But in 1879 two American mathematicians proved that only one-half of all possible initial arrangements, or about 10,000,000,000,000, admitted of a solution.
Williams was almost alone in his time in holding not only that the problem does admit of a solution, but in presenting a novel solution of his own.
Once one accepts that a "reality" predicate is needed to characterize ontological commitment, a puzzle about the logic of ontological commitment admits of a natural solution.
There is then a paradox in the notion of perceiving an event as occurring after another, though one that perhaps admits of a straightforward solution.
You must agree that while we may want to stay the course, we simply can't, because the inner problems of Iraq do not admit of any solution other than the imposition of a new authoritarianism, the very thing we went to war to eliminate.
Frigg and Reiss argue that whether a model admits of analytic solution or not has no bearing on how it relates to the world.
We show that a class of semidefinite programs (SDP) admits a solution that is a positive semidefinite matrix of rank at most r, where r is the rank of the matrix involved in the objective function of the SDP.
Substituting (34) into the right hand side of Equation 30, which admits a solution w 2 = h 12 g 1 g 2, h 12 = ( c 1 − c 2 ) 2 ( c 1 + c 2 ) 2. Open image in new window (35).
If (lambda_{1}<0), then steady state equations of (1) admit a solution (see [1]), psi= sqrt{-lambda_{1} / gamma_{2}}e^{i phi}, qquad u=0,quad phiin[0, 2pi). Equation (1) is invariant when we apply an orthogonal transformation, so (phi=0) in a properly chosen coordinate system of (mathbb{C}). Note that we always assume this coordinate system in this paper.
It follows from Theorem 6 that those algorithms defined by recurrence equations, whose associated functional is a mapping Ψ of type (3), admit a solution.
To find a spacetime in which the philosophical problem posed by bifurcated supertasks admits of the simple solution that has just been mentioned, we will move from the flat spacetime of special relativity to the curved spacetimes of general relativity.
