scholarly journals Mathematical relations for constructing an algorithm for estimating signal parameters under conditions of constraints

2021 ◽  
pp. 153-156
Author(s):  
Я.Я. Эглит ◽  
К.Я. Эглите ◽  
А.А. Ковтун ◽  
Д.А. Глушко
Keyword(s):  
Transport System ◽  
Optimization Problems ◽  
Inequality Constraint ◽  
Statistical Optimization ◽  
Computing Environment ◽  
Dummy Variables ◽  
Signal Parameters ◽  
Main Production ◽  
Mathematical Relationships ◽  
Mathematical Relations

Статья посвящена разработке математических соотношений для построения алгоритма оценивания параметров сигналов в условиях ограничений. При работе транспортной системы возникают довольно сложные проблемы, которые связаны с необходимостью проведения оценки принятых параметров с требованиями соблюдения имеющихся ограничений. Ограничения могут представлять собой как равенства, так и неравенства. Поскольку ограничения-неравенства могут быть сведены путём добавления фиктивных переменных к условиям, а также их можно проверить по шагам, переводя в состав равенства, в статье разработан алгоритм, позволяющий иметь ограничения-равенства. Данная задача относится к классу статистических проблем оптимизации. Для ее решения использованы стандартные функции из подкаталога "optimization" вычислительной среды MatLAB. Построение такого алгоритма даст возможность не только уменьшить складские расходы, но и сократить основное производственное время. The article is devoted to the development of mathematical relationships for constructing an algorithm for estimating signal parameters under constraints. During the operation of the transport system, rather complex problems arise, which are associated with the need to assess the adopted parameters with the requirements of compliance with the existing restrictions. Constraints can be either equality or inequality. Since the inequality constraint can be reduced by adding dummy variables to the equality conditions, and they can also be checked step by step, transforming them into equality, we will develop an algorithm that allows us to have equality constraints. This task belongs to the class of statistical optimization problems. To solve it, standard functions from the "optimization" subdirectory of the MatLAB computing environment will be used. The construction of such an algorithm will make it possible not only to reduce storage costs, but also to reduce the main production time.

The geometry of reflection

Geophysics ◽  
1993 ◽  
Vol 58 (2) ◽  
pp. 293-297
Author(s):  
Shelby C. Worley
Keyword(s):  
Constant Velocity ◽  
Two Dimensional ◽  
Auxiliary Parameter ◽  
Reflection Geometry ◽  
The Creation ◽  
Mathematical Relationships ◽  
Mathematical Relations ◽  
Insight Into

The two‐dimensional (2-D) reflection path from a dipping plane between an offset source‐receiver combination in a constant velocity medium can be described with several parameters (coordinates, offsets, angles, and lengths). Although there are many parameters, only four independent ones are needed to locally determine the reflection geometry. Given four determining parameters, the evaluations of other ones present problems that range from trivial to formidable. The circumscribed circle about the source, receiver, and specular point turns out to have a number of remarkable properties that are useful for the solution of these problems. The radius of the circle is a useful new auxiliary parameter. Triangles constructed in the circle provide nonintuitive mathematical relationships between angles and lengths. The use of mathematical relations derived from the circle has allowed the creation of formulas to fully recover the reflection geometry in a vast majority of valid sets of four known parameters. This circle provides a powerful tool for the calculation of nondetermining parameters as well as new insight into the geometry of reflection with straight raypaths.

scholarly journals Multi-Agent Modeling in Schedule Problems

2019 ◽  
Vol 09 (4) ◽  
pp. 100-111
Author(s):  
T.V. Sivakova ◽  
V.A. Sudakov
Keyword(s):  
Distributed Computing ◽  
Optimization Problems ◽  
Computational Experiments ◽  
Multi Agent Systems ◽  
Computing Environment ◽  
Agent Modeling ◽  
Agent Systems ◽  
Multi Agent

The article explores the use of multi-agent technologies for solving optimization problems. It is shown how multi-agent systems allow working with restrictions in a distributed computing environment. The task of scheduling is formalized. Software was developed and computational experiments were carried out, which showed the effectiveness of the proposed approach.

