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     

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.

     

Intermolecular potential energy surface and spectra of He-HCl with generalization to other rare gas-hydrogen halide complexes

A two-dimensional (rigid monomer) intermolecular potential energy surface (PES) of the He-HCl complex has been obtained from ab initio calculations utilizing the symmetry-adapted perturbation theory (SAPT) and an spdfg basis set including midbond functions. The bond length in HCl was chosen to be equal to the expectation value in the ground vibrational state of isolated HCl. The rigid-monomer potential should be a very good approximation to the complete (three-dimensional) potential for H-Cl distances corresponding to the lowest vibrational levels of the monomer since the He-HCl interaction energy was found to be only weakly dependent on the HCl bond length in this region, at least as compared to systems such as Ar-HF. The calculated points were fitted using an analytic function with ab initio computed asymptotic coefficients. As expected, the complex is loosely bound, with the dispersion energy providing the majority of the attraction. Our SAPT PES agrees with the semiempirical PES of Willey et al. [J. Chem. Phys. 96, 898 (1992)], in finding that, atypically for rare gas-hydrogen halide complexes including the lighter halide atoms, the global minimum is on the Cl side (with intermonomer separation 3.35 A and depth of 32.8 cm(-1)), rather than on the H side, where there is only a local minimum (3.85 A, 30.8 cm(-1)). The ordering of the minima was confirmed by single-point calculations in larger basis sets and complete basis set extrapolations, and also using higher levels of theory. We show that the opposite findings in the recent calculations of Zhang and Shi [J. Mol. Struct: THEOCHEM 589, 89 (2002)] are due to the lack of midbond functions in their basis set. Despite the closeness in depth of the two linear minima, the existence of a relatively high barrier between them invalidates the assumption of isotropy, a feature of some literature potentials. The trends concerning the locations of minima within the family of rare gas-hydrogen halide complexes are rationalized in terms of the physical components of the intermolecular forces and related to monomer properties. The accuracy of the SAPT PES was tested by performing calculations of rovibrational levels. The transition frequencies obtained were found to be in excellent agreement (to within 0.02 cm(-1)) with the measurements of Lovejoy and Nesbitt [J. Chem. Phys. 93, 5387 (1990)]. The SAPT PES predicts a dissociation energy for the complex of 7.74 cm(-1) which is probably more accurate than the experimental value of 10.1+/-1.2 cm(-1). Our analysis of the ground-state rovibrational wave function shows that the He-HCl configuration is favored over the He-ClH configuration despite the ordering of minima. This is due to the greater volume of the well in the former case. We have also determined positions and widths of three low-lying resonance states through scattering calculations. These predictions are expected to be more accurate than values derived from experiment.     

Strukturviskosität von verdünnten Lösungen von Biopolymeren

The importance of the rheological behaviour of solutions of macromolecules is briefly evaluated. The viscosity of the solutions depends on concentration, shear rate and time of shear, this relation being determined by the structure of the dissolved molecules. In dilute solutions shear dependence of viscosity is very frequently caused by the preferential orientation of anisotropic molecules. In such a case the particle dimensions can be calculated from the true limiting viscosity number, an anisotropy factor, the rotational diffusion constant and the effective particle density. These numbers can be derived from the flow curve, which has been extrapolated to zero concentration. It is necessary to measure the flow curve at shear gradients, which are sufficiently low to allow for an extrapolation to vanishing shear rate. By comparing the experimental flow curve with a choice of theoretical ones, the rotational diffusion constant and the anisotropy factor (axial ratio) can be found. From the limiting viscosity number and the axial ratio, the particle density can be calculated.     

Komplexe von 2,6-Dimethylpyridin-1-oxid mit Lanthanidjodiden

Complexes of 2,6-dimethylpyridine 1-oxide with lanthanide iodides of the formulaeLn(2,6-LTNO)₅I₃ whereLn=La, Tb and Yb,Ln(2,6-LTNO)₄I₃ whereLn=Pr and Nd and Er(2,6-LTNO)_4.5I₃ have been prepared and characterised by chemical analysis, infrared and conductance studies. Infrared and conductance data have been interpreted in terms of dimeric (or polymeric) structures involving bridging amine oxide groups.

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Mit 2 Abbildungen     

Über die Synthese von 5-(o-Trifluormethylphenyl)-1H-thieno[3,4—e]-1,4-diazepin-2(3H)-onen

The synthesis of 5-(o-trifluoromethylphenyl)-1H-thieno-[3,4-e]1,4-diazepin-2(3H)-one (7) and its nitration and chlorination in pos. 8 are described.     

Berechnung von mittleren Schwingungsamplituden einiger tetraedrischer Moleküle und Ionen nach der Methode der charakteristischen Schwingungen

Mean amplitudes of vibration of a series of tetrahedralXY ₄ molecules and ions (hydrides, halides, oxides and oxoanions) have been calculated using the “Method of the Characteristic Vibrations” ofA. Müller. The results indicate that this method leads to very good values for most of the investigated species, and especially in the cases of highM _X/M_Y mass ratio.     

Die Hydrohalogenierung von Hexaphenyldigerman und die Schwingungsspektren einiger Ge2(C6H5) n X6−n -Verbindungen

The reactions of Ge₂(C₆H₅)₆ with HCl and HBr lead in nearly quantitative yields to the 1,1,2,2-tetrahalo derivatives Cl₂(C₆H₅)GeGe(C₆H₅)Cl₂ (I) and Br₂(C₆H₅)GeGe(C₆H₅)Br₂ (II), resp. The Si?Ge bond of (C₆H₅)₃SiGe(C₆H₅)₃ is cleaved under the conditions of hydrohalogenation. The vibrational spectra of Ge₂Br₆, Ge₂(C₆H₅)₆, I, and II are reported. The influence of vibrational coupling on ν GeGe in these compounds is discussed in detail, including vibrational calculations.