Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides

In the spirit ofWilkinson's [1, 2] backward error analysis, conditions are established under which a given approximate solution of a system ofn linear equations withn unknowns is the exact solution of a modified system whose coefficients and right-hand sides are within a given neighborhood of those of the original system.     

Method for minimizing a convex-concave function over a convex set

A branch-and-bound method is proposed for minimizing a convex-concave function over a convex set. The minimization of a DC-function is a special case, where the subproblems connected with the bounding operation can be solved effectively.on leave at Mannheim University by a grant from the Alexander von Humboldt Foundation.     

Characterization of weakly efficient points

Weakly efficient points of a mappingF: S Y are characterized, where the feasible setS is given by infinitely many constraints, andY is equipped with an arbitrary convex ordering. In the linear and in the convex case a necessary and sufficient condition is given, which needs no constraint qualification.

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Zusammenfassung Es werden schwach effiziente Punkte einer AbbildungF: S Y charakterisiert, wobei der zulässige BereichS durch unendlich viele Restriktionen bestimmt wird undY mit einem beliebigen konvexen Ordnungskegel versehen ist. Im linearen und im konvexen Fall wird eine notwendige und hinreichende Bedingung angegeben, die keine Regularitätsvoraussetzung benötigt.

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Rudolf Henn zum 65. Geburtstag gewidmet     

Time-Dependent Traffic Equilibria

We consider the existence, characterization, and calculation of equilibria in transportation networks, when the route capacities and demand requirements depend on time. The problem is situated in a Banach space setting and formulated in terms of a variational inequality.     

Flow in networks with amplification and coupling

Summary The network model presented in an earlier paper [1] is generalized by introducing amplification in arcs and coupling between arcs. The appropriate modifications of the earlier results are stated and the usefulness of the new model is illustrated by examples.

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Zusammenfassung Das in einer früheren Arbeit [1] angegebene Netzwerkmodell wird durch Einführung von Verstärkern in Leitungszweigen und Kopplung von Leitungszweigen verallgemeinert. Die entsprechenden Verallgemeinerungen der früheren Ergebnisse werden besprochen, und die Nützlichkeit des neuen Modells wird durch Beispiele illustriert.

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Vorgel. v.:J. Nitsche.     

Neutron scattering study of the field-dependent ground state and the spin dynamics in spin-one-half NH4CuCl3

Elastic and inelastic neutron scattering experiments have been performed on the dimer spin system NH4CuCl3, which shows plateaus in the magnetization curve at m=1/4 and m=3/4 of the saturation value. Two structural phase transitions at T1 approximately 156 K and at T(2)=70 K lead to a doubling of the crystallographic unit cell along the b direction and as a consequence a segregation into different dimer subsystems. Long-range magnetic ordering is reported below T(N)=1.3 K. The magnetic field dependence of the excitation spectrum identifies successive quantum phase transitions of the dimer subsystems as the driving mechanism for the unconventional magnetization process in agreement with a recent theoretical model.     

An example of a bad quasicomplementarity problem

An example is given of a parametric, nonlinear quasicomplementarity problem having the property that, for every value of the parameters, the solution set is nonempty and unbounded.The collaboration of Dirk Schläger in working out the example is gratefully acknowledged.     

A Farkas lemma for difference sublinear systems and quasidifferentiable programming

A new generalized Farkas theorem of the alternative is presented for systems involving functions which can be expressed as the difference of sublinear functions. Various other forms of theorems of the alternative are also given using quasidifferential calculus. Comprehensive optimality conditions are then developed for broad classes of infinite dimensional quasidifferentiable programming problems. Applications to difference convex programming and infinitely constrained concave minimization problems are also discussed.