Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

We study the elliptic sine-Gordon equation in the quarter plane using a spectral transform approach. We determine the Riemann-Hilbert problem associated with well-posed boundary value problems in this domain and use it to derive a formal representation of the solution. Our analysis is based on a generalization of the usual inverse scattering transform recently introduced by Fokas for studying linear elliptic problems.

Influence of adsorption geometry in the heterogeneous enantioselective catalytic hydrogenation of a prototypical enone

Asymmetric catalysis is of paramount importance in organic synthesis and, in current practice, is achieved by means of homogeneous catalysts. The ability to catalyze such reactions heterogeneously would have a major impact both in the research laboratory and in the production of fine chemicals and pharmaceuticals, yet heterogeneous asymmetric hydrogenation of C═C bonds remains hardly explored. Very recently, we demonstrated how chiral ligands that anchor robustly to the surface of Pd nanoparticles promote asymmetric catalytic hydrogenation: ligand rigidity and stereochemistry emerged as key factors. Here, we address a complementary question: how does the enone reactant adsorb on the metal surface, and what implications does this have for the enantiodifferentiating interaction with the surface-tethered chiral modifiers? A reaction model is proposed, which correctly predicts the identity of the enantiomer experimentally observed in excess.

Forward modelling to determine the observational signatures of white-light imaging and interplanetary scintillation for the propagation of an interplanetary shock in the ecliptic plane

Recent coordinated observations of interplanetary scintillation (IPS) from the EISCAT, MERLIN, and STELab, and stereoscopic white-light imaging from the two heliospheric imagers (HIs) onboard the twin STEREO spacecraft are significant to continuously track the propagation and evolution of solar eruptions throughout interplanetary space. In order to obtain a better understanding of the observational signatures in these two remote-sensing techniques, the magnetohydrodynamics of the macro-scale interplanetary disturbance and the radio-wave scattering of the micro-scale electron-density fluctuation are coupled and investigated using a newly constructed multi-scale numerical model. This model is then applied to a case of an interplanetary shock propagation within the ecliptic plane. The shock could be nearly invisible to an HI, once entering the Thomson-scattering sphere of the HI. The asymmetry in the optical images between the western and eastern HIs suggests the shock propagation off the Sun–Earth line. Meanwhile, an IPS signal, strongly dependent on the local electron density, is insensitive to the density cavity far downstream of the shock front. When this cavity (or the shock nose) is cut through by an IPS ray-path, a single speed component at the flank (or the nose) of the shock can be recorded; when an IPS ray-path penetrates the sheath between the shock nose and this cavity, two speed components at the sheath and flank can be detected. Moreover, once a shock front touches an IPS ray-path, the derived position and speed at the irregularity source of this IPS signal, together with an assumption of a radial and constant propagation of the shock, can be used to estimate the later appearance of the shock front in the elongation of the HI field of view. The results of synthetic measurements from forward modelling are helpful in inferring the in-situ properties of coronal mass ejection from real observational data via an inverse approach.

Copper complexes of new benzodioxotetraaza macrocycles with potential applications in nuclear medicine

Two novel benzodioxotetraaza macrocycles [2,9-dioxo-1,4,7,10-tetraazabicyclo[10.4.0]1,11-hexadeca-1(11),13,15-triene (H(2)L1) and 2,10-dioxo-1,4,8,11-tetraazabicyclo[11.4.0]1,12-heptadeca-1(12),14,16-triene (H(2)L2)] were synthesized by a [1 + 1] crablike cyclization. The protonation constants of both ligands were determined by H-1 NMR titration and by potentiometry at 25.0 degrees C in 0.10 M ionic strength in KNO3. The latter method was also used to ascertain the stability constants of their copper(II) complexes. These studies showed that the CuL1 complex has a much lower thermodynamic stability than the CuL2, and the H(2)L2 displays an excellent affinity for copper(II), due to the good fit of copper(II) into its cavity. The copper complexes of the novel ligands were characterized by electronic spectroscopy in solution and by crystal X-ray diffraction. These studies indicated that the copper center in the CuL1 complex adopts a square-pyramidal geometry with the four nitrogen atoms of the macrocycle forming the equatorial plane and a water molecule at axial position, and the copper in the CuL2 complex is square-planar. Several labeling conditions were tested, and only H(2)L2 could be labeled with Cu-67 efficiently (> 98%) in mild conditions (39 degrees C, 15 min) to provide a slightly hydrophilic radioligand (log D = -0.19 +/- 0.03 at pH 7.4). The in vitro stability was studied in the presence of different buffers or with an excess of diethylenetriamine-pentaethanoic acid. Very high stability was shown under these conditions for over 5 days. The incubation of the radiocopper complex in human serum showed 6% protein binding.

