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 METHODS OF FORMULATING AND SOLVING OPTIMIZATION PROBLEMS OF CUTTING LOGS OF LARGE SIZE BY BAR-SAWING METHOD WITH CUTTING OUT ONE BAR AND FIVE PAIRS OF SIDE EDGING BOARDS WITH SUBSEQUENT SAWING LUMBER FOR EDGED BOARDS

2017 ◽  
Vol 7 (1) ◽  
pp. 137-150
Author(s):  
Агапов ◽  
Aleksandr Agapov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Target Function ◽  
Cross Sectional ◽  
Optimization Task ◽  
Cutting Out ◽  
The Mathematical Model ◽  
The Relationship

For the first time the mathematical model of task optimization for this scheme of cutting logs, including the objective function and six equations of connection. The article discusses Pythagorean area of the logs. Therefore, the target function is represented as the sum of the cross-sectional areas of edging boards. Equation of the relationship represents the relationship of the diameter of the logs in the vertex end with the size of the resulting edging boards. This relationship is described through the use of the Pythagorean Theorem. Such a representation of the mathematical model of optimization task is considered a classic one. However, the solution of this mathematical model by the classic method is proved to be problematic. For the solution of the mathematical model we used the method of Lagrange multipliers. Solution algorithm to determine the optimal dimensions of the beams and side edging boards taking into account the width of cut is suggested. Using a numerical method, optimal dimensions of the beams and planks are determined, in which the objective function takes the maximum value. It turned out that with the increase of the width of the cut, thickness of the beam increases and the dimensions of the side edging boards reduce. Dimensions of the extreme side planks to increase the width of cut is reduced to a greater extent than the side boards, which are located closer to the center of the log. The algorithm for solving the optimization problem is recommended to use for calculation and preparation of sawing schedule in the design and operation of sawmill lines for timber production. When using the proposed algorithm for solving the optimization problem the output of lumber can be increased to 3-5 %.

Multi-Objective Optimization Design of Screw Conveyor Using Genetic Algorithm

2013 ◽  
Vol 732-733 ◽  
pp. 402-406
Author(s):  
Duan Yi Wang
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Optimization Design ◽  
Optimization Problem ◽  
Machine Design ◽  
Screw Conveyor ◽  
Optimized Design ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
The Mathematical Model

The weight minimum and drive efficiency maxima1 of screw conveyor were considered as double optimizing objects in this paper. The mathematical model of the screw conveyor has been established based on the theory of the machine design, and the genetic algorithm was adopted to solving the multi-objective optimization problem. The results show that the mass of spiral shaft reduces 13.6 percent, and the drive efficiency increases 6.4 percent because of the optimal design based on genetic algorithm. The genetic algorithm application on the screw conveyor optimized design can provided the basis for designing the screw conveyor.

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>

Research on Multi-Objective Transmission Planning in Electricity Markets

2012 ◽  
Vol 516-517 ◽  
pp. 1429-1432
Author(s):  
Yang Liu ◽  
Xu Liu ◽  
Feng Xian Cui ◽  
Liang Gao
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Genetic Algorithms ◽  
Electricity Markets ◽  
Optimization Problem ◽  
Nsga Ii ◽  
Transmission Planning ◽  
Multi Objective ◽  
Complex Optimization ◽  
The Mathematical Model

Abstract. Transmission planning is a complex optimization problem with multiple deciding variables and restrictions. The mathematical model is non-linear, discrete, multi-objective and dynamic. It becomes complicated as the system grows. So the algorithm adopted affects the results of planning directly. In this paper, a fast non-dominated sorting genetic algorithm (NSGA-II) is employed. The results indicate that NSGA-II has some advantages compared to the traditional genetic algorithms. In transmission planning, NSGA-II is feasible, flexible and effective.

Kinematic Analysis of 5-UPS Parallel Machine Tool Based on Adams

2014 ◽  
Vol 644-650 ◽  
pp. 215-219 ◽  
Author(s):  
Lin Cai
Keyword(s):  
Mathematical Model ◽  
Machine Tool ◽  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Machine ◽  
Inverse Solution ◽  
Robot Kinematics ◽  
Vector Method ◽  
Parallel Machine Tool ◽  
The Mathematical Model

In this paper, the kinematics of 5-UPS parallel machine tool is analyzed, and a kinematic analysis method combining kinematic analysis and computer kinematics software is proposed. Under the premise that the parallel machine tool sector parameters is known, firstly we use the vector method to establish a mathematical model of inverse kinematics, and in accordance with a U-shaped processing trajectory the inverse solution is calculated; Secondly, three-dimensional model of the parallel machine tool is modeled in Adams, and kinematic constraints are set correctly; Finally, the inverse kinematics solution of the mathematical model is used as the Adams drive input, then the positive solutions is carried out. Compared through the Adams simulation results with U-machining path, it is verified that the inverse solution of the mathematical model and parallel machine tool bodies both are correct, it has certain significance for Parallel machine tools and other parallel robot kinematics analysis.

scholarly journals Shakedown of Composite Frames Taking into Account Plastic and Brittle Fracture of Elements

2015 ◽  
Vol 15 (4) ◽  
pp. 5-21 ◽  
Author(s):  
Piotr Alawdin ◽  
George Bulanov
Keyword(s):  
Mathematical Model ◽  
Cyclic Loading ◽  
Brittle Fracture ◽  
Optimization Problem ◽  
Shakedown Analysis ◽  
Composite Frames ◽  
Composite Frame ◽  
Plane Frames ◽  
Low Cyclic Loading ◽  
The Mathematical Model

abstract In the paper the mathematical model of the optimization problem of limit and shakedown analysis for composite plane frames, containing elastic-plastic and brittle elements under low-cyclic loading, is proposed. It is assumed that the load varies randomly within the specified domain, and limited plastic redistribution of forces in such structures occurs. An example of the shakedown analyses of the composite frame is given.

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.

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