A p-version finite element method for nonlinear elliptic variational inequalities in 2D

This article introduces and analyzes a p-version FEM for variational inequalities resulting from obstacle problems for some quasi-linear elliptic partial differential operators. We approximate the solution by controlling the obstacle condition in images of the Gauss–Lobatto points. We show existence and uniqueness for the discrete solution u _p from the p-version for the obstacle problem. We prove the convergence of u _p towards the solution with respect to the energy norm, and assuming some additional regularity for the solution we derive an a priori error estimate. In numerical experiments the p-version turns out to be superior to the h-version concerning the convergence rate and the number of unknowns needed to achieve a certain exactness of the approximation.     

Synthese und Struktur von γ-Halogenpropyl-octa(silasesquioxanen)

Synthesis and Structures of γ-Halopropyl-octa(silasesquioxanes) As a more rapid and versatile synthetic approach, we have studied the FeCl₃-catalyzed hydrolytic polycondensation of suited trichlorosilanes in a biphasic system which yields e.g. the new octa(silasesquioxane) (BrCH₂CH₂CH₂)₈Si₈O₁₂.     

Neutral strange particle exclusive production in charged current high-energy antineutrino interactions

The cross section of the quasi-elastic reactions \(\bar v_\mu p \to \mu ^ + \Lambda (\Sigma ^0 )\) in the energy range 5–100 GeV is determined from Fermilab 15′ bubble chamber antineutrino data. TheQ ² analysis of quasi-elastic Λ events yieldsM _A=1.0±0.3 GeV/c² for the axial mass value. With zero µΛ K ⁰ events observed, the 90% confidence level upper limit \(\sigma (\bar v_\mu p \to \mu ^ + \Lambda {\rm K}^0 )< 2.0 \cdot 10^{ - 40} cm^2 \) is obtained. At the same time, we found that the cross section of reaction \(\bar v_\mu p \to \mu ^ + \Lambda {\rm K}^0 + m\pi ^0 \) is equal to \(\left( {3.9\begin{array}{*{20}c} { + 1.6} \\ { - 1.3} \\ \end{array} } \right) \cdot 10^{ - 40} cm^2 \) .     

Alternativ-Liganden. XXIII. Rhodium(I)-Komplexe mit Donor/Akzeptor-Liganden des Typs (Me2PCH2CH2SiX2 und (2-Me2PC6H4)SiXMe2 (X = F,Cl)

Alternative Ligands. XXIII Rhodium(I) Complexes with Donor/Acceptor Ligands of the Type (Me₂PCH₂CH₂)₂SiX₂ and (2-Me₂PC₆H₄)SiXMe₂ (X = F, Cl) Donor/acceptor ligands of the type (Me₂PCH₂CH₂)₂SiX₂ and (2-Me₂PC₆H₄)SiXMe₂ (X = F, Cl) react with [Rh(CO)₂Cl]₂ (₁) to give the mononuclear complexes RhCl(CO)(Me₂PCH₂CH₂)₂SiX₂ [X = F( 4 ), Cl ( 5 )] and RhCl(CO)[2-Me₂PC₆H₄)SixMe₂]₂ [X = F ( 8 ), Cl ( 9 )], respectively. In case of the ligands (Me₂PCH₂CH₂)₂SiCl₂ ( 3 ) and (2-Me₂PC₆H₆)SiClMe₂ ( 7 ) the Rh(I) complexes formed in the first step partly undergo oxidative addition reactions of SiCl bonds yielding rhodium(III) compounds of low solubility. Only for 8 the coordination shifts Δδ = δ(complex)?δ(ligand) and coupling constants give some indication to possible Rh→Si interactions. However, the molecular structure of 8 determined by X-ray diffraction does not show RhSi or RhF bonding contacts. The new compounds were characterized by analytical (C, H) and spectroscopic investigations (MS, IR,-NMR).     

Strukturen neuer SeII- und TeII-Komplexe mit 2,2-Dicyanethylen-1,1-dithiolat, 2,2-Dicyanethylen-1,1-thioselenolat und 2,2-Dicyanethylen-1,1-diselenolat

Structures of New Se^II and Te^II Complexes Containing 2,2-Dicyanethylene-1,1-dithiolate, 2,2-Dicyanethylene-1,1-thioselenolate, and 2,2-Dicyanethylene-1,1-diselenolate (NBu₄)₂{Se[S₂C?C(CN)₂]₂} ( I ), (AsPh₄)₂ · {Te[SSeC?C(CN)₂]₂} ( II ), and (NBu₄)₂{Te[Se₂C?C(CN)₂]₂} ( III ) containing the bidentate chelate ligands 2,2-dicyanethylene-1,1-dithiolate i-mnt , 2,2-dicyanethylene-1,1-thioselenolate i-mnts , and 2,2-dicyanethylene-1,1-diselenolate i-mns have been prepared and characterized by X-ray structure analysis. The central units consist of [M(X? X)₂E₂]^2? (M = Se, Te; X? X = ligand; E = lone-pair) with fourfold coordinated Se^II and Te^II, respectively. The complex anions [Se(i-mnt)₂E₂]^2? as well as [Te(i-mnts)₂E₂]^2? show a trapezoide distortion with d(Se? S) = 2.276(5); 2.287(5); 2.803(5); 2.789(5) Å and d(Te? Se) = 2.611(2); 2.617(3); d(Te? S) = 2.889(5); 2.935(4) Å. In III there are centrosymmetric complex anions [Te(i-mns)₂E₂]^2? with nearly identical Te? Se-bond-lengths: 2.674(3) and 2.692(2) Å. These Te? Se bonds are elongated compared to usual Te? Se bonds.