Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.     

über einen Satz von G. Ricci-Curbastro und die Gaußsche Krümmung der Minimalflächen III

Ohne Zusammenfassung Richard Rado zum 65. Geburtstag     

Expanding the Chemistry of Molecular U2+ Complexes: Synthesis,Characterization, and Reactivity of the {[C5H3(SiMe3)2]3U}− Anion

The synthesis of new molecular complexes of U²⁺ has been pursued to make comparisons in structure, physical properties, and reactivity with the first U²⁺ complex, [K(2.2.2‐cryptand)][Cp′₃U], 1 (Cp′=C₅H₄SiMe₃). Reduction of Cp′′₃U [Cp′′=C₅H₃(SiMe₃)₂] with KC₈ in the presence of 2.2.2‐cryptand or 18‐crown‐6 generates [K(2.2.2‐cryptand)][Cp′′₃U], 2‐K(crypt) , or [K(18‐crown‐6)(THF)₂][Cp′′₃U], 2‐K(18c6) , respectively. The UV/Vis spectra of 2‐K and 1 are similar, and they are much more intense than those of U³⁺ analogues. Variable temperature magnetic susceptibility data for 1 and 2‐K(crypt) reveal lower room temperature χ_MT values relative to the experimental values for the 5f³ U³⁺ precursors. Stability studies monitored by UV/Vis spectroscopy show that 2‐K(crypt) and 2‐K(18c6) have t_1/2 values of 20 and 15 h at room temperature, respectively, vs. 1.5 h for 1 . Complex 2‐K(18c6) reacts with H₂ or PhSiH₃ to form the uranium hydride, [K(18‐crown‐6)(THF)₂][Cp′′₃UH], 3 . Complexes 1 and 2‐K(18c6) both reduce cyclooctatetraene to form uranocene, (C₈H₈)₂U, as well as the U³⁺ byproducts [K(2.2.2‐cryptand)][Cp′₄U], 4 , and Cp′′₃U, respectively.     

Synthesis of a crystalline molecular complex of Y2+, [(18-crown-6)K][(C5H4SiMe3)3Y

The La(2+) complex [K(18-crown-6)(OEt(2))][Cp″(3)La] (1) [Cp″ = C(5)H(3)(SiMe(3))(2)-1,3], can be synthesized under N(2), but in the presence of KC(5)Me(5), 1 reduces N(2) to the (N═N)(2-) product [(C(5)Me(5))(2)(THF)La](2)(μ-η(2):η(2)-N(2)). This suggests a dichotomy in terms of ligands that optimize isolation of reduced dinitrogen complexes versus isolation of divalent complexes of the rare earths. To determine whether the first crystalline molecular Y(2+) complex could be isolated using this logic, Cp'(3)Y (2) (Cp' = C(5)H(4)SiMe(3)) was synthesized from YCl(3) and KCp' and reduced with KC(8) in the presence of 18-crown-6 in Et(2)O at -45 °C under argon. EPR evidence was consistent with Y(2+) and crystallization provided the first structurally characterizable molecular Y(2+) complex, dark-maroon-purple [(18-crown-6)K][Cp'(3)Y] (3).