The Intramolecular Diels-Alder Furan Approach in Synthesis : 11-oxatricyclo|6.2.1.01,6|undec-9-en-5-one

Although the synthetic potential of the intramolecular variant of the Diels-Alder reaction has now been fully recognized³, little attention has so far been paid to this type of addition using the furan nucleus as the diene partner4–8. The presence of an oxygenated cyclohexene system in several complex natural products (e.g. gibberellic acid, morphine), the diverse possibilities of the substituted 7-oxabicyclo |2.2.1|-2-heptene system for further transformation⁹, the expected enhanced reactivity and stereoselectivity of the intramolecular cycloaddition and the availability of a wide variety of commercial furan derivatives make the sequence a → b → c particularly attractive in total synthesis.     

The Callan-Symanzik equation and dimensional regularization

A study is made of the Callan-Symanzik equation using the dimensional regularization method. The final equation is far more general than in the usual derivation in that the effect of mass terms is explicitly included; moreover the momenta need not be restricted to the deep-Euclidean region when considering asymptotic limits.     

Decay of metastable states in Nd II

The difficulty associated with an accurate determination of transition rates for forbidden lines in lowly ionized heavy elements is illustrated in the case of Nd II. We have investigated the radiative decay of the low-lying metastable levels in Nd⁺ including the two levels K_11/2 and I_13/2. In these two particular cases, using different theoretical approaches, we find that the decay is dominated by the M1 channels but that the E2 contributions are of the same order of magnitude. These levels have also been studied experimentally by lifetime measurements with the heavy ion storage ring CRYRING of Stockholm University. The difficulties encountered when performing such experiments are underlined and discussed.     

On the infrared behaviour of massless φ4 theory for small ϵ

In this paper we compare a formulation that gives the full infrared singular behaviour of massless φ⁴ theory for all continuous dimensions below four with the ?-expansion. These theories give very different result for small ?! We give then arguments that suggest that the ?-expansion when combined with the renormalization group may be based on too strong analyticity assumptions.     

Stahl und Eisen

Ohne Zusammenfassung     

Calculation of cyclotron resonance linewidth due to ionized impurities and longitudinal optical phonons

The cyclotron resonance linewidth for free carriers in semiconductors is calculated, starting from the Kubo formula. Ionized impurity and LO phonon scattering are taken into account. The absorption spectrum is investigated in the Relaxation Kernel approach and the scattering is treated in the lowest order Born approximation. For T>15 K, excellent agreement is obtained with the measurements of Matsuda et al. in InSb. No adjustable parameters are introduced.     

On some multivariate gamma-distributions connected with spanning trees

Any correlation matrixR can be mapped to a graph with edges corresponding to the non-vanishing correlations. In particularR is said to be of a tree type if the corresponding graph is a spanning tree. The tridiagonal correlation matrices belong to this class. If the accompanying correlation matrixR or its inverse is of a tree type, then some representations of the multivariate gamma distribution are obtained with a much simpler structure than the integral or series representations for the general case.     

Intramolecular diels-alder reaction with furan-diene. A novel potential entry to steroids.

Depending on the reaction conditions the intramolecular Diels-Alder reaction of furan-diene $\text{14}$ yields predominantly either one of two adducts $\text{16a}$ and $\text{16b}$, which possess the necessary functionality for eventual transformation into corticosteroids. The dienophile was introduced via alkylation of the enolate, formally obtained upon lithium-liq. ammonia reduction of 3-furyl-2-methyl-2-cyclopentenone ($\text{7}$).