Diels-Alder reaction of furan with some dienophiles

The reaction of furan and maleic acid was carried out in several solvents. The endo-adduct was isolated and the structure established by its spectral properties and conversion into known compounds. The adducts of furan with fumaric acid, diethyl fumarate and diethyl maleate are reported.     

Quantitative information from x-ray diffraction of nylon-6 yarns. I. Development of a model for the analytical description of equatorial x-ray profiles

A wide-angle x-ray method has been developed by which quantitative structural information can be obtained on nylon-6 yarns. To this end, experimental equatorial diffractometer scans measured in transmission were fitted to a mathematical model describing the profiles as the envelopes of three bell-shaped functions. Four different models were investigated using, respectively, Gauss, Lorentz (Cauchy), Logistic, and Pearson-VII functions. The last model, which can be regarded as a generalized Lorentz function, gave the best fit. On the basis of a statistical analysis of the results of well-separated x-ray peaks, two parameters could be fixed. Another reduction of the number of parameters was achieved by interrelating the peak areas of the two outer reflections. These reductions widened the applicability of a computer program based on the aforementioned model to highly overlapping x-ray peaks. So the whole variety of x-ray scans, which can be obtained from nylon-6 yarns made under widely varying process conditions, can be well described. The fitting procedures provide unique solutions and hence objectively determined parameters.     

Utility of the tandem Pauson-Khand reaction in the construction of tetracycles

The scope of the tandem Pauson-Khand reaction has been explored for the regiospecific construction of [5.5.5.5]- and [5.6.6.5]tetracyclic systems via the photolytic method of Livinghouse. The rapid regiospecific entry into the two dicyclopentapentanoid systems 17 and 29 was accomplished from the key diene-diynes 11 and 19b. A photochemically mediated catalytic tandem Pauson-Khand cyclization was employed to prepare the parent ring systems of dicyclopenta[a,e]pentalene (from 19b) and dicyclopenta[a,f]pentalene (from 11) in regiospecific fashion in a one-pot process. Under these conditions, conversion of acyclic diene-diyne 16 into tetracyclic system 17 was achieved in 74% yield, while a similar process was employed to convert 28 into tetracycle 29 in 90% yield. This is much improved over the previous conditions that employed NMO. Six carbon-carbon bonds were generated in this process constituting up to 98% yield for each carbon-carbon bond so formed. Furthermore, tetracyclic [5.6.6.5] systems such as dicyclopenta[b,g]decalins 37, 38, and 40 were prepared from similar diene-diyne precursors via the tandem Pauson-Khand cyclization. Importantly, acetal 36 provided the desired cis-fused [5.6.6.5] system 38a (via 40a/b) in stereospecific fashion. This reaction is unique in that it provides a cis-decalin ring system; moreover, the yield of each of the six carbon-carbon bonds formed in this process was at least 89%. The structure of cis diol 38a was confirmed by X-ray crystallography.     

Non-special divisors on real algebraic curves and embeddings into real projective spaces

We show that there is a large class of non-special divisors of relatively small degree on a given real algebraic curve. If the real algebraic curve has many real components, such a divisor gives rise to an embedding (birational embedding, resp.) of the real algebraic curve into the real projective space ℙ ^r for r≥3 (r=2, resp.). We study these embeddings in quite some detail. Received: October 17, 2001?Published online: February 20, 2003     

The moduli space of stable vector bundles over a real algebraic curve

We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension of \mathbbZ/2{\mathbb{Z}/2} by the fundamental group. By comparison with the space of real or quaternionic connections, some of the basic topological invariants of these spaces are calculated.