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SYMMETRIES OF PARTIAL DIFFERENTIAL EQUATIONS
Gaussier, Herve,Merker, Joel Korean Mathematical Society 2003 대한수학회지 Vol.40 No.3
We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in $\mathbb{C}$. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries of such a system with a Lie group structure. Finally we determine the precise upper bound of the dimension of this Lie group for some specific systems of partial differential equations.
C. Matthias,P. de Souza,H. J Merker 대한비과학회 1997 Journal of rhinology Vol.4 No.2
The morphology of the mucosa from the human paranasal sinuses was investigated by electron microscopy and immunofluorescencemicroscopy. A total of 27 specimens was taken from 11 patients following midfacial fractures. All tissue sampleswere biopsied during surgery after given informed consent. In accordance with light microscopic investigations, the mucosarepresented a highly prismatic epithelium consisting of kinocilia-carrying and mucus-producing (goblet) cells similar to the respiratoryepithelium of other areas. Peculiar findings in the electron microscopic and immunomorphological investigationsrevealed collagen type VII beneath the lamina densa of the basal lamina. To date, this collagen type has only been described toaccompany a multilayered epithelium. Another observation was the small number of basophils and eosinophils. Pronouncedacute reactions of the mucosa in this area cannot be expected, which is in contrast, to that of the nasal mucosa.