Complex formation of trace elements in geochemical systems—VI: Study on the formation of hydroxo fluoro mixed ligand complexes of the lanthanide elements in fluorite bearing system

The complexation of the rare elements Ce, Eu, Tb and Yb in fluorite bearing model solution of the pH 5–9 and the pF 2–5 has been studied by means of the distribution method. Hydroxofluoro mixed ligand complexes were found to be the most important species formed at pH 7 and pF 3 which are the relevant values of hydrothermal fluorite bearing solutions. The stability constants and the distribution of these complexes as a function of pH and pF were determined.     

Untersuchung eines Li-Cr-Ferrits mit Hilfe des Mößbauer-Effekts

The hyperfine-structure spectra of the 14.4 keVγ-ray of the nucleus⁵⁷Fe in the spinel type ferrite (Li ₀₅ ⁺ Fe _1.3 ³⁺ Cr _1.2 ³⁺ O ₄ ^2? ) have been measured through the use of the Mößbauer effect. These measurements were performed on powder samples at different temperatures between 88 °K and 633 °K. For the Fe³⁺ ions at both the tetrahedral (A) and octahedral (B) sites at 88 °K the effective magnetic fieldH at the Fe nuclei is the same and equal to 504±4 kG. The temperature dependence ofH _A however is different fromH _B . Application of an external magnetic field of 20 kG shows that the sign ofH _A is positive and the sign ofH _B is negative. As the temperature is increased a considerable broadening of the magnetic hfs-lines (and especially of the outer pair of lines) is observed. No theoretical discussion directly applicable to these measurements is as yet available. In the paramagnetic phase a well resolved doublet is obtained. It appears that this doublet must be interpreted as a quadrupole splitting.     

Berichtigung

Ohne Zusammenfassung     

Existenzsätze mit der linienmethode für parabolische probleme und periodische lösungen von ut=f(t,x,u,ux,uxx)

The (longitudinal) method of lines transforms a parabolic equation into a first order system of ordinary differential equations by discretization of the spatial variable. It is shown how to obtain existence theorems for nonlinear parabolic equations from those for ordinary differential equations under general growth conditions and weak regularity assumptions. The method is demonstrated in proving a new existence theorem for periodic solutions to u_t=f(t,x,u,u_x,u_xx) with boundary conditions of Dirichlet type.     

Über den Index abgeschlossener Operatoren in Banachräumen

Ohne ZusammenfassungDie vorliegende Fassung stellt eine am 19. 12. 1964 eingereichte Überarbeitung und teilweise Ergänzung des ursprünglichen Manuskriptes dar.     

Bestimmung der Maximalzahl der Nachbargebiete auf nichtorientierbaren Flächen

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