Abstract
SHS investigation development is considered from the geographical and historical viewpoint. 3 stages are described. Within Stage 1 the work was carried out in the Department of the Institute of Chemical Physics in Chernogolovka where the scientific discovery had been made. At Stage 2 the interest to SHS arose in different cities and towns of the former USSR. Within Stage 3 SHS entered the international scene. Now SHS processes and products are being studied in more than 50 countries.
Abstract
We give some basic mathematical ideas of partially ordered sets (posets), which frame into the mathematical way of thinking illustrated in the Erlangen Programme by Felix Klein. The programme entails extracting relevant variables to study, symbolising them and relating them through a function. We show several examples where the mathematical way of thinking, restricted to partial orders, is found in chemistry. The examples are: Geoffroy’s affinity table, benzene’s structure, posetic predictive methods, multicriteria situations and derivation of concepts. Finally we question the ranking process by showing how it disregards its underlying, and not always recognised, posetic nature.
Keywords:
Partial order, partially ordered sets, mathematical way of thinking, erlangen programme, posets, mathematical chemistry, ranking, affinity tables, benzene’s structure, posetic predictive methods, multicriteria approaches, formal concept analysis, mutagenicity, estimation of properties, philosophy of chemistry.
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Authors:Bentham Science Books