MATHEMATICAL APPARATUS FOR CALCULATIMG THE MICROSTRUCTURE OF A HARMONIC KINOFORM LENS

2019 ◽  
Keyword(s):  
Mathematical Apparatus

GEOMETRIC THEORY OF MULTIDIMENSIONAL INTERPOLATION

2020 ◽  
Vol 2020 (1) ◽  
pp. 9-16
Author(s):  
Evgeniy Konopatskiy
Keyword(s):  
Response Function ◽  
Algebraic Curves ◽  
Geometric Theory ◽  
Analytical Description ◽  
Geometric Interpretation ◽  
Affine Geometry ◽  
Mathematical Apparatus ◽  
Multidimensional Interpolation ◽  
Pass Through

The paper presents a geometric theory of multidimensional interpolation based on invariants of affine geometry. The analytical description of geometric interpolants is performed within the framework of the mathematical apparatus BN-calculation using algebraic curves that pass through preset points. A geometric interpretation of the interaction of parameters, factors, and the response function is presented, which makes it possible to generalize the geometric theory of multidimensional interpolation in the direction of increasing the dimension of space. The conceptual principles of forming the tree of the geometric interpolant model as a geometric basis for modeling multi-factor processes and phenomena are described.

Development of gas hydrates the modern technologies

2010 ◽  
Vol 7 ◽  
pp. 202-210
Author(s):  
V.V. Khabirov ◽  
S.V. Khabirov
Keyword(s):  
Porous Medium ◽  
Phase Change ◽  
Gas Hydrates ◽  
Gas Production ◽  
Mathematical Apparatus ◽  
Modern Technologies

The scheme of gas production from gas hydrates on underwater slopes is offered. The existing modern technologies which have to be used are listed. The mathematical apparatus for calculations describes a filtration of polyphase environments in the relative frame elastic porous medium with phase change.

NETWORK MODELS AS A SOLUTION FOR COMPLEX TECHNICAL PRODUCT`S DIAGNOSING PROBLEMS SOLVING

2019 ◽  
pp. 38-42
Author(s):  
S. Yu. Strakhov ◽  
A. A. Karasev
Keyword(s):  
Complex System ◽  
System Analysis ◽  
Network Models ◽  
Functional Testing ◽  
Formal Models ◽  
Mathematical Apparatus ◽  
Complex Technical Systems ◽  
Technical Systems ◽  
Formalized Description ◽  
Diagnostic Software

Authors explore issue of applicability of the methodology of building diagnostic software using network formal models in the functional testing of electronic equipment as part of complex technical systems. Using methods of system analysis allows to perform a decomposition of interdependent subsystems and to reveal basic acts of interaction between the control‑verification equipment and the object of diagnosis. Mathematical apparatus of Petri nets should be employed for the formalized description of such acts and determined the cause‑and‑effect relations in the diagnosed complex system`s processes. Network models properties studying (such as safety and accomplishment of the final positions) allows us to move to the test object`s algorithm`s developing. The article presents an approach of a formalized description for basic acts of interaction between the diagnosis system and the object.

Digital Technologies – Innovative Solutions for Agriculture

2020 ◽  
Vol 67 (1) ◽  
pp. 127-132
Author(s):  
Marina A. Nikitina ◽  
Dmitriy N. Osyanin ◽  
Irina V. Petrunina
Keyword(s):  
Farm Animals ◽  
High Tech ◽  
Mathematical Apparatus ◽  
Online Mode ◽  
Cell Matrix ◽  
Algorithmic Support ◽  
Quality Product ◽  
A Cell ◽  
Parametric Description ◽  
Animal Feeding

High-tech decision support systems based on the knowledge of experts in the field of animal feeding and a rigorous mathematical apparatus make it possible to increase the productivity of the animals and provide a high-quality product with the ability to trace the trophological chain from the field to the counter. (Research purpose) To identify methodological approaches for the development of algorithmic support and software for assessment and optimizing the animals diet. (Materials and Methods) The authors complied a structural-parametric model of a productive animal feeding in a cell matrix form. They represented the whole variety of existing known and unknown relationships between the factors of the farm animal state and the feeding ration characteristics. It was found that when forming a feeding ration, it was necessary to assess the degree of influence on productivity of not individual indicators, but its combination. (Results and discussion) The authors considered parametric descriptions of farm animals; diet with selected groups of indicators, characteristics and properties. It was stated that the parametric description of feeding contained a set of parameters taking into account at least 25 nutritional indicators. They presented a mathematical apparatus for evaluating and optimizing the feeding ration. It was determined that the automation of the process of calculating the daily ration of an animal allowed to change the diets depending on the availability of feed in the farm and their chemical composition in real time. The authors found out that an increase in the productivity of animals and poultry by 30-50 percent was possible due to balanced full-fledged feeding. (Conclusions) The authors showed a systematic approach to the development of software for evaluating and optimizing the animal feeding diet. It was revealed that a computer system in the online mode would help to find the best option for a feeding ration, taking into account multifactor and limitations.

