Theoretical prediction of linear free energy relationships using proton nucleomers

Values of σ and σ⁺, for use in linear free energy relationships, are determined for para hydrogen atoms having nuclear charges other than 1 (nucleomers). Hammett ρ values for a variety of free energies of activation, reaction, and other extrathermodynamic properties (e.g., vibrational frequencies) are computed therefrom and compared to those computed using typical para functional groups. The nucleomer correlations show excellent qualitative agreement with standard correlations but the quantitative agreement is less good, typically underestimating the standard ρ‐value by 10–60%. Copyright © 2007 John Wiley & Sons, Ltd.     

Self-assembly of water cluster in iron(III) oxalate-bridged complexes

The synthesis and crystal structural characterization of the compound of formula {[Fe^II(phen)₃]₂[Fe₂^IIIox₅]}·11H₂O (1) has been reported. The most interesting feature of the solid state structure of 1 consists in the occurrence of decanuclear water clusters made up of self-assembled cyclic hexameric water clusters with a quasi-planar conformation, unclosed trinuclear clusters and individual water molecules. The decanuclear water clusters are connected to the host lattices via an extensive net of strong hydrogen bonds that finally lead to an extended 3D supramolecular organization, wherein hexameric water clusters interconnected with dodecameric hybrid water–O_oxalate clusters can be identified. The comparison of this supramolecular architecture with that found in the already known compound of formula [Fe(bpm)₃]₂[Fe₂(ox)₅]·8H₂O (2) allows some preliminary observations on the design and control of water cluster nuclearity and conformation.     

A comparison between the absorption properties of the regular and F<Subscript><Emphasis Type="Italic">s</Emphasis></Subscript>-defected MgO (100) surface

The electron density, the electrostatic potential and the electric field of the MgO (100) surface, both regular and containing an oxygen vacancy (F _s center), are compared in order to understand the modifications induced in the surface-absorbate interaction by the presence of the defect, with particular attention to the metal-oxide case. The spin-density for a gold atom absorbing on the most characteristic sites of the regular and F _s -defected surface is also shown. It is found that in the defected surface the electron pair in the vacancy protrudes appreciably out of the surface, thus shifting the electrostatic potential to negative values (but producing a similar electric field) and being able to chemically interact with neighboring absorbed species. These results rationalize the rotational invariance and double frustration effects previously described for the metal/F _s -defected MgO (100) surface.     

Inexact constraint preconditioners for linear systems arising in interior point methods

Issues of indefinite preconditioning of reduced Newton systems arising in optimization with interior point methods are addressed in this paper. Constraint preconditioners have shown much promise in this context. However, there are situations in which an unfavorable sparsity pattern of Jacobian matrix may adversely affect the preconditioner and make its inverse representation unacceptably dense hence too expensive to be used in practice. A remedy to such situations is proposed in this paper. An approximate constraint preconditioner is considered in which sparse approximation of the Jacobian is used instead of the complete matrix. Spectral analysis of the preconditioned matrix is performed and bounds on its non-unit eigenvalues are provided. Preliminary computational results are encouraging.     

The q-Deformed Knizhnik–Zamolodchikov–Bernard Heat Equation

We introduce a q-deformation of the genus one sl ₂ Knizhnik–Zamolodchikov–Bernard heat equation. We show that this equation for the dependence on the moduli of elliptic curves is compatible with the qKZB equations, which give the dependence on the marked points. Received: 4 October 2000 / Accepted: 25 March 2001     

New Coumarin Dipicolinate Europium Complexes with a Rich Chemical Speciation and Tunable Luminescence

Europium (III) luminescent chelates possess intrinsic photophysical properties that are extremely useful in a wide range of applications. The lack of examples of coumarin-based lanthanide complexes is mainly due to poor photo-sensitization attempts. However, with the appeal of using such a versatile scaffold as antenna, especially in the development of responsive molecular probes, it is worth the effort to research new structural motifs. In this work, we present a series of two new tris coumarin-dipicolinate europium (III) complexes, specifically tailored to be either a mono or a dual emitter, tuning their properties with a simple chemical modification. We also encountered a rich chemical speciation in solution, studied in detail by means of paramagnetic NMR and emission spectroscopy.     

A systematic approach to reduced GLT

BIT Numerical Mathematics - This paper concerns the spectral analysis of matrix-sequences that are generated by the discretization and numerical approximation of partial differential equations, in...     

Algebraic Boundaries Among Typical Ranks for Real Binary Forms of Arbitrary Degree

Foundations of Computational Mathematics - We show that the algebraic boundaries of the regions of real binary forms with fixed typical rank are always unions of dual varieties to suitable...     

Riemann‐Hilbert problem and matrix discrete Painlevé II systems

Matrix Szeg? biorthogonal polynomials for quasi‐definite matrices of Hölder continuous weights are studied. A Riemann‐Hilbert problem is uniquely solved in terms of the matrix Szeg? polynomials and its Cauchy transforms. The Riemann‐Hilbert problem is given as an appropriate framework for the discussion of the Szeg? matrix and the associated Szeg? recursion relations for the matrix orthogonal polynomials and its Cauchy transforms. Pearson‐type differential systems characterizing the matrix of weights are studied. These are linear systems of ordinary differential equations that are required to have trivial monodromy. Linear ordinary differential equations for the matrix Szeg? polynomials and its Cauchy transforms are derived. It is shown how these Pearson systems lead to nonlinear difference equations for the Verblunsky matrices and two examples, of Fuchsian and non‐Fuchsian type, are considered. For both cases, a new matrix version of the discrete Painlevé II equation for the Verblunsky matrices is found. Reductions of these matrix discrete Painlevé II systems presenting locality are discussed.