Hopf cyclic cohomology and transverse characteristic classes

We refine the cyclic cohomological apparatus for computing the Hopf cyclic cohomology of the Hopf algebras associated to infinite primitive Cartan–Lie pseudogroups, and for the transfer of their characteristic classes to foliations. The main novel feature is the precise identification as a Hopf cyclic complex of the image of the canonical homomorphism from the Gelfand–Fuks complex to the Bott complex for equivariant cohomology. This provides a convenient new model for the Hopf cyclic cohomology of the geometric Hopf algebras, which allows for an efficient transport of the Hopf cyclic classes via characteristic homomorphisms. We illustrate the latter aspect by indicating how to realize the universal Hopf cyclic Chern classes in terms of explicit cocycles in the cyclic cohomology of étale foliation groupoids.     

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.     

Rankine–Hugoniot conditions obtained by using the space–time Hamilton action

In the quadri–dimensional space–time, the variation of Hamilton’s action is a powerful tool to study the process equations for conservative fluid media. In this framework, Hamilton’s principle allows to obtain equation of motions, equation of energy but also Rankine–Hugoniot conditions. The variational method may be a versatile key to obtain the shock-wave conditions for complex media when the equations of processes are not expressed by linear or quasi-linear differential equations.

     

Short communication: Thermal stability of the diazohydroborate [1‐N2B10H9]−: degradation to [B20H18]2− anion

The thermal stability of the monodiazohydroborate NMe₄[1‐N₂B₁₀H₉] was studied by thermogravimetric analysis. Under two different atmospheres (air and argon), the thermal decomposition starts at a temperature between 140 and 160 °C. The decomposition residue obtained was separated on a silica gel column. ¹¹B NMR, IR and electrospray mass spectroscopy analyses of the different fractions separated showed that the above decomposition produces (NMe₄)₂[B₂₀H₁₈] as major product (90%), along with smaller amounts of residual NMe₄[1‐N₂B₁₀H₉] (5%), (NMe₄)₂[B₁₂H₁₂] and boric acid. Copyright © 2003 John Wiley & Sons, Ltd.     

Stereoselective synthesis of new spirobenzodihydropyrancyclohexanes

A stereoselective synthesis of unknown spirobenzodihydropyrancyclohexanes is described starting from arylcyclohexenes alkylated and cyclized via a coumarin intermediate and leading to new amino derivatives which are rigid analogs of dopamine.