Über eine Wahl des Parameters beim Parallelenverfahren (Parallel-Chord-Method)

Computing ◽  
1978 ◽  
Vol 20 (1) ◽  
pp. 17-26 ◽  
Author(s):  
G. Scheu
Keyword(s):  
Parallel Chord ◽  
Chord Method

The use of the parallel-chord method to solve hydrodynamic difference equations

1981 ◽  
Vol 21 (3) ◽  
pp. 178-192
Author(s):  
V.A. Gasilov ◽  
V.F. Tishkin ◽  
A.P. Favorskii ◽  
M.Yu. Shashkov
Keyword(s):  
Difference Equations ◽  
Parallel Chord ◽  
Chord Method

Application of the parallel-chord method to solve implicit difference equations of magnetohydrodynamics

1983 ◽  
Vol 23 (4) ◽  
pp. 104-111
Author(s):  
V.A. Gasilov ◽  
T.K. Korshiya ◽  
B.Ya. Lyubimov ◽  
V.F. Tishkin ◽  
A.P. Favorskii ◽  
...  
Keyword(s):  
Difference Equations ◽  
Parallel Chord ◽  
Chord Method

scholarly journals Theory of the Stereological Analysis of Spheroid Size Distribution – Validation of the Equations

2017 ◽  
Vol 17 (4) ◽  
pp. 67-72
Author(s):  
D. Gurgul ◽  
A. Burbelko ◽  
T. Wiktor
Keyword(s):  
Outer Sphere ◽  
Bimodal Distribution ◽  
Mean Value ◽  
Ductile Cast Iron ◽  
Sample Space ◽  
Cumulative Distribution ◽  
Estimation Errors ◽  
Distribution Parameters ◽  
Chord Method ◽  
Validation Tests

AbstractThe paper presents validation tests for method which is used for the evaluation of the statistical distribution parameters for 3D particles’ diameters. The tested method, as source data, uses chord sets which are registered from a random cutting plane placed inside a sample space. In the sample space, there were individually generated three sets containing 3D virtual spheres. Each set had different Cumulative Distribution Function (CDF3) of the sphere diameters, namely: constant radius, normal distribution and bimodal distribution as a superposition of two normal distributions. It has been shown that having only a chord set it is possible, by using the tested method, to calculate the mean value of the outer sphere areas. For the sets of data, a chord method generates quite large errors for around 10% of the smallest nodules in the analysed population. With the increase of the nodule radii, the estimation errors decrease. The tested method may be applied to foundry issues e.g. for the estimation of gas pore sizes in castings or for the estimation of nodule graphite sizes in ductile cast iron.

Particle-size analysis of powders by the chord method

1975 ◽  
Vol 14 (11) ◽  
pp. 867-870
Author(s):  
L. I. Skorobogat ◽  
L. G. Podobeda
Keyword(s):  
Particle Size ◽  
Particle Size Analysis ◽  
Size Analysis ◽  
Chord Method

An intersecting chord method for minimum circumscribed sphere and maximum inscribed sphere evaluations of sphericity error

2015 ◽  
Vol 26 (11) ◽  
pp. 115005 ◽  
Author(s):  
Fei Liu ◽  
Guanghua Xu ◽  
Qing Zhang ◽  
Lin Liang ◽  
Dan Liu
Keyword(s):  
Chord Method

scholarly journals Methods for Transformation of Rectangular Spatial Coordinates to Geodetic Coordinates

2018 ◽  
Vol 7 (4.38) ◽  
pp. 1179
Author(s):  
Pavel Aleksandrovich Medvedev ◽  
Leonid Vasilevich Bykov ◽  
Vasiliy Leonidovich Bykov ◽  
Marina Vladimirovna Novorodskaya ◽  
Svetlana Ivanovna Sherstneva
Keyword(s):  
Transcendental Equation ◽  
Curvilinear Coordinates ◽  
Quartic Equation ◽  
Iterative Processes ◽  
Geodetic Height ◽  
Rectangular Coordinates ◽  
Spatial Coordinates ◽  
Root Isolation ◽  
Chord Method

The article gives a brief analysis of methods and algorithms for the transformation of spatial rectangular coordinates to curvilinear coordinates - geodetic latitude, geodetic longitude, geodetic height. Two algorithms for solving the equation for determining longitude are considered. Three formulas used to calculate the height are analyzed, with an estimate of their errors due to the approximate latitude. The shortcomings of mathematical solutions to these problems are revealed. A study of different approaches and methods for solving the transcendental equation for determining the latitude, based on the theory of separation of the root of the equation, is performed. Using this technique, iterative processes were performed to calculate the reduced latitude , using trigonometric identities, by introducing an auxiliary angle and transforming it to an algebraic quartic equation, which Borkowski solves by the Ferrari's method. The determination of the root isolation interval allowed using the chord method (proportional parts) to determine the latitude. In all cases, estimates of the convergence of the iterative processes that facilitate the comparative analysis of the proposed solutions are obtained. By further decreasing the separation interval of the root, the accuracy of the non-iterative determination of the latitude is improved by the Newton method.  

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