Catalytic activity of nickel(II), copper(II) and oxovanadium(II)‐dihydroindolone complexes towards homogeneous oxidation reactions

Three novel paramagnetic metal complexes (MH₂ID) of Ni²⁺, Cu²⁺ and VO²⁺ ions with 3‐hydroxy‐3,3’‐biindoline‐2,2’‐dione (dihydroindolone, H₄ID) were synthesized and characterized by different spectroscopic methods. The ligand (H₄ID) was synthesized via homocoupling reaction of isatin in presence of phenylalanine in methanol. Complexation of low valent Ni²⁺, Cu²⁺ ions and high valent VO²⁺ ions with H₄ID carried out in 1: 2 molar ratios. A comparison in the catalytic potential of paramagnetic complexes of low and high valent metal ion was explored in the oxidation processes of cis‐cyclooctene, benzyl alcohol and thiophene by an aqueous H₂O₂, as a green terminal oxidant, in the presence and absence of acetonitrile, as an organic solvent, at 85 °C. NiH₂ID, CuH₂ID and VOH₂ID show good catalytic activity, i.e. good chemo‐ and regioselectivity. VOH₂ID has the highest catalytic potential compared to both Ni²⁺‐ and Cu²⁺‐species in the same homogenous aerobic atmosphere. Catalytic oxidation of other alkenes and alcohols was also studied using NiH₂ID, CuH₂ID or VOH₂ID as a pre‐catalyst by an aqueous H₂O₂. A mechanistic pathway for those oxidation processes was proposed.     

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.