Estimation of intrinsic processes affected by additive fractal noise

Fractal Gaussian models have been widely used to represent the singular behavior of phenomena arising in different applied fields; for example, fractional Brownian motion and fractional Gaussian noise are considered as monofractal models in subsurface hydrology and geophysical studies Mandelbrot [The Fractal Geometry of Nature, Freeman Press, San Francisco, 1982 [13]]. In this paper, we address the problem of least-squares linear estimation of an intrinsic fractal input random field from the observation of an output random field affected by fractal noise (see Angulo et al. [Estimation and filtering of fractional generalised random fields, J. Austral. Math. Soc. A 69 (2000) 1-26 [2]], Ruiz-Medina et al. [Fractional generalized random fields on bounded domains, Stochastic Anal. Appl. 21 (2003a) 465-492], Ruiz-Medina et al. [Fractional-order regularization and wavelet approximation to the inverse estimation problem for random fields, J. Multivariate Anal. 85 (2003b) 192-216]. Conditions on the fractality order of the additive noise are studied to obtain a bounded inversion of the associated Wiener-Hopf equation. A stable solution is then obtained in terms of orthogonal bases of the reproducing kernel Hilbert spaces associated with the random fields involved. Such bases are constructed from orthonormal wavelet bases (see Angulo and Ruiz-Medina [Multiresolution approximation to the stochastic inverse problem, Adv. in Appl. Probab. 31 (1999) 1039-1057], Angulo et al. [Wavelet-based orthogonal expansions of fractional generalized random fields on bounded domains, Theoret. Probab. Math. Stat. (2004), in press]). A simulation study is carried out to illustrate the influence of the fractality orders of the output random field and the fractal additive noise on the stability of the solution derived.     

Electroreduction of some pyridine carboxamides on carbon electrodes in aqueous solutions

The electroreductions of the NAD⁺ model compounds nicotinamide (I), N₁-methyl nicotinamide (II), N′-methyl nicotinamide (III) and isonicotinamide (IV) on carbon electrodes have been studied in aqueous media in the pH range 0–12 by linear-sweep cyclic voltammetry (Scheme 1, I-IV). Logarithmic analyses of the reduction peaks were performed by computing the convolution of the current with time as a function of the potential. On the basis of the experimental results it was concluded that the irreversibility of the electron transfers increased when a glassy carbon electrode was used, and this irreversibility being more marked when a plastic formed carbon electrode was employed. The reduction processes occurred with more difficulty on carbon electrodes than on mercury electrodes. Both the reduction and the reoxidation (when occurred) processes changed with respect to those observed on mercury electrodes, being irreversible electron transfers the rate-determining steps in most cases. Thus, for compounds I, II and III at pH < 2 the reductions occurred by the uptake of two electrons and two H⁺ ions, and the rate determining step was found to be the first one-electron transfer, for I and III, and the irreversible second electron transfer, preceded by the uptake of an H+ ion, for II. At pH>3 the processes consisted of electrodimerization reactions, preceded by the protonation of the heterocyclic nitrogen in cases I and III. The second electron transfer of the electroreduction of IV always appeared irreversible, in contrast with that found for mercury electrodes.     

AstrophysicalS(E) factor of10B(p, α1)7Be at low energies

The absolute cross section of the fusion reaction ¹⁰B(p, ₁)⁷ has been measured at the c.m. energy range E=48 to 159 keV via the 429 keV secondary -ray transition. The studies involved high proton currents and thick solid ¹⁰Btargets. The resulting cross sections have the same energy dependence as those of the ¹⁰B(p,₀)⁷Bereaction but they are lower by a factor 600.Supported in part by the Deutsche Forschungsgemeinschaft (Ro429/18-2 and Ro429/21-3), the Landesamt Nordrhein Westfalen (IVA5-10600387), and the Comision Intel-ministerial de Ciencia y Technologia (AEN90-0932).     

Miscibility of small colloidal spheres with large polymers in good solvent

Nearly athermal colloid-polymer mixtures were studied in the "protein limit." A fluid-fluid transition was observed in mixtures of stearyl-alcohol-coated silica particles and large polystyrene coils in toluene. The ratios of the polymer radius of gyration to the particle radii were q=4.1 and q=5.2. The binodal curves and the critical points were determined. Turbidity measurements and analysis for one set of particles allowed the systems to be mapped onto hard sphere-polymer mixtures. A comparison with recent predictions for the miscibility of model mixtures shows that the experimental binodals lie between the two extreme results for ideal and interacting polymers. The critical colloid volume fraction is also found to decrease with increasing size ratios.     

Stereocontrolled synthesis of iminocyclitols with an ether bridge

Nor-tropane related bicyclic (6+5) iminocyclitols with an ether bridge and different substituents (hydroxymethyl, aminomethyl, and aminoethyl) on C-1 are prepared starting from a β-d-psicofuranosyl cyanide. The method involves an internal nucleophilic attack of a stabilized amide ion on a 5-mesyloxy derivative. The intermediate N-acetyl O-protected iminocyclitols present atropoisomerism due to restricted rotation of the N-CO amido bond. Conformational aspects of the prepared compounds are discussed.     

