Bodies invisible in one direction and bodies of zero total cross section

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We consider a body in a parallel flow of non-interacting particles. One can imagine that the flow is highly rarefied or consists of light rays. The interaction of particles with the body is perfectly elastic. We introduce the notions of a body of zero resistance and an invisible body and prove that all such bodies do exist.
Submitted to proceedings for the 9th International Conference on Mathematical and Numerical Aspects of Waves Propagation June 15-19, 2009 Pau, France

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