Simple Mathematical Relations between the Acetabular Anteversion and Sector Angles

1993 ◽  
Vol 34 (1) ◽  
pp. 99-100
Author(s):  
S. Anda ◽  
I. K. Amdal
Keyword(s):  
Femoral Head ◽  
Hip Joint ◽  
Acetabular Anteversion ◽  
Mathematical Relationships ◽  
Mathematical Relations

Acetabular anteversion is an important parameter of the hip joint. It is measured at CT of the hip, as are the more recently introduced acetabular sector angles. These angles give information on the anterior and posterior support from the acetabulum to the femoral head. Some simple mathematical relationships between these angles are presented.

scholarly journals Fuzzy-Logic Approach to Estimate the Passengers’ Preference when Choosing a Bus Line within the Public Transport System

2021 ◽  
Vol 23 (3) ◽  
pp. A150-A157
Author(s):  
Vitalii Naumov ◽  
Baurzhan Zhamanbayev ◽  
Dinara Agabekova ◽  
Zhumazhan Zhanbirov ◽  
Igor Taran
Keyword(s):  
Fuzzy Logic ◽  
Transport System ◽  
Public Transport ◽  
Optimization Problems ◽  
The Public ◽  
Public Transport System ◽  
Wide Range ◽  
Fuzzy Logic Approach ◽  
Logic Approach ◽  
The Given

For the developed system of public transport, the passengers, as the customers, have a variety of alternatives when choosing the transport mode or even the route for the given mode of public transport. The estimation of the passengers’ preference is the key task for transportation planners for solving the wide range of optimization problems in the field of public transport. A methodology for estimation of the passengers’ preference when choosing the bus line within a public transport system is developed in this paper. The proposed approach is based on the fuzzy-logic mathematical apparatus and uses the surveys’ data to calculate the membership functions defining the passengers’ preference. The case study of the passengers’ survey, held in Talas (Kazakhstan), is used to illustrate the developed methodology.

Parallelization of Evolution Strategy on a Workstation-Cluster and its Application to Discrete Structural Optimization

1994 ◽  
Author(s):  
Jianbo Cai ◽  
Georg Thierauf
Keyword(s):  
Parallel Computing ◽  
Structural Optimization ◽  
Discrete Optimization ◽  
Optimization Problems ◽  
Biological Evolution ◽  
Computing Environment ◽  
Design Point ◽  
Workstation Cluster ◽  
Conventional Optimization ◽  
Discrete Optimization Problems

Abstract Evolution strategies (ESs) imitate biological evolution and have two characteristics that differ from other conventional optimization algorithms: (a) ESs use randomized operators instead of the usual deterministic ones; (b) instead of a single design point, the ESs work simultaneously with a population of design points in the space of variables. The second characteristic allows for an implementation in a parallel computing environment. In this paper the application of ESs for the solution of discrete optimization problems and its parallelization are described.

On Mathematical Models of the Classic Maya Collapse: The Class Conflict Hypothesis Reexamined

1982 ◽  
Vol 47 (3) ◽  
pp. 643-652 ◽  
Author(s):  
John W. G. Lowe
Keyword(s):  
Mathematical Models ◽  
Classic Maya ◽  
Class Conflict ◽  
Mathematical Form ◽  
Collapse Models ◽  
Peasant Revolt ◽  
Maya Collapse ◽  
Mathematical Relationships ◽  
Mathematical Relations ◽  
Good Agreement

Recently, Hamblin and Pitcher (1980) have attempted to buttress the class conflict explanation of the Classic Maya collapse using a series of mathematical models. However, despite the exceptionally good agreement between these mathematical relations and the empirical data, the same cannot be said for the fit between the conceptual and mathematical models. The relations employed are very general, so much so as to often be isomorphic with very different processes. In one case at least, the same model appears to be consistent with several entirely distinct explanations of the collapse, and other mathematical readings of the monument data are by no means precluded. While these particular mathematical relationships fail to make a very strong case that the Classic Maya collapse was engendered primarily through peasant revolt and class conflict, which was very possibly Hamblin's and Pitcher's underlying aim, the attempt to cast explanations of the collapse into mathematical form points the way for the next generation of collapse models.

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