On two-coefficient identification in elliptic variational inequalities

Abstract

This paper is concerned with elliptic variational inequalities that depend on two parameters. First, we investigate the dependence of the solution of the forward problem on these parameters and prove a Lipschitz estimate. Then, we study the inverse problem of identification of these two parameters and formulate two optimization approaches to this parameter identification problem. We extend the output least-squares approach, provide an existence result and establish a convergence result for finite-dimensional approximation. Further, we investigate the modified output least-squares approach which is based on energy functionals. This latter approach can be related to vector approximation.     

On the invariant translation approximation property for discrete groups

Recently J.Roe considered the question of whether for a discrete group the reduced group -algebra is the fixed point algebra of Ad acting on the uniform Roe algebra . is said to have the invariant translation approximation property in this case. We consider a slight generalization of this property which, for exact , is equivalent to the operator space approximation property of . We also give a new characterization of exactness and a short proof of the equivalence of exactness of and exactness of for discrete groups.

     

Singularities of secant maps of immersed surfaces

The secant map of an immersion sends a pair of points to the direction of the line joining the images of the points under the immersion. The germ of the secant map of a generic codimension-c immersion $X\!\!:{\mathbb R}^n \to {\mathbb R}^{n+c}The secant map of an immersion sends a pair of points to the direction of the line joining the images of the points under the immersion. The germ of the secant map of a generic codimension-c immersion X:\mathbb Rⁿ ? \mathbb R^n+cX\!\!:{\mathbb R}^n \to {\mathbb R}^{n+c} at the diagonal in the source is a \mathbb Z₂{\mathbb Z}_2 stable map-germ \mathbb R²ⁿ ? \mathbb R^n+c-1{\mathbb R}^{2n} \to {\mathbb R}^{n+c-1} in the following cases: (i) c≥ 2 and (2n,n + c − 1) is a pair of dimensions for which the \mathbb Z₂{\mathbb Z}_2 stable germs of rank at least n are dense, and (ii) for generically immersed surfaces (i.e., n = 2 and any c≥ 1). In the latter surface case the A^{\mathbb Z₂}{\mathcal A}^{{\mathbb Z}_2}-classification of germs of secant maps at the diagonal is described and it is related to the A{\mathcal A}-classification of certain singular projections of the surfaces.     

Salt-specific stability and denaturation of a short salt-bridge-forming alpha-helix

The structure of a single alanine-based Ace-AEAAAKEAAAKA-Nme peptide in explicit aqueous electrolyte solutions (NaCl, KCl, NaI, and KF) at large salt concentrations (3-4 M) is investigated using approximately 1 mus molecular dynamics (MD) computer simulations. The peptide displays 71% alpha-helical structure without salt and destabilizes with the addition of NaCl in agreement with experiments of a somewhat longer version. It is mainly stabilized by direct and indirect (" i + 4")EK salt bridges between the Lys and Glu side chains and a concomitant backbone shielding mechanism. NaI is found to be a stronger denaturant than NaCl, while the potassium salts hardly show influence. Investigation of the molecular structures reveals that consistent with recent experiments Na (+) has a much stronger affinity to side chain carboxylates and backbone carbonyls than K (+), thereby weakening salt bridges and secondary structure hydrogen bonds. At the same time, the large I (-) has a considerable affinity to the nonpolar alanine in line with recent observations of a large propensity of I (-) to adsorb to simple hydrophobes, and thereby "assists" Na (+) in its destabilizing action. In the denatured states of the peptide, novel long-lived (10-20 ns) "loop" configurations are observed in which single Na (+) ions and water molecules are hydrogen-bonded to multiple backbone carbonyls. In an attempt to analyze the denaturation behavior within the preferential interaction formalism, we find indeed that for the strongest denaturant, NaI, the protein is least hydrated. Additionally, a possible indication for protein denaturation might be a preferential solvation of the peptide backbone by the destabilizing cosolute (sodium). The mechanisms found in this work may be of general importance to understand salt effects on protein secondary structure stability.     

