Symmetrische Functionen

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Ueber die Theorie der ternären cubischen Formen

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Ueber die algebraischen Formen,deren Hesse'sche Determinante identisch verschwindet

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Ueber Gleichungen siebenten Grades mit einer Gruppe von 168 Substitutionen. II

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Polyhedral magnetite nanocrystals with multiple facets: facile synthesis, structural modelling, magnetic properties and application for high capacity lithium storage

Polyhedral magnetite nanocrystals with multiple facets were synthesised by a low temperature hydrothermal method. Atomistic simulation and calculations on surface attachment energy successfully predicted the polyhedral structure of magnetite nanocrystals with multiple facets. X-ray diffraction, field emission scanning electron microscopy, and high resolution transmission microscopy confirmed the crystal structure of magnetite, which is consistent with the theoretical modelling. The magnetic property measurements show the superspin glass state of the polyhedral nanocrystals, which could originate from the nanometer size of individual single crystals. When applied as an anode material in lithium ion cells, magnetite nanocrystals demonstrated an outstanding electrochemical performance with a high lithium storage capacity, a satisfactory cyclability, and an excellent high rate capacity.     

Carbon/carbon nanocomposites fabricated by base catalyzed twin polymerization of a Si-spiro compound on graphite sheets

Defect-free microporous carbon layers on graphite can be produced by DABCO-catalyzed twin polymerization of 2,2'-spirobi[4H-1,3,2-benzodioxasiline] in a slurry polymerization and subsequent thermal transformation of the resulting phenolic resin into carbon.     

Box dimension of Neimark–Sacker bifurcation

In this article we show how a change of a box dimension of orbits of two-dimensional discrete dynamical systems is connected to their bifurcations in a non-hyperbolic fixed point. This connection is already shown in the case of one-dimensional discrete dynamical systems and Hopf bifurcation for continuous systems. Namely, at the bifurcation point the box dimension changes from zero to a certain positive value which is connected to the appropriate bifurcation. We study a two-dimensional discrete dynamical system with only one multiplier on the unit circle, and show a result for the box dimension of an orbit on the centre manifold. We also consider a planar discrete system undergoing a Neimark–Sacker bifurcation. It is shown that box dimension depends on the order of non-degeneracy at the non-hyperbolic fixed point and on the angle–displacement map. As it was expected, we prove that the box dimension is different in the rational and irrational case.     

Weitere Untersuchungen über die ternäre biquadratische Formf =x 1 3 x 2+x 2 3 x 3+x 3 3 x 1

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Ueber die Resultante

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