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The paper is devoted to pseudodifferential boundary value problems in domains with singular points on the boundary. The tangent cone at a singular point is allowed to degenerate. In particular, the boundary may rotate and oscillate in a neighbourhood of such a point. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to singular points.
Abschließende Bemerkungen des Menschenrechtsausschusses zum Bericht Deutschlands gemäß Art. 40 CCPR
(1997)
Three-dimensional bouyancy-driven convection in a horizontal fluid layer with stress-free boundary conditions at the top and bottom and periodic boundary conditions in the horizontal directions is investigated by means of numerical simulation and bifurcation-analysis techniques. The aspect ratio is fixed to a value of 2√2 and the Prandtl number to a value of 6.8. Two-dimensional convection rolls are found to be stable up to a Rayleigh number of 17 950, where a Hopf bifurcation leads to traveling waves. These are stable up to a Rayleigh number of 30 000, where a secondary Hopf bifurcation generates modulated traveling waves. We pay particular attention to the symmetries of the solutions and symmetry breaking by the bifurcations.
We have studied the bifurcation structure of the incompressible two-dimensional Navier-Stokes equations with a special external forcing driving an array of 8×8 counterrotating vortices. The study has been motivated by recent experiments with thin layers of electrolytes showing, among other things, the formation of large-scale spatial patterns. As the strength of the forcing or the Reynolds number is raised the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. The bifurcations lead to several periodic branches, torus and chaotic solutions, and other stationary solutions. Most remarkable is the appearance of solutions characterized by structures on spatial scales large compared to the scale of the forcing. We also characterize the different dynamic regimes by means of tracers injected into the fluid. Stretching rates and Hausdorff dimensions of convected line elements are calculated to quantify the mixing process. It turns out that for time-periodic velocity fields the mixing can be very effective.
Two-dimensional bouyancy-driven convection in a horizontal fluid layer with stress-free boundary conditions at top and bottom and periodic boundary conditions in the horizontal direction is investigated by means of numerical simulation and bifurcation-analysis techniques. As the bouyancy forces increase, the primary stationary and symmetric convection rolls undergo successive Hopf bifurcations, bifurcations to traveling waves, and phase lockings. We pay attention to symmetry breaking and its connection with the generation of large-scale horizontal flows. Calculations of Lyapunov exponents indicate that at a Rayleigh number of 2.3×105 no temporal chaos is reached yet, but the system moves nonchaotically on a 4-torus in phase space.
The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum.
After overcoming the divergence from the general features of Western and international urban development caused by Germany's division, Berlin is catching up with and imitating almost all features of post-modern city formation constituted and demonstrated in the last two decades. Berlin is trying to make good its backwardness and to keep abreast of the metropolis in Europe and the world through a strategy aimed at a cultural re-evaluation of urban structure and architecture. The so-called Prussian style based on the Classicist tradition of the beginning of the 19th century is the historical and asthetic horizon. A small administrative and architectural elite pushing the redefinition of the social, political and asthetic meaning of public space ignores consciously the architectural reality in the Eastern and Western parts of the city. Crucial objectives are the cultural, political and economic recapturing of the traditional centre of Berlin profoundly marked by its socialist past and the protection of middle class interests.
The attitude of the East Germans to the Polish is burdened with the heritage of the past. After 1945 the composition of the population on both sides of the new border along the Oder and Neisse rivers changed drastically. On the eastern side the Germans were expelled and Polish people were settled. On the western side many expelled Germans found a new home. Despite the fact that the GDR signed the Oder-Neisse border treaty, the ruling communist party (SED) did not encourage contacts between the people living on both sides of Oder and Neisse in the following years. The policy of the SED towards the Polish communists during the whole period between 1946-1989 was characterised by arrogance and suspicion, at times falling back on old anti-Polish stereotypes. Especially in the 1980s, the GDR tried to prevent the influence of Solidarnosc and dissident ideas from entering the country. Despite this policy, substantial personal contacts developed, particularly in the 1970s when the border was fully opened. The authors argue that current German-Polish relations should make use of these experiences.
Die Kinderrechtskonvention
(1997)
Lineare Modelle mit latenten Variablen sind seit langem verbreitete Analyse- und Prognoseinstrumente in den Sozialwissenschaften. Auch in der Ökonometrie gibt es einige Anwendungen. Die meistverbreiteten Modellierungs- und Schätzverfahren sind LISREL von Jöreskog und Sörbom (z.B. 1987) und Partial Least Squares (PLS) von H. Wold (1973). Während LISREL mehr modellorientiert und in der Anwendung konfirmativ ist, kann man PLS als datenorientiert und eher deskriptiv oder explorativ bezeichnen. Charakteristisch für Wolds Herangehen ist, daß das PLS-Modell eigentlich nur durch den Algorithmus zu seiner Schätzung definiert wird. Das umfassendste Programmsystem für PLS ist LVPLS von J. B. Lohmöller (1984). Es lehnt sich sehr eng an die Theorie von Wold an und ist trotz mangelnden Nutzerkomforts in seiner Vielseitigkeit und Zuverlässigkeit unübertroffen. Weder Wolds Verfahren noch Lohmöllers Programm sehen die Anwendung auf dynamische Modelle, etwa VARs, explizit vor. Die Einbeziehung verzögerter Variablen ist nur in Form selbständiger Variablen möglich, was zu Inkonsistenzen bei der Gewichtung führt. Im folgenden zweiten Abschnitt wird ein Verfahren skizziert (vgl. Strohe 1995), das sich einerseits sehr eng an den Woldschen Algorithmus anlehnt, das aber andererseits speziell auf die Behandlung von dynamischen Modellen mit verzögerten latenten Variablen ausgerichtet ist. Der dritte Abschnitt bringt dann eine Einführung in das entsprechende ISP™ Computerprogramm DPLS (vgl. Geppert 1995). Er besteht aus einer allgemeinen Programmbeschreibung und einer detaillierten Nutzeranleitung. Hinzu kommt die Bearbeitung eines kleinen ökonometrischen Demonstrationsmodells. Im vierten Abschnitt werden mit einer Simulationsstudie die Eigenschaften des Schätzverfahrens DPLS unter verschiedenen Verteilungsannahmen geprüft. Der Anhang bringt die vollständigen Listings der kommentierten Programm-Macros.
Inhaltsübersicht I. Einführung II. Grundlagen und Durchsetzung von völkerrechtlichen Verpflichtungen 1. Vertragliche Verpflichtung 2. Völkergewohnheitsrechtliche Verpflichtung III. Einbettung von Durchsetzungsmaßnahmen in politische und wirtschaftliche Zusammenhänge 1. Berücksichtigung im Rahmen rechtlicher Kontrolle 2. Abstimmung mit anderen Politikzielen IV. Sonderfall: erodierende Staatsgewalt V. Ausblick