Synthesis of benzo analogs of oxoarcyriaflavins and caulersine

In the course of a program aimed at designing new antitumor agents, we were interested in the synthesis of mixed structures of maleimidophenyl carbazoles and natural product caulersine as potential CDK inhibitors. This was performed through an efficient four-step sequence starting from indole or 3-formyl-N-Boc indole. 5H-Benzocycloheptaindol-6-one derivatives equipped with a fused maleimide (oxophenylarcyriaflavins) or a methyl ester (benzo analog of caulersine) on the central tropone ring were thus obtained.     

Interaction of wetting fronts with an impervious surface — Longer time behaviour

The interaction of a wetting front with an impervious surface can be described very easily in the early stages of interaction by using a superposition principle. After the time when the superposition principle fails to describe the interaction properly, two flow regimes are analysed. For most of the interaction the profile is only affected by the impervious surface near that surface and in particular the inflow into the soil layer is unchanged. Then, only at the very end of the process is the inflow decreasing because of the impervious surface.     

Generalized fractional programming: Algorithms and numerical experimentation

Several algorithms to solve the generalized fractional program are summarized and compared numerically in the linear case. These algorithms are iterative procedures requiring the solution of a linear programming problem at each iteration in the linear case. The most efficient algorithm is obtained by marrying the Newton approach within the Dinkelbach approach for fractional programming.     

A remark on two-dimensional stokes flow solutions

Summary It is shown that the solution of Laplace's equation is useful to obtain a unique Stokes stream function which is valid everywhere under limited circumstances. When the Stokes stream function fails at infinity the use of the Oseen solution is required to obtain a physically acceptable solution.

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Résumé Les solutions de l'équation de Laplace permettent d'obtenir des fonctions de courant au sens de Stokes uniques et valides en tous points de l'espace, dans certains cas seulement. Quand les fonctions de courant au sens de Stokes ne sont pas valides à l'infini l'utilisation de functions de courant au sens d'Oseen est nécessaire pour obtenir une solution physiquement valable.

     

Über die Bildung von Dihydro-1,2-oxazin-N-oxiden durch intramolekulare Addition eines Nitronat-Anions an eine Carbonylgruppe

The Formation of Dihydro-1,2-oxazine N-Oxides through an Intramolecular Addition of a Nitronate Anion to a Carbonyl Group Highly substituted 4-keto-1-nitroalkanes cyclize under basic conditions to dihydro-1,2-oxazine N-oxides. These N-oxides are thermally unstable and decompose to 1,4-diketones, BF₃ catalyzes a similar decomposition, but probably via a different mechanism.     

Electrochemical coupling of mono and dihalopyridines catalyzed by nickel complex in undivided cell

One step nickel-catalyzed electroreductive homocoupling among 2-bromopicolines and 2-bromopyridine has been investigated by our group in an undivided cell and using zinc or iron as sacrificial anode. In this work, it was developed mono and dihalopyridines coupling to obtain possible products from heterocoupling. A series of reactions were carried out in order to develop a synthetic method for the preparation of unsymmetrical 2,2′-bipyridines and 2,2′:6′,2″-terpyridines. Statistical yields (50%) were observed for 2-bromopyridines/2-bromo-6-methylpyridine heterocoupling. In a preliminary study devoted to terpyridines preparation, good results were obtained for 2,6-dihalopyridines homocoupling, affording 2,6-dichloro-2,2′-bipyridine (46%) and 2,6-dibromo-2,2′-bipyridine (56%), at controlled reaction time. At major reaction time, it was observed that the direct electroreduction of the 2,6′-dihalo-2,2′-bipyridines intermediates and 2,6″-dihalo-2,2′:6′,2″-terpyridines products on the cathode surface. A reasonable isolated product yield of 6,6″-dimethyl-2,2′:6′,2″-terpyridine (10%) was only observed in the reaction between 2,6-dichloropyridine and 2-bromo-6-methylpyridine (1:2).     

An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles

The vehicle routing problem with multiple use of vehicles is a variant of the classical vehicle routing problem. It arises when each vehicle performs several routes during the workday due to strict time limits on route duration (e.g., when perishable goods are transported). The routes are defined over customers with a revenue, a demand and a time window. Given a fixed-size fleet of vehicles, it might not be possible to serve all customers. Thus, the customers must be chosen based on their associated revenue minus the traveling cost to reach them. We introduce a branch-and-price approach to address this problem where lower bounds are computed by solving the linear programming relaxation of a set packing formulation, using column generation. The pricing subproblems are elementary shortest path problems with resource constraints. Computational results are reported on euclidean problems derived from well-known benchmark instances for the vehicle routing problem with time windows.