A spectral characterization of the -torus by the first stability eigenvalue

Let be a compact hypersurface with constant mean curvature immersed into the unit Euclidean sphere . In this paper we derive a sharp upper bound for the first eigenvalue of the stability operator of in terms of the mean curvature and the length of the total umbilicity tensor of the hypersurface. Moreover, we prove that this bound is achieved only for the so-called -tori in , with . This extends to the case of constant mean curvature hypersurfaces previous results given by Wu (1993) and Perdomo (2002) for minimal hypersurfaces.

     

Convex Transitive Norms on Spaces of Continuous Functions

A norm on a Banach space X is called maximal when no equivalentnorm has a larger group of isometries. If, besides this, thereis no equivalent norm with the same isometries (apart from itsscalar multiples), the norm is said to be uniquely maximal,which is equivalent to the convex-transitivity of X: the convexhull of the orbits under the action of the isometry group onthe unit sphere is dense in the unit ball of X. The main resultof the paper is that the complex C₀() is convex-transitive inits natural supremum norm if is a connected manifold (withoutboundary). As a complement, it is shown that if is a connectedmanifold of dimension at least two, then the diameter norm isconvex transitive on the corresponding space of real functions.2000 Mathematics Subject Classification 46B15, 47B99     

Spirophosphoranylation d'α-aminoacides—I : Preparation et tautomerie

New spirophosphoranes have been prepared by reaction of &alpha-aminoacids with tricoordinate phosphorus substrates. In one case, 1i, an equilibrium chain-cycle P^IIIP^v has been observed.     

Poincaré-invariant gravitational field and equations of motion of two pointlike objects: The postlinear approximation of general relativity

Using a fast-motion approximation method we obtain the second-order gravitational field and equations of motion for two pointlike objects in algebraically closed form. A regularization procedure is used which is shown to guarantee the consistency of the approximation scheme. The equations of motion are then transformed within the framework of relativistic predictive mechanics into a system of ordinary differential equations.     

Kinetic-fluorimetric determination of microamounts of cerium(IV) by means of sodium 4,8-diamino-1,5-dihydroxyanthraquinone-2,6-disulphonate

Summary A kinetic method for determination of traces of Ce(IV), based on the oxidation of sodium 4,8-diamino-1,5-dihydroxyanthraquinone-2, 6-disulphonate is described. The reaction is monitored by means of the fluorescence of the oxidation product ( _ex=525nm, _em=585 nm), and allows determination of 0.02–0.37 ppm Ce(IV). The proposed method has few interferences.

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Kinetisch-fluorimetrische Bestimmung von Mikromengen Cer(IV) mit Natnum-4,8-diamino-1,5-dihydroxyanthrachinon-2,6-disulfonat

Zusammenfassung Eine kinetische Methode zur Bestimmung von Spuren Cer(IV) mit Hilfe von Natrium-4,8-diamino-1,5-dihydroxyanthrachinon-2,6-disulfonat wurde beschrieben. Dabei wird ein fluoreszierendes Oxydationsprodukt gebildet, das bei 525 nm angeregt mit einer maximalen Emission bei 585 nm fluoresziert. Die Reaktion ermöglicht die Bestimmung von 0,02–0,37 ppm Cer(IV). Die vorgeschlagene Methode wird nur durch wenige Störungen eingeschränkt.

     

Phosphazene spirannique a partir de derives du phophore dicoordine

The reaction of azidoalcohol $\text{2}$ on triazaphosphole $\text{1}$ takes place according to pathway $\text{a}$ and not $\text{b}$, as shown by the isolation of spirannic phosphazene $\text{3}$. The diazadiphosphetidines $\text{4}$, dimers of $\text{3}$ are also caracterized.     

Resolution of Eigen fuzzy sets equations

When R is a fuzzy relation between the elements of a finite set X, the fuzzy subsets A of X such that R·A = A (max-min composition) are called eigen fuzzy sets. In this paper we describe algorithms for the determination of the greatest eigen fuzzy set associated with a given fuzzy relation, thinking of medical diagnosis applications.     

Improved spot test for traces of nickel with dimethylglyoxime in the presence of interferences

Summary A general technique for the detection of nickel with dimethylglyoxime in the presence of considerable amount of interferent cations, even in complex mixtures, has been worked out. The influence of numerous anions in the reaction has been established. The method has been successfully applied to pure salts, minerals and metallic samples.

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Zusammenfassung Ein allgemein anwendbares Verfahren zum Nachweis von Nickel mit Dimethylglyoxim in Gegenwart erheblicher Mengen störender Kationen, auch in Vielfachgemischen, wurde ausgearbeitet. Die Beeinflußbarkeit der Reaktion durch mehrere Anionen wurde festgestellt. Die Methode wurde mit Erfolg auf die Analyse reiner Salze, Minerale und metallischer Proben angewendet.