STUDY OF IRRATIONAL SYSTEMS BY EXTENDING THE LOGICAL-MATHEMATICAL APPARATUS

Servis plus ◽  
2017 ◽  
Vol 11 (1) ◽  
pp. 66-74 ◽  
Author(s):  
Вадим Кортунов ◽  
Vadim Kortunov
Keyword(s):  
Mathematical Apparatus

scholarly journals Inner Damping of Water in Conduit of Hydraulic Power Plant

2021 ◽  
Vol 13 (13) ◽  
pp. 7125
Author(s):  
Daniel Himr ◽  
Vladimír Habán ◽  
David Štefan
Keyword(s):  
Power Plant ◽  
Operating Conditions ◽  
Mathematical Apparatus ◽  
Pressure Pulsations ◽  
Hydraulic Power ◽  
Economic Operation ◽  
Compression And Expansion ◽  
Rotor Stator Interaction ◽  
Start Ups

The operation of any hydraulic power plant is accompanied by pressure pulsations that are caused by vortex rope under the runner, rotor–stator interaction and various transitions during changes in operating conditions or start-ups and shut-downs. Water in the conduit undergoes volumetric changes due to these pulsations. Compression and expansion of the water are among the mechanisms by which energy is dissipated in the system, and this corresponds to the second viscosity of water. The better our knowledge of energy dissipation, the greater the possibility of a safer and more economic operation of the hydraulic power plant. This paper focuses on the determination of the second viscosity of water in a conduit. The mathematical apparatus, which is described in the article, is applied to data obtained during commissioning tests in a water storage power plant. The second viscosity is determined using measurements of pressure pulsations in the conduit induced with a ball valve. The result shows a dependency of second viscosity on the frequency of pulsations.

IDENTIFICATION OF INTERHARMONICS BASED ON WAVELET PACKET TRANSFORM

2021 ◽  
Vol 3 (1) ◽  
pp. 031-036
Author(s):  
S. A. GOROVOY ◽  
◽  
V. I. SKOROKHODOV ◽  
D. I. PLOTNIKOV ◽  
◽  
...  
Keyword(s):  
Fourier Transform ◽  
Simulation Model ◽  
Frequency Domain ◽  
Time Domain ◽  
Wavelet Packet ◽  
High Accuracy ◽  
Wavelet Packet Transform ◽  
Mathematical Apparatus ◽  
Nonlinear Load ◽  
The Time Domain

This paper deals with the analysis of interharmonics, which are due to the presence of a nonlinear load. The tool for the analysis was a mathematical apparatus - wavelet packet transform. Which has a number of advantages over the traditional Fourier transform. A simulation model was developed in Simulink to simulate a non-stationary non-sinusoidal mode. The use of the wavelet packet transform will allow to determine the mode parameters with high accuracy from the obtained wavelet coefficients. It also makes it possible to obtain information, both in the frequency domain of the signal and in the time domain.

The measurement problem of calibration of measuring instrument under specified conditions

2021 ◽  
pp. 9-15
Author(s):  
Sergey F. Levin
Keyword(s):  
Risk Assessment ◽  
Risk Management ◽  
Measurement Problem ◽  
Parametric Identification ◽  
Correction Function ◽  
Measuring Instruments ◽  
Measuring Instrument ◽  
Mathematical Apparatus ◽  
Second Stage ◽  
Assessment Techniques

The problem of calibration of measuring instruments for given conditions based on the correction function is considered as a measurement problem of structural-parametric identification of the calibration diagram. It is shown, that the correction function allows at the first stage to obtain a ratio for correcting the readings, and at the second stage to obtain a corrected measurement result, it is necessary to identify the probability distribution of possible deviations from it. An example of solving the measurement problem of calibration for given conditions is given. Negative aspects of the practice of calibration of measuring instruments are noted: carrying out calibration under normal conditions according to the methods of verification of measuring instruments; presentation of calibration results by tables of joint readings of measuring instruments and standards; the presence in the calculations of the calibration diagram of significant restrictions on the mathematical apparatus of the «Guidelines for the expression of measurement uncertainty», specified by ISO/IEC 31010:2019 “Risk management – Risk assessment techniques”.

Investigation of the Influence of Inertia Forces on the Adhesion of the Coating to the Outer Surface of Bodies of Revolution during Thermal Spraying

2021 ◽  
Vol 316 ◽  
pp. 726-731
Author(s):  
Alexey Yu. Rodichev ◽  
Roman N. Polyakov ◽  
Andrey V. Gorin
Keyword(s):  
Adhesion Strength ◽  
Outer Surface ◽  
External Surface ◽  
Thermal Spraying ◽  
Inertial Forces ◽  
Body Of Revolution ◽  
Mathematical Apparatus ◽  
Bodies Of Revolution ◽  
Steel Base ◽  
Inertia Forces

The article presents the results of a study of the influence of inertial forces on the adhesion of the coating to the external surface of a body of revolution during thermal spraying. A mathematical apparatus is proposed for calculating the inertia forces, acting on a particle of coating, applied to the outer surface of the bodies of revolution. As a result, dependencies have been revealed that allow predicting the adhesion strength of the coating with the steel base during thermal spraying.

scholarly journals Representation of the kinematics of the natural trihedral of a spiral-helix trajectory by quaternion matrices

2021 ◽  
Vol 9 (4) ◽  
pp. 18-29
Author(s):  
Anatolii Alpatov ◽  
Victor Kravets ◽  
Volodymyr Kravets ◽  
Erik Lapkhanov
Keyword(s):  
Computational Experiment ◽  
Nonlinear Problems ◽  
Unit Vector ◽  
Frame Of Reference ◽  
Mathematical Apparatus ◽  
Dynamic Design ◽  
Quaternion Matrices ◽  
Transport Vehicle ◽  
Stationary Frame ◽  
Curvature And Torsion

The spiral-helix trajectory of the transport vehicle programmed motion in the form of a hodograph in the stationary frame of reference is considered. A relative frame of reference associated with the natural trihedral of the trajectory is introduced. The formulas of curvature and torsion of the trajectory, the unit vector of the natural trihedral, the components of the angular velocity of rotation of the natural trihedral in the proper axes and in the stationary frame of reference are set in the quaternionic matrices. The results are verified using the Frenet-Serret formulas. The mathematical apparatus of quaternion matrices is tested with the aim of adapting spatial, nonlinear problems of dynamic design of transport vehicles to a computational experiment.

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