Dynamic coefficient estimation using variational and least-squares techniques

2002 ◽  
Author(s):  
F. Driscoll ◽  
R.G. Lueck
Keyword(s):  
Least Squares ◽  
Dynamic Coefficient ◽  
Coefficient Estimation ◽  
Least Squares Techniques

A Bounded Variation Approach to Inverse Interferometry

1995 ◽  
Author(s):  
B. G. Fitzpatrick ◽  
S. L. Keeling ◽  
S. G. Rock
Keyword(s):  
Least Squares ◽  
Flow Measurement ◽  
Optical Methods ◽  
Optical Data ◽  
Reconstruction Technique ◽  
Direct Inversion ◽  
Variation Approach ◽  
Mathematical Techniques ◽  
Traditional Approaches ◽  
Least Squares Techniques

Abstract A least squares reconstruction technique is examined for determining flow-field densities from optical data. Nonintrusive optical methods have long been used for flow visualization; however, the goal of this work is to devise mathematical techniques with which optical data can be used for quantitative flow measurement. The ill-posedness of density computation from interferogram measurements is recognized as a serious limitation in direct inversion methods. Here, least squares techniques employing compactness constraints are developed to avoid the difficulties encountered in traditional approaches.

scholarly journals The Chemistry of Heteroarylphosphorus Compounds, Part 16.+ An X-Ray Structural Study of (2-Thienyl)bis(2,2′-biphenylylene)phosphorane. A Comparison with Related Methyl and Aryl bis(2,2′-biphenylylene)- spirophosphoranes

1983 ◽  
Vol 38 (4) ◽  
pp. 465-469 ◽  
Author(s):  
David W. Allen ◽  
Lorraine A. March ◽  
Ian W. Nowell ◽  
John C. Tebby
Keyword(s):  
Least Squares ◽  
Electron Density ◽  
Structural Study ◽  
Equatorial Plane ◽  
Title Compound ◽  
X Ray ◽  
Trigonal Bipyramidal ◽  
Thienyl Group ◽  
Density Methods ◽  
Least Squares Techniques

AbstractCrystals of the title compound are monoclinic, a= 18.9 93 (11), b = 8.757(5), c= 13.267(8) Å, β = 106.60(5)°, Z = 4 in space group Cc (Cs4 , No. 9). The structure was determined by Patterson and electron-density methods and refined by least squares techniques to R= 0.081, R′ = 0.085 for 1293 independent reflections classified as observed. The molecule is found to adopt an almost regular trigonal bipyramidal geometry in which the two biphenylylene units span apical-equatorial positions and the 2-thienyl group occupies the remaining equatorial site. The 2-thienyl group, which is disordered, does not lie in the equatorial plane, and there is no indication of C2pπ → P3dπ-t interactions between the heteroaryl group and phosphorus. The steric requirements of the 2-thienyl group appear to be comparable with those of methyl and phenyl groups in bis(2,2′-biphenylylene)spiro-phosphoranes.

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