Determination of physical properties of bitumens by use of near-infrared spectroscopy with neural networks. Joint modelling of linear and non-linear parameters

The fact that bitumens behave as non-Newtonian fluids results in non-linear relationships between their near-infrared (NIR) spectra and the physico-chemical properties that define their consistency (viz. penetration and viscosity). Determining such properties using linear calibration techniques [e.g. partial least-squares regression (PLSR)] entails the previous transformation of the original variables by use of non-linear functions and employing the transformed variables to construct the models. Other properties of bitumens such as density and composition exhibit linear relationships with their NIR spectra. Artificial neural networks (ANNs) enable modelling of systems with a non-linear property-spectrum relationship; also, they allow one to determine several properties of a sample with a single model, so they are effective alternatives to linear calibration methods. In this work, the ability of ANNs simultaneously to determine both linear and non-linear parameters for bitumens without the need previously to transform the original variables was assessed. Based on the results, ANNs allow the simultaneous determination of several linear and non-linear physical properties typical of bitumens.     

Palladium(0)-catalyzed allylation of heterocycles with cyclopentene derivatives

Palladium(0)-catalyzed allylation of imidazoles, 6-methyluracil, 2-pyrimidinone, and Meldrum's acid with cyclopentadiene monoepoxide and cis-cyclopentene-3,5-diol mono and dicarbonate is described.     

Palladium(0)-catalyzed allylation of 4(5)-substituted imidazoles, 5(6)-substituted benzimidazoles,benzotriazole and 5(6)-methylbenzotriazole

Pd(0)-Catalyzed allylations of 4(5)-nitroimidazole, 1 , 2-methyl-4(5)-nitroimidazole, 2 , 4(5)-bromo-imidazole, 7 , 4(5)-methoxyimidazole, 10 , 5(6)-nitrobenzimidazole, 16a , 5(6)-methylbenzimidazole, 16b , benzotriazole, 19 , and 5(6)-methylbenzotriazole, 22 , were studied under several reaction conditions. Nitroimidazoles 1 and 2 were regioselectively allylated under thermodynamic control, leading to 1-allyl-4-nitro derivatives.     

Stepwise Construction of Polynuclear Complexes of Rhodium and Iridium Assisted by Benzimidazole-2-thiol. NMR and X-ray Diffraction Studies

Reactions of [M(2)(&mgr;-Cl)(2)(cod)(2)] (cod = 1,5-cyclooctadiene, M = Rh, Ir) with benzimidazole-2-thiol (H(2)Bzimt) afford the mononuclear complexes [MCl(H(2)Bzimt)(cod)] (M = Rh (1), Ir (2)) for which a S-coordination of the ligand is proposed based on their spectroscopic data. The dinuclear complexes [M(2)(&mgr;-HBzimt)(2)(cod)(2)] (M = Rh (3), Ir (4)) are isolated from the reaction of [M(acac)(cod)] and benzimidazole-2-thiol. They contain the monodeprotonated ligand (HBzimt(-)) bridging the two metals in a &mgr;(2)-(1kappaN,2kappaS) coordination mode and in a relative cis,cis-HT arrangement. Complexes 3 and 4 react with the appropriate species [M(cod)(Me(2)CO)(2)](+) to afford the trinuclear cationic aggregates [M(3)(&mgr;-HBzimt)(2)(cod)(3)](+) (M = Rh (5), Ir (6)) and with the [M'(2)(&mgr;-OMe)(2)(cod)(2)] compounds to give the homo- and heterotetranuclear complexes [MM'(&mgr;-Bzimt)(cod)(2)](2) (M = M' = Rh (7), Ir (8); M = Ir, M' = Rh (9)) containing the dideprotonated ligand (Bzimt(2)(-)). The trinuclear neutral complexes [M(3)(&mgr;-Bzimt)(&mgr;-HBzimt)(cod)(3)] are intermediates detected in the synthesis of the tetranuclear complexes. Protonation of 9 with HBF(4) gives the unsymmetrical complex [Ir(2)Rh(&mgr;-HBzimt)(2)(cod)(3)]BF(4) (10). This reaction involves the protonation of the bridging ligands followed by the removal of one "Rh(cod)" moiety to give a single isomer. The molecular structure of [Rh(2)(&mgr;-Bzimt)(cod)(2)](2) (7) has been determined by X-ray diffraction methods. Crystals are monoclinic, space group P2(1)/n, a = 20.173(5) ?, b = 42.076(8) ?, c = 10.983(3) ?, beta = 93.32(2) degrees, Z = 8, 7145 reflections, R = 0.0622, and R(w) = 0.0779. The complete assignment of the resonances of the (1)H NMR spectra of the complexes 3, 4, and 7-9 was carried out by selective decoupling, NOE, and H,H-COSY experiments. The differences in the chemical shifts of the olefinic protons are discussed on the basis of steric and magnetic anisotropy effects.     

Commutators of linear and bilinear Hilbert transforms

Let , and let and denote the bilinear and linear Hilbert transforms, respectively. It is proved that, for and , maps into and it maps into if and only if . It is also shown that, for the commutator is bounded on for if and only if , where .

     

Palladium nanoparticles stabilised by polyfluorinated chains

Palladium nanoparticles can be prepared by reduction of palladium(II) chloride in the presence of different compounds featuring long perfluorinated carbon chains.     

Sharp estimates for maximal operators associated to the wave equation

The wave equation, ∂ _tt u=Δu, in ℝ ⁿ⁺¹, considered with initial data u(x,0)=f∈H ^s (ℝ ⁿ ) and u’(x,0)=0, has a solution which we denote by . We give almost sharp conditions under which and are bounded from H ^s (ℝ ⁿ ) to L ^q (ℝ ⁿ ).     

Bilinear multipliers on Lorentz spaces

We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform. The author has been partially supported by grants DGESIC PB98-1246 and BMF 2002-04013.