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  • 1
    ISSN: 1434-4475
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Periodica mathematica Hungarica 4 (1973), S. 217-220 
    ISSN: 1588-2829
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Periodica mathematica Hungarica 5 (1974), S. 343-352 
    ISSN: 1588-2829
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Combinatorica 14 (1994), S. 417-433 
    ISSN: 1439-6912
    Keywords: 03 F 20 ; 03 F 30 ; 03 H 15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The Pigeonhole Principle forn is the statement that there is no one-to-one function between a set of sizen and a set of sizen−1. This statement can be formulated as an unlimited fan-in constant depth polynomial size Boolean formulaPHP n inn(n−1) variables. We may think that the truth-value of the variablex i,j will be true iff the function maps thei-th element of the first set to thej-th element of the second (see Cook and Rechkow [5]).PHP n can be proved in the propositional calculus. That is, a sequence of Boolean formulae can be given so that each one is either an axiom of the propositional calculus or a consequence of some of the previous ones according to an inference rule of the propositional calculus, and the last one isPHP n . Our main result is that the Pigeonhole Principle cannot be proved this way, if the size of the proof (the total number or symbols of the formulae in the sequence) is polynomial inn and each formula is constant depth (unlimited fan-in), polynomial size and contains only the variables ofPHP n .
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Combinatorica 8 (1988), S. 235-247 
    ISSN: 1439-6912
    Keywords: 68B15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetL be the set consisting of the firstq positive integers. We prove in this paper that there does not exist a data structure for representing an arbitrary subsetA ofL which uses poly (¦A¦) cells of memory (where each cell holdsc logq bits of information) and which the predecessor inA of an arbitraryx≦q can be determined by probing only a constant (independent ofq) number of cells. Actually our proof gives more: the theorem remains valid if this number is less thanε log logq, that is D. E. Willard's algorithm [2] for finding the predecessor inO(log logq) time is optimal up to a constant factor.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Combinatorica 14 (1994), S. 379-416 
    ISSN: 1439-6912
    Keywords: 05 C 38 ; 05 C 85
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present an algorithm which inn 3 (logn)3 time constructs a 3-regular expander graph onn vertices. In each step we substitute a pair of edges of the graph by a new pair of edges so that the total number of cycles of lengths=⌊clogn⌋ decreases (for some fixed absolute constantc). When we reach a local minimum in the number of cycles of lengths the graph is an expander.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1618-2650
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Microchimica acta 2 (1937), S. 299-305 
    ISSN: 1436-5073
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Summary A test for ferricyanide by means of hydrogen peroxide and para phenetidine is described. It is based on the fact that oxydation of para phenetidine by hydrogen peroxide, being slow in itself, is catalized by ferricyanide (or ferrocyanide + hydrogen peroxide). Sensitivity and “limits of proportion” of this colour reaction are determined.
    Abstract: Résumé L'auteur décrit le décèlement du cyanure ferreux et du cyanure ferrique avec le peroxyde d'hydrogène et la paraphénétidine. L'oxydation de la paraphénétidine par le peroxyde d'hydrogène qui, de coutume, ne se fait que lentement, est catalysée par le cyanure ferrique (cyanure ferreux + peroxyde d'hydrogène). La sensibilité de cette réaction colorante fut déterminée.
    Notes: Zusammenfassung Es wird ein Nachweis von Ferro- und Ferricyanid mit Wasserstoffsuperoxyd und Paraphenetidin beschrieben, der darauf beruht, daß die an sich langsam verlaufende Oxydation des Paraphenetidins durch Wasserstoffsuperoxyd durch Ferricyanid (bzw. durch Ferrocyanid + Wasserstoffsuperoxyd) katalysiert wird. Empfindlichkeit und Grenzverhältnisse dieser Farbreaktion wurden bestimmt.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Microchimica acta 1 (1937), S. 255-259 
    ISSN: 1436-5073
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Summary The well-known method of titrating nitrates with 1/10 n-ferrous sulphate in a strongly acid solution has some disadvantages which are discussed. It is proposed to substitute the 0,1 n-ferrous sulphate solution by a 1 n-solution delivered from a micro-burette. Thus the disadvantages are overcome without loss of accuracy. This is proved by analyses.
    Abstract: Résumé On discute les défauts du mode de titration des nitrates dans un liquide sulfurique très acide avec une solution de sulfate ferreux N/10. L'auteur propose d'employer une solution de sulfate ferreux 1 normale et des microburettes au lieu d'une solution de sulfate ferreux N/10; de cette manière la précision de l'analyse reste la même tout en évitant les défauts mentionnés. Comme preuve l'auteur cite les résultats de plusieurs analyses.
    Notes: Zusammenfassung Die Mängel der bekannten Methode, Nitrate in stark schwefelsaurer Lösung mit 1/10 n-Ferrosulfat zu titrieren, werden diskutiert. Es wird vorgeschlagen, an Stelle der 1/10 n-Ferrosulfatlösung eine 1 normale Lösung zu verwenden und mit Mikrobüretten zu arbeiten, wodurch bei gleicher Genauigkeit die Mängel beseitigt werden, was durch Analysen belegt wird.
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  • 10
    ISSN: 1436-5073
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Summary The authors have found a reaction of vanadium which enables this element to be identified by means of its catalytic action. It is shown that pyrocatechol strongly activates this catalytic action, and increases the sensitivity of the reaction. The sensitivity and limit of this activated colour reaction has been ascertained.
    Abstract: Résumé Les auteurs ont trouvé une réaction du vanadium, où le vanadium est caractérisé par son action catalytique. On a constaté, que le pyrocatéchine peut activer fortement la réaction catalytique, par laquelle la sensibilité est augmentée. On a déterminé la sensibilité et les limites de cette réaction activée.
    Notes: Zusammenfassung Verfasser haben eine Reaktion des Vanadins gefunden, bei der das Vanadin durch seine katalytische Wirkung kenntlich gemacht wird. Es wurde festgestellt, daß Brenzcatechin die katalytische Wirkung des Vanadins stark aktiviert, wodurch die Empfindlichkeit der Reaktion gesteigert werden kann. Empfindlichkeit und Grenzverhältnisse dieser aktivierten Reaktion wurden ermittelt.
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