Stevin numbers and reality

We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:1104.0375, arXiv:1108.2885, arXiv:1108.420

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

Environment influences on the aromatic character of nucleobases and amino acids

Geometric (HOMA) and magnetic (NICS) indices of aromaticity were estimated for aromatic rings of amino acids and nucleobases. Cartesian coordinates were taken directly either from PDB files deposited in public databases at the finest resolution available (≤1.5 Å), or from structures resulting from full gradient geometry optimization in a hybrid QM/MM approach. Significant environmental effects imposing alterations of HOMA values were noted for all aromatic rings analysed. Furthermore, even extra fine resolution (≤1.0 Å) is not sufficient for direct estimation of HOMA values based on Cartesian coordinates provided by PDB files. The values of mean bond errors seem to be much higher than the 0.05 Å often reported for PDB files. The use of quantum chemistry geometry optimization is strongly advised; even a simple QM/MM model comprising only the aromatic substructure within the QM region and the rest of biomolecule treated classically within the MM framework proved to be a promising means of describing aromaticity inside native environments. According to the results presented, three consequences of the interaction with the environment can be observed that induce changes in structural and magnetic indices of aromaticity. First, broad ranges of HOMA or NICS values are usually obtained for different conformations of nearest neighborhood. Next, these values and their means can differ significantly from those characterising isolated monomers. The most significant increase in aromaticities is expected for the six-membered rings of guanine, thymine and cytosine. The same trend was also noticed for all amino acids inside proteins but this effect was much smaller, reaching the highest value for the five-membered ring of tryptophan. Explicit water solutions impose similar changes on HOMA and NICS distributions. Thus, environment effects of protein, DNA and even explicit water molecules are non-negligible sources of aromaticity changes appearing in the rings of nucleobases and aromatic amino acids residues