Convex hull of powers of a complex number,trinomial equations and the Farey sequence

The color of a complex number is defined as the number of vertices of the convex hull of powers of that number. This induces a coloring of the unit disk. The structure of the set of points where the color changes is investigated here. It is observed that there is a connection between this fractal set and some family of trinomial equations. Three algorithms for coloring the unit disk are described, the last one (related to the Farey sequence) arising out of a conjecture. This conjecture is formulated and proved in this presentation.     

Precise and accurate quantitative C NMR with reduced experimental time

In order to detect small variations in ¹³C isotopomers concentrations, high sensitivity, accuracy and precision have to be achieved. To assess such criteria, when using ¹³C NMR, ¹³C bi-labelled ethanol has been proposed as a molecular probe. Advantage has been taken of the pre-established structural relationship between the peak areas of the ¹³C NMR spectrum of this molecule, i.e. the ratio of signal areas is set to a fixed value. It is shown that the quality performance, required by quantitative ¹³C NMR spectroscopy, is not affected by a large reduction of the repetition delay using relaxation reagents.     

A highly enantioselective conjugate reduction of 3-arylinden-1-ones using bakers' yeast for the preparation of (S)-3-arylindan-1-ones

[formula: see text] The bakers' yeast reduction of 3-(1,3-benzodioxol-5-yl)-6-propoxy-1H-inden-1-one 4 has been shown to give (S)-3-(1,3-benzodioxol-5-yl)-2,3-dihydro-6-propoxy-1H-indan-1-one 6 in 65% yield with high enantioselectivity (> 99.0% ee), a key intermediate for the synthesis of the endothelin receptor antagonist SB 217242. In addition, the substituted 3-arylinden-1-ones 10a-e gave equally high enantioselectivity for the 3-arylindan-1-one products 13a-e. Mechanistic studies of the reaction indicate the operative pathway to be an asymmetric conjugate reduction, wherein the hydride transfer from NAD(P)H occurs from the Re-face of the indenone substrate.     

Thermolytic carbonates for potential 5'-hydroxyl protection of deoxyribonucleosides

Thermolytic groups structurally related to well-studied heat-sensitive phosphate/thiophosphate protecting groups have been evaluated for 5'-hydroxyl protection of deoxyribonucleosides as carbonates and for potential use in solid-phase oligonucleotide synthesis. The spatial arrangement of selected functional groups forming an asymmetric nucleosidic 5'-O-carbonic acid ester has been designed to enable heat-induced cyclodecarbonation reactions, which would result in the release of carbon dioxide and the generation of a nucleosidic 5'-hydroxyl group. The nucleosidic 5'-O-carbonates 3-8, 10-15, and 19-21 were prepared and were isolated in yields ranging from 45 to 83%. Thermolytic deprotection of these carbonates is preferably performed in aqueous organic solvent at 90 degrees C under near neutral conditions. The rates of carbonate deprotection are dependent on the nucleophilicity of the functional group involved in the postulated cyclodecarbonation reaction and on solvent polarity. Deprotection kinetics increase according to the following order: 4 < 5 < 10 < 6 < 12 < 7 < 13 < 8 < 14 congruent with 19-21 and CCl4 < dioxane < MeCN < t-BuOH < MeCN:phosphate buffer (3:1 v/v, pH 7.0) < EtOH:phosphate buffer (1:1 v/v, pH 7.0). Complete thermolytic deprotection of carbonates 7, 8, 13, and 14 is achieved within 20 min to 2 h under optimal conditions in phosphate buffer-MeCN. The 2-(2-pyridyl)amino-1-phenylethyl and 2-[N-methyl-N-(2-pyridyl)]aminoethyl groups are particularly promising for 5'-hydroxyl protection of deoxyribonucleosides as thermolytic carbonates.     

Rapid stereoselective separations of amphetamine derivatives with highly sulfated gamma-cyclodextrin

The highly sulfated gamma-CD (HS-gamma-CD) is a chiral selector widely used in CE for the enantioseparation of pharmaceutical compounds. This paper investigated different approaches to reduce the stereoselective analysis time of amphetamine (AT) derivatives according to the chiral selector concentration in the BGE. With high HS-gamma-CD concentration, tested analytes were separated in 3.5 min as anionic complexes with short-end injection technique in reversed polarity mode. However, this procedure presented some limitations in terms of efficiency and resolution, excessive Joule heating and poor compatibility with MS detection. With low HS-gamma-CD concentration, compounds were separated as cations. Conventional approaches to reduce CE analysis time demonstrated critical resolution between some analytes. Therefore, the use of the partial-filling technique compatible with MS detection was carried out. Under optimized conditions, the analysis time for the chiral separation of seven AT like compounds was reduced to 6 min. Moreover, sensitivity of CE-MS was sufficient for the determination of ATs in plasma following a simple liquid-liquid extraction.     

Fluorenyl-containing sulfonated poly(aryl ether ether ketone ketone)s (SPFEEKK) for fuel cell applications

A series of fluorenyl-containing sulfonated poly(aryl ether ether ketone ketone)s (SPFEEKK) were synthesized via aromatic nucleophilic substitution polymerization. The sulfonation content (SC) was controlled by the feed ratios of sulfonated and nonsulfonated monomers. Flexible and strong membranes in the sulfonic acid form were obtained from cast membranes in the sodium salt forms by treatment with acid. The thermal properties, water uptake, swelling ratio, water state, oxidative stability, proton conductivity and methanol permeability were investigated. All the polymers had proton conductivities greater than 1 × 10⁻² S/cm at room temperature, and the conductivity values of m-SPFEEKK-80 and p-SPFEEKK-80 were up to 1.86 × 10⁻¹ and 1.78 × 10⁻¹ S/cm at 100 °C. This series of polymers also possessed good dimensional stability in water and low methanol crossover.     

Steroregularity of Polystyrenes Obtained by New Complex Bases

The stereoregularity of polystyrenes obtained with complex bases and salt complex bases in various solvents was determined by ¹³C-NMR spectroscopy. Polystyrenes produced by complex bases are mostly syndiotactic and obey Bernoullian statistics.