Die Struktur der oberflächlichen Abschlussbezirke in den Ebenen (100) in Eisen. Die Bäumchenstruktur

Zusammenfassung Auf Grund der Gesamtenergiebilanz wird die Bäumchenstruktur erklärt und werden die Abmessungen dieser Abschlussbezirke berechnet. Es wird die Abhängigkeit vom Neigungswinkel der Beobachtungsebene und von der Grösse der Abschlussbezirke und damit auch von der Kristallgrösse ermittelt. Für jede Abmessung der Grundbezirke existiert auch ein maximaler Neigungswinkel der Beobachtungsebene, bis zu welchem die Bäumchenstruktur stabil ist. Diese Neigung verringert sich mit dem Anwachsen der Bezirksabmessung.     

Riccati equations and Lie series

Lie series and a special matrix notation for first-order differential operators are used to show that the Lie group properties of matrix Riccati equations arise in a natural way. The Lie series notation makes it evident that the solutions of a matrix Riccati equation are curves in a group of nonlinear transformations that is a generalization of the linear fractional transformations familiar from the classical complex analysis. It is easy to obtain a linear representation of the Lie algebra of the nonlinear group of transformations and then this linearization leads directly to the standard linearization of the matrix Riccati equations. We note that the matrix Riccati equations considered here are of the general rectangular type.     

Polyferrocenylenes by oxidative coupling of 1,1′-dilithioferrocene with Cu2+ Ion(1)

Summary The oxidative coupling of 1,1 -dilithioferrocene (chelated withN,N,N,N-tetramethylethylenediamine) in the presence of Cu^II halide (Cu²⁺Li=1–1.5) in ether solvents at –70 to 110° gives 30–45% yields of polyferrocenylene. Still higher yields of coupling products result from reactions in which oxidative coupling is paired with thermal coupling,i. e. C-C bond formation through thermal decomposition of organocopper(I) intermediates in the absence of external oxidant (Cu²⁺Li=0.5). Number-average molecular masses of the highest fractions of linear products (2) as separated in the primary work-up process are in the 1500–3400 range, and fractionating precipitation results in subfractions with M_n as high as 5000. Cyclization of dinuclear intermediates, producting up to 10% of [0,0] ferrocenophane (bisfulvalenediiron), competes in all experiments with linear propagation. Experiments conducted with Cu^I halides under conditions leading exclusively to thermal coupling provide even higher conversion to the ferrocenophane (up to 25% yields) at the expense of linear condensation products. Spectroscopic features of the polyferrocenylenes are discussed. In the linear compounds with ¯M_n>800, i.r. absorptions and p.m.r.'s are remarkably invariant with the degree of polymerization, as are the electronic absorption maxima. This shows, in confirmation of earlier reports, that there is insignificant resonance interaction between the cyclopentadienyl rings in the ferrocene system and hence little, if any, electronic delocalization along the polymer chain of heteroannularly interlinked polyferrocenylene structures.     

ВЛИЯНИЕ СТАРЕНИЯ НА Э ЛЕКТРИЧЕСКИЕ СВОЙСТ ВА ПОЛУПРОВОДНИКОВОЙ С ИСТЕМЫ Bi2Te3-Bi2Se3

, Bi₂Te₃-Bi₂Se₃. , , , . .

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Influence of ageing on change in electrical properties of semiconducting systems of Bi₂Te₃-Bi₂Se₃

The paper describes the effect of ageing observed on a semiconducting system Bi₂Te₃ — Bi₂Se₃. It is shown that the change in electrical conductivity and thermoelectric force, which takes place during ageing, is caused by the change in concentration of the free electrons. The influence of this process on the efficiency of equipment employing the Peltier effect is analyzed.

     

The energy of periodic surface structures in ferromagnetism

The periodic domain structures on unfavourably oriented surface layers of ferromagnetic materials were studied both experimentally and theoretically. The connection between the surface structure and the crystallographic orientation of the crystals was confirmed. All the terms contributing to the total energy of the surface layer were calculated. A general solution of the potential problem is given for arbitrary periodic distribution of the charges.

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A note on a generalization of Diliberto’s Theorem for certain differential equations of higher dimension

In the theory of autonomous perturbations of periodic solutions of ordinary differential equations the method of the Poincaré mapping has been widely used. For the analysis of properties of this mapping in the case of two-dimensional systems, a result first obtained probably by Diliberto in 1950 is sometimes used. In the paper, this result is (partially) extended to a certain class of autonomous ordinary differential equations of higher dimension.This research was supported by Grant No. 201/99/0295 of the Grant Agency of the Czech Republic.This revised version was published online in April 2005 with a corrected missing date string.     

Some sufficient conditions for the existence of a 1-factor

The following theorem is proved: Let G be a graph of even order. Assume that there exists a connected spanning subgraph F of G such that for every set U of four vertices in G, if the subgraph of F induced by U is a star, then the subgraph of G induced by U is complete. Then G has a 1-factor. The above theorem is derived from another sufficient condition for the existence of a 1-factor, which is also proved in this paper (Lemma 1).