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  • 1
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 65 (1961), S. 417-419 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    International journal of game theory 21 (1992), S. 249-266 
    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.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Naturwissenschaften 47 (1960), S. 538-539 
    ISSN: 1432-1904
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Natural Sciences in General
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical methods of operations research 34 (1990), S. 195-206 
    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.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Acta informatica 28 (1991), S. 593-601 
    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.
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  • 6
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    Journal of Polymer Science 48 (1960), S. 399-404 
    ISSN: 0022-3832
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The cationic polymerization of 1,3,5-trioxane in methylene dichloride with boron trifluoride, producing polyoxymethylene, was investigated. An ionogenic cocatalyst is not required in this polymerization. During the induction period, initially formed, short polyoxymethylene chains depolymerize to formaldehyde until a constant equilibrium concentration of formaldehyde is reached. This concentration is equal to the ceiling concentration of formaldehyde in cationic polymerization under the conditions chosen for the experiments. The nonstationary state and the strong acceleration of the polymerization of trioxane are due mainly to the lack of an effective kinetic termination reaction. Thus the concentration of growing polyoxymethylene cations increases with time.
    Additional Material: 2 Ill.
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  • 7
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Dans ce travail des mesures de diffusion de la lumière et de diffusion de translation ont été effectuées sur une série de para-oligophénylènes méthylsubstitués.Les masses moléculaires déterminées par diffusion de la lumière sont en très bon accord avec les valeurs calculées à partir de la formule chimique.L'interprétation des mesures de dépolarisation permet d'affirmer que l'on a affaire à des molécules rigides en forme de bâtonnet.Les constantes de diffusion de translation D de ces corps ont été mesurées. Les valeurs ainsi déterminées sont liées aux masses moléculaires par une relation du Type D = K · M-b où b à pour valeur 0.8.
    Notes: In der vorliegenden Arbeit werden Streulicht- und Diffusionsmessungen an methylsubstituierten p-Oligophenylenen beschrieben. Das aus den Streulichtmessungen ermittelte Molekulargewicht stimmt überraschend gut mit dem aus der chemischen Formel errechneten überein. Aus den Untersuchungen über die Depolarisation des Streulichtes ergibt sich eindeutig, daß es sich bei den untersuchten Molekülen um starre Stäbchen handelt.Es wurde ferner die Diffusionskonstante D dieser Stoffe bestimmt. Die so erhaltenen Werte sind mit dem Molekulargewicht durch die Gleichung D = K · M-b verbunden, wobei für b der Wert 0,8 gefunden wurde.
    Additional Material: 6 Ill.
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  • 8
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Additional Material: 1 Tab.
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  • 9
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: The autoxidation of isotactic polypropylene and poly-butylene-1 in solution shows a kinetic difference from that of atactic fractions of these polymers and of polyethylene. Autocatalysis during autoxidation of isotactic fractions is caused by a bimolecular chain initiation step of the hydroperoxides formed whereas that of atactic fractions and of polyethylene is caused by an unimolecular chain initiation step. It is shown that the only reason of this different kinetic behaviour is the difference in tacticity.
    Notes: Die Autoxydation in Lösung von isotaktischem Polypropylen bzw. Polyputylen-1 gehorcht einer anderen kinetischen Beziehung als die entsprechende Autoxydation von ataktischem Polypropylen, Polybutylen-1 und Polyäthylen. Die Autokatalyse der Autoxydation isotaktischer Produkte wird durch einen bimolekularen Kettenstart der gebildeten Hydroperoxyde hervorgerufen, während bei ataktischen Produkten ein monomolekularer Kettenstart beobachtet wird. Die unterschiedliche Kinetik der Autoxydation kann eindeutig auf Taktizitätsunterschiede zurückgeführt werden.
    Additional Material: 5 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Die Makromolekulare Chemie 68 (1963), S. 69-99 
    ISSN: 0025-116X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: The paper deals with aryl-homologous 1,3,5-triphenyl-benzenes. These compounds can be described as branched oligophenylenes with defined star-like molecular structure.The synthesis was carried out by cyclo-trimerization of corresponding methyl-arylketones. For this purpose a new procedure was developed based on the application of compounds which can be used for ketalization (orthoformate) in the presence of gaseous hydrogen chloride. This procedure which is characterized especially by its methodical simplicity and mild reaction conditions proved not only to be very efficient but also of broad application. Using this method not only 1,3,5-triphenyl-benzenes but also 1,3,5-tribiphenylyland 1,3,5-triterphenylyl-benzenes were synthesized with a yield in most cases of 60%. The poor cyclization tendency of methyl-aryl-ketones with substituents in o-position to the acetyl group can be explained by steric effects.For the preparation of methyl-aryl-ketones - used as starting material - especially the mixed ULLMANN-Reaction (i.e., with p-iodo-acetophenone and iodo-toluenes) proved to be very effective.The mechanism of this cyclization reaction is treated below. The appearance and nature of by-products can thus be explained.In comparison with the oligophenylenes of the p-series these triarylbenzenes show lower melting points and higher solubilities. Despite of the increasing bulkiness of the molecules with increasing side chains one can observe a rapid decline in solubility.In contrast from the non-substituted p-oligophenylenes the density decreases with increasing molecular weight. Similar to the p-oligophenylenes methyl groups in the side positions cause a considerable increase in solubility and also a decrease in melting point.
    Notes: Es wird über arylhomologe 1,3,5-Triphenylbenzole berichtet. Diese Verbindungen können als verzweigte Oligophenylene mit definierter, sternförmiger Molekülgestalt angesprochen werden.Die Synthese erfolgte durch cyclisierende Trimerisierung entsprechender Methyl-arylketone. Dazu wurde ein neues Verfahren ausgearbeitet, das auf der Anwendung von Ketalisierungsagenzien (Orthoformiat) als Kondensationsmittel in Gegenwart von Chlorwasserstoff als Katalysator beruht. Dieses Verfahren, dessen besondere Merkmale methodische Einfachheit und milde Reaktionsbedingungen sind, hat sich nicht nur als sehr leistungsfähig, sondern auch als verallgemeinerungsfähig erwiesen. Es wurden sowohl 1,3,5-Triphenyl-, 1,3,5-Tribiphenylyl- wie auch 1,3,5-Triterphenylyl-benzole dargestellt; dabei konnten meist Ausbeuten bis zu 60% d. Th. erreicht werden. Die geringere Cyclisierungsneigung von Methyl-arylketonen mit zur Acetylgruppe o-ständigen Substituenten läßt sich auf sterische Effekte zurückführen.Zur Gewinnung der als Ausgangsprodukte benötigten Methyl-arylketone bewährte sich vornehmlich die gemischte ULLMANN-Reaktion, beispielsweise mit p-Jodacetophenon und p-Jodtoluolen. Es wird der Mechanismus dieser Cyclisierungsreaktion behandelt; dabei werden Rückschlüsse auf Entstehung und Natur von Nebenprodukten gezogen.Im Vergleich zu den Oligophenylenen der p-Reihe zeigen die Triarylbenzole niedrigere Schmelzpunkte und höhere Löslichkeit. Trotz ihrer mit der Länge der Seitenzweige zunehmenden Molekülsperrigkeit kommt es doch gleichsinnig zu einer starken Löslichkeitsabnahme. Zum Unterschied von den unsubstituierten p-Oligophenylenen nimmt aber die Dichte mit dem Molekulargewicht ab. Wie bei den p-Oligophenylenen wirken auch hier seitenständige Methylgruppen stark löslichkeitssteigernd und schmelzpunktssenkend.
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