3D Object Recognition: Symmetry and Virtual Views

Many 3D objects in the world around us are strongly constrained. For instance, not only cultural artifacts but also many natural objects are bilaterally symmetric. Thoretical arguments suggest and psychophysical experiments confirm that humans may be better in the recognition of symmetric objects. The hypothesis of symmetry-induced virtual views together with a network model that successfully accounts for human recognition of generic 3D objects leads to predictions that we have verified with psychophysical experiments.

Notations and conventions in molecular spectroscopy: part 2. Symmetry notation

The field of Molecular Spectroscopy was surveyed in order to determine a set of conventions and symbols which are in common use in the spectroscopic literature. This document, which is Part 2 in a series, establishes the notations and conventions used for the description of symmetry in rigid molecules, using the Schoenflies notation. It deals firstly with the symmetry operators of the molecular point groups (also drawing attention to the difference between symmetry operators and elements). The conventions and notations of the molecular point groups are then established, followed by those of the representations of these groups as used in molecular spectroscopy. Further parts will follow, dealing inter alia with permutation and permutation-inversion symmetry notation, vibration-rotation spectroscopy and electronic spectroscopy.

Notations and conventions in molecular spectroscopy: part 3. Permutation and permutation-inversion symmetry notation

The field of Molecular Spectroscopy was surveyed in order to determine a set of conventions and symbols which are in common use in the spectroscopic literature. This document, which is Part 3 in a series, deals with symmetry notation referring to groups that involve nuclear permutations and the inversion operation. Further parts will follow, dealing inter alia with vibration-rotation spectroscopy and electronic spectroscopy.

Testing symmetry and homogeneity in the almost ideal demand system with co-integrated data using fully modified estimation and the bootstrap

Conventional seemingly unrelated estimation of the almost ideal demand system is shown to lead to small sample bias and distortions in the size of a Wald test for symmetry and homogeneity when the data are co-integrated. A fully modified estimator is developed in an attempt to remedy these problems. It is shown that this estimator reduces the small sample bias but fails to eliminate the size distortion.. Bootstrapping is shown to be ineffective as a method of removing small sample bias in both the conventional and fully modified estimators. Bootstrapping is effective, however, as a method of removing. size distortion and performs equally well in this respect with both estimators.

Synthesis and crystal structure of the thiophene-3-acetonitrile complex fac-[Mo(CO)(3){NCCH2(C4H3S-3)}(3)]

Reaction of fac-[ Mo( CO)(3)( NCMe)(3)] with three equivalents of NCCH2(C4H3S- 3) in acetonitrile gives the tris(thiophene- 3- acetonitrile) complex, fac-[Mo(CO)(3){NCCH2(C4H3S-3)}(3)] (1) in 7% yield. Complex 1 crystallizes out in the orthorhombic space group Pnma with a = 12.714( 17), b = 16.41( 2), c = 11.304(16) Angstrom, Z = 4. The structure has crystallographic m symmetry and the metal is in an almost perfect octahedral environment, with a facial arrangement of carbonyl and thiophene- 3- acetonitrile groups. The thiophene rings are disordered.

Dinuclear complexes of M-II thiocyanate (M = Ni and Cu) containing a tridentate Schiff-base ligand: synthesis, structural diversity and magnetic properties

A dinuclear Ni-II complex, [Ni-2(L)(2)(H2O)(NCS)(2)]center dot 3H(2)O (1) in which the metal atoms are bridged by one water molecule and two mu(2)-phenolate ions, and a thiocyanato-bridged dimeric Cull complex, [Cu(L)NCS](2) (2) [L = tridentate Schiff-base ligand, N-(3-aminopropyl)salicylaldimine, derived from 1:1 condensation of salicylaldehyde and 1,3-diaminopropane], have been synthesized and characterized by IR and UV/Vis spectroscopy, cyclic voltammetry and single-crystal X-ray diffraction studies. The structure of 1 consists of dinuclear units with crystallographic C-2 symmetry in which each Ni-II atom is in a distorted octahedral environment. The Ni-O distance and the Ni-O-Ni angle, through the bridged water molecule, are 2.240(11) angstrom and 82.5(5)degrees, respectively. The structure of 2 consists of dinuclear units bridged asymmetrically by di-mu(1,3)-NCS ions; each Cull ion is in a square-pyramidal environment with tau = 0.25. Variable-temperature magnetic susceptibility studies indicate the presence of dominant ferromagnetic exchange coupling in complex 1 with J = 3.1 cm(-1), whereas complex 2 exhibits weak antiferromagnetic coupling between the Cu-II centers with J = -1.7 cm(-1). ((c) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2005)

Topotactic oxidation of TiGaPO-1, a pyridine-templated titanium gallophosphate with a new octahedral-tetrahedral 3-D framework structure containing Ti-III/Ti-IV

The first 3-D open-framework TiGaPO complex, constructed from (TiO6)-O-III, (TiO6)-O-IV, GaO4, and PO4 polyhedra, contains pyridinium cations in a 1-D pore network and can be oxidized in air at 543 K with retention of the original framework structure.

Dicopper(II) trihydroxide cyanoureate dihydrate

The title compound, poly[[mu-cyanoureato-tri-mu-hydroxidodicopper(II)] dihydrate], {[Cu-2(C2H2N3O)(OH)(3)]center dot 2H(2)O}(n), is a new layered copper(II) hydroxide salt (LHS) with cyanoureate ions and water molecules in the interlayer space. The three distinct copper(II) ions have distorted octahedral geometry: one Cu (symmetry (1) over bar) is coordinated to six hydroxide groups (4OH + 2OH), whilst the other two Cu atoms (symmetries (1) over bar and 1) are coordinated to four hydroxides and two N atoms from nitrile groups of the cyanoureate ions (4OH + 2N). The structure is held together by hydrogen-bonding interactions between the terminal-NH2 groups and the central cyanamide N atoms of organic anions associated with neighbouring layers.

Synthesis, crystal structure and reactivity of copper(II) complexes of tetradentate N2S2 donor ligands

Two new hexa-coordinated mononuclear copper(II) complexes of two ligands L-1 and L-2 containing NSSN donor sets formulated as [Cu(L)(H2O)(2)](NO3)(2) [1a, L = 1,2-bis(2-pyridylmethylthio)ethane (L-1), 1b L = 1,3-bis(2-pyridyl-methylthio)propane (L-2)] were synthesized and characterized by physico-chemical and spectroscopic methods. In 1a the single crystal X-ray crystallography analysis showed a distorted octahedral geometry about copper(II) ion. The crystal packing evidences pairs of complexes arranged about a center of symmetry and connected through a H-bond occurring between aquo ligands and nitrate anions. On reaction with chloride and pseudohalides (N-3(-) and SCN-), in acetonitrile at ambient temperature. complexes 1 changed to monocationic penta-coordinated mononuclear copper(H) species formulated as [Cu(L)(Cl)]NO3 (2), [Cu(L)(N-3)]NO3 (3). and [Cu(L)(SCN)]NO3 (4). These copper(II) complexes have been isolated in pure form from the reaction mixtures and characterized by physico-chemical and spectroscopic tools. The solid-state structure of 2a, established by X-ray crystallography, shows a trigonal bipyramidal geometry about the metal ion with a trigonality index (tau) of 0.561. (C) 2009 Elsevier B.V. All rights reserved.