Related papers: Mathematical Aspects of the Periodic Law
Unveiling numerical trends among either atomic or equivalent weights that somehow preserved resemblances among elements was frequent in the 1860s. Standing out from the crowd, Meyer and Mendeleev went beyond numerical relationships,…
For more than 150 years the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is.…
The numbers of natural chemical elements, minerals, inorganic and organic chemical compounds are determined by 1, 2, 3 and 4-combinations of a set 95 and are respectively equal to 95, 4,465, 138,415 and 3,183,545. To explain these relations…
For studying the objectivity and the quality of a given form of the Periodic system as a single whole we compare plots of functions presenting properties of elements in pairs of periods. Using mathematical statistics we introduce a…
A large variety of periodic tables of the chemical elements have been proposed. It was Mendeleev who proposed a periodic table based on the extensive periodic law and predicted a number of unknown elements at that time. The periodic table…
Periodic table of chemical elements symbolizes an elegant graphical representation of symmetry at atomic level and provides an overview on arrangement of electrons. It started merely as tabular representation of chemical elements, later got…
This paper presents two facets. First, we show that the periodic table of chemical elements can be described, understood and modified (as far as its format is concerned) on the basis of group theory and more specifically by using the group…
Mathematical formula describing the periodicity of the elements in the periodic system is presented.
Perhaps the most significant, if not the most important, achievements in chemistry and physics are the Periodic Table of the Elements in Chemistry and the Standard Model of Elementary Particles in Physics. A comparable achievement in…
In the first part we associate a periodic sequence to a partition and study the connection the distribution of elements of uniform limit of the sequences. Then some facts of statistical independence of these limits are proved
This survey article is the outgrowth of two talks given at the Journ\'ees X-UPS "P\'eriodes et transcendance" at \'Ecole polytechnique. Periods are complex numbers whose real and imaginary parts can be written as integrals of rational…
This paper is a companion article to the review paper by the present author devoted to the classification of matter constituents (chemical elements and particles) and published in the first part of the proceedings of The Second Harry Wiener…
Proposed is system of consistent mathematical models describing physical laws of a system of energy emitting bodies in dynamics, relativity and nuclear physics. It is shown the use of developed models for the description of systems,…
Structures of chemical compounds can be synthesized and categorized through mathematical means. Organic compounds are suitable targets because of their simple valences. Acyclic organic compounds made of hydrogen and second-row elements C,…
Period mappings were introduced in the sixties [G] to study variation of complex structures of families of algebraic varieties. The theory of tautological systems was introduced recently [LSY,LY] to understand period integrals of algebraic…
The theory of aperiodic order is concerned with the development of ideas stimulated by the discovery of quasicrystals. We give a gentle introduction to some mathematical aspects of aperiodic order, aimed at a more general audience.
Periods are numbers represented as integrals of rational functions over algebraic domains. A survey of their elementary properties is provided. Examples of periods includes Feynman Integrals from Quantum Physics and Multiple Zeta Values…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
The empirical laws of chemical kinetics are studied from a microscopic point of view. An analysis based on elementary probability theory and combinatorics is enough to explain the kinetics law observed in experiments. Thus, an out of…
A modification of the standard periodic table of the elements reveals $4n^{2}$ periods, where $n=2,3,\dots$. The new arrangement places hydrogen with halogens and keeps the rare-earth elements in the table proper (without separating them as…