Sentence examples for uniquely determining from inspiring English sources

If we understand the theory of the reals prior to the cuts, we can say that each cut is of the form L = (−∞, r) ∩ Q, R = [r, ∞) ∩ Q, where Q is the set of all rationals and r is a unique real number uniquely determining and uniquely determined by the cut. It is obvious that each real number r uniquely determines a cut in this way (but we need to show that there are no other cuts).

We present a method for uniquely determining the mixing energy density coefficients involved in the N-phase model based on the pairwise surface tensions among the N fluids.

Explicit iterative formulas have been derived for uniquely determining the coefficients of normal forms and associated non-linear transformations up to an arbitrary order.

For there are infinitely many mathematical structures, and there is no way of uniquely determining which of them is actually instantiated or even instantiated only in part in a finite region of the physical world.

Asymptotic series have the virtue of uniquely determining the perturbation coefficients from the eigenvalues as functions and they often give good numeric results if (beta ) is small and one takes only a few terms.

However, detailed modeling by dividing the region into smaller zones (due to the large scatter in the observed intensities) may be the only solution to uniquely determining the dust properties to the South of Spica.

The operator is, however, not uniquely determined by the measure.

The effective layer thickness t can also be uniquely determined from first-principles calculated bending energy49.

Asked why Mancunians seemed uniquely determined to wreck the bikes, he said: "We aren't sure.

Generally, a symmetric tensor decomposition can be uniquely determined by a generating matrix.

One change had to be made to uniquely determine all the cards using our notation.