Comparisons between model equations for long waves

Summary Considered here are model equations for weakly nonlinear and dispersive long waves, which feature general forms of dispersion and pure power nonlinearity. Two variants of such equations are introduced, one of Korteweg-de Vries type and one of regularized long-wave type. It is proven that solutions of the pure initial-value problem for these two types of model equations are the same, to within the order of accuracy attributable to either, on the long time scale during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles.This research was supported in part by the National Science Foundation. A considerable portion of the project was completed while the first author was resident at the Institute for Mathematics and Its Applications, University of Minnesota.     

Some remarks on Zienkiewicz-Zhu estimator

In this article, Zienkiewicz-Zhu estimator is analyzed for the piecewise linear finite element approximate solution of an elliptic problem. The estimator is proved to be equivalent to the error for the Poisson equation with a homogeneous Dirichlet boundary condition for any triangular regular mesh. No assumptions are needed about the regularity of the solution (i.e., solutions with corner singularities are not excluded). The estimator is also proved to be asymptotically exact on subdomains where the solution is smooth when parallel meshes are used. Therefore, its behavior is similar to that of other well-known estimators. © 1994 John Wiley & Sons, Inc.     

The extended loop group: An infinite dimensional manifold associated with the loop space

A set of coordinates in the non-parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of these objects is proposed. The enlarged group behaves locally as an infinite dimensional Lie group. Ordinary loops form a subgroup of this group. The algebraic properties of this new mathematical structure are analyzed in detail. Applications of the formalism to field theory, quantum gravity and knot theory are considered.     

Ab-initio molecular dynamics based on non-local density functional procedure with Gaussian basis; study of structural and temperature behaviour of metallic clusters

An ab-initio molecular dynamics procedure without precalculation of the Born-Oppenheimer energy surface based on an iterative non-local density functional method employing Gaussian atomic basis has been developed. Analytical gradients are calculated and used for the propagation of nuclei. Sufficiently long trajectories can be calculated at an acceptable computational cost, allowing for analysis of dynamical behaviour of small metallic clusters. This is illustrated on an example of the Li₈ cluster. Temperature behaviour of different type of isomers has been investigated. Calculated power spectra allow to identify the presence of more than one isomeric forms along the given trajectories.     

Synthesis of 2-(p-R-benzoylmethylene)-3-(p-R-phenyl)-1H-quinoxalines

The reaction of 1,2-diaminobenzenes with substituted 1,2-dibenzoyl-1,2-dibromoethanes constitutes a convenient synthetic route to the hitherto 2-(p-R-benzoylmethylene)-3-(p-R-phenyl)-1H-quinoxalines. Structures of all products were elucidated by ir, ¹H and ¹³C-nmr, mass spectra data. X-Ray crystallography data confirm assigned structures.     

Physicochemical and structural properties of bacteriostatic sulfonamides: Theoretical study

A theoretical study at the Hartree–Fock and density functional theory levels is performed on sulfonamide‐type bacteriostatic compounds with the aim to provide an insight into their structure–activity relationship. The basicity of the p‐amino group is analyzed by means of the proton affinities and the protonation energies, showing that molecules presenting bacteriostatic activity are less basic, i.e., they are characterized by larger protonation energies and smaller proton affinities. The acidity of the amide group is analyzed through the deprotonation energy. The results reveal that the more acidic molecules present a larger bacteriostatic activity. This result is also confirmed from a study of bond orders. A bond order analysis of the amide group suggests that the electron attracting group in these molecules is responsible for the increase in acidity. The charge of the SO₂ group is also shown to be affected by the presence of the electron attracting group and consequently related to the acidity of the molecules. A geometric analysis shows that structures in which the amino group is more coplanar with respect to the benzenic ring possess larger bacteriostatic activity. A conformational analysis of these molecules illustrates that active molecules have relatively larger torsion energy barriers. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 165–172, 2003     

Computational studies of Cu(II)/Met and Cu(I)/Met binding motifs relevant for the chemistry of Alzheimer's disease

A systematic study of the binding motifs of Cu(II) and Cu(I) to a methionine model peptide, namely, N-formylmethioninamide 1, has been carried out by quantum chemical computations. Geometries of the coordination modes obtained at the B3LYP/6-31G(d) level of theory are discussed in the context of copper coordination by the peptide backbone and the S atom of a methionine residue in peptides with special emphasis on Met35 of the amyloid-beta peptide (Abeta) of Alzheimer's disease. The relative binding free energies in the gas phase, DeltaG(g), are calculated at the B3LYP/6-311+G(2df,2p)//B3LYP/6-31G(d) level of theory, and the solvation affects are included by means of the COSMO model to obtain the relative binding energies in solution, DeltaG(aq). A free energy of binding, DeltaG(aq) = -19.4 kJ mol(-1), relative to aqueous Cu(II) and the free peptide is found for the most stable Cu(II)/Met complex, 12. The most stable Cu(I)/Met complex, 23, is bound by -15.6 kJ mol(-1) relative to the separated species. The reduction potential relative to the standard hydrogen electrode is estimated to be E degrees (12/23) = 0.41 V. On the basis of these results, the participation of Met35 as a low affinity binding site of Cu(II) in Abeta, and its role in the redox chemistry underlying Alzheimer's disease is discussed.     

Preparation and crystal structure of a copper(II) uranyl(VI) binuclear chelate

Summary The structure of the heterobinuclear complex of Cu²⁺ and [UO₂]²⁺ with the tetraanionic ligand derived from the condensation of 1,2-diaminoethane witho-acetoacetylphenol has been determined from diffractometer data and refined to R = 5.2%. The crystals are monoclinic,P2₁/a, witha = 26.22(2),b = 14.79(2),c = 8.10(1) Å and = 104.65(5)°; Z = 4. The ligand employed has two different coordination sets of atoms, N₂O₂ and O₂O₂, two oxygen atoms being common to both donor sets. In the complex the copper atom, which is retained in the inner N₂O₂ chamber, is five coordinate being axially bonded to a solvent molecule, whilst the uranyl ion is incorporated in the outer O₂O₂ chamber. Another molecule of solvent is retained to preserve the preferred seven coordination of uranium.     

Solute-solute-solvent interactions in dilute aqueous solutions of aliphatic diols. Excess enthalpies and gibbs free energies

The heats of dilution and the osmotic coefficients for some aliphatic diols (1,3-propanediol; 1,2-butanediol; 1,3-butanediol; 1,4-butanediol; 2,3-butanediol; 1,5-pentanediol; 1,6-hexanediol) in water at 25°C are reported. The experimental free energy and enthalpy pairwise interaction coefficients were evaluated and are discussed in terms of the hydrophobic-hydrophilic properties of the solutes. The effect of the mutual position of the polar hydrophilic groups in the molecule on the experimental interaction coefficients transposed to the McMillan-Mayer (MM) state is emphasized. The Sawage-Wood additivity of groups (SWAG) approach has been used and critically discussed.Paper presented at J.C.A.T. '86-Ferrara 27–30 Ottobre 1986.     

Model studies on the ring construction of the auriside macrolactone

The preparation of a 12-membered ring macrolactone model of auriside that contains a pendant diene chain bearing a bromide was investigated employing two approaches. The first approach utilized an oxidative rearrangement of a tertiary allylic alcohol on a 12-membered ring. The second approach was based on a 1,4-methylation of an ynone followed by macrolactonization.