Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II. Nachtrag zu Math. Annalen 142, 385–398 (1961)

Ohne Zusammenfassung     

Cycloadditions of adamantanethione S-methylide to CC multiple bonds

Adamantanethione S-methylide (12) is a nucleophilic 1,3-dipole which easily combines with electrophilic acetylenic and ethylenic bonds affording dihydrothiophene and thiolane derivatives, usually in high yields. The S-methylide 12, generated by extrusion of nitrogen from the 2,5-dihydro-1,3,4-thiadiazole 11, can not be isolated, but is intercepted in situ by dipolarophiles; otherwise, 12 furnishes irreversibly the spirothiirane 13. The ¹H nmr spectra and mass spectra establish the regiochemistry for the adducts of methyl propiolate, acrylonitrile, methyl acrylate, benzylidenemalononitrile and methyl α-cyanocinnamate. The 1,3-dipole does not react with common alkenes; the highly strained trans-cyclooctene gives rise to a cycloadduct.     

On the use of the correlation coefficient r for testing the linearity of calibration functions

This paper criticises the use of the correlation coefficient r for testing the linearity of calibration functions and recommends better methods.

     

Fast perfect sampling from linear extensions

In this paper, we study the problem of sampling (exactly) uniformly from the set of linear extensions of an arbitrary partial order. Previous Markov chain techniques have yielded algorithms that generate approximately uniform samples. Here, we create a bounding chain for one such Markov chain, and by using a non-Markovian coupling together with a modified form of coupling from the past, we build an algorithm for perfectly generating samples. The expected running time of the procedure is O(n³lnn), making the technique as fast as the mixing time of the Karzanov/Khachiyan chain upon which it is based.     

Biosynthesis of the Irregular C12-Terpenoid Dehydrogeosmin in Flower Heads of Rebutia marsoneri WERD. (Cactaceae)

Farnesol ( 3a ) is the precursor to the irregular C₁₂ terpenoid (4S, 4aS, 8aS)-1,2,3,4,4a,5,8,8a-octahydro-4,8a-dimethylnaphthalen-4a-ol (= dehydrogeosmin; 1 ). The irregular C-backbone originates from the oxidative removal of a C₃ side chain from a C₁₅ eudesmane-type intermediate (Scheme 2). The bicyclic C-framework is assembled by a formal addition of H₂O across the endocyclic double bonds of a monocyclic germacradiene-type precursor. The biosynthetic pathway follows from administration of the deuteriated farnesols 3b–e to flower heads of the cactaceae Rebutia marsoneri Werd. and mass-spectroscopic analysis of the collected volatiles.     

Intracavity frequency-doubled diode-pumped Nd : LaSc3(BO3)4 lasers

 An intracavity frequency-doubled 10%Nd : LaSc₃(BO₃)₄ (Nd : LSB) laser was investigated in different resonator configurations and in different operation modes under continuous wave (cw) and quasi-cw laser-diode pumping. With a Cr⁴⁺ : YAG passive modulator and a KTP crystal the second-harmonic output power at 531 nm amounted to 190 mW in Q-switched TEM₀₀ mode at 750 mW of pump power. In a sandwich resonator, when all the optical elements were in direct contact with each other, 0.8 W of green output power was obtained in cw mode under 2.7 W of pump power with a slope efficiency of 44%. In the same setup under fiber-coupled diode-laser array pumping (5.6 W of incident power), 1.2 W of green output power was achieved in cw mode and 1.4 W in quasi-cw mode. Received: 30 April 1996/Revised version: 1 July 1996     

Formation of Dianions in Helium Nanodroplets

The formation of dianions in helium nanodroplets is reported for the first time. The fullerene cluster dianions (C₆₀)_n^2? and (C₇₀)_n^2? were observed by mass spectrometry for n≥5 when helium droplets containing the appropriate fullerene were subjected to electron impact at approximately 22 eV. A new mechanism for dianion formation is described, which involves a two‐electron transfer from the metastable He^? ion. As well as the prospect of studying other dianions at low temperature using helium nanodroplets, this work opens up the possibility of a wider investigation of the chemistry of He^?, a new electron‐donating reagent.