Metal complexes of C2-symmetric chiral bipyridine ligands. X-ray structure of [bis(nitrato)(4S,5S)-2,2-dimethyl-4,5-bis(2-pyridyl)-1,3-dioxolane cobalt(II)]

Chelating properties of C₂-symmetric chiral bipyridine ligands are discussed. In particular we report the syntheses of the cobalt(II), nickel(II), zinc(II) and copper(II) complexes of (4S,5S)-2,2-dimethyl-4,5-bis(2-pyridyl)-1,3-dioxolane. All compounds have been characterized by IR spectroscopy, and an X-ray diffraction analysis has been carried out on one of them: Co(L)(NO₃)₂. The ligand coordinates the cobalt atom by the two nitrogen donors N(1) and N(2). A seven-membered chelation ring is formed, presenting a remarkable non-crystallographic twofold pseudosymmetry around the axis connecting Co and the midpoint of the C(6)–C(7) bond. The metal also binds two monodentate nitrates, thus completing a distorted coordination tetrahedron.     

Langmuir–Blodgett films of pyridinium-dicyanomethanide dyes mixtures with photobleachable absorption bands

We report on Langmuir-Blodgett (LB) films characterization of 4-[5-dicyanomethanido)thien-2-y1]-N-(n-hexadecyl)pyridinium (C₁₆H₃₃-PDCNT), and 1-(N-(n-hexadecy]-4-pyridinio)-2-[5-(dicyanomethanido)thien-2-yl]ethene (C₁₆H₃₃-PDCNTE); LB films of the pure compounds and of the mixtures of the two compounds were prepared at 291 K: UV-vis investigation revealed the presence of photobleachable absorption bands, the ones at about 530 nm and 640 nm were due to charge transfer transitions of the monomer of C16H33-PDCNT and C₁₆H₃₃-PDCNTE, respectively; the sharp, photobleachable ones shifted to shorter wavelengths were due to H-aggregates of the two compounds. By changing the molar ratios of the two compounds in the mixtures and in other cases by annealing the LB films, the absorption maxima of the sharp, photobleachable bands due to H-aggregates could be tuned in the range 415–467 nm. These LB films are thus very promising in view of optical data storage applications.     

Dynamical systems and numerical analysis: the study of measures generated by uncountable I.F.S.

Measures generated by Iterated Function Systems composed of uncountably many one-dimensional affine maps are studied. We present numerical techniques as well as rigorous results that establish whether these measures are absolutely or singular continuous.     

A graphical approach to redox titrations

Summary A method for drawing a logarithmic diagram which gives a correct representation of the equilibrium concentrations of the various species taking part in a redox titration is described. The use of this kind of diagrams for evaluating the titration error and for calculating the titration curve is illustrated. The symmetry properties of titration curves and the linearity range of Gran plots are also discussed on the basis of the logarithmic diagrams.

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Graphische Behandlung von Redox-Titrationen

Zusammenfassung Ein Verfahren wird beschrieben zur Aufstellung eines logarithmischen Diagramms, das eine korrekte Darstellung der Gleichgewichtskonzentrationen der verschiedenen Teilnehmer an einer Redoxtitration bietet. Der Gebrauch eines solchen Diagramms zur Auswertung des Titrationsfehlers und zur Berechnung der Titrationskurve wird gezeigt. Aufgrund der logarithmischen Diagramme werden auch die Symmetrieeigenschaften von Titrationskurven und der Linearitätsbereich von Gran-Diagrammen diskutiert.

     

Accuracy of suboptimal solutions to kernel principal component analysis

For Principal Component Analysis in Reproducing Kernel Hilbert Spaces (KPCA), optimization over sets containing only linear combinations of all n-tuples of kernel functions is investigated, where n is a positive integer smaller than the number of data. Upper bounds on the accuracy in approximating the optimal solution, achievable without restrictions on the number of kernel functions, are derived. The rates of decrease of the upper bounds for increasing number n of kernel functions are given by the summation of two terms, one proportional to n ^−1/2 and the other to n ⁻¹, and depend on the maximum eigenvalue of the Gram matrix of the kernel with respect to the data. Primal and dual formulations of KPCA are considered. The estimates provide insights into the effectiveness of sparse KPCA techniques, aimed at reducing the computational costs of expansions in terms of kernel units.