Sentence examples for for any given solution from inspiring English sources

Then, one can easily verify that, for any given solution for the Afriat inequalities (left( 2.B.1right) ), there also exists a solution for condition (left( 2.B.2right) ).

From (2.15) it follows that if for any given solution u ( t ) of (1.1) the phase functions θ j ( t ) satisfy characteristic equation, that is, θ j ( t ) = χ j ( t ), j = 1, 2, then energy conservation laws E j ( t ) = const, j = 1, 2 are satisfied.

For any given solution ((x^,omega ^,lambda^)) of CCEiCP, there exists a corresponding stationary point ((x^,omega^,lambda^,y^)) of NLP 2. From Theorem 4.2, a stationary point of NLP2 is a solution of CCEiCP if and only if the Lagrange multipliers associated with the equality constraints (23) and (24) in NLP2 are exactly zero.

This directly follows from the fact that is constrained with for and hence, in any given solution they cannot be simultaneously one. v Since we have already found a solution where the first and last variables are one, we know that any other solution such as with one or more zeros in these positions becomes suboptimal and can be discarded.

Defining a value proposition that will attract customers who are actually willing to pay for a given solution is more art than science.

However, as with other areas of sustainability, it is important that our enthusiasm for a given solution does not lead us to make claims which are not rigorously thought through and justified.

Absorbance measurements for a given solution of mCP were taken against a baseline solution that contained no mCP.

Any society may accept or reject a given solution to a problem for a variety of reasons.

For any given positive solution ((u,v)= u(x),v(x))) to the problem (1.2), we denote their averages over Ω by bar{u}=frac{1}{|Omega|} int_{Omega}u,dx quad text{and}quad bar{v}= frac{1}{|Omega|} int_{Omega}v,dx, where (|Omega|) is the volume of Ω.

ATP was found to adsorb effectively onto biomimetic apatite: despite smaller values of the affinity constant KS and the exponential factor m, larger adsorbed amounts were reached for ATP as compared to AMP for any given concentration in solution.

For any given, is a solution of the problem (3.1) if and only if (3.6).