scholarly journals OPTIMIZING THE NATURAL ILLUMINATION OF RANDOM SHAPE PREMISES

2016 ◽  
Vol 2 (1) ◽  
pp. 181-184
Author(s):  
Чернышёва ◽  
Kseniya Chernysheva ◽  
Брусенцев ◽  
Aleksandr Brusentsev
Keyword(s):  
Mathematical Model ◽  
Mathematical Problem ◽  
Technical Problem ◽  
Main Task ◽  
Random Shape ◽  
Natural Illumination ◽  
Basic Concepts ◽  
The Mathematical Model

The problem of providing the illumination in diverse industrial premises, despite the numerous methods and ways to solve it is still relevant. In this article, the example of a specific technical problem considers the possibility of optimizing the natural illumination of random shape premises. The main task & basic concepts and definitions from the area of metering lighting which are necessary for solving this task are formulated. The mathematical model of natural illumination and the mathematical problem of optimization of natural illumination are described here. A brief description of the algorithm for solving the problem is given also.

A Ball-Balancing System for Demonstration of Basic Concepts in the State-Space Control Theory

1974 ◽  
Vol 11 (4) ◽  
pp. 367-376 ◽  
Author(s):  
V. Jørgensen
Keyword(s):  
Mathematical Model ◽  
Control Theory ◽  
Physical Properties ◽  
Graduate Education ◽  
State Space ◽  
The State ◽  
Basic Concepts ◽  
Conditions Of Stability ◽  
The Mathematical Model

The Ball-balancing Systems is intended to demonstrate the basic concepts in the state-space control theory in the graduate education. The physical properties of the system are stated and the mathematical model is evaluated. Conditions of stability are discussed.

scholarly journals ON BÄCKLUND TRANSFORMATIONS WITH SPLIT QUATERNIONS

2020 ◽  
pp. 423
Author(s):  
Muhammed Talat Sariaydin
Keyword(s):  
Mathematical Model ◽  
Minkowski Space ◽  
Bäcklund Transformations ◽  
Split Quaternion ◽  
Split Quaternions ◽  
Backlund Transformations ◽  
Null Curves ◽  
Basic Concepts ◽  
The Mathematical Model ◽  
End Results

The present paper deals with the introduction of Bäcklund Transformations with split quaternions in Minkowski space. Firstly, we tersely summarized the basic concepts of split quaternion theory and Bishop Frames of non-null curves in Minkowski space. Then, for Bäcklund transformations defined with each case of non-null curves, we give relationships between Bäcklund transformations and split quaternions. It is also presented some special propositions for transformations constructed with split quaternions. At the end, results obtained with the mathematical model have been evaluated.

scholarly journals Optimizing Vehicle Routing for Simultaneous Pick-up and Delivery considering the Reusable Transporting Containers: Case of Convenient Stores

2020 ◽  
Author(s):  
Intaek Gong ◽  
Kyungho Lee ◽  
Jaewon Kim ◽  
Yunhong Min ◽  
Kwang Sup Shin
Keyword(s):  
Mathematical Model ◽  
Vehicle Routing ◽  
Traffic Congestion ◽  
Optimal Algorithm ◽  
Time Windows ◽  
Mathematical Problem ◽  
Transportation Cost ◽  
Business Environment ◽  
Routing Problem ◽  
The Mathematical Model

A lot of previous research have proposed various frameworks and algorithms to optimize routes to reduce the total transportation cost, which accounts for over 70% of overall logistics cost. However, it is very hard to find the cases applied the mathematical models or algorithms to the practical business environment cases, especially daily operating logistics services like convenient stores. Most of previous research have considered the developing an optimal algorithm which can solve the mathematical problem within the practical time while satisfying all constraints such as the capacity of delivery and pick-up, and time windows. For the daily pick-up and delivery service like supporting several convenient stores, it is required to consider the unit transporting container as well as the demand, capacity of trucks, traveling distance and traffic congestion. Especially, the reusable transporting container, trays, should be regarded as the important asset of logistics center. However, if the mathematical model focuses on only satisfying constraints related delivery and not considering the cost of trays, it is often to leave the empty trays on the pick-up points when there is not enough space in the track. In this research, it has been proposed to build the mathematical model for optimizing pick-up and delivery plans by extending the general vehicle routing problem of simultaneous delivery and pickup with time windows while considering left-over cost. With the numerical experiments, it has been proved that the proposed model may reduce the total delivery cost. It may be possible to apply the proposed approach to the various logistics business which uses the reusable transporting container like shipping containers, refrigerating containers, trays, and pallets.

scholarly journals Operational Optimization of the Electromechanical System in Non-deterministic Conditions

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Technical Problem ◽  
Control Object ◽  
Electromechanical System ◽  
Operational Optimization ◽  
The Moment ◽  
Definition Of ◽  
The Impact ◽  
The Mathematical Model

On the basis of theoretical and practical studies of the electromechanical system, the scientific and technical problem of improving the control system of the electromechanical system during the impact on it of multi-vector perturbations is solved. The result of the study is the integration of differential equations with coefficients dependent on the oscillations of the control object. In the theoretical part, the mathematical model of the electromechanical system was synthesized, which made it possible to investigate ways of minimizing the deviation angles and time intervals required to stabilize the motion of the electromechanical system, which allowed indirectly to realize the associated signal with the stochastic nature of the moment of oscillation of the control object on the coordinate plane. The method of parametric optimization of the mathematical model of the electromechanical system in the function of the angle of inclination is also improved and investigated. Based on the definition of the structure and algorithms of work, the efficiency of the control system of the electromechanical system increases in terms of reducing the stabilization time of the control object.