A case of four-coordinate silver(I) adopting a high energy planar geometry. Experiment and theory

The ligands PhL and MeL are obtained by condensing 2-formylpyridine with benzil dihydrazone and diacetyl dihydrazone, respectively, in 2: 1 molar proportion. With silver( I), PhL yields a double-stranded dinuclear cationic helicate 1 in which the metal is tetrahedral but MeL gives a cationic one-dimensional polymeric complex 2 where silver( I) is distorted square planar and the ligand backbone is nearly planar. In both complexes, metal: ligand ratio is 1: 1. Ab initio calculations on the ligands at the HF/6-31+G* level reveal that while PhL strongly prefers a helical conformation, MeL has a natural inclination to remain in a planar conformation. Density functional theory calculations on model silver( I) complexes show that formation of the linear polymer in the case of MeL is also an important factor in imposing the planar geometry of Ag(I) in 2.

Bis- and tris-(methylphosphonic) acid derivatives of a 14-membered tetraazamacrocycle containing pyridine: synthesis, protonation and complexation studies

Two N-methylphosphonic acid derivatives of a 14-membered tetraazamacrocycle containing pyridine have been synthesized, H4L1 and H6L2. The protonation constants of these compounds and the stability constants of complexes of both ligands with Ni2+, Cu2+ and Zn2+ were determined by potentiometric methods at 298 K and ionic strength 0.10 mol dm(-3) in NMe4NO3. The high overall basicity of both compounds is ascribed to the presence of the phosphonate arms. H-1 and P-31 NMR spectroscopic titrations were performed to elucidate the sequence of protonation, which were complemented by conformational analysis studies. The complexes of these ligands have stability constants of the order of or higher than those formed with ligands having the same macrocyclic backbone but acetate arms. At pH = 7 the highest pM values were found for solutions containing the compound with three acetate groups, followed immediately by those of H6L2, however, as expected, the increasing pH favours the complexes of ligands containing phosphonate groups. The single-crystal structure of Na-2[Cu(HL1)]NO3.8H(2)O has shown that the coordination geometry around the copper atom is a distorted square pyramid. Three nitrogen atoms of the macrocyclic backbone and one oxygen atom from one methylphosphonate arm define the basal plane, and the apical coordination is accomplished via the nitrogen atom trans to the pyridine ring of the macrocycle. To achieve this geometric arrangement, the macrocycle adopts a folded conformation. This structure seems consistent with Uv-vis-NIR spectroscopy for the Ni2+ and the Cu2+ complexes and with the EPR for the latter.

Surface geometry of Cu{531}

We present a combined quantitative low-energy electron diffraction (LEED) and density-functional theory (DFT) study of the chiral Cu{531} surface. The surface shows large inward relaxations with respect to the bulk interlayer distance of the first two layers and a large expansion of the distance between the fourth and fifth layers. (The latter is the first layer having the same coordination as the Cu atoms in the bulk.) Additional calculations have been performed to study the likelihood of faceting by comparing surface energies of possible facet terminations. No overall significant reduction in energy with respect to planar {531} could be found for any of the tested combinations of facets, which is in agreement with the experimental findings.

A new porous 2D coordination polymer built by copper(II) and trimesic acid

A 2D porous material, Cu-3(tmen)(3)(tma)(2)(H2O)(2)(.)6.5H(2)O [tmen = N,N,N',N'-tetramethylethane-1,2-diamine; tmaH(3) = 1,3,5-benzenetricarboxylic acid/trimesic acid], has been synthesized and characterized by X-ray single crystal analysis, variable temperature magnetic measurements, IR spectra and XRPD pattern. The complex consists of 2D layers built by three crystallographically independent Cu(tmen) moieties bridged by tma anions. Of the three copper ions, Cu(1) and Cu(2) present distorted square pyramidal coordination geometry, while the third exhibits a severely distorted octahedral environment. The Cu(1)(tmen) and Cu(2)(tmen) building blocks bridged by tma anions give rise to chains with a zig-zag motif, which are cross-connected by Cu(3)(tmen)-tma polymers sharing metal ions Cu(2) through pendant tma carboxylates. The resulting 2D architecture extends in the crystallographic ab-plane. The adjacent sheets are embedded through the Cu(3)(tmen) tma chains, leaving H2O-filled channels. There are 6.5 lattice water molecules per formula unit, some of which are disordered. Upon heating, the lattice water molecules get eliminated without destroying the crystal morphology and the compound rehydrated reversibly on exposure to humid atmosphere. Magnetic data of the complex have been fitted considering isolated irregular Cu-3 triangles (three different J parameters) by applying the CLUMAG program. The best fit indicates three close comparable J parameters and very weak antiferromagnetic interactions are operative between the metal centers. (C) 2004 Elsevier B.V. All rights reserved.

