Stability properties of collocation methods

Lower bounds for are given for which equidistant s-point collocation methods areA()-stable for arbitrarys.     

Untangling Polygons and Graphs

Untangling is a process in which some vertices in a drawing of a planar graph are moved to obtain a straight-line plane drawing. The aim is to move as few vertices as possible. We present an algorithm that untangles the cycle graph C _n while keeping Ω(n ^2/3) vertices fixed. For any connected graph G, we also present an upper bound on the number of fixed vertices in the worst case. The bound is a function of the number of vertices, maximum degree, and diameter of G. One consequence is that every 3-connected planar graph has a drawing δ such that at most O((nlog n)^2/3) vertices are fixed in every untangling of δ.     

Linear dichroism and magnetic circular dichroism of acenaphth[1,2-a]acenaphthylene

Ultraviolet-visible polarized absorption spectra of acenaphth[1,2-a]acenaphthylene have been determined from low-temperature measurements of linear dichroism in stretched polyethylene. The magnetic circular dichroic spectrum has been measured in solution. Transition energies, polarizations, and relative intensities, as well as the absolute signs of B terms of low-energy transitions are in good agreement with results of π-electron calculations and with simple qualitative arguments, which also account for the close similarity to the known spectra of acenaphthylene.     

Über eine allgemeine Methode zur mathematischen Analyse empirischer Reihen

Ohne ZusammenfassungGerhard Kowalewski zum 60. Geburtstage am 27. März 1936 gewidmet     

Primordial <Superscript>4</Superscript>He Abundance Constrains the Possible Time Variation of the Higgs Vacuum Expectation Value

We constrain the possible time variation of the Higgs vacuum expectation value (v) by recent results on the primordial ⁴He abundance (Y _P ). For that, we use an analytic approach which enables us to take important issues into consideration, that have been ignored by previous works, like the v-dependence of the relevant cross sections of deuterium production and photodisintegration, including the full Klein–Nishina cross section. Furthermore, we take a non-equilibrium Ansatz for the freeze-out concentration of neutrons and protons and incorporate the latest results on the neutron decay. Finally, we approximate the key-parameters of the primordial ⁴He production (the mean lifetime of the free neutron and the binding energy of the deuteron) by terms of (where v ₀ denotes the present theoretical estimate). Eventually, we derive the relation and the most stringent limit on a possible time variation of v is given by: .     

Non‐thermal plasma‐induced apoptosis in yeast Saccharomyces cerevisiae

The effect of non‐thermal plasma generated by the direct current (DC) corona discharge in the mode of transition spark is studied on a yeast Saccharomyces cerevisiae. The exposure to plasma increases production of reactive oxygen species (ROS) in cells, possibly causing the induction of apoptosis. To clarify the mechanism of apoptosis, its induction is tested not only on a wild strain of S. cerevisiae, but also on mutant strains: A deletion mutant Δyca1 without yeast metacaspase proves that in S. cerevisiae the apoptosis occurs partly by the caspase‐independent pathway. A petite strains with mutation in the mitochondria do not show pronounced ROS formation, but in spite of this, apoptosis is detected. Hence, mitochondrial ROS probably do not play an important role in induction of apoptosis.     

Surfaces of prescribed mean curvature in a cone

We show existence of surfaces of prescribed mean curvature in central projection for such values of the mean curvature for which estimates for the corresponding Euler–Lagrange equations are generally not known. This is achieved by extending the variational problem to the space \({BV(\Omega)}\), where graphs in a cone must satisfy a side condition, and using variational methods. Moreover, we give an example of a solution in \({BV(\Omega)}\) which does not solve the Dirichlet problem for the Euler-Lagrange equation.