scholarly journals Complexity of the characteristic semi-groups the direct products of „AG“ asynchronous automata of the strongly connected determined analogs the extensions associated with DFASC2 isomorfisms

2018 ◽  
Vol 19 (6) ◽  
pp. 1007-1011
Author(s):  
Stanisław Bocian
Keyword(s):  
Mathematical Model ◽  
Direct Product ◽  
Direct Products ◽  
Semi Group ◽  
Product Complexity ◽  
Asynchronous Automata ◽  
Strongly Connected ◽  
The Many ◽  
The Mathematical Model ◽  
Computational Processes

The paper presents the assumption and the evidence is carried out of the direct product complexity of character-istic semi-groups of any number (“ ”) of deterministic, finite, asynchronous, highly consistent DFASC2. automata. The characteristic semi-group of the automaton interferes in the computational algorithm of the generalized homoeo-morphism of the automatons. Then determination the com-plexity of the characteristic semi-group enables to estimate the complexity of the computational generalized homoeo-morphism for the other classes of automatons. In the range of the mathematical model the conception of the determined analog of the extension of the automaton associated with the isomorphism g0, g1 ,…, gq-1 where q is the grade of the extensions, with the suitable assumptions it simulates the automaton variable in time. The variable automaton in time is the adequate mathematical model for the many technical and computational processes of the real time. The direct product of automatons can be considered as the realization- parallel calculations accordingly

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

scholarly journals Mathematical Modelling and Simulation of Six Axis Robot for Industrial Application

2020 ◽  
Vol 9 (4) ◽  
pp. 955-959
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Low Cost ◽  
Sine Wave ◽  
Modeling Software ◽  
Paper Work ◽  
The Many ◽  
Mathematical Modelling And Simulation ◽  
The Mathematical Model ◽  
Environment Condition

The proposed paper work is focused on the development of low cost six axis robot. The robot is modelled using mathematical model and it’s compared with the simulation model in the real time environment condition. The modeling of the robot is designed in the modeling software and it is simulated in the Matlab software. This type of solving system is used to solve the many type of real time problems. The simulated result is compared with the mathematical model of the robot. Based on the testing the robot is redesigned in the modeling software. In this work sin wave is given has input and the robot is followed the sine wave.

scholarly journals Lie-Group Modeling and Numerical Simulation of a Helicopter

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2682
Author(s):  
Alessandro Tarsi ◽  
Simone Fiori
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Group Theory ◽  
Lie Group ◽  
Technical Literature ◽  
Lie Group Theory ◽  
Pontryagin Principle ◽  
Group Modeling ◽  
The Many ◽  
The Mathematical Model

Helicopters are extraordinarily complex mechanisms. Such complexity makes it difficult to model, simulate and pilot a helicopter. The present paper proposes a mathematical model of a fantail helicopter type based on Lie-group theory. The present paper first recalls the Lagrange–d’Alembert–Pontryagin principle to describe the dynamics of a multi-part object, and subsequently applies such principle to describe the motion of a helicopter in space. A good part of the paper is devoted to the numerical simulation of the motion of a helicopter, which was obtained through a dedicated numerical method. Numerical simulation was based on a series of values for the many parameters involved in the mathematical model carefully inferred from the available technical literature.

Methods of Increasing the Speed of the Many-Arc Welding

2016 ◽  
Vol 843 ◽  
pp. 274-277
Author(s):  
A.M. Ulanov ◽  
Mikhail Alekhsandrovich Ivanov
Keyword(s):  
Mathematical Model ◽  
Heat Input ◽  
Arc Welding ◽  
Thick Plate ◽  
Steel Structures ◽  
Depth Of Penetration ◽  
Welded Steel ◽  
The Many ◽  
The Mathematical Model ◽  
Geometrical Dimensions

Many-arc submerged welding is used weld thick and long seams of welded steel structures. This article describes a method for increasing the speed of the many-arc welding, with evidence from the parametrical calculation of the four-arc welding mode, using the basic mathematical model of the WeldCalc software. First of all, mathematical model coefficients are calculated based on the existing weld mode. This article presents data for four-arc welding of a 28 mm thick plate. The obtained coefficients are entered in WeldCalc, which checks the compliance of the calculated welding heat input and the actual current while the sample is welded. In case of the values of heat input are discrepant, the software adjusts the coefficients. Data are corrected and and the mathematical model is adjusted according to the participation share coefficient of each arc and to the Ku coefficients of the voltage for each arc. After the welding mode is successfully reconstructed, the welding speed is increased. Thus the parameters of welding mode are changed to increase the aggregate capacity of the power source, but the heat input of welding is not changed. In order to check the new mode, the researchers have welded the rest sample and checked its geometrical dimensions of the joints (height, width, depth of penetration, square of the weld seam). The obtained results are satisfactory.

scholarly journals Isomorphism of the characteristic semi- group of the direct sum and direct product of the asynchronous automatons of the strongly connected and determined analogs of their extensions

2018 ◽  
Vol 19 (12) ◽  
pp. 312-315
Author(s):  
Stanisław Bocian
Keyword(s):  
Direct Product ◽  
Semi Group ◽  
Parallel Calculation ◽  
Direct Sum ◽  
Strongly Connected ◽  
Abstract Class ◽  
Suitable Characteristic

In this article it is presented that the characteristic semi – group of the direct sum and direct product “G” and “AG” of the asynchronous automatons of the strongly connected and determined analogs of their extensions are isomorphism. Taking into account that the characteristic semi – group determines the ability to process the information then the direct sum and direct product can be consider as realization – the sequence and parallel calculation accordingly. The obtained results mean that this ability doesn’t depend on the sequence and parallel realization (the same number of abstract class of the suitable characteristic semi- groups).

scholarly journals Modelling and static stability analyses of the hexa-quad bimorph walking robot

2019 ◽  
Vol 254 ◽  
pp. 02029 ◽  
Author(s):  
Dominik Wojtkowiak ◽  
Krzysztof Talaśka ◽  
Ireneusz Malujda ◽  
Jan Górecki ◽  
Dominik Wilczyński
Keyword(s):  
Mathematical Model ◽  
Great Influence ◽  
Static Stability ◽  
Walking Robots ◽  
Walking Robot ◽  
Centre Of Gravity ◽  
Functional Features ◽  
Robot Configuration ◽  
The Many ◽  
The Mathematical Model

Gait stability of the walking robot has great influence on the many functional features related to walking robots, from mechanical construction to control algorithms and generating steps. The goal of the presented research was a development of the concept of hexa-quad bimorph walking robot. Results of the performed static stability analysis allowed the initial verification of the mathematical model and provided information about the design adequacy and the possibilities of controlling the machine. The research involved analysing the characteristic postures of the robot focused on retaining static stability. To achieve this objective the mathematical model was made to determine the centre of gravity for the robot by using Denavit-Hartenberg notation. On this basis the simulation model was created in Matlab Simulink environment, where the described analyses were conducted. Based on the obtained results, the initial model error was determined at approximately 3%. It was also established that the centre of gravity for the design was not significantly different from the effective centre of gravity for the robot. This made it possible to achieve static stability through adequate alignment of the legs in nearly every robot configuration.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

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