Numerical Kähler-Einstein Metric on the Third del Pezzo

The third del Pezzo surface admits a unique Kähler-Einstein metric, which is not known in closed form. The manifold’s toric structure reduces the Einstein equation to a single Monge-Ampère equation in two real dimensions. We numerically solve this nonlinear PDE using three different algorithms, and describe the resulting metric. The first two algorithms involve simulation of Ricci flow, in complex and symplectic coordinates respectively. The third algorithm involves turning the PDE into an optimization problem on a certain space of metrics, which are symplectic analogues of the “algebraic” metrics used in numerical work on Calabi-Yau manifolds. Our algorithms should be applicable to general toric manifolds. Using our metric, we compute various geometric quantities of interest, including Laplacian eigenvalues and a harmonic (1,1)-form. The metric and (1,1)-form can be used to construct a Klebanov-Tseytlin-like supergravity solution.     

Ueber die Diffusion der Kolloide I

Ohne Zusammenfassungnach Versuchen von H. Kasarnowski.     

Permutation groups generated by cycles of fixed length

Combinatorial conditions on a set of cycles of fixed degree inS _n are studied, so that they generateA _n orS _n . It is shown thatA _n orS _n is so generated if and only if a graph associated with the set of cycles is connected, provided two of the cycles satisfy certain, not too restrictive, criteria. As a corollary, the minimum number of cycles of degreem ≧ 2 that generateA _n or S_n is determined.     

Groups with strongly self-centralizing 3-centralizers

LetG be a finite group with a subgroupM which is the centralizer inG of each of its nonidentity elements and let 3 divide the order ofM. Such groups are classified under the assumption that eitherq=[N _G (M):M]=2^s;s≧0 ands ≠ 3 orq<8. This paper was written while the author was visiting the Department of Mathematics, University of Illinois, Urbana, Illinois 61801.     

The quadrupole moment of the 535 keV state of 133La

The quadrupole moment of the 535 keV $\text{3}\text{2}{}^{\mathrm{?}}$ state of ¹³³La has been derived from a time-differential perturbed angular correlation measurement in an environment of La metal. The effective electric gradient is known from a nuclear quadrupole resonance measurement with the ground state of ¹³⁹La. The result Q = 0.35 ± 0.03 b does not confirm a proposed shape isomerism.     

Semi-regular plane polygons of integral type

A polygon is called semi-regular if its interior angles are equal to one another. The paper deals mainly with semi-regular polygons whose sides have integral lengths.     

Experimental investigation of low lying excited states in201Hg

Zeitschrift für Physik A Hadrons and nuclei - The decay of201Tl to201Hg has been investigated withγ- and conversion electron spectroscopic methods. The 26 keV level in201Hg, proposed...