The Nappi-Witten string in the light-cone gauge

Some of the motivations for as well as the main points of the quantization of the Nappi-Witten string in the light-cone gauge are reviewed.     

Spectral and scattering theory for a Schrödinger operator with a class of momentum-dependent long-range potentials

Let be the selfadjoint operator for the static electromagnetic field where W _j for 0, 1, 2, ..., n is a sum of (i) a short-range potential and (ii) a smooth long-range potential decreasing at as |x|^- with in (0, 1]. Then for >1/2, asymptotic completeness holds for the scattering system (H, H ₀).     

On the one loop equivalence of dual σ models

It is shown that in the one loop order of perturbation theory the coupling constant and parameter(s) of an (Abelian T) dual sigma model get renormalized in the same way as in the ‘original’ model.     

Raman spectroscopic investigation on the microenvironment of the liver tissues of Zebrafish (Danio rerio) due to titanium dioxide exposure

Nano titanium dioxide (nTiO₂), generally considered to be toxicologically inert, is manufactured in large quantities and extensively applied in consumer products. The small size and large surface area endow them with an active group or intrinsic toxicity. Advances in instrumentation are making Raman spectroscopy the tool of choice for an increasing number of (bio) chemical applications. One of the great advantages of this technique is its ability to provide information on the concentration, structure and interaction of biochemical molecules in their microenvironments within intact cells and tissues, non-destructively. Zebrafish (Danio rerio), one of the most important vertebrate model organisms used in developmental biology, are increasingly used in biomedical research, particularly as a model of human disease. In the present work, an attempt is made to study the effect of titanium dioxide, both nano and bulk, on the microenvironment of the liver tissues of Zebrafish using FT-Raman spectroscopy. The results of the present study suggest that TiO₂ exposure demonstrate a marked influence on the microenvironments of the liver tissues of Zebrafish. A shift to a higher wavenumber and an increase in the intensity of the band at ∼1087 cm⁻¹ in the TiO₂ exposed tissues suggest that some of the conformational changes resulting from the alkali recovery process takes place due to TiO₂ exposure. The decreased intensity ratio (I₃₂₂₀/I₃₄₀₀) observed in the titanium-exposed tissues suggests a decreased water domain size, which could be interpreted in terms of weaker hydrogen-bonded molecular species of water in the TiO₂ exposed tissues. The observed shift of COO⁻ bands to higher frequencies shows the disruption of salt bridges as a result of a change in the oppositely charged partners and due to the enhanced random coil conformation. The variation in the intensity ratio of the tyrosyl doublet (I₈₅₈/I₈₂₅) indicates variation in the hydrogen bonding of the phenolic hydroxyl group due to TiO₂ exposure. The results further suggest that the microenvironments are greatly altered due to titanium nano exposure when compared to titanium bulk. In conclusion, the results indicate that FT-Raman spectroscopy might be a useful tool for rapid assessment of nano particle biological interactions.     

On dimensional reduction of gauge theories: Symmetric fields and harmonic expansion

We compare the four-dimensional symmetric fields obtained by the coset space dimensional reduction scheme to the infinite tower of fields given by the harmonic expansion in a 4+N dimensional gauge theory coupled to fermions on a space-timeM ⁴ ×S/R.     

The mechanism of carbonyl reduction by LiBH4: An ab initio investigation

The minimum energy path and the geometry of the transition state for the first stage of the reduction by LiBH₄ of R₂CO (RH, CH₃) to alcohol have been determined by ab initio SCF calculations using a small basis set and subsequently confirmed by further calculations using a larger basis set and CI methods. Attention has been focused on the changes of electron distribution during the reaction, the nature of the bonding, and the effect of chemical substituents. The results lend support to one of the proposed reaction mechanisms. Some supplementary data concerning the role of the solvent are also discussed.     

Electromagnetic mass shift of pions in unified gauge field theories and the light-cone

The electromagnetic mass shift of pions is discussed in unified gauge field theories of weak and electromagnetic interactions to second order of the electric charge and the pion mass, respectively. We calculate the contributions of the next to leading light-cone singularities (quark mass terms) and it is found that these do not contribute to the divergences in the mass shift provided the masses of the bare proton quark and neutron quark are equal. γ, Z, W, φ exchanges are taken into account. Different bare quark masses in general make the mass shift divergent. In the tadpole contribution, the Born term causes a divergence unless we extrapolate first to q² = 0.     

Some relations between additive functions,II

Aequationes mathematicae -