Hyperbolicity in Teichm\"uller space

We review and organize some results describing the behavior of a Teichm\"uller geodesic and draw several applications: 1) We show that Teichm\"uller geodesics do not back track. 2) We show that a Teichm\"uller geodesic segment whose endpoints are in the thick part has the fellow travelling property. This fails when the endpoints are not necessarily in the thick part. 3) We show that if an edge of a Teichm\"uller geodesic triangle passes through the thick part, then it is close to one of the other egdes.Comment: 26 pages, 2 figure

Logik und Kategorienlehre : der "Neuen Grundlegung der Metaphysik" zweiter Teil

http://tartu.ester.ee/record=b2598266~S1*es

Ueber das Wesen der Liebe

http://tartu.ester.ee/record=b2501007~S1*es

Zur Pädagogik der Elementarschulen

https://www.ester.ee/record=b4008519*es

Teichm\"uller's problem in space

Quasiconformal homeomorphisms of the whole space Rn, onto itself normalized at one or two points are studied. In particular, the stability theory, the case when the maximal dilatation tends to 1, is in the focus. Our main result provides a spatial analogue of a classical result due to Teichm\"uller. Unlike Teichm\"uller's result, our bounds are explicit. Explicit bounds are based on two sharp well-known distortion results: the quasiconformal Schwarz lemma and the bound for linear dilatation. Moreover, Bernoulli type inequalities and asymptotically sharp bounds for special functions involving complete elliptic integrals are applied to simplify the computations. Finally, we discuss the behavior of the quasihyperbolic metric under quasiconformal maps and prove a sharp result for quasiconformal maps of R^n \ {0} onto itself.Comment: 25 pages, 2 figure

Observaciones microscópicas sobre los sedimentos en los manglares de El Salvador.

Los sedimentos de los manglares en El Salvador, son generalmente pobres en substancia orgánica, aunque algunos huelan fuertemente a H2S, Para los estudios siguientes puso a nuestra disposición el Prof. Dr. Weyl, material que se distinguía por su contenido en substancia orgánica, el cual era reconocible aun microscópicamente por los abundantes residuos de raíces y su color más oscuro

On the behaviour of Brauer pp-dimensions under finitely-generated field extensions

The present paper shows that if $q \in \mathbb P$ or $q = 0$, where $\mathbb P$ is the set of prime numbers, then there exist characteristic $q$ fields $E _{q,k}\colon \ k \in \mathbb N$, of Brauer dimension Brd$(E _{q,k}) = k$ and infinite absolute Brauer $p$-dimensions abrd$_{p}(E _{q,k})$, for all $p \in \mathbb P$ not dividing $q ^{2} - q$. This ensures that Brd$_{p}(F _{q,k}) = \infty$, $p \dagger q ^{2} - q$, for every finitely-generated transcendental extension $F _{q,k}/E _{q,k}$. We also prove that each sequence $a _{p}, b _{p}$, $p \in \mathbb P$, satisfying the conditions $a _{2} = b _{2}$ and $0 \le b _{p} \le a _{p} \le \infty$, equals the sequence abrd$_{p}(E), {\rm Brd}_{p}(E)$, $p \in \mathbb P$, for a field $E$ of characteristic zero.Comment: LaTeX, 14 pages: published in Journal of Algebra {\bf 428} (2015), 190-204; the abstract in the Metadata updated to fit the one of the pape

Das Alter des Sylter Kaolinsandes

Aus den Profilen des Kaolinsandes am Morsum-Kliff und am Roten Kliff auf Sylt wurden 2 Braunkohlenflöze von je 1 m Mächtigkeit pollenstratigraphisch und die Begleitschichten sedimentpetrographisch untersucht. Bei einem Vergleich der Pollenzusammensetzung mit anderen Horizonten aus dem mittleren Pliozän bis zum mittleren Pleistozän in Nordwestdeutschland zeigt sich eine gute Übereinstimmung mit der oberpliozänen Reuverstufe. Auch alle vorhergehenden pollenanalytischen Untersuchungen von Braunkohlenproben aus den Kaolinsanden kamen zu dem gleichen Resultat. Es bleibt somit bei der Stellung des Kaolinsandes im Oberpliozän. Daher muß die von D. Wirtz und H. Illies vorgenommene Neudatierung des Tertiärprofils am Morsum-Kliff als hinfällig gelten. Auch sind die Überlegungen über die Lage der Plio-Pleistozängrenze auf der Insel Sylt zu revidieren. Die Verwitterung der Kaolinsande hat mit Sicherheit vor der Elster-Vereisung (Mindel) und aller Wahrscheinlichkeit nach im allerjüngsten Pliozän stattgefunden. Im Profil des Roten Kliffs ist der Schwermineralbestand in den tonigen Lagen vor einer nachträglichen Verwitterungsauslese geschützt geblieben. Damit sind gewisse Unterschiede in der Mineral-Assoziation zu erklären. Zum Alter des Limonitsandsteins im Sylter Profil kann auf Grund der vorliegenden Untersuchung keine Stellung genommen werden.researc

What can quasi-periodic oscillations tell us about the structure of the corresponding compact objects?

We show how one can estimate the multipole moments of the space-time, assuming that the quasi-periodic modulations of the X-ray flux (quasi-periodic oscillations), observed from accreting neutron stars or black holes, are due to orbital and precession frequencies (relativistic precession model). The precession frequencies $\Omega_{\rho}$ and $\Omega_z$ can be expressed as expansions on the orbital frequency $\Omega$, in which the moments enter the coefficients in a prescribed form. Thus, observations can be fitted to these expressions in order to evaluate the moments. If the compact object is a neutron star, constrains can be imposed on the equation of state. The same analysis can be used for black holes as a test for the validity of the no-hair theorem. Alternatively, instead of fitting for the moments, observations can be matched to frequencies calculated from analytic models that are produced so as to correspond to realistic neutron stars described by various equations of state. Observations can thus be used to constrain the equation of state and possibly other physical parameters (mass, rotation, quadrupole, etc.) Some distinctive features of the frequencies, which become evident by using the analytic models, are discussed.Comment: accepted in MNRAS; changes made to match version in prin

Analytical approximation of the exterior gravitational field of rotating neutron stars

It is known that B\"acklund transformations can be used to generate stationary axisymmetric solutions of Einstein's vacuum field equations with any number of constants. We will use this class of exact solutions to describe the exterior vacuum region of numerically calculated neutron stars. Therefore we study how an Ernst potential given on the rotation axis and containing an arbitrary number of constants can be used to determine the metric everywhere. Then we review two methods to determine those constants from a numerically calculated solution. Finally, we compare the metric and physical properties of our analytic solution with the numerical data and find excellent agreement even for a small number of parameters.Comment: 9 pages, 10 figures, 3 table