• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1945-1962
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• 2015

This paper is mainly concerned with the formation of delta standing wave for the scalar conservation law with a linear flux function involving discontinuous coefficients by using the self-similar viscosity vanishing method. More precisely, we use the self-similar viscosity to smooth out the discontinuous coefficient such that the existence of approximate viscous solutions to the delta standing wave for the Riemann problem is established and then the convergence to the delta standing wave solution is also obtained when the viscosity parameter tends to zero. In addition, the Riemann problem is also solved with the standard method and the instability of Riemann solutions with respect to the specific small perturbation of initial data is pointed out in some particular situations.

• Clinical and Experimental Pediatrics
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• v.46 no.12
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• pp.1274-1278
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• 2003

Syncope in children and adolescents have a common occurrence according for up to 15% before adulthood. Micturition syncope, a kind of situational syncope, can be considered a form of reflex syncope. It can typically occur in healthy young men after rising from bed in the early morning who experience sudden loss of consciousness during or immediately after urination. The mechanism of micturition syncope is not completely understood, but it has been suggested that vasovagal reflex mediated bradycardia and peripheral vasodilation and decreased venous return due to Valsalva effect and standing position lead to the decrease in cerebral blood flow resulting in syncope. The causes of syncope are variable. So complete history taking, physical examination, electrocardiography, exercise stress test, echocardiography, head-up tilt table test, electroencephalography(EEG), brain magnetic resonance image and urodynamic study should be required for the diagnosis of micturition syncope. There were several reports about micturition syncope. However, literature of micturition syncope at the pediatric age has rarely been reported in Korea so far. Therefore, we report a case of a 9-year-old boy with micturition syncope with typical EEG findings of high amplitude delta wave and flattening during syncope.