相关论文: Tetrahedral Units: For Dodecahedral Super-Structur…
The article studies power complexes and generalized power complexes, and investigates the algebraic structure of their automorphism groups. The combinatorial incidence structures involved are cube-like, in the sense that they have many…
We propose a predictive building-up of tetrahedral molecules, based on a previously derived chirality index, which characterizes a tetrahedral molecule, with n chiral centers, as achiral, diastereoisomer, or enantiomer as a function of the…
We show that exchangeable structures such as Polya urn model and Chinese restaurant process can be constructed from sets with a real number of elements. From this construction, the exchangeability of these structures becomes obvious and the…
Mechanism - collections of rigid elements coupled by perfect hinges which exhibit a zero-energy motion -- motivate the design of a variety of mechanical metamaterials. We significantly enlarge this design space by considering…
The aim of this article is to show the existence, and also give an explicit construction, of infinite sets of orthogonal exponentials for certain families of convex polytopes which include simple-rational polytopes and also non simple…
Real spherical designs and real and complex projective designs have been shown by Delsarte, Goethals, and Seidel to give rise to association schemes when the strength of the design is high compared to its degree as a code. In contrast,…
Pentagon is one of the most beautiful geometric structures in nature, but it is rarely seen simply because five-fold symmetry is mathematically forbidden in a 2D or 3D periodic lattices. Fortunately, pentagon as a structural element is…
The paper puts into discussion the concept of universality, in particular for structures not of the power of Turing computability. The question arises if for such structures a universal structure of the same kind exists or not. For that the…
A product of cochains in a polyhedral complex is constructed. The multiplication algorithm depends on the choice of a parameter. The parameter is a linear functional on the ambient space. Cocycles form a subring of the ring of cochains,…
The design of complex materials and the formation of specific patterns often arise from the properties of the individual building blocks. In this respect, colloidal systems offer a unique opportunity because nowadays they can be synthesized…
There is only one type of tilings of the sphere by $12$ congruent pentagons. These tilings are isohedral.
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…
The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as finite subdivision rules and iterated function systems. In this…
The recent discoveries of many metal superhydrides provide a new route to room-temperature superconductors. However, their stability and structure trends and the large chemical driving force needed to dissociate H2 molecules and form H…
The newly observed $\Theta^+$ resonance is believed to be a pentaquark with the constituent quarks $uudd\bar s$. There are a few options for the constituent quark structure. Some advocate diquark-diquark-antiquark $(ud)$-$(ud)$-$\bar s$…
In this work, we generalize the integer enumeration basis. We also construct bijections between the elements of special sets and the elements of some groups, and treat the special case of the hyperoctohedral groups. Then, we find a code…
In the paper we give a complete classification of schemes of abstract perspectives between two tetrahedrons such that intersecting edges corespond under this perspective to intersecting edges.
We consider different structures, which can be obtained by polymerization of aromatic organic molecules under high pressures. These 2D and 3D covalently bonded organic polymers and their functionalization can pave the way to production of…
Commutative semirings with divisible additive semigroup are studied. We show that an additively divisible commutative semiring is idempotent, provided that it is finitely generated and torsion. In case that a one-generated additively…
Maximally embedding dimension (MED) numerical semigroups are a wide and interesting family, with some remarkable algebraic and combinatorial properties. Associated to any numerical semigroup one can construct a MED closure, as it is well…