scholarly journals A Mathematical Approach To Demand Estimation In Multi-Segment Oligopoly Markets - With An Application To The Automobile Market

2011 ◽  
Vol 2 (9) ◽  
Author(s):  
Robert P. Culp
Keyword(s):  
Mathematical Model ◽  
Automobile Industry ◽  
Mathematical Approach ◽  
Statistical Regression ◽  
Font Size ◽  
Automobile Market ◽  
Market Prices ◽  
Price Elasticities ◽  
Demand Equations ◽  
The Mathematical Model

<p class="MsoNormal" style="text-align: justify; line-height: normal; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">The purpose of this paper is to develop a purely mathematical approach to determining consumer demand. The model developed allows the researcher to derive demand in an oligopoly market from observed firm output and market prices using only assumptions about each firm, modest restrictions on consumer behavior, and limitations on market structure. The advantage of this revealed demand approach is that it does not require the specification of the consumer&rsquo;s utility function or any firm&rsquo;s production function. In addition, this mathematical approach allows for the estimation of own price and cross price elasticities of demand without statistical regression. </span></span></p><p class="MsoNormal" style="text-align: justify; line-height: normal; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">&nbsp;</span></span></p><p class="MsoNormal" style="text-align: justify; line-height: normal; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">The mathematical model developed is applied to the automobile industry assuming a market characterized by Cournot-Nash behavior and divided into five homogenous vehicle segments. A global optimization program is used to mathematically determine the range of values the coefficients of demand must take in each segment to satisfy market equilibrium. These coefficients can be used to estimate own and cross price elasticities of demand and construct demand equations. </span></span></p><p class="MsoNormal" style="text-align: justify; line-height: normal; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">&nbsp;</span></span></p><p class="MsoNormal" style="text-align: justify; line-height: normal; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">The elasticity estimates generated by the mathematical model of the automobile industry are compared to other estimates of elasticity found by statistical estimation. It is shown that the mathematical model generates results that are consistent with the statistical methods of the automobile market used by other researchers.<span style="mso-spacerun: yes;">&nbsp; </span></span></span></p>

scholarly journals Introducing a Conditional Ghost Correction Into the Vector Method

1984 ◽  
Vol 6 (2) ◽  
pp. 117-123 ◽  
Author(s):  
H. Schaeben
Keyword(s):  
Mathematical Model ◽  
Quadratic Programming ◽  
Optimization Problem ◽  
Linear Equations ◽  
Singular System ◽  
Orientation Distribution ◽  
Mathematical Approach ◽  
System Of Linear Equations ◽  
Vector Method ◽  
The Mathematical Model

The concept of conditional ghost correction is introduced into the vector method of quantitative texture analysis. The mathematical model actually chosen here reduces the texture problem to one of quadratic programming. Thus, a well defined optimization problem has to be solved, the singular system of linear equations governing the correspondence between pole and orientation distribution being reduced to a set of equality constraints of the restated texture problem. This new mathematical approach in terms of the vector method reveals the modeling character of the solution of the texture problem provided by the vector method completely.

scholarly journals Examining the relationship between information evaluation and security stock level

10.29007/shrz ◽  
2020 ◽  
Author(s):  
Csaba Imre Hencz ◽  
Tamás Hartványi
Keyword(s):  
Mathematical Model ◽  
Incomplete Information ◽  
Poor Quality ◽  
Mathematical Approach ◽  
Formal Description ◽  
Information Evaluation ◽  
Safety Stock ◽  
Stock Level ◽  
The Mathematical Model ◽  
The Relationship

In this research, we intend to present a novel mathematical approach to logistics which allows (financial) value to be associated with information as a central corporate resource. The inherent logistics processes (transport, production, sales) uncertainty requires continuous inventory monitoring and maintenance of safety stock levels. Literature and practice show that logistics responds to poor quality or incomplete information by increasing inventory.In our research, we are looking for a minimum of safety stock levels based on the processing of information available in space and time and I intend to give a formal description of the mathematical model and present an example of its application.