Diastereoselective Electrophilic Amination of Chiral 1‐Benzoyl‐2,3,5,6‐tetrahydro‐3‐methyl‐2‐(1‐methylethyl)pyrimidin‐4(1H)‐one for the Asymmetric Syntheses of α‐Substituted α,β‐Diaminopropanoic Acids

The chiral compounds (R)‐ and (S)‐1‐benzoyl‐2,3,5,6‐tetrahydro‐3‐methyl‐2‐(1‐methylethyl)pyrimidin‐4(1H)‐one ((R)‐ and (S)‐ 1 ), derived from (R)‐ and (S)‐asparagine, respectively, were used as convenient starting materials for the preparation of the enantiomerically pure α‐alkylated (alkyl=Me, Et, Bn) α,β‐diamino acids (R)‐ and (S)‐ 11 – 13 . The chiral lithium enolates of (R)‐ and (S)‐ 1 were first alkylated, and the resulting diasteroisomeric products 5 – 7 were aminated with ‘di(tert‐butyl) azodicarboxylate’ (DBAD), giving rise to the diastereoisomerically pure (≥98%) compounds 8 – 10 . The target compounds (R)‐ and (S)‐ 11 – 13 could then be obtained in good yields and high purities by a hydrolysis/hydrogenolysis/hydrolysis sequence.     

Molecular distillation

Molecular distillation was studied for the separation of tocopherols from soya sludge, both experimentally and by simulation, under different operating conditions, with good agreement. Evaporator temperatures varied from 100°C to 160°C and feed flow rates ranged from 0.1 to 0.8 kg/h. The process pressure was maintained at 10⁻⁶ bar, the feed temperature at 50°C, the condenser temperature at 60°C, and the stirring at 350 rpm. For each process condition, samples of both streams (distillate and residue) were collected and stored at −18°C before tocopherols analyses. Owing to the differences between molecular weights and vapor pressures of free fatty acids and tocopherols, tocopherols preferentially remained in the residue at evaporator temperatures of 100°C and 120°C, whereas for higher temperatures (140°C and 160°C) and lower feed flow rate, tocopherols tended to migrate to the distillate stream.     

Autoionization of homogeneous nickel(II) diphosphane hydrogenation catalysts. An NMR study and crystal structures of [Ni(o-MeO-dppe)I2] and [Ni(o-MeO-dppe)I2](PF6)2

The synthesis of a number of nickel(II) complexes containing the didentate phosphane ligand 1,2-bis(di(o-methoxyphenyl)phosphino)ethane (o-MeO-dppe) is reported. Two types of complexes have been synthesized, i.e., the mono(chelate) complex (1) of the general formula [Ni(o-MeO-dppe)X2] (where X = Cl, Br or I) and the bis(chelate) complex (2) of the general formula [Ni(o-MeO-dppe)2]Y2 (where Y = PF6 or trifluoroacetate (TFA)). These complexes have been characterized using electronic absorption and NMR spectroscopy. The structures of the mono(chelate) complex [Ni(o-MeO-dppe)I2] (1c) and of the bis(chelate) complex [Ni(o-MeO-dppe)2](PF6)2 (2e) have been determined by X-ray crystallography. [Ni(o-MeO-dppe)I2] crystallizes in the monoclinic space group P2(1)/c with Z = 4, a = 12.1309(1) A, b = 16.5759(3) A, c = 17.6474(2) A, beta = 119.3250(10) degrees. [Ni(o-MeO-dppe)2](PF6)2 crystallizes in the monoclinic space group C2/c with Z = 4, a = 22.5326(3) A, b = 13.6794(2) A, c = 21.7134(3) A, beta = 107.1745(7) degrees. In both structures the nickel ion is in a square-planar geometry with a NiP2I2 and NiP4 chromophore, respectively. Using 1H and 31P[1H] NMR spectroscopy the behavior of the complexes in various solvents has been studied. It appears that in solution these nickel complexes are involved in an autoionization equilibrium: 2[Ni(o-MeO-dppe)X2] <==>[Ni(o-MeO-dppe)2](2+) + ["NiX(4)"](2-). The ionized complex (3) consists of a cationic unit in which a nickel atom is surrounded by two didentate phosphane ligands, and an anionic unit that stoichiometrically consists of a nickel atom and four anions. The position of the autoionization equilibrium is highly dependent on the anion and the solvent used. In a polar solvent in combination with weakly coordinating anions only the ionized complex is observed, whereas in an apolar solvent in combination with coordinating anions only the mono(chelate) complex occurs. A comparison of the behavior of o-MeO-dppe with its unsubstituted analogue dppe in combination with nickel(II) acetate using 31P[1H] NMR spectroscopy shows that the latter is more readily oxidized.     

Unified and generalized Fresnel numbers

The concept of Fresnel number is discussed and expressions are derived for misaligned optical systems. For the case of perfectly aligned optical elements, the usual number,N, based on a Fresnel zone concept is found to be given byN = (a ²/)(D ₁/B ₁ +A ₂/B ₂), whereB ₁,D ₁ andB ₂,A ₂ are the transfer matrix elements of the optical systems before and after a circular aperture of radiusa respectively. A modified definition of the Fresnel number is proposed for Gaussian beam propagation. This parameterN _G, is related to the complex beam parameter and may be represented by the angle = tan^–1 N _G, found in the familiar Collins chart and its dual representation. A general relation for the transformation of this Fresnel number is found. The expressions for Gaussian beam transformation are thus simplified, since the waist-waist transform is given byN _G1 =N _G2 = 0. Finally, these two kinds of Fresnel numbers are written as tensors when applied to cases involving elliptical apertures, astigmatic beams and nonsymmetrical systems.