Influence of perfluorinated carboxylic acids on ion-pair reversed-phase high-performance liquid chromatographic separation of betacyanins and 17-decarboxy-betacyanins

The ability of trifluoroacetic acid, pentafluoropropionic acid and heptafluorobutyric acid to act as ion-pairing agents for betacyanins and 17-decarboxy-betacyanins during HPLC analysis on a Luna C18(2) reversed-phase column is reported. While the perfluorinated carboxylic acids affect the retention of both groups of compounds by changing the pH of the mobile phase, the possibility of ion-pair chromatography for 17-decarboxy-betacyanins was noticed. In order to explain the accessibility of the positive charge for the counter-anion in decarboxy-betacyanins, the mesomeric structures of the polymethine system at low pH (around a value of 1.5), when the carboxylic group in the 2 position is protonated, should be taken into consideration.     

Near rings without zero divisors

Near rings without zero divisors, and a dual structure, near codomains, are studied. It is shown that a near ring is a near field if and only if it is an integral near ring, a near codomain, and has a non-zero distributive element. If the additive group (N, +) of a near integral domainN is cohopfian, then (N, +) possesses a fixed point free automorphism which is either torsion free or of prime order. This generalizes a well-known theorem of Ligh for finite near integral domains. A result ofGanesan [1] on the non-zero divisors in a finite ring is generalized to near rings.     

Spatiotemporal model for the progression of transgressive dunes

Transgressive dune fields, which are active sand areas surrounded by vegetation, exist on many coasts. In some regions like in Fraser Island in Australia, small dunes shrink while large ones grow, although both experience the same climatic conditions. We propose a general mathematical model for the spatiotemporal dynamics of vegetation cover on sand dunes and focus on the dynamics of transgressive dunes. Among other possibilities, the model predicts growth parallel to the wind with shrinkage perpendicular to the wind, where, depending on geometry and size, a transgressive dune can initially grow although eventually shrink. The larger is the initial area the slower its stabilization process. The model’s predictions are supported by field observations from Fraser Island in Australia.     

On systems of binomials in the ideal of a toric variety

Let be a toric set in the affine space . Given a set of binomials in the toric ideal of , we give a criterion for deciding the equality rad( ) = . This criterion extends to arbitrary dimension, and to arbitrary fields, an earlier result which concerned only monomial curves over an algebraically closed field of characteristic zero.