Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

Evaluation of Serpa cheese proteolysis by nitrogen content and capillary zone electrophoresis

Proteolysis of Serpa cheese produced traditionally (B) and semi-industrially (C) was evaluated for the first time by determination of nitrogen content and capillary zone electrophoresis (CZE). A citrate dispersion of cheese was fractionated to determine the nitrogen in pH 4.4, trichloroacetic and phosphotungstic acid soluble fractions (pH 4.4-SN, TCA-SN and PTA-SN, respectively). The pH 4.4-SN was significantly higher for B ( P <0.001), while TCA-SN was significantly higher for C ( P <0.001). PTA-SN was also higher for C but at 60 days ripening no significant difference was found between B and C. Degradation of alpha(s1) - and beta-caseins evaluated by CZE was in good agreement with the maturation index (pH 4.4-SN/TN).

The effect of the addition of sodium compounds in the liquid-phase hydrodechlorination of chlorobenzene over palladium catalysts

The hydrodechlorination of chlorobenzene over supported palladium catalysts has been studied. The palladium catalysts: deactivate as the reaction proceeds due to the HCl formed as by-product. The effect of the addition of sodium compounds has been analysed for the neutralisation of HCl. When NaOH was added to the reaction mixture, no beneficial effect was observed due to the detrimental effect of the alkaline medium on the textural and metallic properties of the catalysts. Doping the support with NaOH prior to impregnation with the metal precursor leads (after calcination and reduction) to catalysts with better activity and tolerance to deactivation, especially those obtained when using PdCl2 as the metal precursor. Low metal dispersion and the capture of chloride by forming NaCl are the: main factors contributing to the: improved catalytic properties. Finally, doping the catalysts with NaOH or NaNO3, after reduction of the metal precursor leads to a moderate increase in initial activity and final conversion, although NaOH impregnation also gave rise to support corrosion and metal dispersion modification. (C) 2001 Elsevier Science B.V, All rights reserved.