Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones

We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of the cone coincides with the one of the half-space. This allows us to give some criteria ensuring existence of isoperimetric regions: for instance, local convexity of the cone at some boundary point.

We also characterize which are the stable regions in a convex cone, i.e., second order minima of perimeter under a volume constraint. From this it follows that the isoperimetric regions in a convex cone are the euclidean balls centered at the vertex intersected with the cone.

     

Regioselective palladium-catalyzed alkylation of allylic halides with benzylic grignard reagents. Two-step synthesis of abietane terpenes and tetracyclic polyprenoid compounds

A highly regioselective palladium-catalyzed alpha-alkylation of allylic bromides 1a,c-e and chloride 1b with substituted and unsubstituted benzylic Grignard reagents is reported. The resulting all-trans polyenehomobenzene derivatives were obtained in excellent yields and regioselectivity. These products were easily converted to abietane-type diterpenes (10-12) and tetracyclic polyprenoid compounds (13, 14) through a Lewis acid-promoted cascade polyene cyclization reaction.     

Titanocene-catalyzed cascade cyclization of epoxypolyprenes: straightforward synthesis of terpenoids by free-radical chemistry

The titanocene-catalyzed cascade cyclization of epoxypolyenes, which are easily prepared from commercially available polyprenoids, has proven to be a useful procedure for the synthesis of C(10), C(15), C(20), and C(30) terpenoids, including monocyclic, bicyclic, and tricyclic natural products. Both theoretical and experimental evidence suggests that this cyclization takes place in a nonconcerted fashion via discrete carbon-centered radicals. Nevertheless, the termination step of the process seems to be subjected to a kind of water-dependent control, which is unusual in free-radical chemistry. The catalytic cycle is based on the use of the novel combination Me(3)SiCl/2,4,6-collidine to regenerate the titanocene catalyst. In practice this procedure has several advantages: it takes place at room temperature under mild conditions compatible with different functional groups, uses inexpensive reagents, and its end step can easily be controlled to give exocyclic double bonds by simply excluding water from the medium.     

Spectrophotometric determination of indium in nickel alloys and zinc ores with 1-(2-pyridylmethylideneamine)-3-(salicylideneamine)thiourea

A sensitive method for the spectrophotometric determination of indium with 1-(2-pyridylmethylideneamine)-3-(salicylideneamine)thiourea is proposed. A yellow complex is formed at pH 4.5 (succinate buffer) in a medium containing 40% dimethylformamide, and the absorbance is measured at 415 nm. The molar absorptivity is 6.2 x 10(4)l.mole(-1).cm(-1). The relative standard deviation of the procedure is 1.5%. The method has been applied to determination of indium in a nickel alloy and three zinc ores, with prior isolation of indium by co-precipitation with ammonia and extraction into n-butyl acetate from 5M hydrobromic acid.     

Regioselective homogeneous hydrogenation of heteroaromatic nitrogen compounds by use of [RuH(CO)(NCMe)2(PPh3)2]BF4 as the precatalyst

Summary The complex [RuH(CO)(NCMe)₂(PPh₃)₂]BF₄ (1) is an efficient and regioselective catalyst precursor for the hydrogenation of polyaromatic nitrogen compounds such as quinoline (Q), isoquinoline (iQ), indole (ln), 5,6- and 7,8-benzoquinoline (BQ) and acridine (A) under relatively mild reaction conditions (125 °C, 4 atm H₂). The order of individual initial rates was: A > Q > 5,6-BQ > 7,8-BQ > ln > iQ, reflecting both steric and electronic effects. For the regioselective homogeneous hydrogenation of A to 9,10-dihydroacridine (DHA) catalysed by complex (1), a kinetic study was carried out; the experimentally determined rate law was r = k ₁ [Ru] [H₂]. These findings are consistent with a mechanism involving the hydrogenation of [RuH(CO)(A)(NCMe)(PPh₃)₂]BF₄ to yield DHA and the unsaturated species [RuH(CO)(NCMe)(PPh₃)₂]BF₄ in the rate-determining step.     

A simple preparation of calibration curve standards of134Cs and137Cs by serial dilution of a standard reference material

Two sets of calibration standards for¹³⁴Cs and¹³⁷Cs were prepared by small serial dilution of a natural matrix standard reference material, IAEA-154 whey powder. The first set was intended to screen imported milk powders which were suspected to be contaminated with¹³⁴Cs and¹³⁷Cs. Therefore the concentration range of the calibration standards were about 40–400 Bq/kg. The precision of the preparation of the standard with about 7 Bq/kg of¹³⁴Cs and 39 Bq/kg of¹³⁷Cs at measurement time was 7.4% and 3.2%, respectively. The preparation of a similar standard by spiking the matrix with radioisotope solutions resulted in a poorer precision, about double that of the former technique. The other set of calibration standards was prepared to measure the environmental levels of¹³⁷Cs in commercial Venezuelan milk powders. Their concentration ranged from 3–10 Bq/kg of¹³⁷Cs. The accuracy of these calibration curves was checked by using IAEA-152 and A-14 milk powders. Their measured values were in good agreement with their certified values. Finally, it is shown that these preparation techniques by serial dilution of a standard reference material were simple, rapid, precise, accurate and cost-effective.This work was partly funded by a research contract PC-075 from the Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICIT).     

Conlometric determination of weak bases applying bismuth electrode pair for the end-point detection

Tertiäre Amine und Salze organischer Säuren werden in Acetanhydrid mit 5% Essigsäure durch anodische Proton-Erzeugung auf Platin in Gegenwart von Hydrochinon mit Hilfe der biamperometrischen Endpunkttechnik mit einem Wismutelektrodenpaar quantitativ bestimmt. Mengen von 0,5–0,9 mg wurden mit einer mittleren Abweichung von <1% analysiert. Die Ergebnisse stimmten zufriedenstellend mit denen aus thermometrischen und photometrischen Titrationen überein.Summary Tertiary amines and salts of organic acids have been quantitatively determined in acetic anhydride with 5% of acetic acid by means of anodic generation of protons on platinum in the presence of hydroquinone, applying a biamperometric end-point detection using an indicating system of bismuth electrodes. Amounts of 0.5–0.9 mg have been analysed with average deviations of <1%. Good agreement was obtained with the results of thermometric and photometric titrations.

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Coulometrische Bestimmung von schwachen Basen unter Anwendung eines Wismut-Elektrodenpaars als Indicatorsystem

     

A highly reactive mononuclear Zn(II) complex for phosphodiester cleavage

The activity of a Zn(II) complex of a tetradentate, tripodal ligand for catalyzing phosphodiester cleavage is enhanced 750-fold by introducing three hydrogen bond donors to the ligand. Inhibition studies show that the Zn-aqua complex is the kinetically active form and that it binds the transition state with a formal dissociation constant of 3 x 108 M-1. The effect of these ligand modifications on the transition-state affinity is comparable to the rate acceleration provided by the metal ion itself. Overall, this mononuclear complex is more active than the most reactive dinuclear Zn(II) complexes reported to date.