Cis-trans isomeric and polymorphic effects on the magnetic properties of water-bridged copper coordination chains

The synthesis and magnetic characterization of vanillin-based Cu(II) mononuclear complexes of formula [Cu(van)(2)(H(2)O)(2)](H(2)O)(x) (van = vanillinate; x = 0, compound 1; x = 2, compounds 2 and 3) were performed. Despite the presence of very similar [Cu(van)(2)(H(2)O)(2)] moieties, the crystal structures exhibit distinct Cu···Cu contacts and display three different through-H-bond exchange-coupling pathways. As a result of the relative positions of the water molecules, the experimental (MAGSUS) exchange-coupling constants are dissimilar, i.e., J(1) = -3.0 cm(-1) (the data have been fitted to the Bleaney-Bowers equation considering a dimer; 2J = -6.0 cm(-1)), J(2) = -4.0 cm(-1) (the data have been fitted to the Bonner-Fischer equation for a chain of monomeric copper(II) units), whereas compound 3 is paramagnetic. Subsequently, the theoretical density functional theory (DFT) and wave function theory-based (DDCI) calculations were carried out to better understand the role of the water molecule as a mediator of the magnetic coupling. The use of localized orbitals allows one to elucidate the role of the H-bonds in generating exchange interactions. Since the exchange-coupling constants are strongly dependent on the mechanisms selectively introduced, the role of the H-bond is demonstrated.     

On the Existence and Uniqueness of a Solution to the Interior Transmission Problem for Piecewise-Homogeneous Solids

The interior transmission problem (ITP), which plays a fundamental role in inverse scattering theories involving penetrable defects, is investigated within the framework of mechanical waves scattered by piecewise-homogeneous, elastic or viscoelastic obstacles in a likewise heterogeneous background solid. For generality, the obstacle is allowed to be multiply connected, having both penetrable components (inclusions) and impenetrable parts (cavities). A variational formulation is employed to establish sufficient conditions for the existence and uniqueness of a solution to the ITP, provided that the excitation frequency does not belong to (at most) countable spectrum of transmission eigenvalues. The featured sufficient conditions, expressed in terms of the mass density and elasticity parameters of the problem, represent an advancement over earlier works on the subject in that (i) they pose a precise, previously unavailable provision for the well-posedness of the ITP in situations when both the obstacle and the background solid are heterogeneous, and (ii) they are dimensionally consistent, i.e., invariant under the choice of physical units. For the case of a viscoelastic scatterer in an elastic solid it is further shown, consistent with earlier studies in acoustics, electromagnetism, and elasticity that the uniqueness of a solution to the ITP is maintained irrespective of the vibration frequency. When applied to the situation where both the scatterer and the background medium are viscoelastic, i.e., dissipative, on the other hand, the same type of analysis shows that the analogous claim of uniqueness does not hold. Physically, such anomalous behavior of the “viscoelastic-viscoelastic” case (that has eluded previous studies) has its origins in a lesser known fact that the homogeneous ITP is not mechanically insulated from its surroundings—a feature that is particularly cloaked in situations when either the background medium or the scatterer are dissipative. A set of numerical results, computed for ITP configurations that meet the sufficient conditions for the existence of a solution, is included to illustrate the problem. Consistent with the preceding analysis, the results indicate that the set of transmission values is indeed empty in the “elastic-viscoelastic” case, and countable for “elastic-elastic” and “viscoelastic-viscoelastic” configurations.     

Reconstruction of viscoelastic tissue properties from MR elastography-type measurements

This study is concerned with an optimization-based approach to the identification of “background” viscoelastic properties of soft tissues from magnetic resonance (MR) elastography-type measurements. In this approach, the triaxial tissue displacements, captured by the MR scanner over a suitable subdomain that is free of major heterogeneities, are split into (i) a boundary subset that is used to formulate the forward (Dirichlet) problem, and (ii) an internal subset, employed as “the data” for the inverse (material characterization) problem. For an elevated performance of the minimization scheme, material sensitivities of the featured cost functional are computed semi-analytically via a boundary-integral formulation, resulting in alternative “direct” and adjoint-field sensitivity formulas. The numerical results, obtained assuming input parameters that are relevant to MR elastography, indicate that the proposed approach may provide an effective means for comprehensive multi-frequency characterization of the “background” viscoelasticity of soft tissues.     

Overcoming the boundary effects in surface spline interpolation

Surface spline interpolation when the domain is all of R^d isknown to converge much faster to the data function f than inthe case when the domain is the unit ball. This difference isunderstood to be due to boundary effects which, as will be shown,also affect the size of the surface spline's coefficients. Wepropose a modified form of surface spline interpolation which,to a great extent, overcomes these boundary effects. This modifiedsurface spline interpolant uses only the values of f at thegiven interpolation points.     

Vibrational Spectra of Magnesium Hydrogenphosphate Trihydrate and of its Manganese Analogue

Abstract

The infrared (IR) and Raman spectra of MgHPO₄. 3H₂O and of a series of partially deuterated analogues as well as the IR spectra of MnHPO₄. 3H₂O have been recorded and interpreted. The analysis of the IR spectra in the HOD bending region rules out the possibility of existence of H₃OC⁺ ions in the structure.     

<Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript>-minimization methods for Hamilton–Jacobi equations: the one-dimensional case

A new approximation technique based on L ¹-minimization is introduced. It is proven that the approximate solution converges to the viscosity solution in the case of one-dimensional stationary Hamilton–Jacobi equation with convex Hamiltonian. This material is based upon work supported by the National Science Foundation grant DMS-0510650. J.-L. Guermond is on leave from LIMSI, UPRR 3251 CNRS, BP 133, 91403 Orsay Cedex, France.     

Branched coverings

Basic results on combinatorial branched coverings between relative geometric cycles are given. It is shown that every geometricn-cycle is a branched covering overS. If the downstairs space of a branched covering is locally simply connected then the branched set is a pure subcomplex of codimension 2. Finally, several Hurwitz-like theorems on existence and representation of branched coverings between relative geometric cycles are derived.This work was supported in part by the Research Council of Slovenia, Yugoslavia.     

Square-planar copper(II) complexes with a novel tetradentate amido-carboxylate ligand. Crystal structure of [Co(H2O)6][Cu(mda)] · 2H2O

A novel O—N—N—O-type tetradentate ligand H₄mda (H₄mda = malamido-N,N-diacetic acid) and the corresponding square-planar copper(II) complexes have been prepared and characterized. The mda^4– ligand coordinates to the copper(II) ion via two pairs of deprotonated ligating atoms (two carboxylate oxygens and two deprotonated amide nitrogens) with in-plane square chelation. A four-coordinate, square-planar geometry has been established crystallographically for the [Co(H₂O)₆][Cu(mda)] · 2H₂O complex. Structural data correlating the square-planar geometry of the [Cu(mda)]^2– unit are discussed in relation to information obtained for similar complexes. The i.r., electronic, absorption and reflectance spectra of the complexes are analysed in comparison with related complexes of known geometries.     

Phosphorescent excited state of [Au2[(Ph2Sb)2O]3]2+: Jahn-Teller distortion at only one gold(I) center

Dinuclear three-coordinate Au(I) complex [Au2{(Ph2Sb)2O}3](ClO4)2 1 displays an interesting phosphorescent behavior in which a large Stokes' shift is observed. Ab initio calculations show that the main distortion for the first triplet excited state, which is responsible for the luminescence behavior of complex 1, is a Jahn-Teller distortion for only one of the Au(I) centers together with a gold-gold distance shortening. This behavior could be extrapolated to other phosphorescent dinuclear three-coordinate Au(I) complexes.