Das Problem der Configurationen

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Local approximations for maximum partial subgraph problem

We deal with MAXH₀-FREE PARTIAL SUBGRAPH. We mainly prove that 3-locally optimum solutions achieve approximation ratio (δ₀+1)/(B+2+ν₀), where B=max_v∈Vd_G(v), δ₀=min_v∈V(H0)d_H0(v) and ν₀=(|V(H₀)|+1)/δ₀. Next, we show that this ratio rises up to 3/(B+1) when H₀=K₃. Finally, we provide hardness results for MAXK₃-FREE PARTIAL SUBGRAPH.     

Left versus right canonical Wiener-Hopf factorization and realization

For an arbitrary rational matrix function, not necessarily analytic at infinity, the existence of a right canonical Wiener-Hopf factorization is characterized in terms of a left canonical Wiener-Hopf factorization. Formulas for the factors in a right factorization are given in terms of the formulas for the factors in a given left factorization. All formulas are based on a special representation of a rational matrix function involving a quintet of matrices.     

Picosecond control of coherent magnetisation dynamics in permalloy thin films by picosecond magnetic field pulse shaping

We have measured the response of a 20×10 μm, 8 nm thin NiFe (80:20) permalloy film due to excitation by short in-plane magnetic field pulses. We will show that using a two-pulse-technique a complete control of the precessional motion of the magnetisation can be achieved on picosecond timescales. Furthermore, we will present numerical calculations which show that a complete suppression of magnetisation ringing after switching can only be realised by a cascade of short field pulses.     

Nonlinear-optical and micro-Raman diagnostics of thin films and nanostructures of ABO3 ferroelectrics

Ferroelectric composite two-dimensional ferroelectric/aluminum oxide nanostructures were studied. A porous aluminum oxide matrix was used as a template into which a ferroelectric precursor was introduced, followed by annealing. The prepared nanostructures were studied using optical second harmonic generation and micro-Raman scattering.     

The role of alkali content in the devitrification mechanisms of SiO2–Fe2O3–Na2O–PbO SYSTEM

Three batch compositions of pure oxides (SiO₂, Fe₂O₃, PbO, Na₂O) with equivalent SiO₂, Fe₂O₃ and PbO contents and a gradually increased Na₂O content were vitrified through heating in a high temperature electric furnace and subsequent quenching. The resulting vitreous products were thermally treated in order to study the devitrification behaviour, under conditions designated from differential thermal analysis experiments. Depending on the Na₂O content, crystal phase separation gave rise to the growth of acmite and hematite or maghemite. A uniformly phase separated glass-ceramic material, with crystallites of similar size and population density, was produced from devitrification of the vitreous product with the higher Na₂O content.