Related papers: An Alternate Graphical Representation of Periodic …
A representation of an object in a category is an abelian group in the corresponding comma category. In this paper we derive the formulas describing linear representations of objects in the category of formal loops and apply them to obtain…
All leptons, quarks, and gauge bosons can be placed in the periodic table of elementary particles. As the periodic table of elements derived from atomic orbital, the periodic table of elementary particles is derived from the two sets of…
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…
We explain how following the representation of 3D crystallographic space groups in geometric algebra it is further possible to similarly represent the 162 socalled subperiodic groups of crystallography in geometric algebra. We construct 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…
The periodic changes in physical and chemical properties of the chemical elements is caused by the periodic change of the ionization energies. The ionization energy of each element is constant and this manifests itself in the periodic…
All leptons, quarks, and gauge bosons can be placed in the periodic table of elementary particles. The periodic table is derived from dualities of string theory and a Kaluza-Klein substructure for the six extra spatial dimensions. As a…
A new graph-based order parameter is introduced for the characterization of atomistic structures. The order parameter is universal to any material/chemical system, and is transferable to all structural geometries. Three sets of data are…
We suggest a geometrical framework to discuss periodic layered structures in the unit disk. The band gaps appear when the point representing the system approaches the unit circle. We show that the trace of the matrix describing the basic…
The group theoretical description of the periodic system of elements in the framework of the Rumer-Fet model is considered. We introduce the concept of a single quantum system, the generating core of which is an abstract $C^\ast$-algebra.…
We propose a computationally lean, two-stage approach that reliably predicts self-assembly behavior of complex charged molecules on a metallic surfaces under electrochemical conditions. Stage one uses ab initio simulations to provide…
In this article, we provide a pedagogical review of the theory of topological quantum chemistry and topological crystalline insulators. We begin with an overview of the properties of crystal symmetry groups in position and momentum space.…
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,…
Topological phases of matter$\unicode{x2013}$comprising both insulators and semimetals$\unicode{x2013}$offer great potential for quantum applications, but identifying new candidates remains challenging due to expensive first-principles…
Carbon is one of the most intriguing elements in the Periodic Table. It forms many allotropes, some being known from ancient times (diamond and graphite) and some discovered ten to twenty years ago (fullerenes, nanotubes). Quite…
System design is often taught through domain-specific solutions specific to particular domains, such as databases, operating systems, or computer architecture, each with its own methods and vocabulary. While this diversity is a strength, it…
Using the Planck scale as an absolute bound of half-life, we give a quick estimate, in the manner of Feynman's fine-structure method, of the highest possible atomic number. We find, upon simple extrapolation, that element 168 would…
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…
We study periodic representations in number systems with an algebraic base $\beta$ (not a rational integer). We show that if $\beta$ has no Galois conjugate on the unit circle, then there exists a finite integer alphabet $\mathcal A$ such…
This paper proposes spatial periodic table developed based on classic electron shell structure model. The periodic table determines location and chemical properties of superheavy elements. 14 new long-living superheavy elements found by…