Complex powers of classical SG-pseudodifferential operators

Abstract Under a suitable ellipticity condition, we show that classical SG-pseudodifferential operators of nonnegative order possess complex powers. We show that the powers are again classical and derive an explicit formula for all homogeneous components. Keywords: Complex power, Weighted symbols, Noncompact manifolds     

Investigation of the photothermally modulated ferromagnetic resonance signal from magnetostatic modes in yttrium iron garnet films

The conventional and photothermally modulated (PM) ferromagnetic resonance (FMR) of magnetostatic modes (MSM) in yttrium iron garnet (YIG) films have been investigated as a function of temperature. Approaching the ferrimagnetic transition at T _c=560 K a strong enhancement of the PM-FMR signal amplitude is observed which is accompanied by a change of the signal shape. The observations are discussed in the framework of a model that takes into account the temperature derivatives of those quantities that contribute to the high-frequency susceptibility. At temperatures still below T _c a paramagnetic line emerges. The MSM disappear in a state of finite magnetization which is explained on the basis of damping of the MSM being important in the vicinity of the magnetic phase transition. Additionally, frequency and power dependent measurements are presented and the imaging ability of PM-FMR is demonstrated.     

On the Causes and Effects of Contaminations during rf Diode Deposition of Cr-Si Alloys

Investigations to the causes and effects of contaminants at the rf diode deposition of CrSi films in a non-heated high vacuum apparatus were carried out comparing an oxygen-free fusion target with an oxygen-containing cermet target. The films of the fusion target contained considerable amounts of oxygen; analogously the oxygen concentration in the films was increased in the case of the cermet target. Moreover, hydrogen was found. The concentration of the contaminants decreased with the sputtering power, however the rate of incorporation increased. For high sputtering rates the contamination process was reproducible and independent of the plant conditioning; the deposited films were depth-homogeneous. The reasons for this behaviour lie in water sources which are activated first of all by the discharge itself. The electrical properties found are explained by the contaminants and the deposition conditions.     

On the evolution of two-dimensional patterns in an inviscid liquid sheet

We perform an analysis of the pattern formation for a moving sheet of inviscid fluid. The sheet, which is assumed to have an infinite horizontal extent, moves at some prescribed velocity into a passive surrounding gas. The sheet’s thickness is assumed much smaller than the horizontal scale of the fluid motion. By considering a system that is symmetric with respect to the horizontal planes, long scale asymptotics are used to reduce the full governing equations in three dimensions to a set of three coupled nonlinear partial differential equations for the horizontal components of the velocity field and the height of the interface profile. The interfacial conditions consisting of the kinematic and normal stress balance are incorporated into these evolution equations. Investigations are carried out as function of the sole dimensionless parameter, namely the Weber number. A small amplitude stability analysis around the planar gas–liquid interface reveals that wave patterns in the form of traveling plane waves occur subcritically, and are therefore unstable. The reduced evolution equations are solved numerically for fixed values of the Weber number. Since the reduced system of equations is homogeneous, the wave motion is generated by initial conditions. Five initial conditions have been imposed: one-dimensional rolls, two-dimensional squares, two-dimensional hexagons, two-dimensional ridges, and smooth peaks. The ensuing evolution of the liquid sheet’s shape and corresponding flow fields are described by illustrations of the changes in the sheet’s morphology with time.     

Observation and analysis ofE mesons in\bar p p annihilation at rest in H2 gas

Antiproton-proton annihilation at rest in a gaseous H₂ target at NTP into the final state π⁺ π^? K ^± π^? (K ⁰) with an undetectedK ⁰ or \(\bar K^0 \) has been investigated. We observe theE(1420) resonance in the invariant mass spectrum (K ⁰)_miss K ^± π^? with massM _E =1413±8 MeV/c² and widthГ ^E =62 ± 16MeV/c² and find evidence for the production of thef ₁(1285). The absolute branching ratio of \(\bar p\) p → π⁺ π^? E ⁰,E ⁰ →K ₀ ^L K ^± π ^? at (61±6)%P wave annihilation is (3.0±0.9)·10^?4 of all annihilations. The observed suppression of theE production fromP wave with respect to theS wave together with some simple selection rules suggest that the quantum numbers of theE(1420) areJ ^pc=0^?+ and not I⁺⁺.     

Thermodynamic properties of transition metals in aqueous solution. 2. The enthalpies of mixing of aqueous solutions of CoCl2, CuCl2, and MnCl2 with NaCl at varying ionic strength at 25°C

Enthalpies of mixing (_m H) aqueous solutions of CoCl₂, CuCl₂, and MnCl₂ with NaCl solutions were measured at constant ionic strengths of 0.5, 1.0, and 3.0 molal at 25°C. The excess enthalpy equations of Pitzer were then fit to the resulting _m H data. The resulting parameters are the temperature derivatives of the activity coefficient mixing parameters in the Pitzer system. The heat of mixing data for CoCl₂ and CuCl₂ were in agreement with earlier isomolal results by other workers.