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The theoretical analysis of the velocity distribution within a lenticular liquid filament flowing down an inclined plane is presented. The solution based on a series expansion, whose validity depends on the smallness of the filament's height to width ratio, is compared graphically with an exact numerical solution. The gas-liquid lenticular interface is determined in such a way that all constants are known directly in terms of measurable physical parameters.

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In this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those induced by constant functions of modulus 1. We then describe the spectrum of the multiplication operators in terms of the range of the symbol. Lastly, we identify the isometries and spectra of a particular class of weighted composition operators on the Bloch space.2000 Mathematics subject classification: primary 47B38; secondary 30D45.