Symmetry of generalized mean-square vibration amplitudes and their effect on mean and equilibrium bond lengths in benzene, pyridine, and N-oxypyridine

1998 ◽  
Vol 65 (2) ◽  
pp. 196-200 ◽  
Author(s):  
K. V. Berezin ◽  
É. K. Kosterina
Keyword(s):  
Mean Square ◽  
Bond Lengths ◽  
Generalized Mean

Inference Based on α-Cut and Generalized Mean with Fuzzy Tautological Rules

2010 ◽  
Vol 14 (1) ◽  
pp. 76-88 ◽  
Author(s):  
Kiyohiko Uehara ◽  
◽  
Takumi Koyama ◽  
Kaoru Hirota ◽  
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Systems ◽  
Fuzzy Rules ◽  
Mean Square ◽  
Basic Properties ◽  
Generalized Mean ◽  
Conventional Methods ◽  
The Difference ◽  
Mean Square Errors

Theoretical aspects are provided for inference based on α-cuts and generalized mean (α-GEMII). In order to clarify the basic properties of the inference, fuzzy tautological rules (FTRs) are focused on, which are composed by setting fuzzy sets in consequent parts identical to those in antecedent parts of initially given fuzzy rules. It is mathematically proved that the consequences deduced with FTRs are closer to given facts as the number of FTRs increases. The aspects provided in this paper are appropriate from axiomatic viewpoints and can contribute to interpretability in fuzzy systems constructed with α-GEMII. They are not obtained in conventional methods based on the compositional rule of inference. Simulations are performed by evaluating difference (mean square errors) between given facts and deduced consequences under the condition that convex and symmetric fuzzy sets are given as facts. Their results show that the difference becomes smaller as the number of FTRs increases. Thereby, it is confirmed that α-GEMII has an advantage in the interpretability with respect to FTRs over the conventional methods.

Generalized mean-square amplitudes of vibration in some XY4 type ions

1969 ◽  
Vol 9 (7) ◽  
pp. 1033-1034
Author(s):  
Nitish K. Sanyal ◽  
A.N. Pandey ◽  
H.S. Singh
Keyword(s):  
Mean Square ◽  
Generalized Mean

A refinement of the crystal structures of K2ReCl6, K2ReBr6, and K2PtBr6

1970 ◽  
Vol 48 (7) ◽  
pp. 1151-1154 ◽  
Author(s):  
H. D. Grundy ◽  
I. D. Brown
Keyword(s):  
Single Crystal ◽  
Crystal Structures ◽  
Root Mean Square ◽  
Mean Square ◽  
X Ray ◽  
Bond Lengths ◽  
Using Data

The crystal structures of K2ReCl6, K2ReBr6, and K2PtBr6 have been refined using data collected on a single-crystal X-ray diffractometer to give weighted agreement indices ranging from 0.026 to 0.054 for 75 to 90 nonequivalent reflections. The following bond lengths were obtained: Re—Cl = 235 pm, Re—Br = 248 pm, Pt—Br = 246 pm, K—Cl = 348 pm, and K—Br = 367 and 364 pm in the Re and Pt compounds, respectively. The differences in the root-mean-square angles of libration of the MX62− ions in these and a number of isomorphous crystals are discussed.

Adaptive equalization algorithms for optimization of a generalized mean square cost

1981 ◽  
Vol 24 (1) ◽  
pp. 23-42
Author(s):  
Antonio Cantoni ◽  
Robin Evans ◽  
Ken Kwong
Keyword(s):  
Adaptive Equalization ◽  
Mean Square ◽  
Generalized Mean

Détermination des constantes de force et des amplitudes moyennes de vibration du sous-sulfure de carbone, C3S2

1968 ◽  
Vol 46 (16) ◽  
pp. 2641-2643 ◽  
Author(s):  
Alpha O. Diallo
Keyword(s):  
Vibrational Frequencies ◽  
Force Constants ◽  
Mean Square ◽  
Mean Amplitudes Of Vibration ◽  
Symmetrical Structure ◽  
Symmetry Coordinates ◽  
Shrinkage Effect ◽  
The Mean ◽  
Generalized Mean

The theory of the generalized mean amplitudes of vibration has been applied to the C3S2 molecule, which possesses a linear symmetrical structure. The numerical values of the force constants and the mean square parallel and perpendicular amplitudes at 298°K of all bonded and non-bonded pairs of atoms are calculated from spectroscopic vibrational frequencies by the Cyvin and Morino–Hirota methods, utilizing the symmetry coordinates. The "shrinkage" effect constants are also evaluated by means of the perpendicular mean square amplitudes.

scholarly journals Generalized Mean-Square Amplitudes of Vibration, Mean Amplitudes of Vibration, and Shrinkage Effects of Some Trigonal Bipyramidal XY5 and XY3Z2 Molecules.

1967 ◽  
Vol 21 ◽  
pp. 473-480 ◽  
Author(s):  
Jon Brunvoll ◽  
Peder Kierkegaard ◽  
Johan Santesson ◽  
Pär Holmberg ◽  
G. Eriksson ◽  
...  
Keyword(s):  
Mean Square ◽  
Mean Amplitudes Of Vibration ◽  
Trigonal Bipyramidal ◽  
Generalized Mean
Sign in / Sign up

Export Citation Format

Share Document