Sentence examples for by taking a suitable from inspiring English sources

Remark 3.1 In the case of multiple roots, we can also have the Green function by taking a suitable limit in (3.3).

Note that μ 1, μ 2, and μ 3 can take any value in R × R × R + by taking a suitable value of h (because the vector h has n variables).

Therefore, by taking a suitable version of the expectations (mathbb {E}^{mathbb {P}}left [X_{t+varepsilon },|,mathcal {F}_{t+delta }right ]), we have Open image in new window.

We notice that (3.1) contains the unknown quantities [u x ], [p x ], and [ρ x ]; eliminating the unknown discontinuities [ρ x ] and [u x ] between these equations by taking a suitable linear combination, we arrive at the first transport equation governing the shock strength: d p dx = k 11 p x + k 12, Open image in new window (3.3).

If non-stationary, the data would be transformed into a stationary time series by taking a suitable difference.

Then we can take a suitable sufficient small such that, and hence is a contraction on ( denotes with substituted by ).

Take a suitable book with hard cover.

The obtained solutions are reduced as special cases to their limiting solutions by taking some suitable parameters equal to zero.

Then, by taking suitable Q, the feedback system is designed so that it is robustly stable against a pre-specified range of perturbations inserted in the feedback loop.

One can go on to define more general classes of random variables by taking suitable limits (for details, see [Younce, 1987]).

The spectral theorem tells us that every self-adjoint operator on H can be obtained by taking suitable limits of operators of this form.