Palladium‐catalyzed reactions in general are carried out under an inert atmosphere because the palladium intermediates involved in the catalytic cycles are often known to be sensitive to oxygen. In this paper, we report that various palladium‐catalyzed reductive couplings proceed smoothly under an air atmosphere and in aqueous medium. Under the air atmosphere reaction conditions, palladium‐triphenylphosphine complex was found to be inactive. By using zinc as the reducing reagent, aryl halides were homo‐coupled to give symmetrical biaryls either in aqueous acetone or in water in the presence of a catalytic amount of 18‐crown‐6 at room temperature. Both aryl iodides and aryl bromides reacted efficiently under the current reaction conditions. The reaction of arylhalosilanes with aryl halides under refluxing conditions in air and water catalyzed by palladium generated unsymmetrical biaryls efficiently in the presence of either KOH or NaF. Such air‐stable couplings are also suitable for a Suzuki‐type coupling and a Stille‐type coupling.
This paper deals with the axisymmetric contact problem for an elastic half-space with a cylindrical cavity when mixed boundary conditions are prescribed on the surface of the cavity. The problem is simplified to that of finding the solution of dual integral equations arising from the mixed boundary conditions. The solution is obtained by the series method, and quantities of physical interest are calculated.
The nonlinear Rayleigh‐Taylor stability of the cylindrical interface between the vapor and liquid phases of a magnetic fluid is studied when the phases are enclosed between two cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. The method of multiple time scale expansion is used for the investigation. A simple nondimensional parameter is found to characterize the stability of the system. Using this parameter, the region of stability is displayed graphically.
The method of multiple scales is used to analyse the nonlinear breakup of a planar jet in the presence of electric field taking into account surface tension. The evolution of the amplitude is governed by a nonlinear Schrödinger equation which gives the criterion for modulational instability. Numerical result is given in the graphical form.
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