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We introduce cyclic diagram monoids, a generalisation of classical diagram monoids that adds elements of arbitrary period by including internal components, with a view towards cryptography. We classify their simple representations and…
Periodic orbits (equivalence classes of closed paths up to cyclic shifts) play an important role in applications of graph theory. For example, they appear in the definition of the Ihara zeta function and exact trace formulae for the spectra…
One of the molecular properties most intuitive to the human perception is the geometrical shape. However, when exploring a large chemical space the determination of shape needs to be automated. We present a fast and simple approach to…
Topological indices are a class of numerical invariants that predict certain physical and chemical properties of molecules. Recently, two novel topological indices, named as Sombor index and reduced Sombor index, were introduced by Gutman,…
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,…
In a previous paper, we developed a table of components of algebraic solutions of a system of equations generated by an inhomogeneous proper-value equation involving K\"ahler's total angular momentum. This table looks as if it were a…
Consider the network of elements connected by adjacency in atomic number and periodic table column. If all elements except H-He are connected by identical springs and constrained to a z-spiral in 2D, a map sans spring-crossing results for…
An introduction to the Quantum Chemistry Package (QCP), implemented in the computer algebra system Maple, is presented. The QCP combines sophisticated electronic structure methods and Maple's easy-to-use graphical interface to enable…
We introduce MetaChem, a language for representing and implementing Artificial Chemistries. We motivate the need for modularisation and standardisation in representation of artificial chemistries. We describe a mathematical formalism for…
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 track the secondary bifurcations of coherent states in plane Couette flow and show that they undergo an incomplete periodic doubling cascade that ends with a crisis bifurcation. We introduce a symbolic dynamics for the orbits and show…
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 theory is used in many textbooks of contemporary physics. However, electromagnetic community often considers group theory as an "exotic" tool. Graduate and postgraduate textbooks on electromagnetics and electrodynamics usually do not…
Ideograms (symbols that represent a word or idea) have great communicative value. They refer to concepts in a simple manner, easing the understanding of related ideas. Moreover, ideograms can simplify the often cumbersome notation used in…
Algebraic models are proposed for the description of the shell-like quarteting of the nucleons both on the phenomenologic and on the semimicroscopic levels. In the previous one the quartet is considered as a structureless object, while in…
Many finite groups, including all finite non-abelian simple groups, can be symmetrically generated by involutions. In this paper we give an algorithm to symmetrically represent elements of finite groups and to transform symmetrically…
A simple method called symbolic representation for piecewise linear functions on the real line is introduced and used to compute the numbers of periodic points of all periods for some such functions. Since, for every positive integer m, the…
We deduce the periodicity 8 for the type of $Pin$ and $Spin$ representations of the orthogonal groups $O(n)$ from simple combinatorial properties of the finite Clifford groups generated by the gamma matrices. We also include the case of…
While the parameters of atomic nuclei, Z and A, indicate a general structural pattern for the nuclei, their exact masses in their fine differences seem not to exhibit the orderly kind of logical system that systematic and orderly nature…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…