end{aligned}It is easy to check that a curve with this property is automatically a geodesic, and that the following three facts are equivalent (for arbitrary ( p>1)) 1. (omega ) is a constant-speed geodesic defined on ( [t_0,t_1]) and joining (x_0) and (x_1), 2.
What is now described is the equivalent for an arbitrary current distribution.
convergence for random variables, are studied with the use of some properties of the geometry of projectors from U. The conditions are equivalent if (xn) is bounded, and are not equivalent for an arbitrary sequence.
As it turns out, and as Kuznetsov has shown, these algorithms are equivalent in their effect to algorithms for finding the maximal complete subgraphs of arbitrary graphs.
In fact for any arbitrary interval [ k, l] is equivalent to such that [ k', l'] is the common subsequence between [ i, j] and [ k, l].
Two arbitrary screws in space are equivalent to the sum of the mutual moment relation.
One arbitrary unit (1 AU) is equivalent to the reciprocal plasma dilution that gives an OD of 1.0 over background.
Mathematically, nonlinear image registration is equivalent to optical flow because optical flow is also represented as an arbitrary 2D-2D function.
Since the order of the recording leads used for the bipolar derivation was arbitrary, the signal from S1 was reversed in polarity, which is equivalent to a depth-to-surface subtraction.
For an arbitrary subshift and for (alpha ge 1), which of the order conditions (alpha )-repetitive, (alpha )-repulsive and (alpha )-finite are equivalent?
