scholarly journals Some Properties of the Basins of Attraction of the Newton’s Method for Simple Nonlinear Geodetic Systems

2021 ◽  
Author(s):  
Krzysztof Kroszczynski ◽  
Damian Kiliszek ◽  
Ireneusz Winnicki
Keyword(s):  
Iterative Method ◽  
Basins Of Attraction ◽  
Self Similarity ◽  
Observation Systems ◽  
Non Local ◽  
Iterative Systems ◽  
Initial Starting ◽  
Convergence Mechanism ◽  
Selection Of

The research presented in this paper concerns the determination of the attraction basins of the Newton’s iterative method which was used to solve the non-linear systems of observational equations associated with the geodetic measurements. The authors considered simple observation systems corresponding to the intersections, or linear and angular resections, used in practice. The main goal was to investigate the properties of the sets of convergent in the initial points of the applied iterative method. An important issue regarding the possibility of automatic and quick selection of such points was also considered. Therefore, the answers to the questions regarding the geometric structure of the basins, their limitations, connectedness or self-similarity were sought. The research also concerned the iterative structures of the basins, i.e. maps of the number of iterations which are necessary to achieve the convergence of the Newton’s method. The determined basins were compared with the areas of convergence that result from theorems on the convergence of the Newton’s method, i.e. the conditions imposed on the eigenvalues and norms of the matrices of the studied iterative systems. One of the essential results of the research is the indication that the obtained basins of attraction contain areas resulting from the theoretical premises and their diameters can be comparable with the sizes of the analyzed geodetic structures. Consequently, in the analyzed cases it is possible to construct methods that enable quick selection of the initial starting points or automation of such selection. The paper also characterizes the global convergence mechanism of the Newton’s method for disconnected basins and, as a consequence, the non-local initial points, i.e. located far from the solution points.

DETERMINING THE DESALINATION UNIT COMPOSITION FOR COSTAL AREAS AND SMALL ISLANDS USE ANALYTIC HIERARCHY PROCESS

2017 ◽  
Vol 9 (1) ◽  
Author(s):  
Imam Setiadi ◽  
Dinda Rita K. Hartaja
Keyword(s):  
Analytic Hierarchy Process ◽  
Energy Demand ◽  
Pairwise Comparison ◽  
Small Islands ◽  
Ahp Method ◽  
Analytic Hierarchy ◽  
Comparison Research ◽  
Hierarchy Process ◽  
Selection Of

Selection of the appropriate composition desalination units can be done with a variety of method approaches, one of the method is the Analytic Hierarchy Process. In determining the desalination unit with AHP method to consider is setting a goal, an alternative criteria and pairwise comparison. Research for the determination of the exact composition of the desalination unit in order to achieve sustainable drinking water suppy in coastal areas and small islands has been conducted. The results of the study are as follows, the energy demand of 50.83%, operator costs of 26.64%, maintenance costs of 14.13% and chemical requirement 8.4%. For an alternative composition desalination unit of RO 10 m3 / day is the best alternative composition with value of 59.61%, the composition of the next alternative is RO 20 m3/ day of 30.40% and the last alternative of the desalination unit composition is RO 120 m3/ day of 09.99%.Key words : Desalination, Mukti Stage Flash Composition, AHP

Optimization of the selection of analysis methods for the determination of naturally occurring radionuclides

Kerntechnik ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. 118-121
Author(s):  
T. Heinrich ◽  
L. Funke ◽  
M. Köhler ◽  
U.-K. Schkade ◽  
F. Ullrich ◽  
...  
Keyword(s):  
Naturally Occurring ◽  
Analysis Methods ◽  
Naturally Occurring Radionuclides ◽  
Selection Of

Determination of the minimum number of technological bases of a part

2020 ◽  
pp. 73-75
Author(s):  
B.M. Bazrov ◽  
T.M. Gaynutdinov
Keyword(s):  
Cost Price ◽  
Labor Input ◽  
Part Surface ◽  
Technological Base ◽  
Size Accuracy ◽  
Minimum Number ◽  
The Cost ◽  
Input Cost ◽  
Selection Of

The selection of technological bases is considered before the choice of the type of billet and the development of the route of the technological process. A technique is proposed for selecting the minimum number of sets of technological bases according to the criterion of equality in the cost price of manufacturing the part according to the principle of unity and combination of bases at this stage. Keywords: part, surface, coordinating size, accuracy, design and technological base, labor input, cost price. [email protected]

Is Hydraulics Over-Used or Under-Used in Storm Drainage?

