A fuzzy extension of Analytic Hierarchy Process based on the constrained fuzzy arithmetic

The aim of the paper is to highlight the necessity of applying the concept of constrained fuzzy arithmetic instead of the concept of standard fuzzy arithmetic in a fuzzy extension of Analytic Hierarchy Process (AHP). Emphasis is put on preserving the reciprocity of pairwise comparisons during the computations. For deriving fuzzy weights from a fuzzy pairwise comparison matrix, we consider a fuzzy extension of the geometric mean method and simplify the formulas proposed by Enea and Piazza (Fuzzy Optim Decis Mak 3:39–62, 2004). As for the computation of the overall fuzzy weights of alternatives, we reveal the inappropriateness of applying the concept of standard fuzzy arithmetic and propose the proper formulas where the interactions among the fuzzy weights are taken into account. The advantage of our approach is elimination of the false increase of uncertainty of the overall fuzzy weights. Finally, we advocate the validity of the proposed fuzzy extension of AHP; we show by an illustrative example that by neglecting the information about uncertainty of intensity of preferences we lose an important part of knowledge about the decision making problem which can cause the change in ordering of alternatives.     

Spectroscopic, morphological, and mechanistic investigation of the solvent-promoted aggregation of porphyrins modified in meso-positions by glucosylated steroids

Solvent-driven aggregation of a series of porphyrin derivatives was studied by UV/Vis and circular dichroism spectroscopy. The porphyrins are characterised by the presence in the meso positions of steroidal moieties further conjugated with glucosyl groups. The presence of these groups makes the investigated macrocycles amphiphilic and soluble in aqueous solvent, namely, dimethyl acetamide/water. Aggregation of the macrocycles is triggered by a change in bulk solvent composition leading to formation of large architectures that express supramolecular chirality, steered by the presence of the stereogenic centres on the periphery of the macrocycles. The aggregation behaviour and chiroptical features of the aggregates are strongly dependent on the number of moieties decorating the periphery of the porphyrin framework. In particular, experimental evidence indicates that the structure of the steroid linker dictates the overall chirality of the supramolecular architectures. Moreover, the porphyrin concentration strongly affects the aggregation mechanism and the CD intensities of the spectra. Notably, AFM investigations reveal strong differences in aggregate morphology that are dependent on the nature of the appended functional groups, and closely in line with the changes in aggregation mechanism. The suprastructures formed at lower concentration show a network of long fibrous structures spanning over tens of micrometres, whereas the aggregates formed at higher concentration have smaller rod-shaped structures that can be recognised as the result of coalescence of smaller globular structures. The fully steroid substituted derivative forms globular structures over the whole concentration range explored. Finally, a rationale for the aggregation phenomena was given by semiempirical calculations at the PM6 level.     

High Performance Liquid Chromatography‐Electrochemistry‐Electrospray Ionization Mass Spectrometry (HPLC/EC/ESI‐MS) for Detection and Characterization of Roscovitine Oxidation Products

On‐line LC‐EC/ESI‐MS has been established as a fast and simple method to mimic some types of oxidation reaction of various drugs and to study the formation and structure of the resulting products. This technique has been applied to a 2,6,9‐trisubstituted purine, R‐roscovitine, which is known to be an inhibitor of some cyclin‐dependent kinases (CDKs) and a potential anticancer drug. Oxidation of R‐roscovitine in an electrochemical cell (EC), operated under various conditions, resulted in appearance of 6 major products. These were further analyzed by high‐resolution mass spectrometry, their structures were elucidated by accurate mass measurement and compared to previously identified R‐roscovitine in vitro/in vivo metabolites. Although none of the observed products was structurally identical to those identified previously in vitro/in vivo, all of them, except for the methoxylated products, resembled similarity due to appearing through the same reaction type. R‐roscovitine in the EC cell underwent N‐dealkylation of the isopropyl moiety, hydroxylation of the aromatic side‐chain, dihydroxylation, methoxylation and dimer formation. The hydroxylation product was identified as Olomoucine II, a R‐roscovitine derivative, which displays 10‐times higher CDK‐inhibiting activity than R‐roscovitine and the occurrence of which, as R‐roscovitine product, has not yet been observed in vitro/in vivo.     

Fulop-Tsutsui interactions on quantum graphs

We examine scale invariant Fulop-Tsutsui couplings in a quantum vertex of a general degree n. We demonstrate that essentially same scattering amplitudes as for the free coupling can be achieved for two (n−1)-parameter Fulop-Tsutsui subfamilies if n is odd, and for three (n−1)-parameter Fulop-Tsutsui subfamilies if n is even. We also work up an approximation scheme for a general Fulop-Tsutsui vertex, using only n δ function potentials.     

The structure of Valdivia compact lines

We study linearly ordered spaces which are Valdivia compact in their order topology. We find an internal characterization of these spaces and we present a counter-example disproving a conjecture posed earlier by the first author. The conjecture asserted that a compact line is Valdivia compact if its weight does not exceed ℵ₁, every point of uncountable character is isolated from one side and every closed first countable subspace is metrizable. It turns out that the last condition is not sufficient. On the other hand, we show that the conjecture is valid if the closure of the set of points of uncountable character is scattered. This improves an earlier result of the first author.