ITERATIVE ILU PRECONDITIONERS FOR LINEAR SYSTEMS AND EIGENPROBLEMS

Iterative ILU factorizations are constructed,analyzed and applied as preconditioners to solve both linear systems and eigenproblems.The computational kernels of these novel Iterative ILU factorizations are sparse matrix-matrix multiplications,which are easy and efficient to implement on both serial and parallel computer architectures and can take full advantage of existing matrix-matrix multiplication codes.We also introduce level-based and threshold-based algorithms in order to enhance the accuracy of the proposed Iterative ILU factorizations.The results of several numerical experiments illustrate the efficiency of the proposed preconditioners to solve both linear systems and eigenvalue problems.     

Synthesis of α-CF3 azanorbornene and azetidines by aza Diels–Alder or iodine-mediated cyclizations: application in ROMP and ligand design

We report the synthesis of several new α-trifluoromethylated nitrogen heterocycles, among which azanorbornene and azetidine derivatives, by aza Diels–Alder or iodine-mediated cyclizations. These building blocks were used as starting materials for the formation of fluorinated polymers by ROMP or for ligand design through substitution and click reactions.     

Alignment Properties of Some Polymeric Layers

Orientational properties of rubbed thin polymer layers with vinylic backbone and different side groups are presented. Some of these polymers lead to the alignment of LC molecules parallel to the rubbing direction whereas other polymers impose a perpendicular orientation. The stability of the obtained alignment as function of the temperature was tested.     

A theoretical study of saturated sp nitrogen rings

Ab initio calculations on molecular structures composed of hexagonal rings of sp³-hybridated nitrogen atoms (the external nitrogen atoms being saturated with hydrogens) are presented. All the studied systems are local minima on the potential energy surface, and dissociate producing nitrogen dimer and ammonia in different proportions. A periodic Hartree–Fock study of the infinite layer is also presented, and it is shown that the molecular structural parameters quickly converge towards the infinite-system values. Accordingly to the computed dissociation energies, these systems have a very high energy content.     

Polynuclear metal complexes of ligands containing phenolic units

The coordination properties of a selected series of acyclic and macrocyclic ligands containing one or more phenolic groups are explored. The formation of polynuclear metal complexes was only considered highlighting the key role played by the phenoxide oxygen atom in binding two metal centres in a bridge disposition. This arrangement allows two metal ions to stay close each other and consequently these dinuclear centres are able to mimic many biological sites, especially those where the two metals can cooperate to form an active centre. Catalytic properties of these polynuclear complexes, when studied, have been reported. Also some of the numerous heterodinuclear metal complexes that have been synthesized are here reviewed, included several crystal structures.     

A numerical method to price European derivatives based on the one factor LIBOR Market Model of interest rates

We consider the problem of pricing European interest rate derivatives based on the LIBOR Market Model (LMM) with one driving factor. We derive a closed-form approximation of the transition probability density functions associated to the stochastic dynamical systems that describe the behaviour of the forward LIBOR interest rates in the LMM. These approximate formulae are based on a truncated power series expansion of the solutions of the Fokker–Planck equations associated to the LMM. The approximate probability density functions obtained are used to price European interest rate derivatives using the method of discounted expectations. The resulting integrals are low dimensional when the most commonly traded European interest rate derivatives are considered, and they can be computed efficiently using elementary numerical quadrature schemes (i.e. Simpson’s rule). The algorithm obtained is very well suited for parallel computing and is tested on the problem of pricing several derivatives including an European swaption and an interest rate spread option. In both cases, the method proposed in this paper appears to be accurate (i.e. relative error of order 10⁻², 10⁻³, or even 10⁻⁴) and approximately between 278 and 63 000 times faster than previous methods based on the Monte Carlo simulation of the LMM stochastic dynamical systems.

The website http://www.econ.univpm.it/pacelli/ballestra/finance/w2 contains material that helps the understanding of this paper and makes available to the interested users the computer programs that implement the numerical method proposed.     

Solvent effects in density functional calculations of uracil and cytosine tautomerism

The effects of the solvent on the tautomeric equilibria of cytosine and uracil are studied using Onsager's reaction field model in the framework of density functional theory. In this model, the solute molecule is placed in a spherical cavity of radius ao immersed in a continuous medium with a dielectric constant e, treating the solute-solvent electrostatic interactions at the dipole level. The cavity radius is evaluated by determining the molecular volume with a quantum mechanical approach. The solvent effect brings significant changes in the geometrical parameters of some cytosine tautomers, but only very small changes to those of the uracil tautomers. Our results are in good agreement with available experimental results and confirm that the polarization of the solute by the continuum has important effects on the absolute and relative solvation energies. Frequency shifts and intensity variations in the infrared spectra due to the presence of the solvent are also presented. © 1995 John Wiley & Sons, Inc.     

Sur la complexité des nombres algébriques

Let b?2 be an integer. We prove that real numbers whose b-ary expansion satisfies some given, simple, combinatorial condition are transcendental. This implies that the b-ary expansion of any algebraic irrational number cannot be generated by a finite automaton. To cite this article: B. Adamczewski et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Computational approaches to shed light on molecular mechanisms in biological processes

Computational approaches based on Molecular Dynamics simulations, Quantum Mechanical methods and 3D Quantitative Structure-Activity Relationships were employed by computational chemistry groups at the University of Milano-Bicocca to study biological processes at the molecular level. The paper reports the methodologies adopted and the results obtained on Aryl hydrocarbon Receptor and homologous PAS proteins mechanisms, the properties of prion protein peptides, the reaction pathway of hydrogenase and peroxidase enzymes and the defibrillogenic activity of tetracyclines.