Mathematical model for comparing proficiency testing results across analytical methods

1991 ◽  
Vol 37 (2) ◽  
pp. 265-269
Author(s):  
James P AuBuchon
Keyword(s):  
Mathematical Model ◽  
Proficiency Testing ◽  
Standard Method ◽  
Blood Collection ◽  
Mathematical Approach ◽  
General Application ◽  
High Degree ◽  
The Mathematical Model ◽  
Over Time ◽  
Insufficient Number

Abstract Proficiency testing (PT) programs may fail to establish a range of acceptable performance in a challenge when an insufficient number of participants use a particular method. In this study I analyzed a mathematical approach to establish acceptable performance in alanine aminotransferase (ALT; EC 2.6.1.2) PT challenges. This approach was derived from the mathematical model used in establishing a nationwide ALT standardization system for blood-collection facilities in 1988. A ratio of results was derived between each method in the PT program and an arbitrarily chosen "standard" method. The intent of this approach was to transform a target value for a challenge as determined in the "standard" method to units applicable to methods utilized less often. However, the high degree of variability over time in the ratios for some methods precluded general application of this approach. Therefore, although this simple mathematical method was successful in implementing an ALT standardization system across different methods, a derivation of this approach did not afford comparison of results in PT challenges.

scholarly journals Experimental Verification of Model Simulation Results of Heating Cycles within the Electric Muffle Furnaces

2020 ◽  
Vol 5 (2) ◽  
pp. 36-46
Author(s):  
Jiří Lucák
Keyword(s):  
Mathematical Model ◽  
Silicon Carbide ◽  
Thermal Insulation ◽  
Experimental Verification ◽  
Model Simulation ◽  
Heating Furnace ◽  
Font Size ◽  
Muffle Furnace ◽  
Simulation Results ◽  
The Mathematical Model

<p><span style="font-family: Times New Roman; font-size: small;">The paper [1] described a mathematical model of the electric muffle furnace. A specific solution of real models has been already solved and presented within this paper. The first one is the muffle heating furnace equipped with a fireproof clay muffle (MODEL I) and thermal insulation of expanded fireproof clay. As the second variant the furnace equipped with a silicon carbide muffle (MODEL II) and with a thermal insulation of fibre ceramic boards of Sibral type is presented. Further the paper presents the results of simulations of the same heating cycles performed using the mathematical model presented in the paper [1] and comparing these results with the progression of the values measured in real furnaces.</span></p><p><span style="font-family: Times New Roman; font-size: small;">Experiment and simulation assessment will be carried out as the final step hereof. Equipment parameters are sources from technical documentations of the manufacturers.</span></p>

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.

Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A. Buikis ◽  
J. Cepitis ◽  
H. Kalis ◽  
A. Reinfelds ◽  
A. Ancitis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Initial Value Problems ◽  
Moisture Transfer ◽  
Bound Water ◽  
Drying Process ◽  
Initial Value ◽  
First Order ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations. 

The mathematical modelling of corrosion in hot dip galvanized steel reinforced concrete

2011 ◽  
Vol 2 (1) ◽  
pp. 1-12
Author(s):  
A. Hegyi ◽  
H. Vermeşan ◽  
V. Rus
Keyword(s):  
Mathematical Model ◽  
Reinforced Concrete ◽  
Numerical Model ◽  
Equation System ◽  
Galvanized Steel ◽  
Steel Reinforced Concrete ◽  
Numeric Model ◽  
Physical And Mathematical Models ◽  
Physical Phenomena ◽  
The Mathematical Model

Abstract In this paper we wish to present the numerical model elaborated in order to simulate some physical phenomena that influence the general deterioration of steel, whether hot dip galvanized or not, in reinforced concrete. We describe the physical and mathematical models, establishing the corresponding equation system, the initial and boundary conditions. We have also presented the numeric model associated to the mathematical model and the numeric methods of discretization and solution of the differential equations system that describes the mathematical model.

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