The adsorption geometry of sulphur on Ir{100}: a quantitative LEED study

A quantitative low energy electron diffraction (LEED) analysis has been performed for the p(2 x 2)-S and c(2 x 2)-S surface structures formed by exposing the (1 x 1) phase of Ir{100} to H2S at 750 K. S is found to adsorb on the fourfold hollow sites in both structures leading to Pendry R-factor values of 0.17 for the p(2 x 2)-S and 0.16 for the c(2 x 2)-S structures. The distances between S and the nearest and next-nearest Ir atoms were found to be similar in both structures: 2.36 +/- 0.01 angstrom and 3.33 +/- 0.01 angstrom, respectively. The buckling in the second substrate layer is consistent with other structural studies for S adsorption on fcc{100} transition metal surfaces: 0.09 angstrom for p(2 x 2)-S and 0.02 angstrom for c(2 x 2)-S structures. The (1 x 5) reconstruction, which is the most stable phase for clean Ir{100}, is completely lifted and a c(2 x 2)-S overlayer is formed after exposure to H,S at 300 K followed by annealing to 520 K. CO temperature-programmed desorption (TPD) experiments indicate that the major factor in the poisoning of Ir by S is site blocking. (c) 2005 Elsevier B.V. All rights reserved.

New dioxadiaza- and trioxadiaza-macrocycles containing one dibenzofuran unit with two amino pendant arms: synthesis, protonation and complexation studies

New dioxadiaza- and trioxadiaza-macrocycles containing one rigid dibenzofuran unit (DBF) and N-(2-aminoethyl) pendant arms were synthesized, N,N'-bis(2-aminoethyl)-[17]( DBF) N2O2 (L-1) and N,N'-bis(2-aminoethyl)-[22](DBF)N2O3 (L-2), respectively. The binding properties of both macrocycles to metal ions and structural studies of their metal complexes were carried out. The protonation constants of both compounds and the stability constants of their complexes with Co2+, Ni2+, Cu2+, Zn2+, Cd2+, and Pb2+ were determined at 298.2 K, in aqueous solutions, and at ionic strength 0.10 mol dm(-3) in KNO3. Mononuclear complexes with both ligands were formed, and dinuclear complexes were only found for L-2. The thermodynamic binding affinities of the metal complexes of L-2 are lower than those of L-1 as expected, but the Pb2+ complexes of both macrocycles exhibit close stability constant values. On the other hand, the binding affinities of Cd2+ and Pb2+ for L-1 are very high, when compared to those of Co2+, Ni2+ and Zn2+. These interesting properties were explained by the presence of the rigid DBF moiety in the backbone of the macrocycle and to the special match between the macrocyclic cavity size and the studied larger metal ions. To elucidate the adopted structures of complexes in solution, the nickel(II) and copper( II) complexes with both ligands were further studied by UV-vis-MR spectroscopy in DMSO-H2O 1 : 1 (v/v) solution. The copper(II) complexes were also studied by EPR spectroscopy in the same mixture of solvents. The crystal structure of the copper complex of L-1 was also determined. The copper(II) displays an octahedral geometry, the four nitrogen atoms forming the equatorial plane and two oxygen atoms, one from the DBF unit and the other one from the ether oxygen, in axial positions. One of the ether oxygens of the macrocycle is out of the coordination sphere. Our results led us to suggest that this geometry is also adopted by the Co2+ to Zn2+ complexes, and only the larger Cd2+ and Pb2+ manage to form complexes with the involvement of all the oxygen atoms of the macrocyclic backbone.

Facile strategies for the synthesis and crystallization of linear trinuclear nickel(II)-Schiff base, complexes with carboxylate bridges: Tuning of coordination geometry and magnetic properties

