相关论文: Formal structure of periodic system of elements
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,…
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 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…
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…
Most elemental metals under ambient conditions adopt simple structures such as BCC, FCC and HCP in specific groupings across the Periodic Table, and on compression, many of these elements undergo transitions to surprisingly complex…
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…
Mathematical formula describing the periodicity of the elements in the periodic system is presented.
A connected component of an affine algebraic group is called periodic if all its elements have finite order. We give a characterization of periodic components in terms of automorphisms with finite number of fixed points. It is also…
We investigate the mathematical structure of unit systems and the relations between them. Looking over the entire set of unit systems, we can find a mathematical structure that is called preorder (or quasi-order). For some pair of unit…
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…
Crystals are paradigms of ordered structures. While order was once seen as synonymous with lattice periodic arrangements, the discoveries of incommensurate crystals and quasicrystals led to a more general perception of crystalline order,…
Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two…
The hydrogen molecule contains the basic ingredients to understand the chemical bond, i.e, a pair of electrons. We show a step to understand The Correspondence Principle for chaotic system in the Chemical World. The hydrogen molecule is…
Closed-form expressions for all matrix elements required for variational calculation of the electronic structure of periodic solids have been derived using a basis of explicitly correlated Gaussians (ECGs). Periodic basis functions are…
The Modern Theory of Polarization, which rigorously defines the spontaneous electric polarization of a periodic solid and provides a recipe for its computation in electronic structure codes, transformed our understanding of ferroelectricity…
In the present paper, as a generalization of the classical periodic rings, we explore those rings whose elements are additively generated by two (or more) periodic elements by calling them additively periodic. We prove that, in some major…
We discuss the possibility of making the {\it initial} definitions of mutually different (possibly interacting, or even entangled) systems in the context of decoherence theory. We point out relativity of the concept of elementary physical…
This article provides formal definitions characterizing well-formed composition of components in order to guarantee their safe deployment and execution. Our work focuses on the structural aspects of component composition; it puts together…
A generalized formal framework for decoherence, that can be used both in open and closed quantum systems, is sketched. In this context, the relationship between the decoherence of a closed system and the decoherence of its subsystems is…
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…