Sentence examples for transform the above from inspiring English sources

It may have taken a half-century of immense destruction at the hands of Europeans to transform the above into axioms that few challenge today.

Let us first transform the above problem to a RHBVP for analytic functions.

Therefore, we attempt to transform the above maximum problem with multiple variables into a single variable optimization problem.

To address this challenging issue, we transform the above non-linear function into a linear function by exploiting the properties of the binary decision variable.

Secondly, we present a binary XOR operation to transform the above n−2 ISTs into the n−2 ISTs rooted at any node that is similar to 0 on CQn.

Then we use the relation of the channel frequency response matrix and the channel impulse response matrix to transform the above noise-perturbed matrix to another noise-perturbed matrix.

Based on conditional probability, we can transform the above-mentioned ASN to the graphical evaluation and review technique networks with ∑ i = 1 M ∑ j = 1 n i 1 Open image in new window parallel paths.

Applying the Addition Theorem for spherical harmonics (A.2) to (14) transforms the above equation to (15).

After transforming the above expression, we obtain A f = b (28).

Inverse-Fourier transforming the above characteristic function will yield: begin{array}rcl@ f_{Z} z) & = & mathcal{F}^{-1}left[Phi_{Z} omega)right] & = & frac{1}{2pi}int_{-infty}^{infty}expleft -iomega zright)prod_{n=1}^{infty}expleft -iomegagma_{U_{n}}^{2}+1}domega end{array} (11).

The PDE in (16) is found to be a bit difficult to solve in terms of dependence variables x and t, therefore in this paper we resort to transforming the above PDE to an ODE for which, in most cases, a solution can be obtained.