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In this paper, we show that symplectic partitioned Runge-Kutta methods conserve momentum maps corresponding to linear symmetry groups acting on the phase space of Hamiltonian differential equations by extended point transformation. We also generalize this result to constrained systems and show how this conservation property relates to the symplectic integration of Lie-Poisson systems on certain submanifolds of the general matrix group GL(n).
Inhalt: 1. Vorbemerkungen 2. Zu einigen philosophischen und theoretisch-linguistischen Grundlagen einer kommunikativ orientierten Betrachtung der Sprache 3. Sprache und menschliche Gesellschaft 4. Der Euphemismus 5. Euphemismen im Golfkrieg - Zur Analyse der Untersuchungsergebnisse 6. Zusammenfassung und Schlußfolgerungen 7. Perspektiven der kommunikativen Sprachforschung bezüglich 215der Untersuchung des politischen Euphemismus - Forschungsausblick und Schlußbemerkungen
In cultured rat hepatocytes the key gluconeogenic enzyme phosphoenolpyruvate carboxykinase (PCK) is known to be induced by glucagon via an elevation of cAMP. Prostaglandin E₂ has been shown to antagonize the glucagon-activated cAMP formation, glycogen phosphorylase activity and glucose output in hepatocytes. It was the purpose of the current investigation to study the potential of PGE₂ to inhibit the glucagon-induced expression of PCK on the level of mRNA and enzyme activity. PCK mRNA and enzyme activity were increased by 0.1 nM glucagon to a maximum after 2 h and 4 h, respectively. This increase was completely inhibited if 10 μM PGE2 was added concomitantly with glucagon. This inhibition by PGE₂ of glucagon-induced PCK activity was abolished by pertussis toxin treatment. When added at the maximum of PCK mRNA at 2 h, PGE₂ accelerated the decay of mRNA and reduced enzyme activity. This effect was not reversed by pertussis toxin treatment. Since in liver PGE₂ is derived from Kupffer cells, which play a key role in the local inflammatory response, the present data imply that during inflammation PGE₂ may reduce the hepatic gluconeogenic capacity via a Gᵢ-linked signal chain.
Rat hepatocytes have previously been reported to possess prostaglandin E₂ receptors of the EP₃-type (EP₃-receptors) that inhibit glucagonstimulated glycogenolysis by decreasing cAMP. Here, the isolation of a functional EP₃ϐ receptor cDNA clone from a rat hepatocyte cDNA library is reported. This clone can be translated into a 362-amino-acid protein, that displays over 95% homology to the EP₃ϐ receptor from mouse mastocytoma. The amino- and carboxy-terminal region of the protein are least conserved. Transiently transfected HEK 293 cells expressed a single binding site for PGE₂ with an apparent Kd of 15 nM. PGE₂ > PGF₂α > PGD₂ competed for [³H]PGE₂ binding sites as did the EP₃ receptor agonists M&B 28767 = sulprostone > misoprostol but not the EP₁ receptor antagonist SC 19220. In stably transfected CHO cells M&B 28767 > sulprostone = PGE₂ > misoprostol > PGF₂α inhibited the forskolin-elicited cAMP formation. Thus, the characteristics of the EP₃ϐ receptor of rat hepatocytes closely resemble those of the EP₃ϐ receptor of mouse mastocytoma.
We have studied bifurcation phenomena for the incompressable Navier-Stokes equations in two space dimensions with periodic boundary conditions. Fourier representations of velocity and pressure have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. Invariant sets, notably steady states, have been traced for varying Reynolds number or strength of the imposed forcing, respectively. A complete bifurcation sequence leading to chaos is described in detail, including the calculation of the Lyapunov exponents that characterize the resulting chaotic branch in the bifurcation diagram.
Linguistics in Potsdam
(1994)