scholarly journals A least-squares minimization procedure to attain optimum spatial fit between homologous (molecular) structures and its application to studying protein structural homology.

1981 ◽  
Vol 29 (10) ◽  
pp. 2737-2742 ◽  
Author(s):  
YUKIHIDE URATA ◽  
YUKIO MITSUI ◽  
KAZUO NAKAMURA
Keyword(s):  
Least Squares ◽  
Molecular Structures ◽  
Structural Homology ◽  
Minimization Procedure ◽  
Least Squares Minimization

Studies in aryltin chemistry. Part 6. Crystal and molecular structures of tetra(p-methylsulphonylphenyl)tin(IV) and tetra(p-methylsulphinylphenyl)tin(IV) monohydrate

1990 ◽  
Vol 68 (8) ◽  
pp. 1277-1282 ◽  
Author(s):  
Ivor Wharf ◽  
Michel G. Simard ◽  
Henry Lamparski
Keyword(s):  
Least Squares ◽  
Crystal Structures ◽  
Direct Method ◽  
Molecular Structures ◽  
Water Molecules ◽  
Monoclinic Space Group ◽  
Molecular Symmetry ◽  
Asymmetric Unit ◽  
Full Matrix ◽  
Space Group

Tetrakis(p-methylsulphonylphenyl)tin(IV) and tetrakis(p-methylsulphinylphenyl)tin(IV) n-hydrate have been prepared and their spectra (ir 1350–400 cm−1; nmr, 1H, 13C, 119Sn) and X-ray crystal structures are reported. The first compound is monoclinic, space group C2/c, Z = 4, with a = 21.589(6), b = 6.207(3), c = 22.861(11) Å, β = 93.80(3)° (22 °C); the structure was solved by the direct method and refined by full-matrix least squares calculations to R = 0.043 for 2755 observed reflections. It has 2 molecular symmetry with the methyl group and one oxygen atom completely disordered in both CH3S(O2) groups in the asymmetric unit. The second compound is tetragonal, space group P42/n, Z = 2, with a = b = 15.408(6), c = 6.379(2) Å (−100 °C); the structure was solved by the Patterson method and refined by full-matrix least squares calculations to R = 0.060 for 1209 observed reflections. It has [Formula: see text] molecular symmetry with the whole asymmetric unit disordered. Water molecules occupy positions on parallel 42 axes but molecular packing requirements prevent all sites having 100% occupancy giving n ~ 1 for the hydrate. Keywords: Tetra-aryltins, crystal structures, sulphone, sulphoxide, hydrogen-bonding.

scholarly journals Solvability classes for core problems in matrix total least squares minimization

2019 ◽  
Vol 64 (2) ◽  
pp. 103-128 ◽  
Author(s):  
Iveta Hnětynková ◽  
Martin Plešinger ◽  
Jana Žáková
Keyword(s):  
Least Squares ◽  
Total Least Squares ◽  
Least Squares Minimization

A new least-squares minimization approach to depth and shape determination from magnetic data

2007 ◽  
Vol 55 (3) ◽  
pp. 433-446 ◽  
Author(s):  
El-Sayed M. Abdelrahman ◽  
Eid. R. Abo-Ezz ◽  
Khalid S. Essa ◽  
T.M. El-Araby ◽  
Khaled S. Soliman
Keyword(s):  
Least Squares ◽  
Magnetic Data ◽  
Shape Determination ◽  
Minimization Approach ◽  
Least Squares Minimization

scholarly journals Analysis of the hydrogen-rich magnetic White Dwarfs in the SDSS

2008 ◽  
Vol 4 (S259) ◽  
pp. 379-380
Author(s):  
Baybars Külebi ◽  
Stefan Jordan ◽  
Fabian Euchner ◽  
Heiko Hirsch
Keyword(s):  
Magnetic Field ◽  
Least Squares ◽  
White Dwarfs ◽  
Optical Spectra ◽  
Digital Survey ◽  
Least Squares Minimization ◽  
Minimization Scheme ◽  
Field Strengths

AbstractWe have calculated optical spectra of hydrogen-rich (DA) white dwarfs with magnetic field strengths between 1 MG and 1000 MG for temperatures between 7000 K and 50000 K. Through a least-squares minimization scheme, we have analyzed the spectra of 114 magnetic DAs from the Sloan Digital Survey (SDSS; 95 previously published plus 14 newly discovered within SDSS).

Dinuclear cobalt(II) complexes of a polyhydroimidazole ligand. Dinuclear (2:1) non-metallocyclic derivatives and dinuclear (1:1) metallocyclic complexes with a large, unoccupied central cavity

1992 ◽  
Vol 70 (11) ◽  
pp. 2771-2776 ◽  
Author(s):  
Santokh S. Tandon ◽  
Laurence K. Thompson ◽  
John N. Bridson ◽  
John C. Dewan
Keyword(s):  
Least Squares ◽  
Bidentate Ligand ◽  
Unit Cell ◽  
Molecular Structures ◽  
Central Cavity ◽  
Monoclinic System ◽  
Full Matrix ◽  
Space Group ◽  
Cell Refinement ◽  
Compound Ii

The ligand BTIM (1,2,4,5-tetrakis(4,5-dihydro-imidazol-2-yl)benzene) reacts with cobalt(II) salts to form two series of complexes. The 1:1, dinuclear, metallocyclic derivatives [Co2(BTIM)2X2]X2 (X = Cl (I), Br (II)) involve two bis-dentate ligands in a metallocyclic structure with a large unoccupied cavity. The 2:1, binuclear derivatives [Co2(BTIM)X4] (X = Cl (III), Br (IV)) involve two metals bound to a single, bis-bidentate ligand. The crystal and molecular structures of II and III are reported. Compound II crystallized in the monoclinic system, space group P21/c, with a = 13.642(6) Å, b = 11.560(3) Å, c = 18.406(7) Å, β = 101.73(3)° and four formula units per unit cell. Refinement by full-matrix least squares gave final residuals of R = 0.060 and Rw = 0.062. Compound III crystallized in the triclinic system, space group [Formula: see text], with a = 8.367(2) Å, b = 14.254(3) Å, c = 7.649(2) Å, α = 100.99(2)°, β = 101.44(2)°, γ = 106.85(1)° and one formula per unit cell. Refinement by full-matrix least squares gave final residuals of R = 0.052 and Rw = 0.045. In the metallocyclic structure (II) the square-pyramidal cobalt(II) centres are separated by 7.599(4) Å, while in the 2:1 derivative the two tetrahedral cobalt(II) centres have a much larger separation (8.736(3) Å).

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