linear algebraic equations for coefficients of these series. If the equation contains some members then it is practically impossible to construct such system and make a definite conclusion. As some initial equations of such systems differ from others, we proposed to use computer for their suitable presentation. Further, we found sufficient conditions on linear Volterra integro-differential equations of the third kind to be correct in analytical functions which generalize the well-known fact of correctness of a Volterra integral equation of the second kind.

Read More### RADIATION TRANSFER IN HIGH DENSITY ATOMIC VAPOURS WITH VARIOUS DETUNINGS OF PROBE LASER FROM RESONANCE TRANSITION

In this work, we studied the process of resonance radiation transfer in dense rubidium vapour with various detuning of the probe laser from 5S1/2 – 5P3/2 atomic transition. At the working atomic concentration of , the spectral half-width of the transition was 4 GHz. The cw probe laser had a spectrum width of 1 MHz. Test pulses of 1 ms duration and the repetition rate of 1 kHz were formed by an acousto-optic modulator. Due to the radiation trapping, the lifetime of excited atoms was much longer than the spontaneous decay time of 26 ns. In the range of detuning from 16 GHz to 220 GHz, the time linearly increased from 28-04-2020 15-21-09. The long lifetime of the excitation can significantly increase the efficiency of the optical saturation of atomic gas media.

Read More### TESTING GPS MODULE U-BLOX 6

In this article will be tested a GPS Module 6 Ublox by the means of PC and connected directly to the MC AVR ATmega 328. This system is one of the basic units of the robot, and should strictly meet the requirements of the positioning accuracy in space.

Read More### GPS UBLOX 6M MODULE PAIRING WITH THE AVR MICROCONTROLLER

This article describes the pairing and setup process GPS module Ublox 6m with AVR microcontroller ATmega 328. Similar modules are actively used in robotics for robot navigation in open space conditions.

Read More### ROBOT OBSTACLE AVOIDANCE SYSTEM BY USING ULTRASONIC RANGEFINDER AND PROPORTIONAL CONTROLLER

In this article will be described the implementation and debugging of robotic platform with obstacle avoidance system using ultrasonic rangefinders and a proportional controller.

Read More### THE OPERATOR ANALOGUE OF INEQUALITY OF CAUCHY-BUNYAKOVSKIY

The article describes the determination of the left and right of the absolute values of the operator and their properties. The operator analogue of the inequality of Cauchy – Bunyakovski is obtained.

Read More### BRAKING EFFICIENCY OF POSITIVELY AND NEGATIVELY CHARGED PARTICLES IN ULTRA-COLD GAS OF MAGNETIZED ELECTRONS

We performed the molecular dynamics simulation of the braking process of charged particles moving in a dense ultra-cold magnetized electron gas. The case of the uniform magnetic field is considered. The motion of ions with a charge +e and –e is considered. The dependence of the braking efficiency on the sign of the charge, as well as on the angle between the ion velocity and the direction of the magnetic field, is investigated. Results of the simulation are compared with available theoretical models, as well as with the previously obtained results.

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