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Isoperimetric inequalities are applied to a moving-boundaryproblem for doubly-connected domains. This problem occurs forexample in electrochemistry, in which case the domains in questionare the electrolyte of an electrolytic cell. The two electrodessurrounding the electrolyte are assumed to grow or dissolve,at different rates in general, by electrochemical reaction.We obtain optimal estimates showing, for example, that the leastchange in volume of each electrode always occurs in sphericalsymmetry. 相似文献
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Moore J Jankiewicz M Anderson AW Gore JC 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2012,214(1):200-211
Spatially selective excitation pulses have been designed to produce uniform flip angles in the presence of the RF and static field inhomogeneities typically encountered in MRI studies of the human brain at 7 T. Pulse designs are based upon non-selective, composite pulses numerically optimized for the desired performance over prescribed ranges of field inhomogeneities. The non-selective pulses are subsequently transformed into spatially selective pulses with the same field-insensitive properties through modification of the spectral composition of the individual sub-pulses which are then executed in conjunction with an oscillating gradient waveform. An in-depth analysis of the performance of these RF pulses is presented in terms of total pulse durations, slice profiles, linearity of in-slice magnetization phase, sensitivity to RF and static field variations, and signal loss due to T(2) effects. Both simulations and measurements in phantoms and in the human brain are used to evaluate pulses with nominal flip angles of 45° and 90°. Target slice thickness in all cases is 2mm. Results indicate that the described class of field-insensitive RF pulses is capable of improving flip-angle uniformity in 7 T human brain imaging. There appears to be a subset of pulses with durations ?10 ms for which non-linearities in the magnetization phase are minimal and signal loss due to T(2) decay is not prohibitive. Such pulses represent practical solutions for achieving uniform flip angles in the presence of the large field inhomogeneities common to high-field human imaging and help to better establish the performance limits of high-field imaging systems with single-channel transmission. 相似文献
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