Rationality of the moduli spaces of plane curves of sufficiently large degree

We prove that the moduli space of plane curves of degree d is rational for all sufficiently large d.     

"Stückelberg interferometry" with ultracold molecules

We report on the realization of a time-domain "Stückelberg interferometer", which is based on the internal-state structure of ultracold Feshbach molecules. Two subsequent passages through a weak avoided crossing between two different orbital angular momentum states in combination with a variable hold time lead to high-contrast population oscillations. This allows for a precise determination of the energy difference between the two molecular states. We demonstrate a high degree of control over the interferometer dynamics. The interferometric scheme provides new possibilities for precision measurements with ultracold molecules.     

A note on plurisubharmonic defining functions in$$\mathbb{C}^2$$

Let Ω ?? \(\mathbb{C}^2\) be a smoothly bounded domain. Suppose that Ω admits a smooth defining function which is plurisubharmonic on the boundary of Ω. Then the Diederich-Fornæss exponent can be chosen arbitrarily close to 1, and the closure of Ω admits a Stein neighborhood basis.     

Optimized production of a cesium Bose–Einstein condensate

We report on the optimized production of a Bose–Einstein condensate of cesium atoms using an optical trapping approach. Based on an improved trap loading and evaporation scheme we obtain more than 10⁵ atoms in the condensed phase. To test the tunability of the interaction in the condensate we study the expansion of the condensate as a function of scattering length. We further excite strong oscillations of the trapped condensate by rapidly varying the interaction strength. PACS 03.75.Kk; 32.80.Pj     

Über Distanzfunktionen mit Werten in angeordneten Halbgruppen

This paper presents a general investigation of the relations between structural properties of a totally ordered abelian semigroupS and the properties of various topological structures, such as topologies, bitopologies and (semi-)uniformities on a spaceX induced byS-valued distance functionsdX×XS satisfyingd(x,y)=0 iffx=y and the triangular inequalityd(x,z)d(x,y)+d(y,z), for allx,y,zX. Since a linearly ordered abelian semigroupS need not be a topological semigroup with respect to its order topology we have to consider two cases: the case where addition inS is continuous at 0S, and the case where it is not. For both cases, we state several metrization theorems, examples and applications. In this connection, we are also concerned with some special basis-properties of topological spaces. Closely connected is the program stated byAlexandroff-Bourbaki (amongst others) to investigate to what extent countability inherent in matrization theory can be replaced by order-theoretic properties.—Distinguishing between symmetric and not necessarily symmetric distancesd _S we obtain a theory containing the theory of _µ -metrics and _µ- quasimetrics.—As far as it concerns not necessarily symmetric distancesd onX, it seems adequate to study the bitopological structure ( _e , _r ) induced onX byd and the inverse distanced ^–1 respectively. This is done in § 4 where, in this respect, we also generalize a well-known theorem ofSion andZelmer.

---

---

Herrn Prof. Dr. E. Hlawka zum 60. Geburtstag gewidmet

---

Die ersten Anregungen zur grundsätzlichen Problemstellung erhielt der erste Autor in einem Seminar über Bewertungstheorie und Analysis in bewerteten Körpern, das unter der Leitung Herrn Prof. Dr.E. Hlawkas am Mathematischen Institut der Universität Wien abgehalten wurde.