Sentence examples for minimum of a solution from inspiring English sources

In Theorem 3, unimprovable bounds of the difference between the maximum and the minimum of a solution are established.

Some compositions beginning with a bare minimum of pieces involve a solution of more than 20 moves.

The extracts were dried under vacuum and re-suspended in a minimum volume (10 µl) of a solution at 0.1% formic acid and 5% acetonitrile and 4 µl of peptide extract were analysed.

With the two skilled lemmas (Lemmas 2.3, 2.4 in [10]) on the properties of the singular term f, we can show that the negative local minimum point is a solution of problem (1.3).

Standard numerical techniques such as gradient descent converge to a local minimum of the solution space, and different procedures often find different local minima.

The minimum concentration of a sugar solution required to prevent the growth of most pathogenic bacteria is 29% (w/v) along with a water activity value (aw) of between 0.86 and 0.89.

The minimum of the solution (Equation 12) is justified by the positive Hermitian characteristic of the covariance matrix Rnn,k.

This method requires the use of a minimum of 20 calibration solutions with varying target analyte and interference concentrations and adopts a second-order calibration function.

The optimization problem associated with an and/or graph G consists of finding a minimum weight solution subgraph H of G, where the weight of a solution subgraph is the sum of the weights of its edges.

Concerning semi-classical bound states, it was proved in [18] that for ħ > 0 small and admits a least energy solution which concentrates near the global minimum of W. A multiplicity result for solutions was obtained in [4] by using a topological argument.

As we have noted earlier, in that paper, a new definition of lower and upper solutions with corners is used that allows one to construct a sequence of upper solutions over the function minimum of the solutions in.