A framework for existence tests based on the topological degree and homotopy

The invariance of the topological degree under certain homotopies is used to derive a framework for tests to computationally prove the existence of zeros of nonlinear mappings in . These tests use interval arithmetic to enclose the range of a function over a box and are provably more general than many other tests like the Moore–Kioustelidis test, a test based on the Krawczyk operator, and another degree–based test published recently. A numerical example is included.     

Influence of absorbed pump profile on the temperature distribution within a diode side-pumped laser rod

In this paper, an analytical model for temperature distribution of the side-pumped laser rod is extracted. This model can be used for side-pumped laser rods whose absorbed pump profile is a Gaussian profile. Then, it is validated by numerical results which exhibit a good agreement with the analytical results. Afterwards, by considering a general expression for super-Gaussian and top-hat profiles, and solving the heat equation, the influence of profile width and super-Gaussian exponent of the profile on temperature distribution are investigated. Consequently, the profile width turns out to have a greater influence on the temperature compared to the type of the profile.     

Asynchronous Richardson iterations: theory and practice

Numerical Algorithms - We consider asynchronous versions of the first- and second-order Richardson methods for solving linear systems of equations. These methods depend on parameters whose values...     

Die Integralkurven einer gewöhnlichen Differentialgleichung erster Ordnung in der Umgebung rationaler Unbestimmtheitsstellen

Ohne Zusammenfassung     

Analysis of t-butylphenol acetylene condensed resin with methyl-methine linkages in vulcanized rubber by pyrolysis-gas chromatography/mass spectrometry

Methyl-methine linkages of Novolac, a commercially available t-butylphenol acetylene condensed (TBPA) resin, have been identified by recognition of pyrolysis pathways using pyrolysis-gas chromatography/mass spectrometry (Py-GC/mS) in vulcanized rubber. The diagnostic mass spectrum of t-butylphenol with methyl-methine linkages between phenolic rings was observed at m/z 192, corresponding to 4-t-butyl-2-ethyl-6-methylphenol. Other molecular ions were observed at m/z 178, 164, and 150 in the characteristic pyrolyzates. The ion at m/z 192 in the TBPA resin was observed to be characteristic for methyl-methine linkages between the phenolic groups, and the analytical pyrolysis-GC/mS method was thus able to identify the resin at low levels in vulcanized rubber. Copyright 1999 John Wiley & Sons, Ltd.     

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.