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\[ f_0(x,v) = \left(\frac{9}{10 \sqrt{2\pi}} \mathrm{e}^{-0.5 v^2} + \frac{2}{10 \sqrt{2\pi}} \mathrm{e}^{-2 (v-4.5)^2} \right) (1+\alpha \cos(kx)), \]
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