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Institute
- Fachbereich Medizintechnik und Technomathematik (1578) (remove)
Purpose — to compare the chemical elemental composition of vitreous cavity content taken from cadaveric eyes compared to samples taken from the eyes with terminal stage refractory glaucoma with decompensated intraocular pressure (IOP). Material and methods. The vitreous contents of the eyes from 2 groups were studied. The 1st group included 15 cadaveric eyes; the 2nd group included 15 eyes with refractory glaucoma in the terminal stage of the disease with decompensated IOP in patients with hypertension pain. The vitreal content samples were taken in the course of antiglaucoma surgery aimed at preserving the eye as an organ and involving employment of drainage in the vitreous cavity. The study of virtual contents was carried out on energy dispersive spectrometer Oxford X-Max 50 integrated into scanning electron microscope Zeiss EVO LS10. Results. Increased concentrations of Kalium and Phosphorus were detected in the vitreous content of cadaveric eyes compared with the vitreal content from the eyes with terminal glaucoma with decompensated IOP taken in vivo (K — 0.172/0.093; P — 0.045/0.025 mmol/L). In the vitreous cavity in the eyes with end-stage glaucoma with decompensated IOP, the concentration of Nitrogen was higher in comparison with human cadaver eyes (2.030/1.424 mmol/L). Conclusion. The increased concentrations of Kalium and Phosphorus in the vitreous content of cadaveric eyes is associated with postmortem autolytic processes and with the release of intracellular content in the destruction of cell membranes. The increased Nitrogen concentration in the vitreal contents of the eyes with terminal stage glaucoma with decompensated IOP may be associated with the presence of osmotically active nitrogen-containing compounds in the eyes with increased IOP.
Über die Äquivalenz zweier Transmissionsrandwertprobleme aus der elektromagnetischen Streutheorie
(1994)
Für die Approximation stetiger, 2π-periodischer Funktionen auf der reellen Achse durch trigonometrische Polynome wurde ein direkter Satz von D. Jackson 1911 [8] und die Umkehrung von S. N. Bernstein 1912 [1] bewiesen und die Ergebnisse von A. Zygmund [25] 1945 verallgemeinert. 1949 stellte M. Zamansky [25] eine Beziehung zwischen der Approximationsordnung und dem Wachstum bezϋglich n der Ableitungen der Approximationspolynome her; auf die Approximationsordnung für die Ableitungen der Funktion schloβ S. B. Steckin 1951.
Die Umkehrung des Ergebnisses von M. Zamansky bewies G. Sunouchi 1968 [21,22], womit die Aquivalenz aller Aussagen gezeigt ist.
Die Übertragung der Ergebnisse auf Approximationsoperatoren in Banachräumen stammt von K. Scherer und P. L. Butzer [3, 4], wobei gewisse Voraussetzungen an die Operatorfolge (eine verallgemeinerte Bernsteinsche Ungleichung und eine sogenannte Jacksonsche Ungleichung) gestellt werden. An die Stelle der strukturellen Eigenschaften der Funktion, die durch das Verhalten des Stetigkeitsmoduls der Funktion charakterisiert werden, treten in allgemeinen Banachräumen Eigenschaften des von J. Peetre [17] eingefϋhrten K-Funktionals.
In dieser Arbeit wird die Approximation von Funktionen, die auf der Einheitskugel Sᵏ im Rᵏ definiert sind, durch Linearkombinationen von Kugelfunktionen untersucht. Es wird für diesen Fall eine Bernstein-Ungleichung und die Jackson-Ungleichung bewiesen, wenn man die Ableitung durch den Laplace-Operator auf Sᵏ ersetzt. Damit ist der oben zitierte allgemeine Satz von Butzer-Scherer anwendbar. Weiter kann man hier an Stelle des K-Funktionals einen verallgemeinerten Stetigkeitsmodul setzen. Anschlieβend wird der Spezialfall der zonalen Funktionen und ihre Approximation durch algebraische Polynome untersucht.