Sentence examples for use the linearity of from inspiring English sources

(4.2) To use the linearity of the transform (g to u [ g ] - u [ 0 ]), we add and subtract the term (u ( x,T 0 )) to the functional (J_{alpha} ( g )).

We then use the linearity of botharguments of the covariance bracket to express the variance of the quadratureoperator as S ϕ = ∫ − ∞ ∞ [ e i ϕ e − i ϕ ] G [ 〈 a ˜ ˆ i , a ˜ ˆ i 〉 〈 a ˜ ˆ i , a ˜ ˆ i † 〉 〈 a ˜ ˆ i † , a ˜ ˆ i 〉 〈 a ˜ ˆ i † , a ˜ ˆ i † 〉 ] × G T [ e i ϕ e − i ϕ ] d ω ′. (67).

Using the linearity of the trace, for any operator one can write, where.

When dose conversion algorithm was used, the linearity of sensitivity was better about 38%.

Then using the linearity of φ-function, we have.

(75), (76) and (77) by (hat {sigma }_{j}), taking the trace and using the linearity of the trace operation.

To show the existence of Ω, let us define it on the polynomials (2.11) by (2.12), (2.13) and then we expand Ω to over the whole space (mathbb{C}_{2N} [ lambda ] ) by using the linearity of Ω.

Indeed, if we take, where the first coordinate function is given by, and such that t 1 satisfies (2.33), then, using the linearity of Riemann-Liouville derivative, we have.

Finally, using the linearity of W, tilde f= sumlimits_{i=1}^{N} m_{i}^{r_{i}} + W^{-1} text{Lap}_{lambda}), (33). is shoW^{-1} text{erturbed function of the smoothed consumption sum.

Decomposing the EPR-Bohm wave function using the component of spin in the direction associated with the magnet for particle 1, the evolution of the wave function as particle 1 passes its magnet is easily grasped: The evolution of the sum is determined (using the linearity of Schrödinger's equation) by that of its individual terms, and the evolution of each term by that of each of its factors.

Substituting the y i using the linearity of the wavelet transform and the definition of m r yields begin{array}rcl@ {kern-1.9pt}W^{-1}left(Dleft(cright)right)& = &W^{-1}left(T_{r}left(Wleft(m_{1}right)right)+T_{r}left(Wleft(m_{2}right)right)right) & = & W^{-1}left(T_{r}left(Wleft(m_{1}right)right)right) + W^{-1}left(T_{r}left(Wleft(m_{2}right)right)right) & = & m^{r}_{1}+m^{r}_{2} end{array} (18).