Schmelzreaktionen mit Aluminiumchlorid 5. Mitteilung [1] Nebenreaktionen bei der Carbazolierung von Di-(1-anthrachinonyl)-amin in Pyridin-Aluminiumchlorid-Schmelzen

Some by-products of the carbazolation of di-(1-anthraquinonyl)-amine in aluminium chloride-pyridine fusions rich in aluminium chloride are shown to result from pyridiniosubstitution and higher condensation of the 1, 2; 7, 8-diphthaloyl-carbazole primarily formed.     

Zur Abhängigkeit der Lösung von ut + (h(u))x = 0 von ihren Anfangswerten

The above equation has some remarkable properties. In general a global solution exists in a weak sense only, and this solution is not reversible in time. Furthermore it is known, that the solutions for different initial values can coincide for all t ? t₀ > 0, and the set of the initial values with this property is convex. Conditions assuring that this set contains only one element are given. This means a weak form of time-reversibility. As a global solution exists only in the weak sense, the classical question concerning dependence of the solution on the initial values needs some modification. This problem is dealt with in suitable L₁-norms. It is shown, that the L₁-norm of the difference of two weak solutions with respect to the space variable does not increase in time.     

Tensor norms and operators in the category of Banach spaces

The theory of dual functors in the category of Banach spaces is applied to the study of tensor norms in the sense of Grothendieck. The dual functors of the tensor norms arising from the projective and inductive tensor product as well as from more general tensor norms, such as the norms d_p of Saphar, are identified as various spaces of operators, which include p-integral and absolutely p-summing operators. Properties of these operators are then easily derived by categorical means. Applications of the methods provide simplified proofs of composition theorems and the characterization of dual spaces of type (L).The author acknowledges the hospitality of the University of Massachusetts at Amherst during the year when the first draft of this paper was written as well as support from the Natural Sciences and Engineering Research Council of Canada.     

An invariance principle for reversible Markov processes. Applications to random motions in random environments

We present an invariance principle for antisymmetric functions of a reversible Markov process which immediately implies convergence to Brownian motion for a wide class of random motions in random environments. We apply it to establish convergence to Brownian motion (i) for a walker moving in the infinite cluster of the two-dimensional bond percolation model, (ii) for ad-dimensional walker moving in a symmetric random environment under very mild assumptions on the distribution of the environment, (iii) for a tagged particle in ad-dimensional symmetric lattice gas which allows interchanges, (iv) for a tagged particle in ad-dimensional system of interacting Brownian particles. Our formulation also leads naturally to bounds on the diffusion constant.     

Stability determining factors in anomeric coumerosides

The thermodynamic equilibrium between the anomeric coumerosides 3 and 4 differs drastically from that which exists between their C(2)-epimers 7 and 8. Stability determining factors which govern the position of these equilibria include in addition to steric interactions the Δ2 effect and the anomeric effect. The latter is discussed in terms of orbital overlap between nonbonding electrons on oxygen and anti-bonding σ orbitals. The α-configuration of the glycoside linkages of coumermycin A₁ was secured by X-ray analysis of compound 12.     

Schmelzreaktionen mit Aluminiumchlorid 3. Mitteilung [1] Zur Kenntnis der Pyridinio-anthrachinon-Derivate aus der Pyridin-Aluminiumchloridschmelze von Aminoanthrachinonen

In continuation of previous work, the behaviour of amino-anthraquinones on fusion in pyridine - aluminium chloride in the presence of oxidants is studied. Instead of dimerisation the reaction leads to salts of pyridinio-aminoanthraquinones and further to condensed “anthraimidazopyridine” derivatives.