On well-ordered mono-unary algebras

Given a linearly ordered set (A, _R ) and an R-monotone function f: AA, we give a necessary and sufficient condition on A, f, _R , involving generating sets and forbidden subalgebras, for _R to be a well-ordering.Partially supported by Hungarian National Foundation for Scientific Research Grant nr. 1813.     

Umpolung of the allylpalladium reactivity: mechanism and regioselectivity of the electrophilic attack on bis-allylpalladium complexes formed in palladium-catalyzed transformations

The structure and reactivity of various bis-allylpalladium complexes occurring as catalytic intermediates in important synthetic transformations have been studied by applying density functional theory at the B3PW91(DZ + P) level. It was found that n1,n3 coordinated bis-allylpalladium complexes are readily formed from the corresponding n3,n3 complexes, especially in the presence of pi-acceptor phosphine ligands. The theoretical calculations indicate dsigma-->pi type hyperconjugative interactions occurring in the n1-coordinated allyl moiety of the n3,n3 coordinated complexes. These hyperconjugative interactions influence the structure of the complexes and dramatically increase the reactivity of the double bond in the n1-moiety. The DFT results indicate a remarkably low activation barrier for the electrophilic attack on the n1-allyl functionality. In bridged n1,n3 complexes, the electrophilic attack occurs with a very high regioselectivity, which can be explained on the basis of d-pi type hyperconjugative interactions.     

Sandwich structures at oil-water interfaces under alkaline conditions

Equilibrium liquid crystal (LC) layer on an interface between crude oils and water was observed at high pH. This layer is composed mainly of sodium naphthenates produced in situ at the water/oil interface. Transient LC layer was also evolved at the interface of aqueous phase of sodium hydroxide solutions and oleic phase of naphthenic acid (NA) solutions as result of a chemical reaction between NaOH and NA. This chemical reaction causes transport process resulting in a disturbance of the interface. Optical observation of this interface disturbance reviled that the interface covered with LC shows considerably lower flexibility as compared to LC free interface. The LC layer eventually dissolves in the water phase at low oil-to-water ratio, while at high oil-to-water ratio it can form an equilibrium phase, which spreads spontaneously at the oil-water interface.     

Analysis of primary aliphatic short-chain monoamines by LC in water samples

Several derivatization procedures with o-phthaldialdehyde-N-acetylcysteine (OPA-NAC) were compared for a rapid analysis of primary aliphatic short-chain monoamines in water samples by HPLC using a LiChorospher analytical separation column (100RP₁₈ mm i.d., 5 μm). Both the solution and the solid-support assisted off-line derivatization on C₁₈ SPE cartridges were inadequate options because of beginning degradation processes of the instable isoindol derivatives during their transfer to the analytical column. This problem was precluded with the on-column or solid-support assisted on-line derivatization. In the last mentioned procedure, the derivatization took place in a Hypersil C₁₈ precolumn ( mm i.d., 30 μm) connected with an additional preconcentration step resulting in better detection limits (0.002-0.040 μg ml⁻¹ requiring only 150 μl of water sample) than in the on-column procedure (0.08-0.16 μg ml⁻¹). The improved sample handling, the better control of parameters affecting reaction rates, the fully automation of this method with only 10 min analysis time for each sample are further advantageous. The potential of the solid-support assisted on-line derivatization was outlined and applied to water samples from several sources. Recovery values near 100% were obtained.     

Discrete groups of slow subgroup growth

It is known that the subgroup growth of finitely generated linear groups is either polynomial or at least $n^{\frac{{\log n}}{{\log \log n}}} $ . In this paper we prove the existence of a finitely generated group whose subgroup growth is of type $n^{\frac{{\log n}}{{(\log \log n)^2 }}} $ . This is the slowest non-polynomial subgroup growth obtained so far for finitely generated groups. The subgroup growth typen ^logn is also realized. The proofs involve analysis of the subgroup structure of finite alternating groups and finite simple groups in general. For example, we show there is an absolute constantc such that, ifT is any finite simple group, thenT has at mostn ^{c logn} subgroups of indexn.