Related papers: Classifying chemical elements and particles: from …
The problem of expressing an element of K_2(F) in a more explicit form gives rise to many works. To avoid a restrictive condition in a work of Tate, Browkin considered cyclotomic elements as the candidate for the element with an explicit…
The periodic changes in the physical and chemical properties of the chemical elements are caused by the periodic change of the ionization energies, which are constant for each element that manifested in the Periodic Table. However, as has…
Group-theoretical approach is applied to study behavior of lossless two-level atoms in a standing-wave laser field. Due to the recoil effect, the internal and external atomic degrees of freedom become coupled. The internal dynamics is…
Periodic and semi periodic patterns are very common in nature. In this paper we introduce a topological toolbox aiming in detecting and quantifying periodicity. The presented technique is of a general nature and may be employed wherever…
We introduce two partially overlapping classes of pathwise dualities between interacting particle systems that are based on commutative monoids (semigroups with a neutral element) and semirings, respectively. For interacting particle…
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…
The atoms of the Schanuel topos can be described as the pairs $(n,G)$ where $n$ is a finite set and $G$ is a subgroup of $\operatorname{Aut}(n)$. We give a general criterion on an atomic site ensuring that the atoms of the topos of sheaves…
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,…
We can recognize two modes in which 'quantum appears' in macro domains: (i) a 'micro-physical appearance', where quantum laws are assumed to be universal and they are transferred from the micro to the macro level if suitable 'quantum…
We study permutations on n elements preserving orientation (parity) of every subset of size k. We describe all groups of these permutations. Unexpectedly, these groups (except for some special cases) are either trivial, cyclic or dihedral.…
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,…
We show that many important varieties and sets of varieties of semigroups may be defined by relatively simple and transparent first-order formulas in the lattice of all semigroup varieties.
This brief overview stresses the importance of laboratory data and theory in analyzing astronomical observations and understanding the physical and chemical processes that drive the astrophysical phenomena in our Universe. This includes…
A study of the $\lambda$- and $N$-atomic configurations under dipolar interaction with $2$ modes of electromagnetic radiation is presented. The corresponding quantum phase diagrams are obtained by means of a variational procedure. Both…
An introduction to nuclear theory is given starting from the quantum chromodynamics foundations for quark and gluon fields, then discussing properties of pions and nucleons, interactions between nucleons, structure of the deuteron and light…
The "standard" iso-singlet scalar particle $\sigma$ is reconsidered in the reduced normal-ordering (RNO) framework to the effective SU(2) theory. Recent reanalysis of the $\pi\pi$-phase shift [1] is used.
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
We give a simple proof of the well-known fact: any group of n elements is cyclic if and only if n and \phi(n) are coprime. This note is accessible for students familiar with permutations and basic number theory. No knowledge of abstract…
In this article, we compare two different notions of partially defined group strutures, namely partial groups and pregroups, as introduced by Chermak and Stallings respectively. In particular we prove that the category of pregroups can be…
The traditional display of elements in the periodic table is convenient for the study of chemistry and physics. However, the atomic number alone is insufficient for training statistical machine learning models to describe and extract…