Three new linear trinuclear nickel(II) complexes, [Ni-3(salpen)(2)(OAc)(2)(H2O)(2)]center dot 4H(2)O (1) (OAc = acetate, CH3COO-), [Ni-3(salpen)(2)(OBz)(2)] (2) (OBz=benzoate, PhCOO-) and [Ni-3(salpen)(2)(OCn)(2)(CH3CN)(2)] (4) (OCn = cinnamate, PhCH=CHCOO-), H(2)salpen = tetradentate ligand, N,N'-bis(salicylidene)-1,3-pentanediamine have been synthesized and characterized structurally and magnetically. The choice of solvent for growing single crystal was made by inspecting the morphology of the initially obtained solids with the help of SEM study. The magnetic properties of a closely related complex, [Ni-3(salpen)(2)(OPh)(2)(EtOH)] (3) (OPh = phenyl acetate, PhCH2COO-) whose structure and solution properties have been reported recently, has also been studied here. The structural analyses reveal that both phenoxo and carboxylate bridging are present in all the complexes and the three Ni(II) atoms remain in linear disposition. Although the Schiff base ligand and the syn-syn bridging bidentate mode of the carboxylate group remain the same in complexes 1-4, the change of alkyl/aryl group of the carboxylates brings about systematic variations between six- and five-coordination in the geometry of the terminal Ni(II) centres of the trinuclear units. The steric demand as well as hydrophobic nature of the alkyl/aryl group of the carboxylate is found to play a crucial role in the tuning of the geometry. Variable-temperature (2-300 K) magnetic susceptibility measurements show that complexes 1-4 are antiferromagnetically coupled (J = -3.2(1), -4.6(1). -3.2(1) and -2.8(1) cm(-1) in 1-4, respectively). Calculations of the zero-field splitting parameter indicate that the values of D for complexes 1-4 are in the high range (D = +9.1(2), +14.2(2), +9.8(2) and +8.6(1) cm(-1) for 1-4, respectively). The highest D value of +14.2(2) and +9.8(2) cm(-1) for complexes 2 and 3, respectively, are consistent with the pentacoordinated geometry of the two terminal nickel(II) ions in 2 and one terminal nickel(II) ion in 3. (C) 2009 Elsevier Ltd. All rights reserved.

Trinuclear cu(ll) complexes containing peripheral ketonic oxygen bridges and a mu(3)-OH core: Syntheses, crystal structures, spectroscopic and magnetic properties

Four new trinuclear copper(II) complexes, [(CuL1)(3)(mu(3)-OH)](ClO4)(2)center dot H2O (1), [(CuL2)(3)(mu(3)-OH)](CIO4)(2) (2), [(CuL3)(3)-(mu(3)-OH)](ClO4)(4)center dot H2O (3), and [(CuL4)(3)(mu(3)-OH)](ClO4)(2)center dot H2O (4), where HL1 = 8-amino-4,7,7-trimethyl-5-azaoct-3-en-2-one, HL2 = 7-amino-4-methyl-5-azaoct-3-en-2-one, HL3 = 7(ethylamino)-4-methyl-5-azahept-3-en-2-one, and HL4 = 4-methyl-7-(methylamino)-5-azahept-3-en-2-one, have been derived from the four tridentate Schiff bases (HL1, HL2, HL3, and HL4) and structurally characterized by X-ray crystallography. For all compounds, the cationic part is trinuclear with a CU3OH core held by three carbonyl oxygen bridges between each pair of copper(II) atoms. The copper atoms are five-coordinate with a distorted square-pyramidal geometry; the equatorial plane consists of the bridging oxygen atom of the central OH group together with three atoms (N, N, O) from one ligand whereas an oxygen atom of a second ligand occupies the axial position. Magnetic measurements have been performed in the 2-300 K temperature range. The experimental data could be satisfactorily reproduced by using an isotropic exchange model, H = -J(S1S2+S2S3+S1S3) yielding as best-fit parameters: J = -66.7 and g = 2.19 for 1, J = -36.6 and g = 2.20 for 2, J = -24.5 and g = 2.20 for 3, and J = -14.9 and g = 2.05 for 4. EPR spectra at low temperature show the existence of spin frustration in complexes 3 and 4, but it has not been possible to carry out calculations of the antisymmetric exchange parameter, G, from magnetic data. In frozen methanolic solution, at 4 K, hyperfine splitting in all complexes and spin frustration in complex 4 seem to be confirmed. ((c) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2005)

Disparity with respect to a local reference plane as a dominant cue for stereoscopic depth relief

Earlier studies showed that the disparity with respect to other visible points could not explain stereoacuity performance, nor could various spatial derivatives of disparity [Glennerster, A., McKee, S. P., & Birch, M. D. (2002). Evidence of surface-based processing of binocular disparity. Current Biology, 12:825-828; Petrov, Y., & Glennerster, A. (2004). The role of the local reference in stereoscopic detection of depth relief. Vision Research, 44:367-376.] Two possible cues remain: (i) local changes in disparity gradient or (ii) disparity with respect to an interpolated line drawn through the reference points. Here, we aimed to distinguish between these two cues. Subjects judged.. in a two AFC paradigm, whether a target dot was in front of a plane defined by three reference dots or, in other experiments, in front of a line defined by two reference dots. We tested different slants of the reference line or plane and different locations of the target relative to the reference points. For slanted reference lines or plane, stereoacuity changed little as the target position was varied. For judgments relative to a frontoparallel reference line, stereoacuity did vary with target position, but less than would be predicted by disparity gradient change. This provides evidence that disparity with respect to the reference plane is an important cue. We discuss the potential advantages of this measure in generating a representation of surface relief that is invariant to viewpoint transformations. (c) 2006 Elsevier Ltd. All rights reserved.

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.