Solutions of the WDVV Equations and Integrable Hierarchies of KP Type

We show that reductions of KP hierarchies related to the loop algebra of SL_n with homogeneous gradation give solutions of the Darboux-Egoroff system of PDE's. Using explicit dressing matrices of the Riemann-Hilbert problem generalized to include a set of commuting additional symmetries, we construct solutions of the Witten– Dijkgraaf–E. Verlinde–H. Verlinde equations.     

Rank,covering number and a simple spectrum

For a dynamical system (X, B, T, μ) we investigate the connections between metric invariants, the rankr(T) and the covering numberF ^*(T) and a spectral property for having a simple spectrum. Given a positive integerr≥2, a real numberb, 0<b<1 such thatr·b≥1, we construct examples of systems withr(T)=r, F ^*(T)=b and having a simple spectrum.     

(Systemic) phototoxicity of drugs and other xenobiotics.

Xenobiotics extensively used in drugs, cosmetics, food and agricultural chemicals can produce adverse biological effects. These toxic effects are separated into classes, e.g. hepatotoxicity, genotoxicity and neurotoxicity. Skin allergy, part of immunotoxicity, is also a subdivision of toxicology. When light is an essential condition for toxicity, the xenobiotic is called phototoxic. Thus it fits into the logic of toxicology that photoallergic compounds are a subdivision of phototoxic compounds. Phototoxicons as a group do not differ from the group of phototherapeutics with regard to their eventual biological effects. The primary photoreactions, secondary molecular processes, biomolecules involved and cellular and tissue damage are similar. The difference between the two groups is in the appreciation of the photobiological effects: adverse vs. desired. The aim of research is to determine the part of the molecular structure which makes a given compound phototoxic. With that knowledge the structure of the phototoxicon can be changed. This can result in a derivative which still has the desired properties of the parent compound, but is no longer phototoxic. This aim can be reached by combining data from both in vitro and in vivo research. The variety and number of phototoxic compounds is large. This, together with the limited research effort devoted to this subject so far, means that for most phototoxic xenobiotics a relationship between structure and in vivo photoreactivity is not available. In this review, emphasis is placed on xenobiotics whose in vitro and in vivo photochemistry have been studied. Furthermore, possible phototoxic effects which do not concern the skin but involve inner organs (systemic effects) are considered. References in this review mostly concern investigations over the last 10 years. For older literature or for additional information, references to other reviews are given. Important groups of phototoxic xenobiotics not dealt with in this article were already sufficiently covered in the reviews referred to.     

Foams and surface rheological properties of β-casein, gliadin and glycinin

Interfacial rheological properties and their suitability for foam production and stability of two vegetable proteins were studied and compared to β-casein. Proteins used ranged from flexible to rigid/globular in the order of β-casein, gliadin and soy glycinin. Experiments were performed at pH 6.7. Network forming properties were characterised by the surface dilational modulus (determined with the ring trough) and the critical falling film length (L_still) at which a stagnant protein film will break. Gliadin had the highest dilational modulus, followed by glycinin and β-casein, whereas glycinin formed the strongest film against fracture in the overflowing cylinder. The rate of decrease in the surface tension was studied at the air–water (Wilhelmy plate method) and the oil–water interface (bursting membrane) and the dynamic surface tension during compression and expansion in the caterpillar. Gliadin had the lowest equilibrium interfacial tensions and β-casein the lowest dynamic surface tension during expansion. Hardly any foam could be formed at a concentration of 0.1 g/l by shaking. At a concentration of 1.4 g/l most foam was formed by β-casein, followed by gliadin and glycinin. It seems that in the first place the rate of adsorption is important for foam formation. For the vegetable proteins, adsorption was slow. This resulted in lower foamability, especially for glycinin.     

U(2, 2) Symmetry as a Common Basis for Quantum Theory and Geometrodynamics

We formulated some criticisms of the Diracequation and its Clifford-algebraic philosophy; inparticular, we show that, within a general-relativisticcontext, they seem to contain hidden action-at-distance concepts. We suggest a new model based on thefour-component Klein-Gordon equation locally invariantunder the U(2,2) gauge group. The usual Dirac equationis then obtained as a certain approximation. The geometrodynamical sector shows reasonablecorrespondence with general relativity.