Multianvil high-pressure/high-temperature synthesis, crystal structure, and thermal behaviour of the rare-earth borogermanate Ce6(BO4)2Ge9O22

The new monoclinic cerium borogermanate Ce₆(BO₄)₂Ge₉O₂₂ was synthesized under high-pressure and high-temperature conditions in a Walker-type multianvil apparatus at 10.5 GPa and 1200 °C. Ce₆(BO₄)₂Ge₉O₂₂ crystallizes with two formula units in the space group P2₁/n with lattice parameters a=877.0(2), b=1079.4(2), c=1079.1(2) pm, and β=95.94(3)°. As the parameter pressure favours the formation of compounds with cations possessing high coordination numbers, it was possible to produce simultaneously BO₄-tetrahedra and GeO₆-octahedra in one and the same borogermanate for the first time. Furthermore, the cerium atoms show high coordination numbers (C.N.: 9 and 11), and one oxygen site bridges one boron and two germanium atoms (O^[3]), which is observed here for the first time. Besides a structural discussion, temperature-dependent X-ray powder diffraction data are presented, demonstrating the metastable character of this high-pressure phase.     

Linear and Nonlinear Wavetransformation and Absorption in the Inhomogeneous Plasma Capacitor

The parametric decay process in inhomogeneous layers existing near the plasma boundaries or in front of antennas and probes in a plasma has been investigated. The linear enhancement of the pump field near ω = ω_p, the threshold fieldstrength, the wavenumber selection rules and the influence of spontaneous low frequency fluctuations are discussed in detail using a one-dimensional model of the inhomogeneous plasma capacitor. According to this model the instabilities appear in the layers with maximum linear transformation and (linear) absorption. In addition, a strong nonlinear part of absorption in the presence of the instability has been observed. The level of the spontaneous low frequency fluctuations influences strongly the spectrum of the parametrically excited ion waves. The experiments show a redistribution of the transferred ion acoustic wave energy over the whole wave continuum up to ω_pi, if a sufficient strong spontaneous fluctuation level exists in the plasma. It is impossible, however, to excite ion acoustic turbulence by the decay of the high frequency pump field under the present conditions. The conditions for the linear field enhancement are disturbed by the action of the ponderomotive forces changing the density profile near the critical point before reaching the strong pump amplitude being necessary for the excitation of a cascade of decay processes.     

Rest point theorems for autonomous control systems

The classical Poincaré-Bendixson theory in the plane is generalized to multivalued vector fields. For control systems $\text{x}\text{?}\text{= f(x, u)}$ where the state x is in Rⁿ and the control u is valued in a compact subset of R^m we study the existence (and nonexistence) of rest states. Some special emphasis is focused on the case n = 2.     

Messungen der Dispersion und Dämpfung hochfrequenter Raumladungswellen (Oberflächenwellen) im Säulenplasma einer Niederdruckentladung

Electron surface wave propagation is studied on the positive column of a mercury discharge. The dispersion curve is measured by an interferometric method. The result confirms the hydrodynamical theory. The damping of the waves is determined by collisionless processes like Landau-damping.     

On the max-min pursuit game

The max-min linear pursuit game with quadratic performance measure is examined by means of an approximation by a finite sequence of ‘open-loop’ max-min control stages. It is shown that under mild conditions the finite approximation provides a satisfactory representation of the actual game. The limiting behaviour (as the number of stages approaches infinity) is also discussed.     

Eigenvalues and stability properties of multiplication operators and multiplication semigroups

We investigate uniform, strong, weak and almost weak stability of multiplication semigroups on Banach space‐valued ‐spaces. We show that, under certain conditions, these properties can be characterised by analogous ones of the pointwise semigroups. We prove a spectral mapping theorem for the point spectra of the pointwise and global semigroups and apply this as a major tool for determining almost weak stability.     

High‐Pressure Synthesis and Characterization of New Actinide Borates,AnB4O8 (An=Th,U)

New actinide borates ThB₄O₈ and UB₄O₈ were synthesized under high‐pressure, high‐temperature conditions (5.5 GPa/1100 °C for thorium borate, 10.5 GPa/1100 °C for the isotypic uranium borate) in a Walker‐type multianvil apparatus from their corresponding actinide oxide and boron oxide. The crystal structure was determined on basis of single‐crystal X‐ray diffraction data that were collected at room temperature. Both compounds crystallized in the monoclinic space group C2/c (Z=4). Lattice parameters for ThB₄O₈: a=1611.3(3), b=419.86(8), c=730.6(2) pm; β=114.70(3)°; V=449.0(2) ų; R₁=0.0255, wR₂=0.0653 (all data). Lattice parameters for UB₄O₈: a=1589.7(3), b=422.14(8), c=723.4(2) pm; β=114.13(3)°; V=443.1(2) ų; R₁=0.0227, wR₂=0.0372 (all data). The new AnB₄O₈ (An=Th, U) structure type is constructed from corner‐sharing BO₄ tetrahedra, which form layers in the bc plane. One of the four independent oxygen atoms is threefold‐coordinated. The actinide cations are located between the boron–oxygen layers. In addition to Raman spectroscopic investigations, DFT calculations were performed to support the assignment of the vibrational bands.