Behaviour of Solochrome Dark Blue B as a colloidal electrolyte

Summary The electrical conductance of Solochrome Dark Blue B at various dilutions and temperatures have been measured. TheWaldens product has been calculated at different temperatures and it varies with the temperature. The reagent has been found to behave as a colloidal electrolyte. The temperature of zero conductance has been determined to be –20 °C and temperature coefficient per degree centigrade per hundred of conductance 35 °C varies between 1.81 and 1.87.

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Zusammenfassung Die elektrische Leitfähigkeit von Solochrome Dark Blue B bei verschiedener Verdünnung und verschiedenen Temperaturen wurde gemessen, dasWaldensche Produkt bei verschiedenen Temperaturen berechnet. Es variiert mit der Temperatur. Das Reagens benimmt sich wie ein Kolloid. Die Temperatur der Null-Leitfähigkeit wurde zu –20 °C bestimmt und der Temperaturkoeffizient pro Grad in Prozenten der Leitfähigkeit bei 35 °C liegt zwischen 1,81 und 1,87.

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With 2 figures and 3 tables     

A correlational inequality for linear extensions of a poset

Suppose 1, 2, and 3 are pairwise incomparable points in a poset onn≥3 points. LetN (ijk) be the number of linear extensions of the poset in whichi precedesj andj precedesk. Define λ by $$\lambda = \frac{{N(213)N(312)}}{{\left[ {N(123) + N(132)} \right]\left[ {N(231) + N(321)} \right]}}$$ Two applications of the Ahlswede-Daykin evaluation theorem for distributive lattices are used to prove that λ?(n?1)²/(n+1)² for oddn, and λ?(n?2)/(n+2) for evenn. Simple examples show that these bounds are best-possible. Shepp (Annals of Probability, 1982) proved thatP(12)?P(12/13), the so-calledxyz inequality, whereP(ij) is the probability thati precedesj in a randomly chosen linear extension of the poset, thus settling a conjecture of I. Rival and B. Sands. The preceding bounds on λ yield a simple proof ofP(12)<P(12/13), which had also been conjectured by Rival and Sands.     

Weighted majority games and the matrix of homogeneity

If a weighted majority game (not necessarily constant sum or super additive) is described by the weights (voting strength) of the players involved and a majority level, then it is desirable to know whether the game is in addition homogeneous. The paper provides a recursive procedure defining a test for homogeneity. This procedure involves the computation of a number theoretical function, the matrix of homogeneity. If this matrix is knownall majority levels with respect to which the given set of weights represents a homogeneous simple weighted majority game are known at once.

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Zusammenfassung Ein gewichtetes Majoritätsspiel (nicht notwendig superadditiv oder mit Konstantsummeneigenschaft) kann beschrieben werden durch die Gewichte (die Abstimmungsstärke) der beteiligten Spieler und durch eine Mehrheitsschranke. Wenn eine solche Darstellung gegeben ist, so ist es wünschenswert, das Spiel zusätzlich auf die Eigenschaft der Homogenität hin zu untersuchen. Die vorliegende Arbeit stellt eine rekursive Prozedur zur Verfügung, die einen Test auf Homogenität einer vorgelegten Darstellung eines Spieles impliziert. Die Prozedur ermöglicht die Berechnung einer zahlentechnischen Funktion, der Homogenitätsmatrix. Wenn diese Matrix bekannt ist, kann man bei einem vorgegebenen Gewichtssatz alle Majoritätsschranken angeben, bezüglich welcher die vorgelegten Gewichte ein homogenes einfaches gewichtetes Majoritätsspiel darstellen.

     

Application of the ellipsoid method in an interactive procedure for multicriteria linear programming

The research reported in this paper is concerned with an application of the ellipsoid algorithm in the interactive multicriteria linear programming step method (STEM) byBenayoun et al. [1971]. Due to this application we eliminate some drawbacks of the original version of STEM and, moreover, we avoid extra computations connected with sensitivity analysis in every iteration. Specifically, we use the ellipsoid algorithm to minimize the Euclidean norm in the criterion space instead of the Chebyshev norm, which ensures that every solution submitted to the decision maker is efficient. As follows from a computational experiment, in comparison with the application of the simplex method, the proposed modification of STEM shows a smaller increase of the computational effort when the number of criteria increases. However, the absolute computation time becomes worse for problems of larger size.

