Synthesis, crystal structure, magnetic behavior and thermal property of three polynuclear complexes: [M(dca)(2)(H2O)2](n)center dot(hmt)(n) [M = Mn(II), Co(II)] and [Co(dca)(2)(bpds)](n) [dca, dicyanamide; hint, hexamethylenetetramine; bpds, 4,4 '-bipyridyl disulfide]

Three mu(1.5)-dicyanamide bridged Mn(II) and Co(II) complexes having molecular formula [Mn(dca)(2)(H2O)(2)](n)center dot(hmt)(n) (1), [Co(dca)(2) (H2O)(2)](n)center dot(hmt)(n) (2) and [Co(dca)(2)(bpds)](n) (3) [dca = dicyanamide; hmt = hexamethylenetetramine; bpds = 4,4'-bipyridyl disulfide] have been synthesized and characterized by single crystal X-ray diffraction study, low temperature (300-2 K) magnetic measurement and thermal behavior. The X-ray diffraction analysis of 1 and 2 reveals that they are isostructural, comprising of 1D coordination polymers [M(dca)(2)(H2O)(2)](n) [M = Mn(II), Co(II) for 1 and 2. respectively] with uncoordinated hmt molecules located among the chains. The [M(dca)(2)(H2O)(2)](n) chains and the lattice hint molecules are connected through H-bonds resulting in a 3D supramolecular architecture. The octahedral N4O2 chromophore surrounding the metal ion forms via two trans located water oxygens and four nitrogens from four nitrile dca. Complex 3 is a 1D chain formed by two mu(1.5)-dca and one bridging bpds. The octahedral N-6 coordination sphere surrounding the cobalt ions comprises four nitrogens from dca and two from bpds. Low temperature magnetic study indicates small antiferromagnetic coupling for all the complexes. Best fit parameters for 1: J = -0.17 cm(-1), g = -2.03 with R = 6.1 x 10(-4), for 2, J = -0.50 cm(-1), and for 3, J = -0.95 cm(-1). (c) 2005 Elsevier B.V. All rights reserved.

Synthesis, structure and properties of cobalt(II/III) seleno-bisphenolate complexes containing NN bidentate co-ligands: kinetic studies on the reduction of a cobalt(III) complex by ascorbic acid in 80% MeCN-20% water

Two cobalt complexes, [Co(L-Se)(phen)]center dot CH2Cl2 (1) and [Co(L-Se)(N,N-Me(2)en)(CH3COO-)] (2) have been synthesized and characterized by elemental analyses, magnetic measurements, i.r. studies etc. Single crystal X- ray studies reveal that in complex (1) cobalt atom is in +2 oxidation state with trigonal bipyramidal geometry, while in complex (2) it is in +3 oxidation state and surrounded octahedrally. The asymmetric unit of complex (2) contains two crystallographically independent discrete molecules. Complex (1) was found to be paramagnetic with mu(eff) = 2.19 BM indicating a low spin cobalt(II) d(7) system, whereas complex (2) is found to be diamagnetic with cobalt(III) in low spin d(6) state. The kinetic studies on the reduction of (2) by ascorbic acid in 80% MeCN-20% H2O (v/v) at 25 degrees C reveal that the reaction proceeds through the rapid formation of inner-sphere adduct, probably by replacing the loosely coordinated AcO- group, followed by electron transfer in a slow step and is supported by a large Q (formation constant) value.

