Determination of geopotential coefficients by efficient numerical integration techniques

This article concerns the evaluation of the ‘logsine’ integralWe shall encounter it in several guises. Indeed, standard integration techniques used below readily show that (1) has the same value as the following integrals:En passant, it is worth noting that forms (6) and (7) are the best behaved for numerical integration.I first met the logsine integral as a callow youth in that strange hinterland of results that you may not have met at school but were not guaranteed to meet later on either.

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Adopting Image Integration Techniques to Simulate Satellite Images

Iraqi Journal of Science ◽

10.24996/ijs.2020.61.12.32 ◽

2020 ◽

pp. 3445-3455

Author(s):

Heba Khudhair Abbas ◽

Farah Faris ◽

Sale Sami ◽

Al Zahraa Fadel

Keyword(s):

Satellite Images ◽

Signal To Noise Ratio ◽

Accurate Information ◽

Integration Process ◽

Image Region ◽

Contrast Measure ◽

Integration Techniques ◽

Mathematical Relationships ◽

Nearest Neighborhood

Mathematical integration techniques rely on mathematical relationships such as addition, subtraction, division, and subtraction to merge images with different resolutions to achieve the best effect of the merger. In this study, a simulation is adopted to correct the geometric and radiometric distortion of satellite images based on mathematical integration techniques, including Brovey Transform (BT), Color Normalization Transform (CNT), and Multiplicative Model (MM). Also, interpolation methods, namely the nearest neighborhood, Bi-linear, and Bi-cubic were adapted to the images captured by an optical camera. The evaluation of images resulting from the integration process was performed using several types of measures; the first type depends on the determination of quality in the regions of the edges using a contrast measure as well as the number of edges and threshold. The second type is the global one that is based on the parameters of the image region, including the Mean (µ), Standard Deviation (SD), and Signal to Noise Ratio (SNR). The parameters also included the Amount of Information Added (AIA) to the original image, such as those for the total (AIAt) , edges (AIAe), and homogenous (AIAh) regions. The results showed the efficiency of the integration process in the image fusion with different resolutions in one image integrated resolution. The quality measures used were also capable in evaluating the most efficient techniques and determining the accurate information of the resulting image.

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Calcul des éléments dipolaires et quadrupolaires de la matrice de transition moléculaire dans Na2

Canadian Journal of Physics ◽

10.1139/p90-058 ◽

1990 ◽

Vol 68 (4-5) ◽

pp. 365-368 ◽

Cited By ~ 1

Author(s):

K. Hussein ◽

O. Babaky

Keyword(s):

Numerical Integration ◽

Electronic States ◽

Transition Elements ◽

Simple Method ◽

Selection Rules ◽

Variable Formula ◽

Method Of Calculation ◽

Analytical Integration ◽

Fifth Order

In this paper, we study a calculation of the transition elements [Formula: see text] between electronic states of the diatomic molecules Na2. We show the necessary selection rules for the determination of these operators by a method of analytical integration on the variable [Formula: see text], combined with a numerical integration to fifth order. The values found by this simple method of calculation are very reasonable and show that the important transitions [Formula: see text], [Formula: see text]; and [Formula: see text] of the dimer Na2 are dipolar. [Traduit par la revue]

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Determination of Planetary Masses from the Motions of Comets

Symposium - International Astronomical Union ◽

10.1017/s0074180900006549 ◽

1972 ◽

Vol 45 ◽

pp. 209-226

Author(s):

W. J. Klepczynski

Keyword(s):

Least Squares ◽

Numerical Integration ◽

Numerical Experiments ◽

Close Approach ◽

Variational Equations ◽

Orbit Correction ◽

Partial Derivatives ◽

Least Squares Solution ◽

The Masses

A brief survey is given of past determinations of the masses of the principal planets from analyses of the motions of comets. Some numerical experiments using comets which have close approaches to Jupiter are made. As a result of these experiments, it is concluded that the conventional least squares solution for the correction to the mass of Jupiter is inadequate for comets which have a close approach to Jupiter. It is further concluded that perhaps, in some cases, the apparent presence of nongravitational forces is merely a manifestation of the failure of the conventional orbit correction process to adjust correctly the orbits of objects which undergo very large perturbations, and it also may be a consequence of errors in the adopted planetary masses. It is suggested that the use of partial derivatives obtained through the numerical integration of the variational equations may overcome the difficulties.

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On the numerical integration in generalized/extended finite element method analysis for crack propagation problems

Engineering Computations ◽

10.1108/ec-02-2020-0067 ◽

2020 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Bruna Caroline Campos ◽

Felício Bruzzi Barros ◽

Samuel Silva Penna

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Fracture Mechanics ◽

Numerical Integration ◽

Extended Finite Element Method ◽

Extended Finite Element ◽

Content Type ◽

Integration Techniques ◽

Integration Strategies ◽

Element Method

Purpose The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered. Design/methodology/approach Numerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results. Findings Known numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities. Originality/value This study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies.

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