Associative formal power series in two indeterminates

Investigating the associativity equation for formal power series in two variables we show that the transcendental associative formal power series are of order one or two and that they can be represented by an invertible formal power series in one variable. We also discuss the convergence of associative formal power series.     

Über Gruppen Von Iterativen Wurzeln Der Formalen Potenzreihe F(x) = x

Let ?¦x¦ be the ring of formal power series in one indeterminate x over ?, denote by Γ the group of invertible series in ?¦x¦, and by E_Γ the set of all iterative roots of x in Γ. Then we will show that E_Γ is neither a subgroup of Γ nor a family of commuting series. We describe all subgroups of Γ lying in E_Γ, they are abelian and isomorphic to subgroups of the group E of complex roots of unity. Furthermore we determine the maximal subgroups of Γ in E{Γ} and use them to investigate how the subgroups in E _I are related.     

The quadrupole moment of the neutron-halo nucleus11Li

The quadrupole moment ratio of⁹Li and¹¹Li was measured by a combination of in-beam laser induced nuclear polarization and Β-NMR in LiNbO₃. The result ¦Q(¹¹Li)/Q(⁹Li)¦=1.14(16) is consistent with cluster models describing¹¹Li as composed of a⁹Li core and a far extended halo of two loosely bound neutrons.     

Über die Einwirkung von Säureamiden auf Aldehyde

Ohne ZusammenfassungIch komme hiemit einer angenehmen Pflicht nach, meinem hochverehrten Lehrer, dem Herrn Hofrat Prof. Dr. Ad. Lieben, für die mir bei der Ausführung dieser Arbeit freundlichst erteilten Ratschläge meinen innigsten Dank auszusprechen.     

Efficient numerical integration of arbitrarily broken cells using the moment fitting approach

The finite cell method is based on a fictitious domain approach, providing a simple and fast mesh generation of structures with complex geometries. However, this simplification leads to intersected cells where the standard Gauss quadrature does not perform well. To perform the numerical integration of these cells, we use the moment fitting approach that generates an individual quadrature rule for every broken cell. In this paper, we will perform a non-linear optimization approach to find the optimal position and number of the integration points. The findings show that the proposed method leads to efficient quadrature rules that require less integration points than other existing integration methods. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Minimal antiderivatives and monotonicity

We consider settings in convex analysis which give rise to families of convex functions that contain their lower envelope. Given certain partial data regarding a subdifferential, we consider the family of all convex antiderivatives that comply with the given data. We prove that this family is not empty and, in particular, contains a minimal antiderivative under a fairly general assumption on the given data. It turns out that the representation of monotone operators by convex functions fits naturally in these settings. Duality properties of representing functions are also captured by these settings, and the gap between the Fitzpatrick function and the Fitzpatrick family is filled by this broader sense of minimality of the Fitzpatrick function.