Blaschke-Süss type theorems for closed plane curves

A C¹-class of plane closed curves is considered, which contains all ovals and rosettes. This class is divided into some subclasses for which greatest lower bounds of numbers of antipodal and arc-antipodal sets are determined.     

Syntheses with organoboranes. IX. Vinyl- and 1-alkenyldichloroboranes as ethylene and 1-alkene equivalents for the Diels–Alder reaction

Vinyl- and 1-alkenyldichloroboranes were used as dienophiles for the Diels–Alder reaction with representative aliphatic and cyclic 1,3-dienes. The organoborane adducts were transformed into the corresponding olefins either by protonolysis or by oxidation–mesylation–reduction. Direct protonolysis of the adducts gave in most cases mixtures of olefins whereas the reduction of mesylates with lithium triethylborohydride produced pure olefins in good yields.     

Vtbrational spectra of the triclinic K3[ReO2(CN)4] single crystal

Infrared spectra of K₃[ReO₂(CN)₄] have been recorded using polarized radiation and oriented single crystals. The dichroic behaviour of the bands is analyzed and discussed on the basis of molecular geometry and the oriented molecular model. Experimentally determined dichroic ratios are used to obtain a full set of vibrational frequencies. By combining these data with those obtained from Raman spectra, the fundamental internal and lattice vibrations are assigned.     

Tetraaryl-methane analogues in group 14—V. Distortion of tetrahedral geometryin terms of through-space π–π and π–σ interactions andNMR sagging in terms of π–σcharge transfer

44 members of thecompound series Ph_4−nMR_n (M=Si, Ge, Sn, Pb; R=o-, m-, p-Tol; n=0–4) were synthesized (15 newcompounds). The crystal structures of Ph₃Sn (o-Tol) and PhSn (o-Tol)₃ were determined and compared to 16 known structures. Subject to the distanced (M–C), an interplay between through-space π–π repulsion and π–σ attraction leads to either elongated or compressed tetrahedral geometry. ²⁹ Si-, ¹¹⁹ Sn- and ²⁰⁷ Pb-NMR chemical shifts were determined in solution and in the solid state. ⁷³ Ge chemical shifts were measured only in solution. Anupfield or downfield sagging of the chemical shifts along each series is rationalized in terms of a π–σcharge transfer which is constrained by torsion of the aromatic groups.     

Solubility of Solid 2-Methyl-1,3-butadiene (Isoprene) in Liquid Argon and Nitrogen at the Standard Boiling Points of the Solvents

The solubility of solid 2-methyl-1,3-butadiene (isoprene) in liquid argon at a temperature of 87.3 K and in liquid nitrogen at 77.4 K has been measured by the filtration method. The hydrocarbon contents in solutions were determined using gas chromatography. GC–MS was used to identify impurities in the solute. The experimental value of the mole fraction solubility of solid isoprene in liquid argon at 87.3 K is (1.41 ± 0.27) × 10^–6 and (1.56 ± 0.36) × 10^–7 in liquid nitrogen at 77.4 K. The Preston–Prausnitz method was used for calculation of the solubilities of solid hydrocarbon in liquid argon in the temperature range 84.0–110.0 K and in liquid nitrogen from 64.0 to 90.0 K. The solvent–solute interaction parameters l ₁₂ were also calculated. At 90.0 K liquid argon is a better solvent for isoprene than is liquid nitrogen. The experimental values of the solubilities of isoprene in liquid argon and nitrogen were compared with results obtained for selected unsaturated and aromatic hydrocarbons.     

A Novel Synthesis of tert- Alkyl Sulfides

tert- Alkyl sulfides are conveniently prepared from α-(1H-benzotriazol-1-yl)alkyl sulfides by displacement of the 1H-benzotriazol-1-yl group with Grignard reagents. The 1-[α-(alkylthio)alkyl]- and 1-[α-(arylthio)alkyl]-1H-benzotriazole intermediates are easily available by several routes: (i) displacement of the halogen from appropriate halides by sodium salts of thiols, (ii) condensation of 1H-benzotriazole and thiols with carbonyl compounds, or (iii) lithiation of N-substituted 1H-benzotriazoles and subsequent treatment with electrophiles.     

Phase Diagram for the RbBr–CuBr System

The phase diagram for the RbBr–CuBr system has been determined. In the system two intermediate compounds are formed: RbCu₂Br₃, melting congruently at 537 K and Rb₃CuBr₄, melting incongruently at 544 K. The coordinates of the two eutectic points are: 501 K, 54 mole% CuBr and 522 K, 74 mole% CuBr. This revised version was published online in July 2006 with corrections to the Cover Date.     

Studies on 16-Membered Azothia- and Azoxythiacrown Ethers as Ion Carriers in Ion Selective Membranes

16-Membered azothia- and azoxythiacrown ethers have been studied as ion carriers in ion-selective membranes. Their selectivities towards alkali, alkaline earth, transition and heavy metal cations were evaluated. The complex formation constants for these compounds with chosen cations have been determined using segmented sandwich membranes method.