Anodic reductions—V The reduction of diketones by unipositive magnesium anodically generated

A series of diketones of the general formula C₆H₅CO(CH₂nCOC₆H₅ has been prepared and subjected to “anodic reduction” in sodium iodide-pyridine solution between magnesium electrodes. In every case hydrolysis of the anolyte following electrolysis yielded a 1:2-diol as the reduction product as evidenced by titration with standard lead tetraacetate solution. The diketones, 1:3-dibenzoylpropane (n = 3) and 1:4-dibenzoylbutane (n = 4), gave cis-1:2-diphenylcyclopentane-1:2-diol and cis-1:2-diphenylcyclohexane-1:2-diol, respectively. On the assumption that the other diketones also gave cyclic 1:2-diols, there is a striking correlation between the initial mean valence number (V_i) of the magnesium entering solution from the anode and the size of the ring; the lowest V_i values were obtained in those instances where the diketones originally in solution gave the most stable cyclic diols. Interpretations are offered for these results and for corrosion phenomena observed.     

The cationic polymerization of fluoral—III. Thermodynamics of polymerization in solution

The equilibrium between fluoral in dichloromethane solution and live condensed liquid polyfluoral has been investigated between 22 and 43°C. Equilibrium monomer concentrations gave: ΔH_ac°(298 K) = -50-8 ± 2·3 kJ mol^?1 and ΔS_sc° (298 K) = -142·7 ± 7·4 J K^-1 mol^-1. With the aid of calibration and monomer vaporization data, thermodynamic values for the polymerization of liquid monomer to liquid polymer were also calculated: ΔH_tc° (298 K) = -47 ± 3 kJ mol^-1 and ΔS_1e° (298 K) = -97 ± 10 J K^-1 mol^-1.     

Complex Data Processing: Fast Wavelet Analysis on the Sphere

In the general context of complex data processing, this article reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the plane and on the sphere. Two fast algorithms are also presented for the analysis of signals on the sphere with steerable wavelets.     

Cosmological Applications of a Wavelet Analysis on the Sphere

The cosmic microwave background (CMB) is a relic radiation of the Big Bang and as such it contains a wealth of cosmological information. Statistical analyses of the CMB, in conjunction with other cosmological observables, represent some of the most powerful techniques available to cosmologists for placing strong constraints on the cosmological parameters that describe the origin, content and evolution of the Universe. The last decade has witnessed the introduction of wavelet analyses in cosmology and, in particular, their application to the CMB. We review here spherical wavelet analyses of the CMB that test the standard cosmological concordance model. The assumption that the temperature anisotropies of the CMB are a realisation of a statistically isotropic Gaussian random field on the sphere is questioned. Deviations from both statistical isotropy and Gaussianity are detected in the reviewed works, suggesting more exotic cosmological models may be required to explain our Universe. We also review spherical wavelet analyses that independently provide evidence for dark energy, an exotic component of our Universe of which we know very little currently. The effectiveness of accounting correctly for the geometry of the sphere in the wavelet analysis of full-sky CMB data is demonstrated by the highly significant detections of physical processes and effects that are made in these reviewed works.