Orbits in finite incidence structures

Geometriae Dedicata -     

Über Kennzeichnungen endlicher Gruppenräume

Ohne ZusammenfassungMeinem verehrten Lehrer Günter Picken zum 70. Geburtstag gewidmet     

Study of the mechanism of hydroformylation at industrial reaction conditions

With a newly developed analytical technique, i.e. high temperature/pressure IR cell coupled to the reactor, it was possible to study the mechanism of hydroformylation at reaction conditions. It has been conclusively found that the hydrogenolysis of the acyl cobalt complex is performed by HCo(CO)₄ and not by molecular H₂, as proposed byHeck andBreslow.Therefore the formation of HCo(CO)₄ from Co₂(CO)₈ is an intermediate step in the sequence of hydroformylation reaction steps. The rate of hydroformylation of any of the olefins is smaller than the rate of formation of HCo(CO)₄ from Co₂(CO)₈. The IR spectra reveal that always more than 30% of the cobalt is in the form of HCo(CO)₄ under the reaction conditions.It is found that the formation of HCo(CO)₄ from Co₂(CO)₈ is the slowest and most temperature-dependent step of the hydroformylation reaction. Also the reaction between olefin and HCo(CO)₄ is slower than the hydrogenolysis of the acyl complex.The experiments were carried out under industrial oxo conditions. The diffusional effects were eliminated.With 6 FiguresPart of the Ph.D. dissertation 1974. N. H. Alemdarolu, J. M. L. Penninger, andE. Oltay, Mechanism of Hydroformylation, Part II. Mh. Chem.107, 1043 (1976).     

Duality in vector optimization

In this paper the problem dual to a convex vector optimization problem is defined. Under suitable assumptions, a weak, strong and strict converse duality theorem are proved. In the case of linear mappings the formulation of the dual is refined such that well-known dual problems of Gale, Kuhn and Tucker [8] and Isermann [12] are generalized by this approach.     

Über ein verallgemeinertes Dirichletsches Problem für die Minimalflächengleichung und hebbare Unstetigkeiten ihrer Lösungen

Ohne ZusammenfassungDiese Arbeit ist unter Contract Nonr 710 (54) zwischen der Universität von Minnesota und dem Office of Naval Research vorbereitet worden.