Locating the vertices of a steiner tree in an arbitrary metric space

Given a tree each of whose terminal vertices is associated with a given point in a compact metric space, the problem is to optimally associate a point in this space to each nonterminal vertex of the tree. The optimality criterion is the minimization of the sum of the lengths, in the metric space, over all edges of the tree. This note shows how a dynamic programming solution to this problem generalizes a number of previously published algorithms in diverse metric spaces, each of which has direct and significant applications to biological systematics or evolutionary theory.     

Über die π-Elektronenstruktur der 1,2-Dipyridyl-äthylene, 2. Mitt.: Die Spektralübergänge

Zusammenfassung Es werden die charakteristischen Größen der Spektralübergänge der 1,2-Dipyridyl-äthylene berechnet und an Hand des Vergleichs mit gemessenen Werten diskutiert.Mit 1 Abbildung     

Phenomenological analysis of the linear magnetic birefringence in dysprosium iron garnet

Experimental data on linear magnetic birefringence (LMB), previously reported at 1.15 μm wavelength in the 4.2-300 K temperature range and with an applied field up to 20 kOe, in dysprosium iron garnet (DyIG) are analyzed in terms of electric dipole transition within the three magnetic sublattices. Assuming that the garnet symmetry is cubic and that the contribution of the Fe³⁺ ions to LMB is the same as yttrium iron garnet (YIG), the 2nd order magneto-optical (MO) coefficient (Γ₂) of the Dy³⁺ ions is deduced. In the spontaneous state, Γ₂ is linear temperature dependent as previously found for the 1st order (MO) coefficient. It is shown that Γ₂ must be field dependent to explain the evolution of the LMB.     

Échanges inter et intra-molćulaires du proton entre deux atomes d'azote de cycles chélatés hydrazone-imine et azo-énamine

Inter- and intra-molecular exchanges of chelated proton are evaluated by NMR in arylhydrazones derived from β-keto-imines and β-diimines.     

Gravity induced vortices and stepwise growth of these vortices in vertical counterflow of liquid helium

Detailed measurements of the second sound excess attenuation in vertical counterflow show the existence of a zero critical velocity and of steps which can be interpreted as a Josephson A.C. effect related to vortex motion.     

Effets de cryptands et activation de bases—II: Genese d'enolates et essais d'activation de LiH,NaH et KH dans l'ether,le THF et le benzene

The generation of the lithium, sodium and potassium enolates of cyclohexanone using LiH, NaH and KH has been investigated. The utilization of macrocyclic ligands (which selectively complex the metal cation) activated the alkaline hydride reagent. However, the most dramatic effect was the activation of the enolate, enabling proton abstraction from the solvent.     

Une nouvelle synthese de l'ellipticine et ses analogues structuraux

Two new syntheses of the 6H-pyrido [4,3-b] carbazole system are described. The first method involves the cyclization of a (2-alkyl-skatyl)-piperidone whereas the second leads to ellipticine by the participation of the indole nucleus in the rearrangement of tertiary acetylenic alcohols in acidic medium.