Parahydrogen induced polarization of barbituric acid derivatives: 1H hyperpolarization studies

Homogeneous hydrogenation of barbituric acid derivatives with parahydrogen yields a substantial increase of the (1)H NMR signals of the reaction products. These physiologically relevant compounds were hydrogenated at both ambient and elevated temperatures and pressures using a standard cationic rhodium catalyst. The resulting nonthermal nuclear spin polarization (hyperpolarization) is limited by the spin-lattice relaxation time T(1) of the corresponding nuclei in the products, being shorter than the time constant of the hydrogenation. The signal-to-noise ratio of the NMR spectra could be further increased upon signal averaging the antiphase PHIP signals of 25 successive scans following 30 degrees pulse experiments and a delay of 10 s.     

Formaldehyde Formation on Vanadium Oxide Surfaces V2O3(0001) and V2O5(001): How does the Stable Methoxy Intermediate Form?

Hydroxy‐mediated methoxy formation or stabilization is probably an important process in many methanol adsorption systems. Hydrogen atoms originating from the scission of the methanol O? H bond react with the substrate and form water. This process may result 1) in the production of additional surface defects as reactive centers for methoxy formation and 2) in the stabilization of methoxy groups by suppression of methanol formation.

     

Secondary bonding interactions in biomimetic [2Fe-2S] clusters

A series of synthetic [2Fe-2S] complexes with terminal thiophenolate ligands and tethered ether or thioether moieties has been prepared and investigated in order to provide models for the potential interaction of additional donor atoms with the Fe atoms in biological [2Fe-2S] clusters. X-ray crystal structures have been determined for six new complexes that feature appended Et (1(C)), OMe (1(O)), or SMe (1(S)) groups, or with a methylene group (2(C) ), an ether-O (2(O)), or an thioether-S (2(S)) linking two aryl groups. The latter two systems provide a constrained chelate arrangement that induces secondary bonding interactions with the ether-O and thioether-S, which is confirmed by density functional theory (DFT) calculations that also reveal significant spin density on those fifth donor atoms. Structural consequences of the secondary bonding interactions are analyzed in detail, and effects on the spectroscopic and electronic properties are probed by UV-vis, M?ssbauer, and (1)H NMR spectroscopy, as well by SQUID measurements and cyclic voltammetry. The potential relevance of the findings for biological [2Fe-2S] sites is considered.     

Synthese und Kristallstruktur des Goldclusters [Au16(AsPh3)8Cl6]

Synthesis and Structures of the Gold Cluster [Au₁₆(AsPh₃)₈Cl₆] Reduction of Ph₃AsAuCl with NaBH₄ in ethanol yields the gold cluster [Au₁₆(AsPh₃)₈Cl₆]. It can be crystallized from dichloromethane/diisopropyl ether in form of dark red, light sensitive crystals with the space group P2₁/n and a = 1777.68(8), b = 3372.7(1), c = 2696.2(1)pm, β = 94.166(6)°, Z = 4). The inner skeleton of the 16 Au atoms consists of a centered icosahedron of which one of the corners binds to three additional Au atoms forming a tetrahedron pendent. The shortest Au–Au distances of 264.3 to 266.6 pm correspond to the bonds to the three external Au atoms. Within the icosahedron the distances between the central atom and the peripheral atoms (273.0–279.1 pm) are distinctly shorter than the distances between the peripheral atoms (283.6–299.0 pm).     

Integration of electron density and molecular orbital techniques to reveal questionable bonds: the test case of the direct Fe-Fe bond in Fe2(CO)9

The article illustrates the advantages of partitioning the total electron density rho(rb), its Laplacian (inverted Delta)2 rho(rb), and the energy density H(rb) in terms of orbital components. By calculating the contributions of the mathematically constructed molecular orbitals to the measurable electron density, it is possible to quantify the bonding or antibonding character of each MO. This strategy is exploited to review the controversial existence of direct Fe-Fe bonding in the triply bridged Fe2(CO)9 system. Although the bond is predicted by electron counting rules, the interaction between the two pseudo-octahedral metal centers can be repulsive because of their fully occupied t(2g) sets. Moreover, previous atoms in molecules (AIM) studies failed to show a Fe-Fe bond critical point (bcp). The present electron density orbital partitioning (EDOP) analysis shows that one sigma bonding combination of the t(2g) levels is not totally overcome by the corresponding sigma* MO, which is partially delocalized over the bridging carbonyls. This suggests the existence of some, albeit weak, direct Fe-Fe bonding.