An HPLC-DAD and LC-MS study of condensation oscillations with S(+)-ketoprofen dissolved in acetonitrile

In our earlier studies, a spontaneous chiral conversion of the selected low-molecular-weight carboxylic acids (i.e., amino acids, hydroxy acids, and profen drugs) dissolved in aqueous ethanol medium, running in vitro was described. Then it became clear that this spontaneous chiral conversion is accompanied by the spontaneous condensation of the discussed compounds. With several acids, it was established that this condensation is also oscillatory in nature. The theoretical models were developed aiming to give a rough explanation of the observed non-linear processes. In this paper, the results of these studies on the dynamics of condensation with S(+)-ketoprofen, a very popular profen drug, when stored for certain amount of time dissolved in a non-aqueous medium (i.e., acetonitrile) is presented. These investigations were carried out with the aid of two independent high-performance liquid chromatographic systems with the diode array detection and of a third high-performance liquid chromatographic system equipped with mass spectrometric detection. In one cycle of chromatographic measurements, it was possible to monitor condensation of S(+)-ketoprofen in 25-min intervals for 30 h, thus obtaining kinetic information on the progress of this process. Mass spectrometric detection confirmed the presence of new species in the stored solution with molecular weights much higher than that of S(+)-ketoprofen, which can be attributed to the condensation products. The obtained data show that condensation of S(+)-ketoprofen dissolved in acetonitrile progresses in a rapid manner, and that the observed oscillatory concentration changes with S(+)-ketoprofen and with the main condensation product characterize with an irregularity and shallow amplitudes. A theoretical model was referenced that jointly describes the oscillatory chiral conversion and the oscillatory condensation with the low-molecular-weight chiral carboxylic acids.     

Acyclic homomorphisms to stars of graph Cartesian products and chordal bipartite graphs

Homomorphisms to a given graph $H$ ($H$-colourings) are considered in the literature among other graph colouring concepts. We restrict our attention to a special class of $H$-colourings, namely $H$ is assumed to be a star. Our additional requirement is that the set of vertices of a graph $G$ mapped into the central vertex of the star and any other colour class induce in $G$ an acyclic subgraph. We investigate the existence of such a homomorphism to a star of given order. The complexity of this problem is studied. Moreover, the smallest order of a star for which a homomorphism of a given graph $G$ with desired features exists is considered. Some exact values and many bounds of this number for chordal bipartite graphs, cylinders, grids, in particular hypercubes, are given. As an application of these results, we obtain some bounds on the cardinality of the minimum feedback vertex set for specified graph classes.