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Lemanczyk","submitted_at":"2010-02-13T22:10:20Z","abstract_excerpt":"We consider special flows over two-dimensional rotations by $(\\alpha,\\beta)$ on $\\T^2$ and under piecewise $C^2$ roof functions $f$ satisfying von Neumann's condition $\\int_{\\T^2}f_x(x,y)\\,dx\\,dy\\neq 0\\neq \\int_{\\T^2}f_y(x,y)\\,dx\\,dy.$ Such flows are shown to be always weakly mixing and never partially rigid. For an uncountable set of $(\\alpha,\\beta)$ with both $\\alpha$ and $\\beta$ of unbounded partial quotients the strong mixing property is proved to hold. 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