Molecular Topology. 14. Molord Algorithm and Real Number Subgraph Invariants

An algorithm, MOLORD, is proposed for defining real number invariants for subgraphs of various sizes in molecular graphs. The algorithm is based on iterative line derivati ves and accounts for heteroatoms by means of their electronegativities. It can be used in topological equivalence perception as well as to provide local and global descriptors for QSPR or QSAR studies. The algorithm is implemented on a TURBO PASCAL, TOPIND program and examplified on a set of selected graphs

On the cohomology of tautological bundles over the Quot scheme of curves

We consider tautological bundles and their exterior and symmetric powers over the Quot scheme of zero dimensional quotients over the projective line. We prove several results regarding the vanishing of their higher cohomology, and we describe the spaces of global sections via tautological constructions. To this end, we make use of the embedding of the Quot scheme into the product of two Grassmannians, which over the projective line was studied by Str{\o}mme as an explicit local complete intersection. This allows us to construct resolutions with vanishing cohomology for the tautological bundles and their exterior and symmetric powers.Comment: 21 page

Universal behaviour of ideal and interacting quantum gases in two dimensions

I discuss ideal and interacting quantum gases obeying general fractional exclusion statistics. For systems with constant density of single-particle states, described in the mean field approximation, the entropy depends neither on the microscopic exclusion statistics, nor on the interaction. Such systems are called {\em thermodynamically equivalent} and I show that the microscopic reason for this equivalence is a one-to-one correspondence between the excited states of these systems. This provides a method, different from the bosonisation technique, to transform between systems of different exclusion statistics. In the last section the macroscopic aspects of this method are discussed. In Appendix A I calculate the fluctuation of the ground state population of a condensed Bose gas in grandcanonical ensemble and mean field approximation, while in Appendix B I show a situation where although the system exhibits fractional exclusion properties on microscopic energy intervals, a rigorous calculation of the population of single particle states reveals a condensation phenomenon. This also implies a malfunction of the usual and simplified calculation technique of the most probable statistical distributions.Comment: About 14 journal pages, with 1 figure. Changes: Body of paper: same content, with slight rephrasing. Apendices are new. In the original submission I just mentioned the condensation, which is now detailed in Appendix B. They were intended for a separate paper. Reason for changes: rejection from Phys. Rev. Lett., resubmission to J. Phys. A: Math. Ge

Short-term effects of very low dose cadmium feeding on copper, manganese and iron homeostasis:A gastropod perspective

The available information on the interplay between low-dose cadmium intake and copper, manganese, and iron homeostasis in invertebrates is limited. We have currently studied the accumulation of these trace metals in the hepatopancreas of adult snails, Cantareus aspersus, following 14 and 28 days of exposure to low doses of dietary cadmium, up to 1 mg/kg dw (dry weight). The cadmium dose, but not the duration of exposure, had a significant effect on hepatopancreas copper deposition, the values being significantly elevated compared to controls. A significant peak in manganese levels at 14 days was found in snails administered the lowest cadmium dose. These increases occurred even in the absence of cadmium increase in the hepatopancreas. Our data suggest that low dose cadmium feeding can produce a transient disturbance in hepatopancreas copper and manganese homeostasis. Such responses may serve as early biomarkers of physiological changes occurring during the initial stages of cadmium intoxication

Comparative study of fission product release of homogeneous and heterogeneous high-burn up MOX fuel by Knudsen Effusion Mass Spectrometry supported by EPMA, SEM/TEM and thermal diffusivity investigations

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