(Ni-2), (Ni-3), and (Ni-2 + Ni-3): A Unique Example of Isolated and Cocrystallized Ni-2 and Ni-3 Complexes

Structural and magnetic characterization of compound {[Ni-2(L)(2)(OAC)(2)][Ni-3(L)(2) (OAc)(4)]) center dot 2CH(3)CN (3) (HL = the tridentate Schiff base ligand, 2-[(3-methylaminb-propylimino)-methyl]-phenol) shows that it is a rare example of a crystal incorporating a dinuclear Ni(II) compound, [Ni-2(L)(2)(OAc)(2)], and a trinuclear one, [Ni-3(L)(2)(OAC)(4)]. Even more unusual is the fact that both Ni (II) complexes, [Ni-2(L)(2)(OAc)(2)] (1) and [Ni-3(L)(2)(OAc)(4)(H2O)(2)] center dot CH2Cl2 center dot 2CH(3)OH (2), have also been isolated and structurally and magnetically characterized. The structural analysis reveals that the dimeric complexes [Ni-2(L)(2)(OAc)(2)] in cocrystal 3 and in compound 1 are almost identical-in both complexes, the Ni(II) ions possess a distorted octahedral geometry formed by the chelating tridentate ligand (L), a chelating acetate ion, and a bridging phenoxo group with very similar bond angles and distances. On the other hand, compound 2 and the trinuclear complex in the cocrystal 3 show a similar linear centrosymmetric structure with the tridentate ligand coordinated to the terminal Ni(II) and linked to the central Ni(II) by phenoxo and carboxylate bridges. The only difference is that a water molecule found in 2 is not present in the trinuclear unit of complex 3; instead, the coordination sphere is completed by an additional bridging oxygen atom from an acetate ligand. Variable-temperature (2-300 K) magnetic susceptibility measurements show that the dinuclear unit is antiferromagnetically coupled in both compounds (2J = -36.18 and -29.5 cm(-1) in 1 and 3, respectively), whereas the trinuclear unit shows a very weak ferromagnetic coupling in compound 3 (2J = 0.23 cm(-1)) and a weak antiferromagnetic coupling in 2 (2J = -8.7(2) cm(-1)) due to the minor changes in the coordination sphere.

Synthesis and properties of new trinuclear Mo(II) complexes containing imidazole and benzimidazole ferrocene units

The reaction of FcCOC1 (Fc = (C5H5) Fe(C5H4)) with benzimidazole or imidazole in 1: 1 ratio gives the ferrocenyl derivatives FcCO(benzim) (L1) or FcCO(im) (L2), respectively. Two molecules of L1 or L2 can replace two nitrile ligands in [Mo(eta(3)-C3H5)( CO)(2)(CH3CN)(2)Br] or [Mo(eta(3)-C5H5O)(CO)(2)(CH3CN)(2)Br] leading to the new trinuclear complexes [Mo(eta(3)-C3H5)(CO)(2)(L)(2)Br] (C1 for L = L1; C3 for L = L2) and [Mo(eta(3)-C5H5O)(CO)(2)(L)(2)Br] (C-2 for L = L1; C4 for L = L2) with L1 and L2 acting as N-monodentade ligands. L1, L2 and C2 were characterized by X-ray diffraction studies. [Mo(eta(3)-C5H5O)(CO) 2(L1)(2)Br] was shown to be a trinuclear species, with the two L1 molecules occupying one equatorial and one axial position in the coordination sphere of Mo(II). Cyclic voltammetric studies were performed for the two ligands L1 and L2, as well as for their molybdenum complexes, and kinetic and thermodynamic data for the corresponding redox processes obtained. In agreement with the nature of the frontier orbitals obtained from DFT calculations, L1 and L2 exhibit one oxidation process at the Fe(II) center, while C1, C3, and C4 display another oxidation wave at lower potentials, associated with the oxidation of Mo(II). (C) 2007 Elsevier B. V. All rights reserved.

