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These interval partition diffusions are a key ingredient to construct a diffusion on the space of real trees whose existence has been conjectured by David Aldous.
Our construction is a piece of a more elaborate diffusion on the space of real trees, stationary with respect to the law of the Brownian Continuum Random Tree, whose existence has been conjectured by David Aldous.
On one hand, it allows us to prove the NP-completeness of the Cleaning problem, which was conjectured by Messinger et al. [M.-E. Messinger, R.J. Nowakowski, P. Prałat, Cleaning a network with brushes, Theoret. Comput. Sci. 399 (2008) 191 205].
In the literature, all existing such functions have the homogeneous property, and it was conjectured by Gong and Song that difference balanced functions must be d-homogeneous for some d with gcd d,q−1)="1.
It was conjectured by Euler in 1782 and was first proved by Tarry in 1900 by means of an exhaustive enumeration of equivalence classes of Latin squares of order six.
Inequality (1.1) was conjectured by Erdös [1] in 1935.
Inequality (1.2) was conjectured by Erdös and later proved by Lax [1].
It was conjectured by Bedford [5] that this equivalence holds for any p∈K.
The class of groups of polynomial growth coincides with the class of virtually nilpotent groups as was conjectured by Milnor and confirmed by Gromov [24].
Einstein manifolds are real-analytic in the interior and it was conjectured by Lassas and Uhlmann that they were uniquely determined up to isometry by the DN map.
It was conjectured by Yau [53] that the smallest positive eigenvalue of the operator (-Delta _Sigma ) is equal to (2), provided that (Sigma ) is embedded.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com