On multi-way metricity, minimality and diagonal planes

Validity of the triangle inequality and minimality, both axioms for two-way dissimilarities, ensures that a two-way dissimilarity is nonnegative and symmetric. Three-way generalizations of the triangle inequality and minimality from the literature are reviewed and it is investigated what forms of symmetry and nonnegativity are implied by the three-way axioms. A special form of three-way symmetry that can be deduced is equality of the diagonal planes of the three-dimensional cube. Furthermore, it is studied what diagonal plane equalities hold for the four-dimensional tesseract.     

Exploratory analysis of chromatographic fingerprints to distinguish rhizoma Chuanxiong and rhizoma Ligustici

Identification and quality control of products of natural origin, used for preventive and therapeutical goals, is required by regulating authorities, as the World Health Organization. This study focuses on the identification and distinction of the rhizomes from two Chinese herbs, rhizoma Chuanxiong (from Ligusticum chuanxiong Hort.) and rhizoma Ligustici (from Ligusticum jeholense Nakai et Kitag), by chromatographic fingerprints. A second goal is using the fingerprints to assay ferulic acid, as its concentration provides an additional differentiation feature. Several extraction methods were tested, to obtain the highest number of peaks in the fingerprints. The best results were found using 76:19:5 (v/v/v) methanol/water/formic acid as solvent and extracting the pulverized material on a shaking bath for 15 min. Then fingerprint optimization was done. Most information about the herbs, i.e. the highest number of peaks, was observed on a Hypersil ODS column (250 mm × 4.6 mm ID, 5 μm), 1.0% acetic acid in the mobile phase and employing within 50 min linear gradient elution from 5:95 (v/v) to 95:5 (v/v) acetonitrile/water. The final fingerprints were able to distinguish rhizoma Chuanxiong and Ligustici, based on correlation coefficients combined with exploratory data analysis. The distinction was visualized using Principal Component Analysis, Projection Pursuit and Hierarchical Clustering Analysis techniques. Quantification of ferulic acid was possible in the fingerprints of both rhizomes. The time-different intermediate precisions of the fingerprints and of the ferulic acid quantification were shown to be acceptable.     

N,N'-dialkyl- and N-alkyl-N-mesityl-substituted N-heterocyclic carbenes as ligands in Grubbs catalysts

Various symmetrically and asymmetrically substituted N-heterocyclic carbene (NHC) ligands bearing aliphatic nitrogen-containing side groups have been synthesised. In our attempts to isolate the corresponding second-generation Grubbs catalysts, we were unsuccessful when using the symmetrical aliphatic NHC ligands. For the asymmetrical ligands bearing an aliphatic moiety on one side and an aromatic mesityl group on the other side, substitution of a phosphine ligand was achieved. The performance of a so-formed series of Ru-based metathesis initiators has been evaluated for the ring-opening metathesis polymerisation (ROMP) of cycloocta-1,5-diene and the ring-closing metathesis (RCM) of diethyl diallylmalonate.     

Book Review The End of Certainty: Time,Chaos, and the New Laws of Nature. Ilya Prigogine. New York: Free Press, 1997. Pp. viii + 228

Nonlinear Dynamics, Psychology, and Life Sciences -     

Computation of molecular weight distributions by polynomial approximation with complete adaptation procedures

The choice of appropriate reference functions is still the major drawback for collocation techniques to be used during the computation of molecular weight distributions (MWDs) in polymerization reactions and other problems constituted by systems of differential‐difference equations. Complete adaptation procedures provide significant improvement of numerical approximations obtained, but convergence to the real solution is not assured and oscillatory numerical approximations may be obtained when the actual solution experiences large variations during time integration. An alternative method to compute the reference function in an adaptative manner, called here the integration of the reference function procedure, is presented. The technique is used to allow the computation of MWDs in two polymerization problems: the metallocene‐based propene polymerization and the methyl methacrylate/butyl acrylate emulsion polymerization. The integration of the reference function procedure allowed the proper computation of broad, bimodal and fast changing distributions with polynomials of very low order (below 4), where other approximation techniques failed. The method may be easily implemented and does not require any pre‐processing before implementation.     

Synthesis and radical polymerization of pyrocarbonate‐functionalized monomers: application to positive‐tone photoresists

The synthesis of two new tert‐butyl carbonic anhydride monomers, 4‐vinylbenzoic and methacrylic tert‐butylcarbonic anhydride was achieved successfully. Radical polymerization at 45°C yielded tert‐butyl pyrocarbonate protected materials. Thermographic analysis showed that both polymers decompose cleanly at 135°C. The lithographic performance of both materials was evaluated in the presence of 2,4,6‐tris‐(trichloromethyl)‐s‐triazine as photoacid generating species. It was demonstrated that the large polarity change results in a positively working chemically amplified photoresist system.     

1‐Methoxyhexane‐3‐thiol,a Powerful Odorant of Clary Sage (Salvia sclarea L.)

The peculiar and highly diffusive odor signal of flowering clary‐sage plants (Salvia sclarea L.) was identified to derive from trace amounts of 1‐methoxyhexane‐3‐thiol ( 1 ) by mass‐spectrometry analysis and confirmed by comparison with synthetic racemic thiol (±)‐ 1 . The enantiomers (S)‐ and (R)‐ 1 were prepared by enantioselective synthesis, and the absolute configuration of (S)‐ 1 was fully corroborated by X‐ray‐diffraction analysis of the crystalline thioester (1′S,1S)‐ 2 . Compound (S)‐ 1 is one of the most powerful odorants known, with a detection threshold of 0.04⋅10⁻³ ng/l air, and is, with its herbaceous‐green, alliaceous, and perspiration profile, key to the fragrance of clary‐sage flowers and of the freshly distilled essential oil. As a consequence of its unique odor, 1 was also suspected to be part of the volatiles of a Ruta species where it was subsequently identified together with its homologue, 1‐methoxyheptane‐3‐thiol ( 3 ), 1‐methoxy‐4‐methylpentane‐3‐thiol ( 4 ), and the known 4‐methoxy‐2‐methylbutane‐2‐thiol ( 5 ). The syntheses of (±)‐ 3 and (±)‐ 4 as well as of the enantiomer (R)‐ 4 are described. In both natural fractions, the ratio (S)‐ 1 /(R)‐ 1 was slightly in favor of the (S)‐enantiomer. Natural 4 has (R)‐configuration.