Anion-templated assembly of pseudorotaxanes: importance of anion template, strength of ion-pair thread association, and macrocycle ring size

A wide range of pseuclorotaxane assemblies containing positively charged pyridinium, pyridinium nicotinamide, imidazolium, benzimidazolium and guanidinium threading components, and macrocyclic isophthalamide polyether ligands have been prepared using a general anion templation procedure. In noncompetitive solvent media, coupling halide anion recognition by a macrocyclic ligand with ion-pairing between the halide anion and a strongly associated cation provides the driving force for interpenetration. Extensive solution H-1 NMR binding studies, thermodynamic investigations, and single-crystal X-ray structure determinations reveal that the nature of the halide anion template, strength of the ion-pairing between the anion template and the cationic threading component, and to a lesser extent favorable second sphere pi-pi aromatic stacking interactions between the positively charged threading component and macrocyclic ligand, together with macrocyclic ring size, affect the efficacy of pseudorotaxane formation.

Trigonal pyramidal (CuN4)-N-I cores assembled by a family of tetradentate N-donor Schiff bases. Substituent effects on the Cu(II/I) potential

Copper(l) complexes of 1:3 condensates of tris(2-aminoethyl)amine and p-X-benzaldehydes (X = K Cl, NMe2 and NO2) of the type [Cu(ligand)]ClO4 are synthesised. The X-ray crystal structures of the copper(l) complexes with X = K, Cl and NMe2 are determined. In these complexes copper(l) is found to have trigonal pyramidal N-4 coordination sphere with the apical N forming a longer bond (2.191-2.202 Angstrom) than the trigonal ones (2.003-2.026 Angstrom). The Cu(II/I) potentials in these complexes span a range of 0.71-0.90 V vs SCE increasing linearly with the resonance component of the Hammett sigma for the para substituent X. It is concluded that trigonal pyramidal geometry is destabilising for copper(II).

The geometry of optimal control solutions on some six dimensional lie groups

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E-3, the spheres S-3 and the hyperboloids H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions are illustrated.

Integrating control systems defined on the frame bundles of the space forms

This paper considers left-invariant control systems defined on the orthonormal frame bundles of simply connected manifolds of constant sectional curvature, namely the space forms Euclidean space E-3, the sphere S-3 and Hyperboloid H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1, 3). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. In the Euclidean case the elements of the Lie algebra se(3) are often referred to as twists. For constant twist motions, the corresponding curves g(t) is an element of SE(3) are known as screw motions, given in closed form by using the well known Rodrigues' formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.

Optimal 3D surface reconstruction from multiview photographic images

This paper describes a new method for reconstructing 3D surface using a small number, e.g. 10, of 2D photographic images. The images are taken at different viewing directions by a perspective camera with full prior knowledge of the camera configurations. The reconstructed object's surface is represented a set of triangular facets. We empirically demonstrate that if the viewing directions are uniformly distributed around the object's viewing sphere, then the reconstructed 3D points optimally cluster closely on a highly curved part of the surface and are widely, spread on smooth or fat parts. The advantage of this property is that the reconstructed points along a surface or a contour generator are not undersampled or underrepresented because surfaces or contours should be sampled or represented with more densely points where their curvatures are high. The more complex the contour's shape, the greater is the number of points required, but the greater the number of points is automatically generated by the proposed method Given that the viewing directions are uniformly distributed, the number and distribution of the reconstructed points depend on the shape or the curvature of the surface regardless of the size of the surface or the size of the object.

Integrating Hamiltonian systems defined on the Lie groups SO(4) and SO(1,3)

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E³, the spheres S³ and the hyperboloids H³ with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions is illustrated.

Oriented vehicles travelling in spherical space

This paper tackles the path planning problem for oriented vehicles travelling in the non-Euclidean 3-Dimensional space; spherical space S3. For such problem, the orientation of the vehicle is naturally represented by orthonormal frame bundle; the rotation group SO(4). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to control systems defined on Lie groups. The oriented vehicles, in this case, are constrained to travel at constant speed in a forward direction and their angular velocities directly controlled. In this paper we identify controls that induce steady motions of these oriented vehicles and yield closed form parametric expressions for these motions. The paths these vehicles trace are defined explicitly in terms of the controls and therefore invariant with respect to the coordinate system used to describe the motion.

