On the internal stepsize of an extrapolation algorithm for IVP in ODE

We propose an extrapolation algorithm for initial value problems in ordinary differential equations. In the algorithm, an appropriately chosen stepsizeH is divided into smaller stepsizes by a sequence and a new stopping rule is proposed. The sequences applied to the algorithm are Romberg {2,4,8,16,32,...}, Bulirsch {2,4,6,8,16...} and Harmonic {2,4,6,8,10,12,...} types. The proposed algorithm is compared numerically with the algorithm introduced by Stoer. In view of the accuracy of numerical solutions, the relatively small number of calculations, the stability and reliability of the algorithm, we found that the algorithm with the Romberg sequence is the best.     

119Sn Mössbauer study of the CePtSn Kondo compound

We have measured¹¹⁹Sn Mössbauer spectra of the CePtSn and (Ce_0.9La_0.1)NiSn compounds in the range from 1.5 to 293 K. In CePtSn, the spectra observed above 8 K are well explained by an electric quadrupole interaction. The spectral shape changes below 8 K due to the presence of a magnetic hyperfine field produced by the ordering of the Ce magnetic moments. We have analyzed these spectra assuming an incommensurate magnetic structure. The temperature dependence of the magnetic hyperfine field matches with anS=1/2 mean field curve with a step at 5 K. In (Ce_0.9La_0.1)NiSn, no magnetic order exists down to 1.5 K.     

Observation of resonance recombination lines in electron excited auger spectra of Gd

Combined measurements of electron excited N_4,5 Auger spectra and photoelectron emission on clean and oxidized Gd lead to a distinction between Auger lines originating from 4d → continuum and 4d → 4? resonance excitations. Several Auger structures are identified as due to the direct recombination of 4d⁹4?⁸ states with the 4f and valence electrons. The shape of the most prominent Auger line for oxidized Gd agrees perfectly with the Fano profile of the 4? photoemission intensity.     

Total Valuation Rings of Ore Extensions

We consider extensions of a total valuation ring V of a skew field K to the Ore extension K(X;σ, δ) for an endomorphism σ of K and a σ-derivation δ. It is shown that there exists an extension R of V with X ∈ R, such that ${\overline X}$ is transcendental over V/J(V) if and only if (σ,δ) is compatible with V, where ${\overline X} = X + J(R^(1))$ . In the case V is invariant, it is established that there is an invariant extension R of V in K(X;σ,δ) such that ${\overline X}$ is transcendental if and only if σ(a)V = aV and δ(a) ∈ aV for all a ∈ K.     

Spontaneous luminescence due to high density electron-hole plasma in GaAs under nano- and pico-second pulse excitation

Spontaneous luminescence due to high density electron-hole plasma in GaAs is observed at 4.2 K under nano- and pico-second pulse excitation. From the pico-second time-resolved spectra, it is found that the hot carriers are cooled down rapidly within 150 psec, and the changes of spectra are not appreciable in the later stage. One may consider, together with results of the spectral shape analysis, that the electron-hole liquid formation is improbable at least within the time range observed.