Formal structure of periodic system of elements
Wilmer Leal1,2, Guillermo Restrepo2,3
1Bioinformatics Group, Department of Computer Science, Leipzig University, Leipzig, Germany.
Proceedings. Mathematical, Physical, and Engineering Sciences
|May 21, 2019
Summary
Researchers developed a formal mathematical structure for the periodic system, defining it as an ordered hypergraph. This generalized framework can be applied to chemical elements and other scientific disciplines.
Area of Science:
- Chemistry
- Physics
- Mathematics
- Information Science
Background:
- The periodic system of chemical elements has driven scientific inquiry for over 150 years.
- A unified, formal definition of a periodic system remains elusive.
- Existing periodic systems lack a generalized mathematical foundation.
Purpose of the Study:
- To establish a formal mathematical structure for periodic systems.
- To demonstrate the applicability of this structure to the periodic system of chemical elements.
- To generalize the concept of periodic systems for broader scientific application.
Main Methods:
- Utilized relations of order and similarity to define a mathematical structure.
- Represented the periodic system as an ordered hypergraph.
- Quantified order relationships within and among subsets of similar chemical bonds.
Main Results:
- A formal, ordered hypergraph structure for periodic systems was developed.
- The current periodic system of chemical elements was shown to be an instance of this general structure.
- A tailored periodic system for the polarizability of single covalent bonds was devised.
Conclusions:
- The generalized periodic system provides a unified mathematical framework.
- This framework can be applied to create new periodic systems, such as for chemical bond polarizability.
- The concept of periodic systems can be extended to diverse scientific and humanities fields.
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