Sentence examples for with respect to the elements from inspiring English sources

Again, the laws of the different countries vary greatly with respect to the elements that must be present to make a transfer voidable as a preference, especially those of a subjective character such as intent on the part of the debtor or knowledge of the debtor's financial status on the part of the creditor.

To this end, let be the vector of partial derivatives of with respect to the elements of, where denotes the matrix derivative operator[28, Definition 2].

Step 2: Linguistic judgments on each alternative and criterion with respect to the elements on the level immediately above can be obtained from experts through questionnaires, surveys, interviews, expert panels, and direct observations.

Note that the minimization problem in (9) is separable with respect to the elements of s and we just need to find the minimizer of the single-variable cost function β 2 ( s − z ) 2 + τ | s |, which is the well-known shrinkage-threshold operator: S ( z ) = z − τ β z > τ β 0 | z | ≤ τ β z + τ β z < − τ β (11).

Taking the first partial derivate of (1) with respect to the elements of W in (3), say W j, j = 1, 2, …, n, being equal to zero, we see that the minimization of (1) reduces to finding the solution of n non-linear algebraic relations: {displaystyle sum_{i=1}^k{rho}^{k-i}{mathbf{X}}_{ij} psi left(frac{eleft i,mathbf{W}right)}{s}right)}=0,kern0.24em j=1,2,dots, n (5).

These differences with respect to the elements of regulated permissive regimes, are summarized in Table 1.

Results showed that the responses of both cultivars were different with respect to the element accumulation concentration and accumulation times.

Therefore the mapping F is 2-regular at the point x ∗ = ( 0, 0 ) with respect to the element h = [ h z, h ε ].

For a better knowledge of this evolution and, expecially, of the element origin, we have calculated the enrichment factors (EFs) with respect to the element abundance in the upper continental crust.

If the mapping F is p-regular ( p = 2 ) at the point x ∗ = ( 0, 0 ) with respect to the element h = [ h z, h ε ], where h z = z sin t, z ∈ R, h ε = ε ¯, then there exist solutions x = x ( t, ε ) = ε z sin t + r , ∥ r ∥ = o of equation (2) for ε ∈ , where σ > 0 is sufficiently small.

If the mapping F is p-regular at the point x ∗ = ( 0, 0 ) with respect to the element h = [ h z, h ε ], where z = ( z 1, z 2 ), h z = z 1 u 1 + z 2 u 2, h ε = ε ¯, then there exist solutions u = u ( y, ε ) = ε ( z 1 u 1 + z 2 u 2 ) + r , ∥ r ∥ = o of equation (4) for ε ∈ , where σ > 0 is sufficiently small.