A real analytic constructive proof of the lojasiewicz theorem

In this paper we eliminate the complex analytic part from original Lojasiewicz's proof and show a constructive method of producing a saucissonnage for a set of polynomials.     

On square roots of the Haar state on compact quantum groups

The paper is concerned with the extension of the classical study of probability measures on a compact group which are square roots of the Haar measure, due to Diaconis and Shahshahani, to the context of compact quantum groups. We provide a simple characterisation for compact quantum groups which admit no non-trivial square roots of the Haar state in terms of their corepresentation theory. In particular it is shown that such compact quantum groups are necessarily of Kac type and their subalgebras generated by the coefficients of a fixed two-dimensional irreducible corepresentation are isomorphic (as finite quantum groups) to the algebra of functions on the group of unit quaternions. An example of a quantum group whose Haar state admits no nontrivial square root and which is neither commutative nor cocommutative is given.     

Horizontal bridges in polar dielectric liquids

When a high-voltage direct-current is applied to two beakers filled with polar liquid dielectrica like water or methanol, a horizontal bridge forms between the two beakers. By repeating a version of Pellat’s experiment, it is shown that a horizontal bridge is stable by the action of electrohydrodynamic pressure. Thus, the static and dynamic properties of the phenomenon called a ‘floating water bridge’ can be explained by the gradient of Maxwell pressure, replenishing the liquid within the bridge against any drainage mechanism. It is also shown that a number of liquids can form stable and long horizontal bridges. The stability of such a connection, and the asymmetry in mass flow through such bridges caused by the formation of ion clouds in the vicinity of the electrodes, is also discussed by two further experiments.     

A HF Loaded Lewis-Acidic Aluminium Chlorofluoride for Hydrofluorination Reactions

The very strong Lewis acid aluminium chlorofluoride (ACF) was loaded with anhydrous HF. The interaction between the surface of the catalyst and HF was investigated using a variety of characterization methods, which revealed the formation of polyfluorides. Moreover, the reactivity of the HF-loaded ACF towards the hydrofluorination of alkynes was studied.