Application of the method of least squares to molecular intensity component curves in gas electron diffraction

1971 ◽  
Vol 12 (3) ◽  
pp. 480-480
Author(s):  
N. I. Ganotchenko ◽  
N. V. Alekseev
Keyword(s):  
Electron Diffraction ◽  
Least Squares ◽  
Gas Electron Diffraction ◽  
Method Of Least Squares ◽  
Molecular Intensity

Strukturbestimmung von Chlorfluorthiocarbonyl durch Elektronenbeugung / The Structure of Thiocarbonyl-chloro-fluoride as determined by Gas-Electron-Diffraction

1975 ◽  
Vol 30 (4) ◽  
pp. 549-553 ◽  
Author(s):  
F. Gleisberg ◽  
A. Haberl ◽  
W. Zeil
Keyword(s):  
Electron Diffraction ◽  
Experimental Determination ◽  
Least Squares ◽  
Qualitative Agreement ◽  
Gas Electron Diffraction ◽  
Mean Square ◽  
Rotational Constants ◽  
Valence Force ◽  
Experimental Values

Abstract Gas electron diffraction (GED) intensities of CSFCl were measured and resulted in an ra- structure of this molecule. An rav-structure was obtained by combining our GED-data and the rotational constants reported by Kohrmann and Zeil. Both structures were found to be consistent within their uncertainties. The planar structure of CSFCl has been confirmed. A least squares analysis resulted in the following rg-distances and bond angles: r(C-Cl) =1.7178±0.0009 Å, r(C=S) =1.5931 ±0.0008 Å, r(C-F) =1.3387±0.0014 Å, ∢ S = (C-Cl)=127.28 ± 0.09°, ∢(S=C-F)= 123.58 ±0.12°.Inclusion of rotational constants into the GED-analysis allowed an experimental determination of all mean square amplitudes (MSA). We have used the valence force constants obtained by Kohrmann to evaluate the MSA theoretically. Qualitative agreement was found between the theoretical and experimental values of the MSA.

scholarly journals A Method of Least-Squares for Refining Electron-Diffraction Internuclear Distances using Spectroscopical Shrinkage Effects.

1962 ◽  
Vol 16 ◽  
pp. 1528-1528 ◽  
Author(s):  
S. J. Cyvin ◽  
Ulf Persmark ◽  
Svend Erik Rasmussen ◽  
A. Block-Bolten ◽  
J. M. Toguri ◽  
...  
Keyword(s):  
Electron Diffraction ◽  
Least Squares ◽  
Method Of Least Squares ◽  
Internuclear Distances

The limit state of concrete and reinforced concrete rods at complex and longitudinal-transverse bending

2020 ◽  
pp. 60-73
Author(s):  
Yu V Nemirovskii ◽  
S V Tikhonov
Keyword(s):  
General Solution ◽  
Least Squares ◽  
Nonlinear Differential Equations ◽  
Limit State ◽  
Algebraic Equations ◽  
Method Of Least Squares ◽  
Elasticity Limit ◽  
Limit Values ◽  
Symbolic Calculations ◽  
Deformation Diagrams

The work considers rods with a constant cross-section. The deformation law of each layer of the rod is adopted as an approximation by a polynomial of the second order. The method of determining the coefficients of the indicated polynomial and the limit deformations under compression and tension of the material of each layer is described with the presence of three traditional characteristics: modulus of elasticity, limit stresses at compression and tension. On the basis of deformation diagrams of the concrete grades B10, B30, B50 under tension and compression, these coefficients are determined by the method of least squares. The deformation diagrams of these concrete grades are compared on the basis of the approximations obtained by the limit values and the method of least squares, and it is found that these diagrams approximate quite well the real deformation diagrams at deformations close to the limit. The main problem in this work is to determine if the rod is able withstand the applied loads, before intensive cracking processes in concrete. So as a criterion of the conditional limit state this work adopts the maximum permissible deformation value under tension or compression corresponding to the points of transition to a falling branch on the deformation diagram level in one or more layers of the rod. The Kirchhoff-Lyav classical kinematic hypotheses are assumed to be valid for the rod deformation. The cases of statically determinable and statically indeterminable problems of bend of the rod are considered. It is shown that in the case of statically determinable loadings, the general solution of the problem comes to solving a system of three nonlinear algebraic equations which roots can be obtained with the necessary accuracy using the well-developed methods of computational mathematics. The general solution of the problem for statically indeterminable problems is reduced to obtaining a solution to a system of three nonlinear differential equations for three functions - deformation and curvatures. The Bubnov-Galerkin method is used to approximate the solution of this equation on the segment along the length of the rod, and specific examples of its application to the Maple system of symbolic calculations are considered.

Combined gas electron diffraction and mass spectrometric experimental setup at Bielefeld University

2020 ◽  
Vol 91 (7) ◽  
pp. 073103
Author(s):  
Yury V. Vishnevskiy ◽  
Sebastian Blomeyer ◽  
Christian G. Reuter ◽  
Oleg A. Pimenov ◽  
Sergey A. Shlykov
Keyword(s):  
Electron Diffraction ◽  
Mass Spectrometric ◽  
Gas Electron Diffraction ◽  
Experimental Setup
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