… We use the gradient descent scheme to optimize this cost function. Since we have analytically
derived the derivative of the cost function, the gradient descent technique would be very …

… frequency shifts. This frequency shift will detune the cavities and might reflect the RF power.
… In this section, we present the theoretical background required to derive the analytical …

… gradients are employed to increase the selectivity of conventional magnetic resonance methods.
Radio frequency gradient … understanding and developing RF gradient experiments. The …

A simple analytical model for the planar radio-frequency (rf) sheath in … analytic expression
for the screening function is introduced. By means of this expression approximate analytical …

… pulse with piecewise constant gradient trajectories and radio frequency (RF) waveforms …
this analytic solution we formulate a non-linear program for finding sub-pulse durations, gradient …

… The pulse design strategy is developed and analytically … appropriate time varying gradients
after the radio-frequency (RF) … a gradient and a RF pulse implicitly imposes that frequency …

… Moreover, it admits to simple analytical solutions to compare … due to large temperature
gradients just beneath the tissue surface (… We consider analytical results to even more simplified …

… of a high plasma potential gradient between the source and … any ion accelerated in any
potential gradient. A disk-shaped … We find that this first-order analytic result agrees to within five …

… analytical expressions are derived for the particle trajectory and beam envelope of photo-electrons
generated by a laser pulse on a photocathode inside a Radio-Frequency … gradient Kr …

… appreciable spatial gradients in the fields. The typical situation in radio-frequency discharges
… For analytical purposes we can go slightly further and consider a slab model, in which the …