Optimization Over the Efficient Set of Multi-objective Convex Optimal Control Problems

We consider multi-objective convex optimal control problems. First we state a relationship between the (weakly or properly) efficient set of the multi-objective problem and the solution of the problem scalarized via a convex combination of objectives through a vector of parameters (or weights). Then we establish that (i) the solution of the scalarized (parametric) problem for any given parameter vector is unique and (weakly or properly) efficient and (ii) for each solution in the (weakly or properly) efficient set, there exists at least one corresponding parameter vector for the scalarized problem yielding the same solution. Therefore the set of all parametric solutions (obtained by solving the scalarized problem) is equal to the efficient set. Next we consider an additional objective over the efficient set. Based on the main result, the new objective can instead be considered over the (parametric) solution set of the scalarized problem. For the purpose of constructing numerical methods, we point to existing solution differentiability results for parametric optimal control problems. We propose numerical methods and give an example application to illustrate our approach.     

Particle Decays and Stability on the de Sitter Universe

We study particle decay in de Sitter space–time as given by first-order perturbation theory in a Lagrangian interacting quantum field theory. We study in detail the adiabatic limit of the perturbative amplitude and compute the “phase space” coefficient exactly in the case of two equal particles produced in the disintegration. We show that for fields with masses above a critical mass m _c there is no such thing as particle stability, so that decays forbidden in flat space–time do occur here. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is comparable with de Sitter radius. Particles with mass lower than critical have a completely different behavior: the masses of their decay products must obey quantification rules, and their lifetime is zero.     

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.     

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.     

Synthèse d'hétérocycles en catalyse par transfert de phase

A general study of the chemical behavior of heterocyclic anions, dianions and dianionic reagents under phase transfer catalysis conditions allowed us to synthesize various heterocyclic compounds such as imidazo[2,1-b]thiazole and derivatives; imidazo[2,1-b]thiazine and imidazo[2,1-b]benzothiazepine. Reaction conditions e.g., catalyst, solvent, temperature, etc., are indicated.     

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.     

Hydrierung prochiraler Olefine mit Rhodium-Komplexen von optisch aktiven Amidinen

[RhCl(C₈H₁₄)₂]₂ together with the optically active amidines C₆H₅C(=NR)NHCH(CH₃) (C₆H₅) I–V or their Li derivatives after activation with molecular hydrogen gives catalysts which at room temperature and 1.1 bar H₂-pressure hydrogenate the prochiral substrates (Z)-[N-acetylamino]-cinnamic acid, itaconic acid, -methylcinnamic acid, -methylcinnamic aldehyde, and -methylcinnamic alcohol as well as cyclohexene, benzene and toluene. Good hydrogenation activity of the new catalysts is in contrast to low optical induction which only in the hydrogenation of -methylcinnamic alcohol with 1.5 to 2% leads to values different from zero.

3. Mitt.:H. Brunner undW. Pieronczyk, J. Chem. Res., im Druck.     

Action du N-bromosuccinimide sur les dioxolannes en série bicyclo [2.2.1 ]heptanique. Limitation des transpositions de wagner-meerwein

Vicinal benzoyloxy-trans-bicyclo [2.2.1] heptanic bromhydrins, otherwise difficult to obtain are formed from N-bromosuccinimide and norbornanes bearing a 2-aryl-1,3 dioxolane skeleton. The greater stability of the intermediate dioxolenium ion reduces the tendency towards both Wagner-Meerwein rearrangement and neighbouring group participation by chlorine, processes usually observed when a less stable intermediate is involved. Nevertheless, methoxycarbonyl neighbouring group participation and Wagner Meerwein rearrangment occur in methoxycarbonylbicyclo [2.2.1]heptane and in a bornanic compound respectively.