Die ɛ-Störung linearer und quadratischer Optimierungsaufgaben und ihre Anwendung auf das Hildreth-Verfahren

Zusammenfassung Durch eine -Störung in der Diagonalen der quadratischen Form kann man eine lineare oder quadratisch semidefinite Optimierungsaufgabe zu einer streng definiten quadratischen Aufgabe machen, so daß Lösungsverfahren, die die Formmatrix als nichtsingulär voraussetzen müssen, anwendbar werden. Bekanntlich konvergiert die Lösungx der -gestörten Aufgabe für 0 gegen den Lösungsvektorx ^m von minimalem Betrag der ursprünglichen Aufgabe. Wir zeigen darüber hinaus, daß im linearen Fall immer und im eigentlich quadratischen in gewissen Fällen schon für 0<<* die beiden Lösungenx undx ^m übereinstimmen. Im linearen Fall ist die obere Grenze * durch die Lösung eines linearen Ungleichungssystems gegeben.Im zweiten Abschnitt wenden wir dasHildreth-Verfahren mittels der -Störung auf lineare und quadratisch semidefinite Aufgaben an, diskutieren Konvergenz- und Genauigkeitsfragen und kommen zu dem Schluß, daß man in der Praxis sowohl bei Rechnung von Hand als auch bei maschineller Rechnung zu befriedigenden Ergebnissen kommt.

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Summary Linear and quadratic semidefinite programming problems may be transformed into strongly definite quadratic problems by means of an -perturbation of the quadratic form so that procedures which presuppose the matrix of the form to be nonsingular, may be applied. As is well known, the solutionx of the -perturbated problem converges to the solutionx ^m of minimal length of the original problem as 0. We show that always in the linear case and in the quadratic case under certain circumstances, both solutionsx andx ^m are equal if 0 <<*. In the linear case, the upper limit * is given by the solution of a system of linear inequalities.In the second part of this paper we apply the method ofHildreth to linear and quadratic semidefinite programming problems by the -perturbation. We discuss questions of convergence and exactness, and conclude that in practice calculation by hand as well as by computer leads to satisfying results.

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Der Verfasser ist Herrn Prof. Dr.W. Vogel, Bonn, für einen Hinweis zu Dank verpflichtet.

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Vorgel. v.:H. P. Künzi     

Unusual coupling reactions of aldehydes and alkynes: a novel preparation of substituted phthalic acid derivatives by automated synthesis

Based upon a highly versatile multicomponent methodology, a new one-pot synthesis of substituted phthalic acid derivatives from alpha,beta-unsaturated aldehydes was developed. The reaction involves the intermediacy of an acetamidodiene species which undergoes Diels-Alder addition to diethyl acetylenedicarboxylate. The resultant acetamidocyclohexadiene is subject to elimination of acetamide under the reaction conditions to give rise to substituted diethyl phthalates in good yields. This domino condensation-cycloaddition-elimination sequence has been applied to a variety of alpha,beta-unsaturated aldehydes. Furthermore, we demonstrated the exploitation of parallelized and automated synthesis technology for the rapid screening of reaction conditions and compositions. Detailed studies revealed the catalytic role of the employed acetamide and the occurrence of a stereoselective 1,4-syn elimination pathway under standard conditions.     

Capability of ICP-MS (pneumatic nebulization and ETV) for Pt-analysis in different matrices at ecologically relevant concentrations

ICP-MS both with conventional nebulization and with ETV (Electro Thermal Vaporization) have been applied for the determination of Pt in different matrices, e.g. occupational samples like urine and dust samples. It can be used also for other matrices like soil, plants, tissues etc. dependent on the concentration ranges and on a suitable decomposition method. The evaluation, based on the different Pt-isotopes and the quality criteria (detection limit, precision, accuracy) is discussed. Very low determination limits in the range of 1 ng/l can be achieved by ICP-MS-ETV using the standard addition method. This method allows to determine Pt in urine without any sample pretreatment.Dedicated to Professor Dr. Peter Brätter on the occasion of his 60th birthday     

Characterization of synthetic polyelectrolytes by capillary electrophoresis

Capillary electrophoresis in entangled polymer solutions was applied to determine the molecular mass and polydispersity of polyelectrolytes. The separation selectivities of different polyethylene glycols as buffer additive can be correlated to their average molecular mass. A universal curve correlating the selectivity and the molecular mass could be obtained by using the instrinsic viscosity of the polyethylene glycol. The separation of poly(2-vinylpyridine) standards was compared to the separation of poly(4-vinylpyridine) standards. An indirect detection system was developed to characterize the cationic polyelectrolyte polydiallyldimethyl ammonium chloride. Various polymers with oppositely charged groups (polycarboxybetaines) were investigated with respect to structure dependence, pH dependence and molecular mass dependence of interand intramolecular association.     

Novel polyelectrolytes with regular structure synthesis,properties and applications

Cationic polyelectrolytes and polymeric betaines with narrow molecular weight distribution as well as block copolymers containing charged and uncharged blocks of different hydrophilicity/hydrophobicity were synthesized by different routes of radical polymerization. The cationic polyelectrolytes were characterized with respect to solution properties and electrolyte behaviour. The block copolymers serve as powerful stabilizers in precipitation and emulsion polymerization processes.