Einige Aspekte in der Zuordnungstheorie

Zusammenfassung Gegeben seien endliche MengenX, Y undZ X × Y, Z _x ={y¦(x,y) Z},Z _y ={x¦(x,y) Z}.Man nenntA X (bzw.B Y)zuordenbar, wenn es eine Injektion:A Y (bzw.: B X) mit(x) Z _x (bzw.(y) Z _y ) gibt, und (A, B) mit #A=#B > 0 einZuordnungspaar, wenn eine Bijektionf:A B mitf(x)Z _x B (bzw.f ^–1 (y) Z _y A) existiert. Die Bijektionf heißtZuordnungsplan fürA, B.In der vorliegenden Arbeit werden Fragen nach der Existenz von optimal zuordenbaren Mengen und optimalen Zuordnungspaaren behandelt, wenn man auf den MengenX undY Ordnungen vorgibt, wobei auch Nebenbedingungen berücksichtigt werden. In manchen Fällen lassen sich anhand der Beweise Zuordnungspläne oder ihre Berechnungsvorschrift explizit angeben.Zum Schluß werden die Aussagen an konkreten, dem Bereich der Wirtschaftswissenschaften entnommenen Beispielen erläutert.

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Summary LetX, Y be finite sets andZ X × Y, Z _x ={y¦(x,y) Z},Z _y ={x¦(x,y)Z}. A X (resp.B Y) is calledassignable if there is an injection: A Y (resp.: B X) with (x) Z _x (resp.(y) Z _y ), (A, B) with #A=#B > 0 anassigned pair if there is a bijection f:A B withf (x) Z _x B (resp.f ^–1(y) Z _y A). The bijectionf is called aplan forA andB.In this paper problems are discussed concerning the existence of optimal assignable sets and optimal assigned pairs ifX andY are totally ordered, additional constraints are also considered. In some cases the proofs give explicit constructions of plans. The results are illustrated by application to problems occurring in Operations Research.

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Diese Arbeit ist mit Unterstützung des Sonderforschungsbereiches 72 an der Universität Bonn entstanden.     

Magnetic dichroism in K-shell photoemission from laser excited Li atoms

Magnetic dichroism in the angular distribution has been demonstrated for single-electron photoemission from inner ns(2) subshells of gaseous atomic targets using the example of K-shell photoionization of polarized Li atoms laser prepared in the 1s(2)2p (2)P(3/2) excited state. The effect is pronounced for the conjugate shakeup and conjugate shakedown photoelectron lines, and less important, though observable, for the main and direct shakeup lines. The phenomenon is caused by configuration interaction in the final continuum state and is quantitatively described by the close-coupling R-matrix calculations.     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Intensity inversion between main and satellite lines in atomic photoionization

The 1s photoionization of atomic Li was studied by photoelectron spectroscopy in the photon energy region between 85 and 140 eV for the ground state and the three lowest excited configurations Li(*) 1s(2)nl, nl=2p, 3s, 3p. The importance of electron correlations was investigated by comparing the multielectron transitions, so-called shake-up and conjugate shake-up satellites, and the direct process, so-called main lines. The relative intensity of the satellites increases with the level of initial excitation of the Li atom. The shake-up process dominates for states with an n=3 valence electron and the satellites become stronger than the main lines. This spectacular effect can be explained by the spatial overlap of the initial and final state wave functions. Surprisingly, the spatial overlap affects shake-up and conjugate shake-up lines in the same way.     

Outstanding spin-orbit-activated interchannel coupling in the Cs and Ba 3d photoemission

Partial 3d5/2 photoionization cross sections of atomic Cs and Ba as well as the asymmetry parameter beta of the angular distribution of the Cs 3d5/2 photoelectrons were investigated near the threshold of the 3d3/2 channel at about 750 eV and 800 eV, respectively. Strong electron correlations, in particular, the spin-orbit activated interchannel coupling between the 3d5/2 and 3d3/2 channels, govern the observed spectra. The most striking effect was found for beta5/2 of Cs with a dramatic increase from beta=1.0 to beta=1.5 in the energy region where the mixing between both channels causes a pronounced minimum in the partial 3d5/2 cross section. This result indicates the decisive influence of the interference term on the asymmetry parameter beta with its dependence on the phase difference between the outgoing p and f waves.     

Quantum oscillations and the Sermi surface of LuB12

To examine the Fermi surface of LuB₁₂, measurements of the de Haas-van Alphen (dHvA) effect were made at temperatures between 0.35 and 2 K in magnetic fields up to 12 Tesla. Oscillations in the susceptibility occurred above 5 Tesla in any field direction relative to the single crystal sample. From the Fourier transform of the data obtained, we conclude the Fermi surface of both conduction bands to have multiple extremal cross sections. For some of these orbits, the temperature dependence of the dHvA signal was investigated to determine the corresponding cyclotron mass. For a better understanding, a Full Potential Linearized Augmented Plane Wave-(FLAPW-) band structure calculation was carried out and the shapes of the Fermi surfaces were determined. In addition, we investigated the transverse magnetoresistance as a function of the field and the field direction. Its anisotropy, as well as the Shubnikov-de Haas (SdH) oscillations occurring in certain geometries, are in agreement with the results of the dHvA measurements.     

About the influence of mechanical comminution processes on saturation magnetization of strontium ferrites

The influence of the mechanical comminution process on the coercive field of hardmagnetic ferrites is well known. But, there is a strong effect on the saturation magnetization of strontium ferrite as well. Using a special type of a vibration mill the saturation magnetization decreases to 0.084 T and increases up to 0.22 T by further enlarging the milling time. The saturation magnetization approaches up to 0.41 T again by subsequent annealing. Preliminary investigations aiming at an interpretation are given.