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The next step is to show that we may reduce to a n-symmetric set.
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The second step in the proof is to reduce to the case of n-symmetric sets.
These solutions reduce to a single unique solution when symmetric solutions are looked for.
The next step is to pass from an n-symmetric to an axially symmetric set.
For a circularly symmetric Gaussian, this reduces to a Euclidian distance and the likelihood requires four multiplications.
If the potential in such an equation is radially symmetric, this equation can be reduced to a half-linear equation of the form (1.4).
For U 1 = − U 2 and U 3 = 0, Eq. (74) reduces to a simple shearing motion and the solution so obtained is a symmetric solution.
To this aim, following the terminology introduced in [76] we say that (Esubset mathbb {R}^n) is an n-symmetric set if it is symmetric with respect to the n coordinate hyperplanes.
reduced to an inconvenience.
In particular, for (alpha =N), (2.6) reduces to an equality.
The idea is to reduce to spherically symmetric decreasing functions exactly as in Sect. 4 we reduced the proof of the quantitative isoperimetric inequality to axially symmetric sets.
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