Structural Diversity Within the Series of 68-Electron M4L n E2 (L = 2-Electron Ligand; M = Fe, Ru, Os, Co; E = CH, N, P, NR, PR, S) Organometallic Clusters: A Theoretical Investigation

Four different skeletal structural arrangements with very different connectivities are known for 6-vertex/68-electron of M₄E₂ core (M = transition metal; E = main-group atom or ligand). DFT calculations on a large number of title model compounds allow to rationalize the preferences between these structural shapes with respect to the nature of the metal and main-group elements constituting the cluster cage. In particular, the electronegativity of M and the “size” (first-row vs. second-row element) of E play an important role in the stability preference of a particular isomer. For several compounds, although only one type of structure is known, other low-energy isomeric forms are also likely to exist. Moreover, two structural types, so far unreported, are predicted to be stable enough for being synthesized.     

Kraichnan Flow in a Square: An Example of Integrable Chaos

The Kraichnan flow provides an example of a random dynamical system accessible to an exact analysis. We study the evolution of the infinitesimal separation between two Lagrangian trajectories of the flow. Its long-time asymptotics is reflected in the large deviation regime of the statistics of stretching exponents. Whereas in the flow that is isotropic at small scales the distribution of such multiplicative large deviations is Gaussian, this does not have to be the case in the presence of an anisotropy. We analyze in detail the flow in a two-dimensional periodic square where the anisotropy generally persists at small scales. The calculation of the large deviation rate function of the stretching exponents reduces in this case to the study of the ground state energy of an integrable periodic Schrödinger operator of the Lamé type. The underlying integrability permits to explicitly exhibit the non-Gaussianity of the multiplicative large deviations and to analyze the time-scales at which the large deviation regime sets in. In particular, we indicate how the divergence of some of those time scales when the two Lyapunov exponents become close allows a discontinuity of the large deviation rate function in the parameters of the flow. The analysis of the two-dimensional anisotropic flow permits to identify the general scenario for the appearance of multiplicative large deviations together with the restrictions on its applicability.     

A Tabu Search with Slope Scaling for the Multicommodity Capacitated Location Problem with Balancing Requirements

In this paper, a tabu search heuristic is combined with slope scaling to solve a discrete depot location problem, known as the multicommodity location problem with balancing requirements. Although the uncapacitated version of this problem has already been addressed in the literature, this is not the case for the more challenging capacitated version, where each depot has a fixed and finite capacity. The slope scaling approach is used during the initialization phase to provide the tabu search with good starting solutions. Numerical results are reported on various types of large-scale randomly generated instances. The quality of the heuristic is assessed by comparing the solutions obtained with those of a commercial mixed-integer programming code.     

Torsion de groupes munis d'une donnée radicielle

We consider groups endowed with root data associated with non-necessarily finite root systems. We generalise to these groups the twisting methods of Chevalley groups initiated by Steinberg and Ree. The resulting theorem (proved in 1988) can be applied to Kac–Moody groups: see for instance two papers published by J. Ramagge in 1995 [J. Ramagge, On certain fixed point subgroups of affine Kac–Moody groups, J. Algebra 171 (2) (1995) 473–514; J. Ramagge, A realization of certain affine Kac–Moody groups of types II and III, J. Algebra 171 (3) (1995) 713–806].     

Bonding Analysis of Square-Antiprismatic and Fused Square-Antiprismatic Copper(I)-Selenium Clusters

The electronic structure of the Cu_2(4n+2)Se_4n+2(PH₃)₈ (n = 1–4) D _4h series of model clusters has been analyzed by means of density functional theory calculations. The fused square antiprismatic structure of the metal framework is found to be always preferred over the fused cuboctahedral one because it reinforces the Cu-P bonds. Thus, the presence of the terminal phosphine ligands tends to strengthen the Cu...Cu (d¹⁰...d¹⁰) bonding by mixing bonding combinations of the vacant Cu 4s and 4p orbitals into the occupied 3d combinations. The calculations indicate that the compounds corresponding to n = 3 and 4 should be easily two-electron-reduced, leading to stable dianionic species.     

Schmidt rearrangement of 1,2,3,5,10,10a-hexahydropyrrolo[1,2-b]-isoquinoline-3,10-diones

The Schmidt rearrangement of 1,2,3,5,10,10a-hexahydropyrrolo[1,2-b]isoquinoline-3,10-diones has been studied. The structure of the lactams obtained has been determined by chemical reactivity and characterized by means of ir, ¹H and ¹³C nmr spectroscopy.     

New cobalt(II) coordination polymer based on carboxyphenyl-tpy ligand: Photoluminescence,crystal structures and magnetic properties,without orbital contribution

One coordination polymer, [Co(3-ctpy)₂(H₂O)₂]_n*2nEtOH (1), was synthesized by a solvothermal method mixing the complex precursor cobalt(II) acetylacetonate (Co(acac)₂*2H₂O) with 4′-(4-carboxyphenyl)-3,2′:6′,3″-terpyridine (3-Hctpy). This paramagnetic complex has been isolated as a neutral, air and thermal stable solid and has been characterized by elemental analysis, FT-IR and single-crystal X-ray diffraction analysis. The thermal stability and photoluminescence properties were studied in the solid state. The magnetic behavior presents an interesting challenge since the Co(II) ion has a spin 3/2, which leads to multiple possibilities under the influence of an energy crystal field, from the identification of the ground state to possible transitions to excited states. The usual orbital contribution of the magnetic moment has been extinguished, due to an axially distorted octahedral environment for cobalt, changing the O_h symmetry (with ⁴T_1g ground state) to D_4h (with ⁴A_2g ground state). This decrease in symmetry is responsible for the quenching of the orbital contribution, as will be discussed in this article.     

Hecke algebras at roots of unity and crystal bases of quantum affine algebras

We present a fast algorithm for computing the global crystal basis of the basic -module. This algorithm is based on combinatorial techniques which have been developed for dealing with modular representations of symmetric groups, and more generally with representations of Hecke algebras of typeA at roots of unity. We conjecture that, upon specializationq1, our algorithm computes the decomposition matrices of all Hecke algebras at an ^th root of 1.Partially supported by PRC Math-Info and EEC grant n⁰ ERBCHRXCT930400.     

An Integrated Framework for Generating and Revising Factory Schedules

Practical solutions to the production scheduling problem must provide two broad capabilities:

1. i)
   an ability to efficiently generate schedules that reflect the actual constraints and objectives of the manufacturing environment, and
    
2. ii)
   an ability to incrementally revise these schedules over time in response to unexpected executional circumstances. In this paper, we advocate a common view of predictive and reactive scheduling as an incremental problem solving process that is opportunistically focused by characteristics of the current solution constraints.
    

We describe the architecture of OPIS (opportunistic intelligent scheduler), which defines a general framework for configuring scheduling systems according to this view. We then examine the scheduling knowledge (e.g. analysis and scheduling methods, schedule generation or revision strategies) that is exploited within this architecture by the current OPIS scheduler. Experimental studies with the OPIS scheduler have demonstrated the potential of this constraint-directed scheduling methodology in both predictive and reactive scheduling contexts.