• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.669-689
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• 2020

Cohomological degrees (or extended degrees) were introduced by Doering, Gunston and Vasconcelos as measures for the complexity of structure of finitely generated modules over a Noetherian ring. Until now only very few examples of such functions have been known. Using a Cohen-Macaulay obstruction defined earlier, we construct an infinite family of cohomological degrees.

• Investigative Magnetic Resonance Imaging
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• v.1 no.1
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• pp.103-107
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• 1997

Purpose: To investigate the localization and functional lateralization of the supplementary motor area (SMA) in motor activation tests in comparison to that of the primary motor area. Materials and Methods: Seven healthy volunteers obtained echoplanar imaging blood oxygen level dependent technique. This study was carried on 1.5T Siemens Magnetom Vision system with the standard head coil. Parameters of EPI were followed as; TR/TE : 1.0/66.0msec, flip angle: $90^{\circ}$, field of view: $22cm{\times}22cm,{\;}matrix:{\;}128{\times}128$, slice number/slice thickness/gap: 1O/4mm/0.8mm with fat suppression technique. Motor task as finger opposition in each hand consisted of 3 sets of alternative rest and activation periods. Postprocessing were done on Stimulate 5.0 by using cross-correlation statistics. To compare the functional lateralization of the SMA in the right and left hand tests, each examination was evaluated for the percent change of signal intensity and the number of activated voxels both in the SMA and in the pri¬mary motor area. Hemispheric asymmetry was defined as difference of summation of the activted voxels between each hemisphere. Results: Percent change of signal intensity in the SMA (2.49 -3.06%) is lower than that of primary motor area(4.4 -7.23%). Percent change of signal intensity including activated voxels were observed almost equally in the right and left SMA. As for summation of activated voxels, primary motor area had significant difference between each hemisphere but not did the SMA. Conclusion: Preferred contralateral dominant hemisphere and hemispheric asymmetry were detected in the primary motor area but not in the SMA.