Punktweise Abschätzungen zur Ermittlung des Einflusses von Störtermen bei Verzweigungsproblemen

Zusammenfassung Am Beispiel einer nichtlinearen Randwertaufgabe vierter Ordnung wird mit Hilfe von Einschließungsaussagen gezeigt, welchen Einfluß Störterme, die sich beispielsweise aus Materialunvollkommenheiten ergeben, auf die Lösung ausüben. Im allgemeinen sind diese Terme nicht exakt bekannt. Deshalb wurden bei solchen Problemen bisher für die Störterme plausible Ansätze verwendet. Hier werden wir statt dessen mit Hilfe von Einschließungsaussagen aus einer punktweisen Abschätzung der Störterme eine punktweise Abschätzung der Lösung gewinnen.

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Summary In this article we discuss the buckling imperfection sensitivity of a column resting on a nonlinear elastic foundation. Usula methods require a special knowledge about the form of the imperfection. Here we use Range-Domain Implication to provide a pointwise bound for the solutions of the corresponding boundary problem if a pointwise bound for the imperfection may be assumed.

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Die Drucklegung dieses Berichtes wurde durch Mittel des Vereins der Freunde und Förderer der Universität zu Köln unterstützt.     

The generalized Wiener Theorem for groups with finite dimensional irreducible representations

It is shown that the generalized Wiener Theorem for ideals in group algebras of locally compact Abelian groups extends to group algebras of locally compact groups with finite-dimensional irreducible representations (Moore groups).     

Berechnung der isotropen Kopplungskonstanten für die Wechselwirkung zwischen den Kernspins inHD

The coupling constant is calculated by using several basis sets of Gaussian functions differing in size and parameters. For the first time the result of 42.40 cps is in very satisfactory agreement with experiment (42.7?+0.5 cps). The calculations justify our conclusions that 1^st one has to determine classes of excited states which are complete respective to the chosen basis set, 2^d the restriction to the class of singly excited states is adequate and 3^d correlation effects must be included but a perturbational approach is sufficient. These restrictions are essential for handling large basis sets which makes our method transferable to larger molecules.     

Towards sympathetic cooling of trapped ions with laser-cooled Mg + ions for mass spectrometry and laser spectroscopy

Sympathetic cooling by laser cooled Mg ions has been proposed as a method for fast cooling of highly charged ions to a very low temperature. The paper describes the construction of the solid state laser system at 279.63 nm required for laser cooling of the Mg ions. The laser system is composed of a fiber laser at 1,118.54 nm and two successive second harmonic generation (SHG) ring cavities for frequency quadrupling. In the first SHG cavity, non-critical phase matching of a lithium triborate (LBO) crystal is used for doubling from 1,118.54 to 559.27 nm. The second SHG cavity uses critical phase matching of a β-barium borate (BBO) crystal for doubling from 559.27 to 279.63 nm. With the aid of Boyd–Kleinmann theory, optimum experimental parameters are calculated and used for an efficient SHG. Besides this, the paper intends to be a shortcut for practical applications of the Boyd–Kleinmann theory for SHG.     

Thermoluminescence characterization of traps involved in the photodarkening of ytterbium-doped silica fibers

The photodarkening (PD) mechanisms of ytterbium-doped silica optical fibers have still not been elucidated, although hardening routes have been proposed. Most basic questions are still under debate about the assignment of the darkening excitation bands into the UV range, the nature of absorbing centers (photoionized centers or trapped carriers?), or of traps accepting photo-released carriers (electron or hole traps?). We used thermoluminescence measurements to characterize traps populated by different radiation types. It is notably demonstrated that photodarkening involves silica hole traps. The popular idea that color centers are formed upon carrier trapping is not consistent with our observations.     

NZ‐flows in strong products of graphs

We prove that the strong product G₁? G₂ of G₁ and G₂ is ?₃‐flow contractible if and only if G₁? G₂ is not T? K₂, where T is a tree (we call T? K₂ a K₄‐tree). It follows that G₁? G₂ admits an NZ 3 ‐flow unless G₁? G₂ is a K₄ ‐tree. We also give a constructive proof that yields a polynomial algorithm whose output is an NZ 3‐flow if G₁? G₂ is not a K₄ ‐tree, and an NZ 4‐flow otherwise. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 267–276, 2010