Mathematical Aspects of the Periodic Law

We review different studies of the Periodic Law and the set of chemical elements from a mathematical point of view. This discussion covers the first attempts made in the 19th century up to the present day. Mathematics employed to study the periodic system includes number theory, information theory, order theory, set theory and topology. Each theory used shows that it is possible to provide the Periodic Law with a mathematical structure. We also show that it is possible to study the chemical elements taking advantage of their phenomenological properties, and that it is not always necessary to reduce the concept of chemical elements to the quantum atomic concept to be able to find interpretations for the Periodic Law. Finally, a connection is noted between the lengths of the periods of the Periodic Law and the philosophical Pythagorean doctrine.Comment: 20 pages, PDF fil

An\ue1lise de caracteres morfol\uf3gicos e comportamentais em abelhas africanizadas, caucasianas e em descendentes dos seus cruzamentos

<abstract language="eng">Twetve external morphological traits and seven traits of food-gathering behavior were studied in africanized and caucasian (A. m. caucasica), bees. Discriminant analysis showed that neither the length of the fourth segment of the abdomen, nor bee weight can be considered as the traits with the highest discriminatory power between africanized and caucasian bees, with any in-bred bees. In the case of in-bred bees the discriminam traits had a lower interorbital width and time to reach the feeder. Multivariate comparisons between the data of in-bred colonies and twenty hibrid colonies, suggest dominance of the genes group of the africanized subspecies