Managing groups of files in a rule oriented data management system (iRODS)

The iRODS system, created by the San Diego Supercomputing Centre, is a rule oriented data management system that allows the user to create sets of rules to define how the data is to be managed. Each rule corresponds to a particular action or operation (such as checksumming a file) and the system is flexible enough to allow the user to create new rules for new types of operations. The iRODS system can interface to any storage system (provided an iRODS driver is built for that system) and relies on its’ metadata catalogue to provide a virtual file-system that can handle files of any size and type. However, some storage systems (such as tape systems) do not handle small files efficiently and prefer small files to be packaged up (or “bundled”) into larger units. We have developed a system that can bundle small data files of any type into larger units - mounted collections. The system can create collection families and contains its’ own extensible metadata, including metadata on which family the collection belongs to. The mounted collection system can work standalone and is being incorporated into the iRODS system to enhance the systems flexibility to handle small files. In this paper we describe the motivation for creating a mounted collection system, its’ architecture and how it has been incorporated into the iRODS system. We describe different technologies used to create the mounted collection system and provide some performance numbers.

Singularities of optimal control problems on some 6-D lie groups

This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.

Estimation of distances in virtual environments using size constancy

It is reported in the literature that distances from the observer are underestimated more in virtual environments (VEs) than in physical world conditions. On the other hand estimation of size in VEs is quite accurate and follows a size-constancy law when rich cues are present. This study investigates how estimation of distance in a CAVETM environment is affected by poor and rich cue conditions, subject experience, and environmental learning when the position of the objects is estimated using an experimental paradigm that exploits size constancy. A group of 18 healthy participants was asked to move a virtual sphere controlled using the wand joystick to the position where they thought a previously-displayed virtual cube (stimulus) had appeared. Real-size physical models of the virtual objects were also presented to the participants as a reference of real physical distance during the trials. An accurate estimation of distance implied that the participants assessed the relative size of sphere and cube correctly. The cube appeared at depths between 0.6 m and 3 m, measured along the depth direction of the CAVE. The task was carried out in two environments: a poor cue one with limited background cues, and a rich cue one with textured background surfaces. It was found that distances were underestimated in both poor and rich cue conditions, with greater underestimation in the poor cue environment. The analysis also indicated that factors such as subject experience and environmental learning were not influential. However, least square fitting of Stevens’ power law indicated a high degree of accuracy during the estimation of object locations. This accuracy was higher than in other studies which were not based on a size-estimation paradigm. Thus as indirect result, this study appears to show that accuracy when estimating egocentric distances may be increased using an experimental method that provides information on the relative size of the objects used.

3D surface point and wireframe reconstruction from multiview photographic images

This paper describes a new method for reconstructing 3D surface points and a wireframe on the surface of a freeform object using a small number, e.g. 10, of 2D photographic images. The images are taken at different viewing directions by a perspective camera with full prior knowledge of the camera configurations. The reconstructed surface points are frontier points and the wireframe is a network of contour generators. Both of them are reconstructed by pairing apparent contours in the 2D images. Unlike previous works, we empirically demonstrate that if the viewing directions are uniformly distributed around the object's viewing sphere, then the reconstructed 3D points automatically cluster closely on a highly curved part of the surface and are widely spread on smooth or flat parts. The advantage of this property is that the reconstructed points along a surface or a contour generator are not under-sampled or under-represented because surfaces or contours should be sampled or represented with more densely points where their curvatures are high. The more complex the contour's shape, the greater is the number of points required, but the greater the number of points is automatically generated by the proposed method. Given that the viewing directions are uniformly distributed, the number and distribution of the reconstructed points depend on the shape or the curvature of the surface regardless of the size of the surface or the size of the object. The unique pattern of the reconstructed points and contours may be used in 31) object recognition and measurement without computationally intensive full surface reconstruction. The results are obtained from both computer-generated and real objects. (C) 2007 Elsevier B.V. All rights reserved.