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A system has been designed to convert the Gaussian intensity profile of a laser beam into a more uniform distribution. This paper postulates a number of afocal lens arrangements for this purpose and details the effect of one particular combination in balancing the higher-order terms and achieving collimation of a diffraction limited output between the l/e points.
There is hope that the structure of molecular variation within populations can give evidence for recent adaptive evolution. New work on Drosophila genes that seem to have been subject to adaptive changes illustrates the difficulties in calculating the statistical significance of data trends that seem to show this.
This paper offers an alternative proof of the so-called fundamental theorem of the theory of games or the minimax theorem. The proof uses a particularization of Farkas' theorem involving the expression of one vector as a convex combination of a set of vectors. It is demonstrated that the minimax theorem holds as a consequence of this specialization of Farkas' theorem of the alternative.