Covering partially directed graphs with directed paths

We consider graphs which contain both directed and undirected edges (partially directed graphs). We show that the problem of covering the edges of such graphs with a minimum number of edge-disjoint directed paths respecting the orientations of the directed edges is polynomially solvable. We exhibit a good characterization for this problem in the form of a min-max theorem. We introduce a more general problem including weights on possible orientations of the undirected edges. We show that this more general weighted formulation is equivalent to the weighted bipartite b-factor problem. This implies the existence of a strongly polynomial algorithm for this weighted generalization of Euler's problem to partially directed graphs (compare this with the negative results for the mixed Chinese postman problem). We also provide a compact linear programming formulation for the weighted generalization that we propose.     

Generalized inverses and the maximal radius of regularity of a Fredholm operator

Operators possessing analytic generalized inverses satisfying the resolvent identity are studied. Several characterizations and necessary conditions are obtained. The maximal radius of regularity for a Fredholm operatorT is computed in terms of the spectral radius of a generalized inverse ofT. This provides a partial answer to a conjecture of J. Zemánek.     

Dissipative terms of thermal nature in the theory of an ideal monoatomic superfluid

A dissipative model of helium II was built up in previous works, using a 13-field extended thermodynamic theory formulated by Liu and Müller. In this work a generalization of such model is presented, where an extended thermodynamics with 14 fields due to Kremer is used. It is shown that the fourteenth field is able to account for the experimental data concerning the second sound attenuation. Further, the proposed theory is able to explain the Osborne experiment. Finally, a comparison with the two-fluid model is performed, emphasizing the different ways in which the dissipative phenomena are explained by the two theories.     

1H NMR investigation of ring mobility of 1,5-benzodiazepine-2,4-diones

The ring mobility of some 1,5-benzodiazepine-2,4-diones and 1,4-benzodiazepin-2-one has been investigated by the temperature dependence of their ¹H NMR spectra. The activation parameters have been obtained, and the influence of N-1 substitution on the ring mobility is discussed, taking into account previously reported data for similar compounds.     

The variability of composition of the volatile fraction of olive oil

Aroma of olive oil is a very complex mixture of components. Analysis of head space of a series of virgin olive oil samples indicate a great variability of volatile substances composition in olives and these data probably should be related to the story of olives after collecting.     

Influence of chlorine substitution on the self-assembly of zinc phthalocyanine

The adsorption and ordering of zinc phthalocyanine (ZnPc) and octachloro zinc phthalocyanine (ZnPcCl(8)) on an Ag(111) surface is studied in situ by scanning tunneling microscopy under ultrahigh vacuum. Two-dimensional self-assembled supramolecular domains are observed for these two molecules. We show how substituting chlorine atoms for half of the peripheral hydrogen atoms on ZnPc influences the self-assembly mechanisms. While intermolecular interactions are dominated by van der Waals forces in ZnPc molecular networks, ZnPcCl(8) molecular packing undergoes a sequential phase evolution driven by the creation of C-Cl...H-C hydrogen bonds between adjacent molecules. At the end of this evolution, the final molecular assembly involves all possible hydrogen bonds. Our study also reveals the influence of molecule-substrate interactions through the presence of fault lines generating a stripe structure in the molecular film.