For example, in 1994 L . Stankovic proposed a novel technique, now mostly referred to as S-method, resulting in the reduction or removal of cross terms.
12.
For a superposition of states, the expectation value of the position will change based on the cross term which is proportional to \ cos ( \ omega t ).
13.
If the solution to the simpler problem is " not " linear, then it doesn't solve the original problem because of the cross terms appearing when expanding the squares.
14.
When this re-indexing is substituted into the DFT formula for " nk ", the N _ 1 n _ 2 N _ 2 k _ 1 cross term vanishes ( its exponential is unity ), and the remaining terms give
15.
Note that cross terms of the form \ langle A _ 1 ( l, m, t ) A _ 2 ^ * ( l, m, t ) \ rangle are not included due to the assumption that the source is incoherent.
16.
Even if the energy associated with each eigenvalue considered separately is decaying exponentially in time ( as predicted by the Orr Sommerfeld analysis for the Couette flow ), the cross terms arising from the non-orthogonality of the eigenvalues can increase transiently.
17.
The fact that none of the metric coefficients are functions of time make the metric stationary : the additional fact that there are no " cross terms " involving both time and space components ( such as dx dt ) make it static.
18.
In this case, when we calculate the mutual coherence function for an extended coherent source, we would not be able to simply integrate over the intensity function of the source; the presence of non-zero cross terms would give the mutual coherence function no simple form.
19.
A difference frequency only appears in the detector output current when both the LO and signal illuminate the detector at the same time, causing the square of their combined fields to have a cross term or " difference " frequency modulating the average rate at which free electrons are generated.
