Hermite and Smith normal form algorithms over Dedekind domains

We show how the usual algorithms valid over Euclidean domains, such as the Hermite Normal Form, the modular Hermite Normal Form and the Smith Normal Form can be extended to Dedekind rings. In a sequel to this paper, we will explain the use of these algorithms for computing in relative extensions of number fields.

     

Variable sampling interval Shewhart control charts for monitoring the multivariate coefficient of variation

In many industrial manufacturing processes, the ratio of the variance to the mean of a quantity of interest is an important characteristic to ensure the quality of the processes. This ratio is called the coefficient of variation (CV). A lot of control charts have been designed for monitoring the CV of univariate quantity in the literature. However, the CV control charts for multivariate quantity have not received much attention yet. In this paper, we investigate a variable sampling interval (VSI) Shewhart control chart for monitoring multivariate CV. The time between two consecutive samples is allowed to vary according to the previous value of the multivariate CV, which will help the chart to detect the process shifts faster. The comparison with the fixed sampling interval Shewhart chart is implemented to highlight the advantage of the VSI method. Finally, an illustrative example is demonstrated on real data.     

Host-guest interaction between cyclen based macrotricyclic ligands and phosphate anions. A potentiometric investigation

The host-guest interaction between orthophosphate, pyrophosphate and triphosphate anions and three cyclen based macrotricyclic ligands possessing ortho- (TOC), meta- (TMC) and para-xylenyl (TPC) linkers was investigated by potentiometric measurements. The ternary species present in solution and their stability constants have been determined. The different behaviours are explained in terms of hydrogen bond formation and coulombic attraction between the organic host and the inorganic guest. The selectivity, illustrated with species distribution diagrams, is discussed. The results unambiguously showed the importance of the distance between the two cyclen cores and emphasized the increasing of the triphosphate species selectivity together with the cavity size of the ligand. A comparison of the present results with those obtained with their mono-bridged homologues is also discussed.     

Optisch aktive übergangsmetall-komplexe : XXV. Substituenteneinflüsse auf die intramolekulare epimerisierung von tetragonal-pyramidalen molybdanund wolfram-komplexen

The synthesis, IR, ¹H NMR and UV spectra of optically active square pyramidal cyclopentadienyldicarbonyl-molybdenum and -tungsten complexes with Schiff bases, derived from methyl-substituted pyridine carbaldehyde(2) and S-(—)-α-methylbenzylamine, are described. The epimerisation of these complexes, measured polarimetrically at 75–97°C in DMF, follows a 1^st order rate law and represents a regular pentatopal skeletal rearrangement. The inductive effect of a methyl group in the para position of a pyridine ring leads to a retardation of the epimerisation compared to unsubstituted complexes. The rate constants decrease even more if an ortho methyl group is introduced into the pyridine system, since additional steric effects are introduced. If the metal complex contains a 4,6-dimethyl-substituted Schiff base as a chelating ligand, the contributions of a 4- and a 6-methyl group are additive. A benzene ring fused to the 5,6-positions of the pyridine system also leads to stabilisation of the configuration.     

IsoméRisation avant la perte d'eau des ions aldéhydes et cétones protonés en spectrométrie de masse

Isomerization of Protonated Aldehyde and Ketone Ions in the Mass-Spectrography Before the Loss of Water In mass spectrometry, protonated aldehyde and ketone ions isomerize before the loss of a molecule of water. In order to specify this process, the spectra of deuterium labelled protonated aldehydes and ketones have been compared to the spectra of the corresponding isomer ions.     

The Synthesis of 3,5-Diamino-1,2,4-oxadiazoles. 1st Communication

Reaction of the 1-substituted-3-cyano-isothioureas 6 with hydroxylamine gave mixtures of the 5-amino-3-substituted-amino-1,2,4-oxadiazoles 1 and the isomeric 3-amino-5-substituted-amino-1,2,4-oxadiazoles 8 in which 1 usually predominated. The structural assignment of these products is discussed. In a second method, the 2-hydroxy-1-methyl-1-phenyl-guanidine 15 was converted to the corresponding 3-disubstituted-amino-5-trichloromethyl-1,2,4-oxadiazole 16 , a precursor to the 5-amino derivatives 17 by nucleophilic displacement of the trichloromethyl group.     

Disclosure of the imidazolium cation coordination and stabilization mode in ionic liquid stabilized gold(0) nanoparticles

A surface-enhanced Raman spectroscopy (SERS) study of imidazolium ionic liquid stabilized gold(0) nanoparticles (GNPs) furnished previously unknown knowledge about the coordination and stabilization mode of the imidazolium cation. GNPs were prepared by hydrazine reduction of a chloroauric acid solution in 1-triethylene glycol monomethyl ether-3-methylimidazolium methanesulfonate 2 as ether-functionalized room-temperature ionic liquid (RTIL). UV-vis spectroscopy showed the presence of GNP aggregates as absorptions extended to the NIR region. A parallel coordination mode for the imidazolium cation of RTIL 2 on the GNP surface was observed by SERS, which occurred without the simultaneous coordination of the 1-triethylene glycol monomethyl ether-functionality. Instead of this, the ether-functionality was directed away from the GNP surface and acted as steric barrier between the GNPs/GNP aggregates, thus preventing further aggregation. These new insights suggest that the imidazolium cation is responsible for electrosteric stabilization.