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  • 1
    Electronic Resource
    Electronic Resource
    HYDROCARBON SYNTHESIS ON PURE IRON (1961)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 65 (1961), S. 417-419 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/j100821a007
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  • 2
    Electronic Resource
    Electronic Resource
    The Shapley value for cooperative games under precedence constraints (1992)
    Springer
    International journal of game theory 21 (1992), S. 249-266 
    Details
    ISSN: 1432-1270
    Keywords: Cooperative Game ; Shapley Value ; Precedence Constraint ; Marginal Contribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Cooperative games are considered where only those coalitions of players are feasible that respect a given precedence structure on the set of players. Strengthening the classical symmetry axiom, we obtain three axioms that give rise to a unique Shapley value in this model. The Shapley value is seen to reflect the expected marginal contribution of a player to a feasible random coalition, which allows us to evaluate the Shapley value nondeterministically. We show that every exact algorithm for the Shapley value requires an exponential number of operations already in the classical case and that even restriction to simple games is #P-hard in general. Furthermore, we outline how the multi-choice cooperative games of Hsiao and Raghavan can be treated in our context, which leads to a Shapley value that does not depend on pre-assigned weights. Finally, the relationship between the Shapley value and the permission value of Gilles, Owen and van den Brink is discussed. Both refer to formally similar models of cooperative games but reflect complementary interpretations of the precedence constraints and thus give rise to fundamentally different solution concepts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01258278
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  • 3
    Electronic Resource
    Electronic Resource
    Buchbesprechungen (1968)
    Springer
    Mathematical methods of operations research 12 (1968), S. 281-296 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01918338
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  • 4
    Electronic Resource
    Electronic Resource
    Buchbesprechungen (1966)
    Springer
    Mathematical methods of operations research 10 (1966), S. 58-64 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01918285
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  • 5
    Electronic Resource
    Electronic Resource
    Buchbesprechungen (1969)
    Springer
    Mathematical methods of operations research 13 (1969), S. 65-70 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01919551
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  • 6
    Electronic Resource
    Electronic Resource
    Über die orientierte Aufwachsung von Diol-oligo-urethanen auf verstreckter Polyamidfolie (1960)
    Springer
    Naturwissenschaften 47 (1960), S. 538-539 
    Details
    ISSN: 1432-1904
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00639350
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  • 7
    Electronic Resource
    Electronic Resource
    Optimization and optimality test for the Max-Cut Problem (1990)
    Springer
    Mathematical methods of operations research 34 (1990), S. 195-206 
    Details
    ISSN: 1432-5217
    Keywords: Max-cut ; decision problem ; optimization problem ; polynomial transformation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Wir zeigen, daß folgende Probleme polynomial äquivalent sind: 1) Gegeben ein (gewichteter) GraphG, ein cutC vonG. Entscheide obC optimal ist oder nicht. 2) Gegeben ein (gewichteter) GraphG, ein cutC vonG. Entscheide, obC optimal ist oder nicht, und falls nicht, finde einen besseren cutC′. Eine Konsequenz hiervon ist, wie wir sehen werden, daß ein Optimalitätstest Orakel einen polynomialen Algorithmus zur approximativen Lösung von Max Cut Problemen liefert. Insbesondere folgt, daß das Erkennen von maximalen cuts in ungewichteten Graphen NP-schwer ist.
    Notes: Abstract We show that the following two problems are polynomially equivalent: 1) Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not. 2) Given a (weighted) graphG, and a cutC ofG, decide whetherC is maximal or not, and in case it is not, find a better solutionC′. As a consequence, an optimality testing oracle may be used to design a polynomial time algorithm for approximately solving the (weighted) Max-Cut Problem. This in turn implies that recognizing optimal cuts in an unweighted graph is NP-hard.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01415982
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  • 8
    Electronic Resource
    Electronic Resource
    Buchbesprechung (1965)
    Springer
    Mathematical methods of operations research 9 (1965), S. 55-56 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01976182
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  • 9
    Electronic Resource
    Electronic Resource
    Some order dimension bounds for communication complexity problems (1991)
    Springer
    Acta informatica 28 (1991), S. 593-601 
    Details
    ISSN: 1432-0525
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Summary We associate with a general (0, 1)-matrixM an ordered setP(M) and derive lower and upper bounds for the deterministic communication complexity ofM in terms of the order dimension ofP(M). We furthermore consider the special class of communication matricesM obtained as cliques vs. stable sets incidence matrices of comparability graphsG. We bound their complexity byO((logd)·(logn)), wheren is the number of nodes ofG andd is the order dimension of an orientation ofG. In this special case, our bound is shown to improve other well-known bounds obtained for the general cliques vs. stable set problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01463947
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  • 10
    Electronic Resource
    Electronic Resource
    Principles of gel chromatography and possibilities for its development (1967)
    Weinheim : Wiley-Blackwell
    Angewandte Makromolekulare Chemie 1 (1967), S. 150-173 
    Details
    ISSN: 0003-3146
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Die Gelchromatographie kann als eine netzwerk-limitierte Verteilung aufgefaßt werden. Dies führt zu dem Schluß, daß keine normierende Eichbezeichnung, zwischen Molekulargewicht und Elutionsvolumen existiert, die ausschließlich, der gelösten Substanz abhängige Parameter enthält.Die Darstellung von Gelen mit unterschiedlicher chemischer Struktur wird be schrieben, und die Möglichkeiten, die Porengröße zu variieren, werden diskutiert. Die Untersuchung des Einflusses der physikalischen und chemischen Struktur auf die Trennung und die Trennleistung zeigte, daß das Elutionsvolumen durch die chemische Natur des Gels beeinflußt wird; die Trennleistung wird hingegen im wesentlichen durch die physikalische Struktur bestimmt.
    Notes: Gel chromatography can be considered as a network-limited partition. This leads to the conclusion that it is impossible to find a generalizing relationship between the molecular weight and the elution volume using parameters depending only on the solute.The preparation of gels with different chemical structure is discussed and possible methods for the alteration of pore size are described. Investigations of the influence of the physical and chemical structure on separation and separation efficiency have shown that the elution volume depends to some extent on the chemical nature, but the separation efficiency is mainly a function of the physical structure.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/apmc.1967.050010110
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