Related papers: Viruses and Fullerenes - Symmetry as a Common Thre…
We propose and study theoretically a novel family of cage molecules, the porous carbon nitride fullerenes (PCNFs), which can be considered the zero-dimensional counterparts of the two-dimensional porous graphitic carbon nitrides, in…
The reactions of fullerene C60 with atomic fluorine have been studied by unrestricted broken spin-symmetry Hartree-Fock (UBS HF) approach implemented in semiempirical codes based on AM1 technique. The calculations were focused on a…
Inside the discipline of graph theory exists an extension known as the hypergraph. This generalization of graphs includes vertices along with hyperedges consisting of collections of two or more vertices. One well-studied application of this…
We develop a rigorous, equation-free category-theoretic foundation for fungal organisation. A fungal organism is formalised as a functor from a category $\Env$ of structured environmental states and admissible transformations to a category…
The algebraic or ring structure of anyons, called the fusion rule, is one of the most fundamental research interests in contemporary studies on topological orders (TOs) and the corresponding conformal field theories (CFTs). Recently, the…
Using density-functional theory calculations, we investigate the addition energy (AE) of quantum dots formed of fullerenes or closed single-wall carbon nanotubes. We focus on the connection between symmetry and oscillations in the AE…
Small cationic fullerene fragments, produced by electron impact ionization of C60, were mass-selected and accumulated in cryogenic Ne matrixes. Optical absorption spectroscopy of these fragments with up to 18 carbon atoms revealed linear…
The full symmetry groups for all single- and multi-wall carbon nanotubes are found. As for the single-wall tubes, the symmetries form nonabelian nonsymorphic line groups, enlarging the groups reported in literature. In the multi-wall case,…
Odd electrons of benzenoid units and correlation of these electrons having different spins are the main concepts of the molecular theory of graphene. In contrast to the theory of aromaticity, the molecular theory is based on the fact that…
We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…
A very useful result concerning flatness in Algebraic Geometry is EGA's ``fiber'' criterion. We propose similar fiber criteria to verify flatness of a module while avoiding ``finiteness'' assumptions. Motivated by a Tannakian viewpoint…
In a seminal paper Caspar and Klug established a theory that provides a family of polyhedra as blueprints for the structural organisation of viral capsids. In particular, they encode the locations of the proteins in the shells that…
Recently, the NA61/SHINE collaboration at the CERN SPS reported evidence of isospin-symmetry violation in high-energy nuclear collisions [Nature Commun. 16, 2849 (2025)]. The effect was observed in the relative yields of charged and neutral…
We establish a bijective correspondence between affine connections and a class of semi-holonomic jets of local diffeomorphisms of the underlying manifold called symmetry jets in the text. The symmetry jet corresponding to a torsion free…
A vital constituent of a virus is its protein shell, called the viral capsid, that encapsulates and hence provides protection for the viral genome. Assembly models are developed for viral capsids built from protein building blocks that can…
Viruses are biological nanosystems with a capsid of protein-made capsomer units that encloses and protects the genetic material responsible for their replication. Here we show how the geometrical constraints of the capsomer-capsomer…
In the present paper we investigate the mechanics of systems of affinely-rigid bodies, i.e., bodies rigid in the sense of affine geometry. Certain physical applications are possible in modelling of molecular crystals, granular media, and…
We develop category-theoretic framework for universal homogeneous objects, with some applications in the theory of Banach spaces, linear orderings, and in topology of compact spaces.
Fullerene cages allow the confinement of single molecules and the construction of molecular assemblies whose properties strongly deviate from those of free species. In this work, we employ the density-matrix renormalization group method to…
We give an explicit combinatorial description of the deformation theory of the Abelian category of (quasi)coherent sheaves on any separated Noetherian scheme $X$ via the deformation theory of path algebras of quivers with relations, by…