Über das Auftreten von Wirbeln und Strudeln (geschlossener und spiraliger Integralkurven) in der Umgebung rationaler Unbestimmtheitsstellen

Ohne Zusammenfassung     

Comparison of Brown's and Newton's method in the monotone case

Summary In many cases when Newton's method, applied to a nonlinear sytemF(x)=0, produces a monotonically decreasing sequence of iterates, Brown's method converges monotonically, too. We compare the iterates of Brown's and Newton's method in these monotone cases with respect to the natural partial ordering. It turns out that in most of the cases arising in applications Brown's method then produces better iterates than Newton's method.     

The Effect of Solvation in Conducting Polymers

The incorporation of solvent molecules into solid-state organic conductors affects both electrical and mechanical properties of the conducting complexes. Evidence for this has been appearing from the numerous laboratories currently involved in conducting polymer research. On compiling these examples, common rationale for the observed effects can be formulated based largely on the behavior of smaller molecules as found in the organic literature. Nonetheless, the examples must be considered on a case-to-case basis. In assigning the source of solvent effects, the determination of whether solvation is occurring on the charged polymer backbone or on the (oppositely charged) dopant counterion is critical. Among the proposed causes of solvent effects are solvent-separated ion pairing, charge depinning, and plasticization.