Über den Zusammenhang zwischen dem Maximalbetrage einer analytischen Funktion und dem grössten Betrage bei gegebenem Argumente der Funktion

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The mechanism of emission in the red photoluminescence band of porous silicon

Porous silicon (PS) exhibits several photoluminescence (PL) bands, whose spectral position and intensity depend strongly on the actual conditions of preparation of PS, its treatment, and subsequent use. The PS PL band peaking at about 1.8 eV and usually assigned to the intrinsic emission of silicon nanocrystals was studied. It was shown that the temperature-induced variation of the PL kinetics in the 80 to 300-K interval follows a complex pattern and depends noticeably on the actual point on the band profile. The temperature behavior of PL decay in the 1.8-eV band is determined by the electron-hole recombination rate within a nanocrystal and the cascade carrier transitions from small to large nanocrystals, with an attendant decrease in energy.     

Contribution of “unusual” domain walls to the magnetoresistance of multilayer magnetic structures

The contribution to electrical resistance due to scattering of charge carriers by domain walls is analyzed. It is revealed that “unusual” domain walls are created by frustrations in ferromagnet-antiferromagnet multilayer magnetic structures. The thickness of an unusual domain wall is substantially less than that of a usual domain wall. It is shown that scattering of charge carriers by unusual domain walls can contribute significantly to the magnetoresistance of ferromagnet-antiferromagnet multilayer magnetic structures. An analysis of the contribution made by the Levy-Zhang mechanism to the magnetoresistance demonstrates that the initial estimate obtained for this contribution is considerably exaggerated.     

On removable even circuits in graphs

Let G be a connected graph with minimum degree at least 3. We prove that there exists an even circuit C in G such that G−E(C) is either connected or contains precisely two components one of which is isomorphic to a 1-bond. We further prove sufficient conditions for there to exist an even circuit C in a 2-connected simple graph G such that G−E(C) is 2-connected. As a consequence of this, we obtain sufficient conditions for there to exist an even circuit C in a 2-connected graph G for which G−E(C) is 2-connected.     

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