• Honam Mathematical Journal
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• v.45 no.4
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• pp.585-597
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• 2023

We introduce the rotational hypersurface x = x(u, v, s, t) constructed by double rotation in five dimensional Euclidean space 𝔼⁵. We reveal the first and the second fundamental form matrices, Gauss map, shape operator matrix of x. Additionally, defining the i-th curvatures of any hypersurface via Cayley-Hamilton theorem, we compute the curvatures of the rotational hypersurface x. We give some relations of the mean and Gauss-Kronecker curvatures of x. In addition, we reveal Δx=𝓐x, where 𝓐 is the 5 × 5 matrix in 𝔼⁵.

• Korean Journal of Child Studies
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• v.12 no.2
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• pp.51-66
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• 1991

The purpose of study I was to investigate developmental processes and sex differences in the acquisition of topological seriation and Euclidean horizontal/vertical concepts. The purpose of Study II was to investigate the effects of basic geometric activity on the acquisition of space concepts. The subjects of Study I were 164 five- and six-year-old children. The children were grouped by age in 6 month units. The subjects of Study II were 45 children who showed immature space concepts. The data were analyzed by two-way ANOVA, $Scheff{\acute{e}}^{\prime}s$ posthoc test, and paired comparison t-test. On Study I, significant differences were found among the age groups in each of the dependent variables. Sex differences were found on all tasks except cued Euclidean tasks. In Study II, basic geometric activity of 3 weeks duration was found to be effective in the acquisition of the horizontal/vertical concepts in children whose space concept had been immature.

• Journal of Korean Neurosurgical Society
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• v.38 no.5
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• pp.359-365
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• 2005

Objective : The study investigates the extent of brain shift and its effect on the accuracy of the stereotaxic procedure. Methods : Thirty-five patients underwent 40stereotactic procedures between June 2002 and March 2004. There were 26 males, mean age 59years old. There were 34procedures for Parkinson's disease, 2 for essential tremor, 3 for cerebral palsy, 1 for dystonia. Patients were divided in four groups based on postoperative pneumocephalus : under 5cc [9 procedures], between $5{\sim}10cc$ [13procedures], between $10{\sim}15cc$ [11 procedures] and more than 15cc [7procedures]. The coordinates of the anterior commissure[AC], posterior commissure[PC], and target were defined in pre-and intraoperative magnetic resonance image scans and the amount of air volume was measured with @Target (BrainLab, Heimstetten, Germany]. Results : The mean AC-PC was 26.5mm for patients with less than 5cc, 26.9mm for $5{\sim}10cc$, 25.8mm for $10{\sim}15cc$ and 26.2mm for more than 15cc. The length of AC-PC line and coordinates of AC, PC was also not statistically different, Euclidean distance as well as ${\Delta}x$, ${\Delta}y$, ${\Delta}z$ of AC, PC, and target were also not statistically different among the groups [p>,1]. There was a variance in target of $0.7{\sim}7.6mm$, Euclidean distance of 2.5mm, related to electrophysiology but not to brain-shift. Conclusion : The amount of air accumulated in the intracranial space and compressing the cortical surface has no effect on the localization of subcortical stereotactic target and landmarks.