1994 ◽  
Vol 29 (1-2) ◽  
pp. 53-61
Author(s):  
Ben Chie Yen
Keyword(s):  
Unsteady Flow ◽  
Computational Time ◽  
Time Step ◽  
Flow Routing ◽  
Kinematic Wave Equation ◽  
Storm Drainage ◽  
Saint Venant Equations ◽  
Unsteady Flow Routing ◽  
Selection Of

Urban drainage models utilize hydraulics of different levels. Developing or selecting a model appropriate to a particular project is not an easy task. Not knowing the hydraulic principles and numerical techniques used in an existing model, users often misuse and abuse the model. Hydraulically, the use of the Saint-Venant equations is not always necessary. In many cases the kinematic wave equation is inadequate because of the backwater effect, whereas in designing sewers, often Manning's formula is adequate. The flow travel time provides a guide in selecting the computational time step At, which in turn, together with flow unsteadiness, helps in the selection of steady or unsteady flow routing. Often the noninertia model is the appropriate model for unsteady flow routing, whereas delivery curves are very useful for stepwise steady nonuniform flow routing and for determination of channel capacity.

Determination of integral indicators characterizing the possibility of accommodating the evacuated population in the territory of the Republic of Kazakhstan

2020 ◽  
pp. 154851292097028
Author(s):  
Yernar Zh Akimbayev ◽  
Zhumabek Kh Akhmetov ◽  
Murat S Kuanyshbaev ◽  
Arman T Abdykalykov ◽  
Rashid V Ibrayev
Keyword(s):  
Statistical Data ◽  
Armed Conflicts ◽  
Security Issues ◽  
Inaccurate Information ◽  
The Subject ◽  
The Republic ◽  
The Impact ◽  
Integrated Indicators ◽  
Selection Of

Studying the historical facts of past wars and armed conflicts and natural and man-made emergencies, today in the Republic of Kazakhstan one of the most important security issues is the preparation and organization of the evacuation of the population from possible dangerous zones, taking into account the emergence of new threats to the country’s security. The paper presents an algorithm for constructing universal scales of the distribution function of opportunities by types of support and rebuilding them into subject scales using display functions. The purpose of the paper is to determine the integral indicators characterizing the possibility of accommodation of the evacuated population and the impact on resources during relocation. On the subject scales of cities and districts of the region, indicators of the possibility of relocation of a certain amount of the evacuated population by types of support and indicators characterizing the impact on the district’s resources during resettlement of a certain amount of the evacuated population are determined. It was concluded that the use of integrated indicators allows the selection of areas to accommodate the evacuated population without the use of statistical data, in conditions of incomplete and inaccurate information. The presented method does not replace traditional methods based on classical methods of territory assessment by the level of life sustenance, but also allows their reasonable combination with the experience of specialists in this field, taking into account the incompleteness, uncertainty, and inconsistency of the initial data of the study area, which does not allow the application of existing methods.

scholarly journals Genetic Similarity of Avena sativa L. Varieties as an Example of a Narrow Genetic Pool of Contemporary Cereal Species

Plants ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 1424
Author(s):  
Magdalena Cieplak ◽  
Sylwia Okoń ◽  
Krystyna Werwińska
Keyword(s):  
Genetic Diversity ◽  
Avena Sativa ◽  
Genetic Similarity ◽  
Breeding Programs ◽  
Central European ◽  
Cereal Species ◽  
Genetic Pool ◽  
Selection Of ◽  
High Genetic Similarity

The assessment of the genetic diversity of cultivated varieties is a very important element of breeding programs. This allows the determination of the level of genetic differentiation of cultivated varieties, their genetic distinctiveness, and is also of great importance in the selection of parental components for crossbreeding. The aim of the present study was to determine the level of genetic diversity of oat varieties currently grown in Central Europe based on two marker systems: ISSR and SCoT. The research conducted showed that both these types of markers were suitable for conducting analyses relating to the assessment of genetic diversity. The calculated coefficients showed that the analyzed cultivars were characterized by a high genetic similarity. However, the UPGMA and PCoA analyses clearly indicated the distinctiveness of the breeding programs conducted in Central European countries. The high genetic similarity of the analyzed forms allow us to conclude that it is necessary to expand the genetic pool of oat varieties. Numerous studies show that landraces may be the donor of genetic variation.

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