Sentence examples for the transformation where from inspiring English sources

The variance covariance matrix for Cartesian coordinates can be obtained from that for fractional coordinates by the transformation where the transformation matrix needed to transform the entire variance covariance matrix in one operation would be block diagonal, with the orthogonalization matrix O repeated at the appropriate positions along the diagonal.

The discontinuity on can be eliminated by the use of the transformation, where is given by (3.15).

The transformations T to separate the two types of transformations that | | T 1 (q i ′ ) − p i ′ | | > | | T 1 (p j ′ ) − q j ′ | | and | | T 2 (q i ′ ) − p i ′ | | | | T 2 (p j ′ ) − q j ′ | | are the transformations where (3) | | T (q i ′ ) − p i ′ | | 2 − | | T (p j ′ ) − q j ′ | | 2 = 0. Let ∙denote dot product.

For the BGK (Bhatnagar Gross Krook) equation in the large scale hyperbolic limit, the density of particles can be transformed as the Hopf Cole transformation, where the phase function converges uniformly to the viscosity solution of an effective Hamilton Jacobi equation, referred to as the kinetic eikonal equation.

The centroids of the particles are then located using the distance transformation, where the distance to the background region is computed for each foreground (particle) pixel.

To highlight the response pattern of taxa to fire, SEA composites were displayed as anomalies using the following transformation: where xi' is the transformed value of the ith sample, and µ is the mean xi value (Figure 1K,L).

The Weyl connection is invariant under the gauge transformation where the gauge function is \(\lambda(x) = e^{\theta(x)}\).

The reduction is based on the following transformation, where we set the priorities for the patient, ward, and the holding, recovery, radiology, pathology and logistic department to zero.

It can be brought to the form diagonal in phonon variables by the unitary transformation where (20).

Employing the Schröder transformation, where is a differentiable solution of the relation, we can similarly as in the case verify that the property (4.16) remains preserved with being replaced by on its right-hand side.

To approximate the original constraints and reduce the power consumption, β c=− lnρ c/ε c (β p=− lnρ p/ε p) can be adopted in the constraint transformation, where ε c>1 (ε p>1) is the adjustment parameter, and can be obtained by the training process and the bisection search [16].