Bredt Compounds and the Bredt Rule

The Bredt rule, which proved useful in earlier decades mainly as an exclusion criterion in the assignment of structures, has in recent years become the stimulus for efforts to synthesize strained bicyclic systems with a bridgehead double bond. On the basis of the ring-strain forces operating in such systems, an extended Bredt rule is discussed. The “Bredt comgounds” to which this rule applies, which include bicyclic systems not prevoously consodered from this point of view (e.g. bridged methylenecyclopropanes), form a clearly circumscribed, interesting field within the chemistry of highly-strained hydrocarbons with ring unsaturation.     

A phenomenological investigation of the shower particle pseudorapidity fluctuations in hadron-nucleus collisions

From the experimental matrix $\text{?(N}{}_{\mathrm{<mtext>g</mtext>}}\text{; n}{}_{\mathrm{<mtext>s</mtext>}}\text{, Δη}{}_{\mathrm{i}}\text{)}$ (the number of events with a given number N_g of particles with velocity 0.3c<v<0.7c, and n_s, the number of shower particles (v > 0.7c) in a pseudo-rapidity interval Δη_i) obtained from the Heidelberg-Igel hadron-nucleus experiment at CERN, we extract the shower particle multiplicity distributions as a function of ν, the number of nucleons that interacted with the projectile. We use a theoretically justified statistical correlation between ν and N_g (recoil protons) and the assumption that the correlation between n_s and N_g is given merely through ν. The data used are for incoming energies 50 and 150 GeV with a proton or pion as the projectile and Cu or Pb as the target. We find that the shower particle multiplicity distributions are of a Poissonian character in each η bin and for each value of ν. The average multiplicities $\text{〈n}{}_{\mathrm{<mtext>s</mtext>}}\text{〉(ν)}\text{Δη}{}_{\mathrm{i}}$ are approximately the same for the two targets and for the different projectile, possibly with a small excess for the pion projectile.The results are compared to a rather general theoretical model of the soft interaction type. The predictions from this model for the shower particle pseudorapidity distributions are very close to the derived values.     

Semiclassical calculation of energy transfer in polyatomic molecules. V. Differential cross sections for excitation of CO2 and N2O colliding with Li+ at E ≈ 4.72 eV

A semiclassical model has been used to calculate differential cross sections for vibrational excitation of CO₂ and N₂O at the center of mass collision energy E≈ 4.72 eV. Also the average rotational excitation as a function of the scattering angle is reported. Comparison is made with experimental data and previous more approximate theoretical calculations.     

Author index to volume 48

The vibrational energy transfer in a polyatomic molecule is described by introducing an irreducible set of operators. Each operator represents a specific interaction induced by the intermolecular potential. We present a graphic method which significantly facilitates the solution if the number of quantum modes (M) is large.     

Ansätze zur begründung theoretischer terme in der mathematik—Die theorie des unendlichen bei Johann Schultz

In dem Artikel wird der Beitrag des Königsberger Mathematikers Johann Schultz (1739–1805) zur Theorie des Unendlichen diskutiert. Im Gegensatz zur vorherrschenden Benutzung des Unendlichen als einer heuristischen Fiktion begründet Schultz die Realität des mathematischen Unendlichen und entwickelt, aus Anlaß seines Versuchs, das Parallelenpostulat zu beweisen, eine Theorie zum Operieren mit diesem Begriff. Trotz der Inkonsequenzen seiner Theorie, die sich vor allem in der Anwendung auf eine “Geometrie des Unendlichgroßen” auswirken, hat Schultz in seiner Theorie wichtige Fortschritte erzielt, so die Trennung der Begriffe von Zahl und Größe, die Einführung des Begriffs der Menge als Verallgemeinerung des Zahlbegriffs für das Unendliche und die Trennung des Unendlich-Kleinen vom Unendlich-Großen. Da die zeitgenössischen Mathematiker nicht die Inkonsequenzen von Schultz' Theorien und die fehlerhafte Anwendung in der Geometrie erkannten, vermuteten sie den Fehler im theoretischen Ansatz, der daher—bis auf Ausnahmen—nicht weiterentwickelt wurde.This article discusses a publication by the Königsberg mathematician Johann Schultz (1739–1805) on a theory of the infinite. Rather than develop the infinite as a useful heuristic fiction, Schultz establishes the reality of the mathematical infinite and develops this concept to prove the parallel postulate. Despite the inconsistencies of his theory, which appeared particularly in applications to a “Geometry of the Infinite,” Schultz achieved important advances in his theory, including the distinction between the concepts of number and magnitude, the introduction of the concept of set as a generalization of the number concept for the infinite, and the separation of the infinitely-small from the infinitely-large. Since contemporary mathematicians did not recognize the inconsistencies of Schultz' theories and their faulty application in geometry, they assumed the errors to lie in his theoretical foundations, which therefore, with but few exceptions, were not developed further.