Sentence examples for dependence of the vector from inspiring English sources

This translates into shifting the respective vertex v i from the set V ~ to V ^, reducing the vector κby the same element, and solving the implicit equation of the form (4) f i (x i, κ, F = 0 for x i to get the set x ¯ i of fixed point coordinates of the variable x i in dependence of the vector κ. The set F has to be updated accordingly. Equation (4) has to be solved numerically.

We can omit the dependence on the vector of parameters ξ and write simply G x)=G(x;ξ).

Further, we can omit sometimes the dependence on the vector ξ of the parameters and write simply G x)=G(x;ξ).

Further, we can omit sometimes the dependence on the vector ξ of parameters and write simply G x)=G(x;ξ).

For notation simplicity, we omitted the dependence of the steering vector v on the actual spatial frequency ν ¯.

In order to examine the dependence of the wave vector k y on collisional effects, the real and imaginary parts of k y are plotted distinctly in Figures6 and7 for three different values of ν ′ Open image in new window.

Since an explicit form of the dependence of the state vector on the parameters is not known, the use of reparametrization techniques is not feasible.

Although PARALIND model can be viewed as an extension of PARAFAC model, uniqueness of PARALIND does not follow directly from the uniqueness property of PARAFAC because of the linear dependence of the loading vectors.

Notice that the complicated dependence of the wave vectors (k_{i}) and (alpha_{i}) with the potential, (W_{i}), may be transferred to the Fermi energies by changing variables in the integrals of the system (A.15) so that the lower limit of integration (the bottom of the ith well) is zero: (epsilon' = epsilon+ e mathcal{W}_{i}).

For the substitution of an individual compound (c, c′), such coefficients can always be found, due to the linear dependence of the mass vectors: s c ′, r is obtained as.

The first indication of at least two di-μ-oxo bridges with Mn Mn distance of 2.7 Å was established in the 1980s, followed by the finding of a mono-μ-oxo Mn Mn distance of 3.3 Å and the orientation dependence of the Mn Mn vectors.