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Zusammenfassung In dieser Arbeit wird über eine Anwendungsmöglichkeit der Khachiyan-Shor-Algorithmus (Ellipsoid-Algorithmus) im Rahmen des STEM-Verfahrens zur interaktiven Lösung linearer Vektoroptimierungsmodelle berichtet. Auf diese Weise können einige spezifische Nachteile des STEM-Verfahrens in seiner Originalversion vermieden werden. Durch die Verwendung der Euklidischen Norm anstelle der beim STEM-Verfahren üblichen Tschebyscheff-Norm wird garantiert, daß dem Entscheidungsträger nur effiziente Lösungen vorgeschlagen werden. Die numerischen Erfahrungen zeigen, daß der Lösungsaufwand der hier vorgeschlagenen Modifikation des STEM-Verfahrens mit steigender Anzahl von Zielfunktionen weniger stark zunimmt als bei der üblichen Version. Dies gilt jedoch nicht hinsichtlich der allgemeinen Problemgröße.

     

Preparative uv-laser photochemistry of the azoalkane spiro(2,3-diazabicyclo [2.2.1]hept-2-ene-7′,1-cyclopropane): Trapping of the 1,4-Diradical 2-(3-Cyclopentenyl) ethyl by Molecular Oxygen

Photo-extrusion of nitrogen from the azoalkane 1 in the presence of molecular oxygen gave besides the hydrocarbons 3 and 5, the endoperoxide 10 and hydroperoxide 11, the former via trapping of the 1,4-diradical 4 by triplet oxygen, the latter by ene-reaction-6f hydrocarbon 5 with singlet oxygen.     

Equivariant framability of involutions on homotopy spheres

Let G be the group Z₂. Denote byR ^n,k theR ^n+k with non trivial G-action on the first n coordinates. Let ^n,k be the trivial bundle with fibreR ^n,k. We say that a G-manifold M is (n,k)-framable if t(M)= =^n,k in KO_G(M) with t(M) the tangent bundle of M. We show that if G acts on a homotopy sphere ^n+k such that the fixed point set is a k-dimensional homotopy sphere then is (n,k)-framable.     

A critical evaluation of high performance liquid chromatography-electrospray ionisation-mass spectrometry and capillary electrophoresis-electrospray-mass spectrometry for the detection and determination of small molecules of significance in clinical and forensic science

A critical review of applications for the period 2000-2003, taken from the Web of Knowledge database, of the techniques high performance liquid chromatography-electrospray ionisation-mass spectrometry (HPLC-ESI-MS) and capillary electrophoresis-electrospray ionisation-mass spectrometry (CE-ESI-MS) to the detection and determination of small molecules of significance in clinical and forensic science is presented. The molecules of mass less than 500 Da are chosen according to selected structural classes in which they give ESI signals primarily as [M+H](+) ions although other ions such as [M-H](-), [M+Na](+) and [M+NH(4)](+) are also reported. The structural classes are drugs with amine-containing side chains, drugs with N-containing saturated ring structures, 1,4-benzodiazepines, carbohydrates, benzimidazoles, other heterocycles, sulphonylureas, anthracyclines, sulphonamides, penicillins, cephalosporins, tetracyclines, nitrocatechols, steroids, flavonoids, oxazaphosphorines, cannabinols, and miscellaneous molecules. Details are given on the fragmentations, where available, that these ionic species exhibit in-source and in ion-trap, triple quadrupole and time-of-flight mass spectrometers. The review then gives a critical evaluation of these recent HPLC-ESI-MS and CE-ESI-MS analytical methods for the detection and determination of small molecules of clinical and forensic significance. Analytical information on, for example, sample concentration techniques, HPLC and CE separation conditions, recoveries from biological media and limits of detection (LODs) are provided.     

Comparing Intrinsic Reactivities of the First‐ and Second‐Generation Ruthenium Metathesis Catalysts in the Gas Phase

An experimental comparison of the gas‐phase reactivity of the 14‐electron reactive intermediates produced by phosphine dissociation from the first‐ and second‐generation ruthenium metathesis catalysts, (L)Cl₂Ru?CHR (L=PCy₃ or NHC), supports Grubbs's contention that the second‐generation catalysts show hundred‐fold higher phenomenological activity despite a slower phosphine dissociation because of a much more‐favorable partitioning of the 14‐electron active species towards product‐forming steps. The gas‐phase study finds, in ring‐opening metathesis of norbornene as well as acyclic metathesis of ethyl vinyl ether, that the first‐generation systems display evidence for a higher barrier above that for phosphine dissociation; the second‐generation systems, on the other hand, behave as if there is no significantly higher barrier.