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.

---

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.

---

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.

     

Die Ungleichungen von Vietoris

The inequalities $$P_{k,l} = \frac{1}{{B(l + 1,k)}}\int\limits_0^{l/(k + l)} {x^l (1 - x)^{k - 1} dx = I_{l/(k + l)} (l + 1,k)< \frac{1}{2}}$$ and $$\Phi _{k,l,\mu } = \frac{1}{{B(k,k\mu + 1)}}\int\limits_0^1 {x^{k - 1} (1 - x)^{k\mu } I_x (l + 1,l\mu )dx< \frac{1}{2}}$$ are shown to be valid for any positive real numbersk, l, μ.     

Registrierende Messung des mechanischen Verlustes von Kunststoffproben

Zusammenfassung Ein neues Verfahren, das eine unmittelbare und kontinuierliche Registrierung des mechanischen Verlustwinkels über einen weiten Temperaturbereich erm?glicht, wird beschrieben. Die Probe wird einer periodischen Biegung (f=2,5 Hz) unterworfen; die Zeit des Kraftnulldurchgangs relativ zur Bewegung ist dem Verlustwinkel proportional und wird elektronisch ermittelt. Das Me\ergebnis ist weitgehend von der Probenform und deren ?nderung w?hrend der Messung (Krümmung der Probe, thermische Ausdehnung usw). unabh?ngig. Der Deutschen Forschungsgemeinschaft sei für die Unterstützung dieser Arbeit verbindlichst gedankt.     

Homogeneous algebraic varieties defined by Jordan pairs

Every Jordan pair defines an algebraic varietyX containing as a dense open subset.X is projective (affine) if and only if is separable (radical). The Picard group ofX is generated by the irreducible factors of the generic norm of . If is separable then the automorphism group ofX is the projective group of .     

Virus Particles Monitored by Fluorescence Spectroscopy: A Potential Detection Assay for Macromolecular Assembly¶

Native fluorescence spectroscopy was used for in situ investigations of two lipid‐containing bacteriophages from the cystovirus family as well as their Pseudomonad host cells. Both the viruses φ6 and φ12 and their bacterial host proteins contain the amino acid tryptophan (trp), which is the predominant fluorophore in UV. Within proteins, trp's structural environment differs, and the differences are reflected in their spectroscopic signatures. It was observed that the peak of the trp emission from both viruses was at 330 nm, a significantly shorter wavelength than trp in either the Pseudomonad host cells or the amino acid's chemical form. This allowed us to monitor the viral attachment process and subsequent lytic release of progeny virus particles by measurement of the trp emission spectra during the infection process. This work demonstrates that fluorescence may offer a novel tool to detect viruses and monitor viral infection of cells and may be part of a biodefense application.     

The relation between the molecular weight and intrinsic viscosity of polymethyl acrylate

Summary A series of unfractionated and fractionated samples of polymethyl acrylate of different low molecular weights have been prepared by homogeneous solution. polymerization in dimethyl formamide in presence of , '-azo-(-cyano-n-valeric acid) as initiator under a variety of conditions. The number-average molecular weights have been determined by end-group titrations and vapour pressure osmometry. The following []-M relationships for polymethyl acrylate have been obtained.[] = 33.5 x 10^–5M^0.63 for unfractionated samples in benzene at 25 °C. [] = 3.89 x 10^–5M^0.843 for fractionated samples in benzene at 35 °C.With 2 tables     

Synthesis of [18,19,21,22‐13C4]‐Labeled Tautomycin as an NMR Probe of Protein Phosphatase Inhibitor

We have accomplished the synthesis of ¹³C‐labeled tautomycin at the C18, C19, C21, and C22 positions starting from 100 % [¹³C]triethylphosphonoacetate for the purpose of elucidating the dynamics and conformation of the C17–C26 moiety. NMR spectroscopy of ¹³C‐labeled tautomycin revealed strong binding with protein phosphatase type 1 and new features in the ¹³C NMR spectrum, such as the very small three‐bond coupling constants (²J).     

Die Ringinversions-Barriere in [2.2]Metacyclophan

From racemization studies on optically active [2.2]metacyclophanes substituted in position 4, the parameters of activation for the inversion of the tenmembered ring were found to be: G ₄₂₃ =31.5 kcal/mole, H =27.5 kcal/mole and S =–10 Cl/mole.Racemization does not occurvia bond forming or breaking; the value for the inversion barrier is not affected by substituents in position 4 and therefore corresponds to the value of unsubstituted [2.2]metacyclophane, whereas substituents in the bridge exert a distinct influence. These results can easily be explained on the basis of the isoconformational concept.

---

---

Mit 5 Abbildungen

---

Herrn Prof. Dr.O. Hoffmann-Ostenhof mit besten Wünschen zum 60. Geburtstag gewidmet.     

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.