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Aus dem Inhalt: 1 Abraham Wald (1902-1950) 2 Einführung der Grundbegriffe. Einige technische bekannte Ergebnisse 2.1 Martingal und Doob-Ungleichung 2.2 Brownsche Bewegung und spezielle Martingale 2.3 Gleichgradige Integrierbarkeit von Prozessen 2.4 Gestopptes Martingal 2.5 Optionaler Stoppsatz von Doob 2.6 Lokales Martingal 2.7 Quadratische Variation 2.8 Die Dichte der ersten einseitigen Überschreitungszeit der Brown- schen Bewegung 2.9 Waldidentitäten für die Überschreitungszeiten der Brownschen Bewegung 3 Erste Waldidentität 3.1 Burkholder, Gundy und Davis Ungleichungen der gestoppten Brown- schen Bewegung 3.2 Erste Waldidentität für die Brownsche Bewegung 3.3 Verfeinerungen der ersten Waldidentität 3.4 Stärkere Verfeinerung der ersten Waldidentität für die Brown- schen Bewegung 3.5 Verfeinerung der ersten Waldidentität für spezielle Stoppzeiten der Brownschen Bewegung 3.6 Beispiele für lokale Martingale für die Verfeinerung der ersten Waldidentität 3.7 Überschreitungszeiten der Brownschen Bewegung für nichtlineare Schranken 4 Zweite Waldidentität 4.1 Zweite Waldidentität für die Brownsche Bewegung 4.2 Anwendungen der ersten und zweitenWaldidentität für die Brown- schen Bewegung 5 Dritte Waldidentität 5.1 Dritte Waldidentität für die Brownsche Bewegung 5.2 Verfeinerung der dritten Waldidentität 5.3 Eine wichtige Voraussetzung für die Verfeinerung der drittenWal- didentität 5.4 Verfeinerung der dritten Waldidentität für spezielle Stoppzeiten der Brownschen Bewegung 6 Waldidentitäten im Mehrdimensionalen 6.1 Erste Waldidentität im Mehrdimensionalen 6.2 Zweite Waldidentität im Mehrdimensionalen 6.3 Dritte Waldidentität im Mehrdimensionalen 7 Appendix
A numerical MHD model is developed to investigate acceleration and heating of both thermal and auroral plasma. This is done for magnetospheric flux tubes in which intensive field aligned currents flow. To give each of these tubes, the empirical Tsyganenko model of the magnetospheric field is used. The parameters of the background plasma outside the flux tube as well as the strength of the electric field of magnetospheric convection are given. Performing the numerical calculations, the distributions of the plasma densities, velocities, temperatures, parallel electric field and current, and of the coefficients of thermal conductivity are obtained in a self-consistent way. It is found that EIC turbulence develops effectively in the thermal plasma. The parallel electric field develops under the action of the anomalous resistivity. This electric field accelerates both the thermal and the auroral plasma. The thermal turbulent plasma is also subjected to an intensive heating. The increase of the plasma of the Earth's ionosphere. Besides, studying the growth and dispersion properties of oblique ion cyclotron waves excited in a drifting magnetized plasma, it is shown that under non-stationary conditions such waves may reveal the properties of bursts of polarized transverse electromagnetic waves at frequencies near the patron gyrofrequency.
We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of well-known characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information.
In a recent paper with N. Tarkhanov, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.
Harness-Prozesse
(2010)
Harness-Prozesse finden in der Forschung immer mehr Anwendung. Vor allem gewinnen Harness-Prozesse in stetiger Zeit an Bedeutung. Grundlegende Literatur zu diesem Thema ist allerdings wenig vorhanden. In der vorliegenden Arbeit wird die vorhandene Grundlagenliteratur zu Harness-Prozessen in diskreter und stetiger Zeit aufgearbeitet und Beweise ausgeführt, die bisher nur skizziert waren. Ziel dessen ist die Existenz einer Zerlegung von Harness-Prozessen über Z beziehungsweise R+ nachzuweisen.
Basing on recent solar models, the excitation of ion-acoustic turbulence in the weaklycollisional, fully and partially-ionized regions of the solar atmosphere is investigated. Within the frame of hydrodynamics, conditions are found under which the heating of the plasma by ion-acoustic type waves is more effective than the Joule heating. Taking into account wave and Joule heating effects, a nonlinear differential equation is derived, which describes the evolution of nonlinear ion-acoustic waves in the collisional plasma.
The Voyager 2 Photopolarimeter experiment has yielded the highest resolved data of Saturn's rings, exhibiting a wide variety of features. The B-ring region between 105000 km and 110000 km distance from Saturn has been investigated. It has a high matter density and contains no significance features visible by eye. Analysis with statistical methods has let us to the detection of two significant events. These features are correlated with the inner 3:2 resonances of the F-ring shepherd satellites Pandora and Prometheus, and may be evidence of large ring paricles caught in the corotation resonances.
For a sequence of Hilbert spaces and continuous linear operators the curvature is defined to be the composition of any two consecutive operators. This is modeled on the de Rham resolution of a connection on a module over an algebra. Of particular interest are those sequences for which the curvature is "small" at each step, e.g., belongs to a fixed operator ideal. In this context we elaborate the theory of Fredholm sequences and show how to introduce the Lefschetz number.