scholarly journals Analysis of Fracture Characteristic of a Gas Main Pipe on the Basis of the Additive Mathematical Model of the Cyclic Random Process and Polynomial Function

2018 ◽  
Vol 115 ◽  
pp. 012047 ◽  
Author(s):  
I V Lytvynenko ◽  
P O Maruschak ◽  
S V Panin ◽  
A P Sorochak
Keyword(s):  
Mathematical Model ◽  
Random Process ◽  
Polynomial Function ◽  
Fracture Characteristic ◽  
Main Pipe ◽  
Gas Main ◽  
Cyclic Random Process

scholarly journals Cyclic Linear Random Process As A Mathematical Model Of Cyclic Signals

2015 ◽  
Vol 9 (4) ◽  
pp. 219-224 ◽  
Author(s):  
Sergiy Lupenko ◽  
Nadiia Lutsyk ◽  
Yuri Lapusta
Keyword(s):  
Mathematical Model ◽  
Random Process ◽  
Science And Technology ◽  
Random Processes ◽  
Stochastic Signals ◽  
Cyclic Random Process ◽  
The Mathematical Model

Abstract In this study the cyclic linear random process is defined, that combines the properties of linear random process and cyclic random process. This expands the possibility describing cyclic signals and processes within the framework of linear random processes theory and generalizes their known mathematical model as a linear periodic random process. The conditions for the kernel are given and the probabilistic characteristics of generated process of linear random process in order to be a cyclic random process. The advantages of the cyclic linear random process are presented. It can be used as the mathematical model of the cyclic stochastic signals and processes in various fields of science and technology.

Mathematical model of gas consumption process in the form of cyclic random process

2021 ◽  
Author(s):  
Iaroslav Lytvynenko ◽  
Serhii Lupenko ◽  
Oleg Nazarevych ◽  
Grigorii Shymchuk ◽  
Volodymyr Hotovych
Keyword(s):  
Mathematical Model ◽  
Random Process ◽  
Cyclic Random Process ◽  
Gas Consumption

Analysis of multiple cracking of nanocoating as a cyclic random process

2013 ◽  
Vol 49 (2) ◽  
pp. 164-170 ◽  
Author(s):  
I. V. Lytvynenko ◽  
S. A. Lupenko ◽  
P. O. Marushchak
Keyword(s):  
Random Process ◽  
Multiple Cracking ◽  
Cyclic Random Process

scholarly journals An approximate mathematical model for estimating the influence of vibrations on attached elements of a mobile robot video system

2021 ◽  
pp. 20-26
Author(s):  
A. A. Lobaty ◽  
M. М. Tatur ◽  
A. K. Ibrahim
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Mobile Robot ◽  
Random Process ◽  
Random Vibration ◽  
Experimental Studies ◽  
Mobile Platform ◽  
Special Equipment ◽  
Video System ◽  
Vibration Process

The problem of constructing and applying of mathematical model for assessing the influence of vibrations on the attached elements of the video system of a mobile robot is solved. This robot is considered as a mobile platform for placing of the special equipment for various purposes. The analysis of mathematical models and the results of experimental studies of vibrations of multi-support wheeled machine and its structural elements has been conducted. On the basis of this analysis, the form of a stochastic mathematical model of vibrations of the structure of a mobile robot has been substantiated. The vibration model is specified as a correlation function or spectral density of a random process for various conditions of the robot’s movement. Differential equations of the shaping filter for modeling а random vibration process with given characteristics are presented. Differential equations for the probabilistic moments of the vibration process are presented. Based on the equations for the probabilistic moments and the proposed formula, an assessment of events, which consist in exceeding the vibration amplitude of a given level was carried out. These events are named as outliers of a random process and characterize the range within the basic properties of the equipment installed on the mobile platform are preserved. An analytical study of a mathematical model to determine the intensity of emissions of a random vibration process has been carried out. The probabilistic characteristics of the vibration process and the intensity of emissions are determined. The obtained theoretical results make it possible to assess the performance of the elements of a video system installed on a mobile platform and to formulate the basic requirements for tolerances for their parameters. The results of computer modeling clearly showed the efficiency of the proposed mathematical model for assessing the influence of vibrations.

scholarly journals COMPUTER SIMULATION OF DETERMINING SILTATION VOLUMES OF WATER RESERVOIR STORAGE ON THE AKSAY RIVER

2020 ◽  
Vol 46 (4) ◽  
pp. 102-112
Author(s):  
M. R. Magomedova ◽  
Z. A. Kurbanova ◽  
B. A. Shangereeva
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Random Process ◽  
Process Model ◽  
Probabilistic Approach ◽  
Water Reservoir ◽  
Temporal Correlation ◽  
Programming System ◽  
Reservoir Storage ◽  
Hydrological System

Objectives. The development of a mathematical model for the increased turbidity zones of the Aksay river in order to determine the siltation volumes of the Aksay water reservoir storage.Method. The mathematical model is developed using the theory of probability and the theory of random process outliers. The model takes the normal distribution of the horizontal and vertical components of the instantaneous flow velocities into account, as well as the Rayleigh law of the distribution of their maxima. The proposed model is used to calculate the “turbidity tail” of the Aksay river.Result. Due to the multifactorial nature of the continuously associated processes of siltation and deposition of suspended and bottom sediments in the upper pounds of the Aksay reservoir storage hydrological system, a mathematical model of the reservoir accretion process is developed. This model provides the reliability of accretion forecasting with spatial and temporal correlation with the siltation process model, which is actually feasible on the basis of computer simulation.Conclusion. The developed model, which is based on a probabilistic approach and the theory of random process outliers, reflects the overall process of sediment transport in open channels. The development and execution of simulation programmes is carried out using the Microsoft Developer Studio (MDS) and the Fortran Power Station algorithmic language, which comprises not only a programming system, but also a set of tools for supporting large software projects integrated into MDS. 

scholarly journals THE CHOICE AND SUBSTANTIATION OF THE MATHEMATICAL MODEL OF ELECTRORETINOGRAM IN THE FORM OF LINEAR STOCHASTIC PROCESS

2014 ◽  
pp. 95-99
Author(s):  
S. V. Dzubin ◽  
A. V. Matsiuk ◽  
S. V. Martsenko ◽  
M. V. Pryimak
Keyword(s):  
Mathematical Model ◽  
Stochastic Process ◽  
Random Process ◽  
Applied Research ◽  
The Mathematical Model ◽  
Eye Retina

The mathematical model of electroretinogram as a linear random process which takes into account the mechanism of eye retina biopotentials forming and is suitable for solving of the measuring and diagnosing problems is developed in the work. The approach is proposed, the method is developed and the statistics are given to estimate the kernel of the linear random process as electroretinogram model. The obtained results may be used in the applied research of eye diagnosis.

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