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Abstract. An optical measuring method has been applied to determine the dynamic surface tension of aqueous solutions of heptanol. The method uses the frequency of an oscillating liquid droplet as an indicator of the surface tension of the liquid. Droplets with diameters in the range between 100 and 200µm are produced by the controlled break-up of a liquid jet. The temporal development of the dynamic surface tension of heptanol-water solutions is interpreted by a diffusion controlled adsorption mechanism, based on the ”three- layer ” model of Ward & Tordai. Measured values of the surface tension of bi-distilled water, and the pure dynamic and static (asymptotic) surface tensions of the surfactant solutions are in very good agreement with values obtained by classical methods

Global representation of Segre numbers by Monge-Amp\`ere products

On a reduced analytic space $X$ we introduce the concept of a generalized cycle, which extends the notion of a formal sum of analytic subspaces to include also a form part. We then consider a suitable equivalence relation and corresponding quotient $\mathcal{B}(X)$ that we think of as an analogue of the Chow group and a refinement of de Rham cohomology. This group allows us to study both global and local intersection theoretic properties. We provide many $\mathcal{B}$-analogues of classical intersection theoretic constructions: For an analytic subspace $V\subset X$ we define a $\mathcal{B}$-Segre class, which is an element of $\mathcal{B}(X)$ with support in $V$. It satisfies a global King formula and, in particular, its multiplicities at each point coincide with the Segre numbers of $V$. When $V$ is cut out by a section of a vector bundle we interpret this class as a Monge-Amp\`ere-type product. For regular embeddings we construct a $\mathcal{B}$-analogue of the Gysin morphism

Depth of modular invariant rings

It is well-known that the ring of invariants associated to a nea-modular representation of a finite group is Cohen-Macaulay and hence has depth equal to the dimension of the representation. For modular representations the ring of invariants usually fails to be Cohen-Macaulay and computing the depth is often very difficult. In this paper(1) we obtain a simple formula for the depth of the ring of invariants for a family of modular representations. This family includes all modular representations of cyclic groups. Tn particular, we obtain an elementary proof of the celebrated theorem of Ellingsrud and Skjelbred [6]