By properly using the difference scheme to deal with the convolution term, an imaginary time method is given to compute the ground states and then a time-splitting method is obtained for dynamics of dipolar BECs.
The other two methods make use of linear elastic fracture mechanics (LEFM): we call these the imaginary crack method (ICM) and finite fracture mechanics (FFM).
To compute the ground state, an imaginary time method is adopted [14].
The second part involved the analysis of functional connectivity from the time-varying source density of each ROI by using of the imaginary coherence method, which essentially measures how the phases between two sources are coupled to each other with minimum crosstalk effects between sources [47].
Using this solution and the imaginary emission method (that is described by Ponomarjov M.G. in Physical Review E, 54, 5591 5598, 1996; Planetary and Space Science, 43, 1419 1427, 1995) in one specific case the analytical and numerical results are obtained, which describe developing magnetic field aligned 3D stratifications of plasma disturbances and wakes.
One of the efficient and popular techniques for the constraint (6) is through the following construction [13]: we choose a time step size τ > 0 and set t k = k τ for k = 0, 1,.... Applying the imaginary time method [18] without considering the constraint (6), and then projecting the solution back to the unit nonconvex set S at the end of each time interval [t k, t k +1] to satisfy the constraint.
We recorded the resting-state magnetoencephalographic activities of 28 patients with FM and 28 age- and sex-matched controls, and analyzed the source-based functional connectivity between the insula and the DMN at 1 40 Hz by using the minimum norm estimates and imaginary coherence methods.
The mesh adaptivity is used with two different numerical algorithms to compute stationary vortex states: an imaginary time propagation method and a Sobolev gradient descent method.
The imaginary interference cancelation method provides a mean to estimate in a similar way the channel as in CP-OFDM and its performances are closer to CP-OFDM ones.
