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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.
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].
Inequality (1.1) was conjectured by Erdös [1] in 1935.
It was conjectured by Bedford [5] that this equivalence holds for any p∈K.
Inequality (1.2) was conjectured by Erdös and later proved by Lax [1].
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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.
Also, because no adjusted data were reported for male and female levels, the impact of such an adjustment cannot be conjectured by the reader.
Intrinsic to this modelling is identification of a distinct relevant feature subset specific to each sample cluster, that is, for the microarray domain, each subclass will have its own gene set, as has been conjectured by Shedden et al (2003); Ein-Dor et al (2005).
We also show the non-existence of a 2-fold perfect (10, 9, 1 -Mendelsohn design which was conjectured to exist by Dénes.
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