A New Mathematical Model of the Force in Pneumatic Tire-Snow Chain Systems

2006 ◽  
Author(s):  
Juan C. Botero ◽  
Massimiliano Gobbi ◽  
Giampiero Mastinu
Keyword(s):  
Mathematical Model ◽  
Theoretical Model ◽  
Traction Force ◽  
Experimental Tests ◽  
Safety Device ◽  
Transmitted Force ◽  
Basic Concepts ◽  
External Forces ◽  
The Mathematical Model ◽  
Made In

In this paper a new theoretical model to estimate the transmitted force in a snow-chain safety device is presented. Starting with a detailed analysis of the significant external forces acting on the system, the mathematical model is developed using some basic concepts of the contact mechanics theory. A MATLAB® code was developed in order to perform numerical simulations and experimental tests were carried out to validate the model. The results obtained show that for certain conditions of the driving surface and the tire's tread the force transmitted along the chain can be several times the longitudinal traction force applied to the tire itself. The importance of the interaction between the blocks on the tire and the chain segments is discussed. Some conclusions and recommendations are made in order to improve the design process of this kind of devices.

scholarly journals Optimization of Operation Strategy for Collection Systems of Biohazard Wastes in Hospitals Based on Autonomous Robots: A Heuristic Approach

2020 ◽  
pp. 33-43
Author(s):  
Tamás Bányai ◽  
Izteleuova Maral ◽  
Béla Illés ◽  
Ágota Bányai ◽  
Péter Tamás
Keyword(s):  
Mathematical Model ◽  
Health Care ◽  
Industrial Revolution ◽  
New Technologies ◽  
Autonomous Robots ◽  
Health Care Systems ◽  
Mathematical Problem ◽  
Optimal Solution ◽  
Waste Collection ◽  
The Mathematical Model

The increasing rate of hospital admission led to increased volume of both municipal and biohazard wastes. The fourth industrial revolution opens up new perspectives to improve the conventional processes of hospitals and other institutions of health care systems. The application of new technologies integrated into the solutions of Industry 4.0 makes it possible to improve the efficiency of processes of hospitals not only in the field of medicine, but also in the field of other services, like logistics and supply chain. Within the frame of this article the authors are focusing on the development of new operation strategies for biohazard waste collection in hospitals using smart bins and autonomous waste collection vehicles/robots. The literature review helps to identify research gaps in the field of biohazard waste collection in hospitals. After that, the article describes the mathematical model of the waste collection system including smart bins, autonomous collection vehicles, users (patients and health professionals). The mathematical model has a time-based objective function, while time-, capacity- and safety-related constraints are also taken into consideration. The mathematical problem is an NP-hard problem; therefore, we use the non-linear regression and evolutive options of Excel Solver to find the optimal solution. The numerical scenarios validate the model and show the advantages of using new technologies in health care institutes, like hospitals.

The centrally cracked Brazilian disc: implications and solutions in case of closing cracks

2014 ◽  
Vol 23 (3-4) ◽  
pp. 59-77 ◽  
Author(s):  
Christos F. Markides ◽  
Dimitrios N. Pazis ◽  
Stavros K. Kourkoulis
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Fundamental Problem ◽  
Mathematical Problem ◽  
Radial Pressure ◽  
Contact Stresses ◽  
Displacement Fields ◽  
Brazilian Disc ◽  
Wide Range ◽  
The Mathematical Model

AbstractA recently presented closed-form analytic solution for the displacement field and stress field in a cracked Brazilian disc, under uniform radial pressure along two symmetric arcs of its periphery, revealed that for a wide range of crack-axis inclinations, the lips of the crack tend to overlap each other, leading to a kind of an “unnatural” geometrical configuration. It is here proven that this behavior is a consequence of the inability of the mathematical model to simulate the change of the boundary conditions that appears (for some special configurations) in the physical problem and render the mathematical problem an “ill-posed” one. Indeed, what happens in praxis is that for a given interval of crack inclination angles, the initially stress-free lips are coming in contact and contact stresses appear violating the boundary conditions initially adopted in the mathematical model. This problem is here solved by superposing to the above-mentioned solution the respective one of an auxiliary mixed fundamental problem solved according to Muskhelishvili’s complex potentials method. In this way, physically acceptable displacement fields and stress fields are obtained all over the cracked disc independently from the crack inclination angle. In addition, the contact stresses developed along the crack lips are determined. Moreover, naturally sound formulae for the corresponding stress intensity factors (in case of cracks with lips in contact to each other) are obtained, which are of crucial engineering importance. The solution obtained enlightens some critical aspects related to the practical application of the cracked Brazilian disc as a tool for the standardized determination of the fracture toughness of brittle rock-like materials and concrete.

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

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