Library

Description / Table of Contents: Zusammenfassung Während die Aufgabe der konvexen Interpolation im Falle kubischer Splines im allgemeineen nicht lösbar ist, kann jetzt gezeigt werden, daß sie bei Verwendung von Exponentialsplines Lösungen besitzt sofern die vorkommenden Parameter hinreichend roß sind, und es werden konkrete hinreichende und notwendige Lösbarkeitsbedingungen hergeleitet. Da eindeutige Lösbarkeit in der Regel nicht vorliegt, wird eine Auswahlfunktion eingeführt und das entstehende quadratische Optimierungsproblem nach Dualisierung numerisch behandelt.

Description / Table of Contents: Zusammenfassung Das Problem, konvexe Interpolationssplines mit minimaler mittlerer Krümmung zu ermitteln, führt auf eine speziell strukturierte quadratische Optimierungsaufgabe. In der vorliegenden Note wird eine zugehörige duale Aufgabe aufgestellt, die ohne Nebenbedingungen auskommt, deren Zielfunktion stückweise quadratisch ist und die daher eine effektive numerische Behandlung erlaubt.

Description / Table of Contents: Zusammenfassung Unter positiver Interpolation wird die Aufgabenstellung verstanden, zur einer nichtnegativen Datenmenge nichtnegative Interpolierende zu konstruieren. Im Fallen rational-quadratischer Splines wird eine notwendige und hinreichende Bedingung für die Durchführbarkeit positiver Interpolation hergeleitet, und es wird gezeigt, daß diese sich bei passender Wahl der vorkommenden Parameter stets erfüllen läßt.

Description / Table of Contents: Zusammenfassung Gegenstand der Arbeit ist die flächentreue Approximation von Histogrammen durch rational-quadratischeC 1-Splines unter Zusatzbedingungen wie Konvexität oder Monotonie. Für derartige Aufgaben werden hinreichende und notwendige Existenzbedingungen in algorithmischer Form angegeben, und es ergibt sich, daß sich diese Bedingungen bei konvexen oder monotonen Histogrammen durch passende Wahl der Rationalitätsparameter stets erfüllen lassen. Da die genannten Aufgaben, sofern überhaupt, im allgemeinen nicht eindeutig lösbar sind, werden Histosplines mit minimaler Gesamtkrümmung ermittelt.

Description / Table of Contents: Abstract. Monitoring of ventilation in infants is difficult and often not very reliable. In this study, transcutaneous measurement of blood gas tensions was used to investigate the influence of four different modes of ventilation on oxygenation and ventilation in anaesthetized infants. Methods. In a randomised study, transcutaneously measured PO2 (tcPO2) and PCO2 (tcPCO2) tensions were continuously registered in 42 ASA class I and II infants between 3 and 24 weeks of age undergoing minor surgical procedures (inguinal hernia repair). Two breathing systems combined with different modes of ventilation were evaluated: manual ventilation with Kuhn's T-piece system and face mask (group A; n=11) or endotracheal tube (group B; n=10); manual ventilation with paediatric circuit system and face mask (group C; n=11); and mechanical ventilation with paediatric circle system, endotracheal tube, and positive end-expiratory pressure (PEEP) 3 cm H2O (group D; n=10). Transcutaneous values were measured by a combined tcPO2/PCO2 electrode (E 5277, Radiometer). Anaesthesia was maintained by controlled ventilation with N2O/O2 (67%/33%) and halothane 0.5 – 1.5 vol.%. Surgical and anaesthetic techniques were standardized and the anaesthetist was blinded to the measured values. Results. Preoperative mean tcPO2 values while spontaneously breathing air ranged between 69 and 75 mm Hg in all patients. During anaesthesia and controlled ventilation (FiO2=0.33), there was a significant increase in tcPO2 (P〈0.01) in 3 groups: in groups A and D mean tcPO2 increased to 90 – 100 mm Hg and in group C to 110 – 120 mm Hg. In contrast, tcPO2 in group B reached only 75 – 80 mm Hg, which was not considered significant. Postoperatively, tcPO2 immediately reached baseline values in all patients (Fig. 2). Compared to preoperative values, the alveolar-tcPO2 difference (AtcDO2) significantly increased during anaesthesia in all groups (Fig. 3). The tcPCO2 measurements revealed marked alveolar dysventilation, with hyperventilation supervening in groups A, B, and D; in group C, however, most (7 of 11) infants were normoventilated (Fig. 4). Conclusions. Adverse effects of anaesthesia on pulmonary function in infants are caused by loss of the PEEP effect induced by the physiological subglottic stenosis. Endotracheal intubation and the increase in chest wall compliance during anaesthesia lead to a decrease in functional residual capacity (FRC) associated with premature airway closure and ventilation/perfusion mismatch. These pathophysiological disturbances result in a marked increase in AaDO2 and low arterial PO2 values despite high FiO2, as could be observed when intubated infants had been ventilated with a high-flow T-piece system (group B). Mechanical ventilation with a paediatric circuit system and endotracheal tube allows the use of low PEEP levels (group D), which may replace the lost subglottic function and partially restore the FRC. Ventilation by mask does not disturb the functional subglottic stenosis, and the impairment of pulmonary function will depend solely on the decrease in FRC caused by increased chest wall compliance (group A). If mask ventilation is combined with a paediatric circuit system (group C), the pressure relief valve produces a low PEEP of 2 to 3 cm H2O, which may partially counteract the decrease in FRC. With regard to oxygenation, the paediatric circle system proved to be superior to the high-flow T-piece system independent of whether children were ventilated via a face mask or an endotracheal tube. The group-specific differences in degree of dysventilation with manual ventilation show that the type of breathing system is important with regard to the size of the tidal volume delivered. Thus, tidal volumes will be unintentionally increased by the high fresh gas flow needed when a T-piece system is used. The lower flow and preadjusted pressure limit may prevent the delivery of excessive tidal volumes with the paediatric circuit system. The high incidence of dysventilation with mechanically controlled ventilation might be caused by the limited applicability of ventilation nomograms during anaesthesia for this age group.

Description / Table of Contents: Abstract Inorganic glass melts are showing a characteristic die swell, when in the case of slow motion a strong adhesion between the streaming fluid and the wall of the die channel exists. The reason for this phenomenon is the rearrangement of the velocity profile from a parabolic to a box-type design form. The experimental investigations have demonstrated, that above a certain channel length, this means at distinct flow conditions inside the die channel, the value for the extension of the cross-sectional area is constant of about 29%. Particularly it is independent of the shape of the used die profiles. From this result, it is to deduce that this value must correspond to that of the two-dimensional case of the infinite extended slit. In a theoretical analysis the computation of this case was performed, starting from the Stokes-equation by the finite element method. By means of the resulting pressure and velocity distribution, the contour of the emerging rod and its final thickness could be determined. A comparison between experimental and computational results shows good agreement. So the appreciable independence of the magnitude of the die swell from the profile of the extruded rod is confirmed.