Factor Groups, Permutation Representations, Finite Point Groups

AbstractIn this paper, a stabilized numerical method with high accuracy is proposed to solve time-fractional singularly perturbed convection-diffusion equation with variable coefficients. The tailored finite point method (TFPM) is adopted to discrete equation in the spatial direction, while the time direction is discreted by the G-L approximation and the L1 approximation. It can effectively eliminate non-physical oscillation or excessive numerical dispersion caused by convection dominant. The stability of the scheme is verified by theoretical analysis. Finally, one-dimensional and two-dimensional numerical examples are presented to verify the efficiency of the method.

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Darstellung, Schwingungsspektren und Normalkoordinatenanalyse von Chloro-Bromo-Rhodaten(III) / Preparation, Vibration Spectra and Normal Coordinate Analysis of Chloro-Bromo-Rhodates(III)

Zeitschrift für Naturforschung B ◽

10.1515/znb-1989-1014 ◽

1989 ◽

Vol 44 (10) ◽

pp. 1221-1227 ◽

Cited By ~ 7

Author(s):

W. Preetz ◽

W. Kuhr

Keyword(s):

Exchange Chromatography ◽

Trans Isomers ◽

Normal Coordinate ◽

Valence Force ◽

Trans Influence ◽

Diethylaminoethyl Cellulose ◽

Point Groups ◽

First Time ◽

Ir And Raman ◽

Good Agreement

The mixed chloro-bromo-rhodates(III) [RhClnBr6-n]3-, n = 1-5, have been separated for the first time by ion exchange chromatography on diethylaminoethyl-cellulose. Due to the stronger trans-effect of Br, as compared with Cl, on treatment of [RhBr6]3- with conc. HCl nearly pure cis/fac-isomers for n = 2, 3, 4 are formed. The reaction of [RhCl6]3- with conc. HBr yields mixtures of the cis/trans-isomers for n = 2, 4, which cannot be separated, but mer-[RhCl3Br3]3 is formed stereospecifically. The IR and Raman spectra of all isolated mixed ligand complexes are completely assigned according to point groups Oh, D3d, C4v, C3v and C2v, supported by normal coordinate analyses based on a general valence force field. The good agreement of calculated and observed frequencies confirms the assignments. Due to the stronger trans-influence of Br as compared to Cl, in all asymmetric Cl—Rh—Br axes the Rh—Br bonds are strengthened and the Rh—Cl bonds are weakened, indicated by valence force constants for Rh—Br approximately 14% higher, for Rh—Cl 10% lower, as compared with the values calculated for symmetric Br—Rh—Br and Cl—Rh—Cl axes, respectively.

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