相关论文: Tetrahedral Units: For Dodecahedral Super-Structur…
A simple cut-and-patch method is presented for the construction and classification for fullerenes belonging to the octahedral point groups, $O$ or $O_h$. In order to satisfy the symmetry requirement of the octahedral group, suitable numbers…
The fundamental principles underlying the arrangement of elements into solid compounds with an enormous variety of crystal structures are still largely unknown. This study presents a general overview of the structure types appearing in an…
Uniqueness theorems are considered for various types of almost periodic objects: functions, measures, distributions, multisets, holomorphic and meromorphic functions.
Density-functional theory based global geometry optimization is used to scrutinize the possibility of using endohedrally-doped hydrogenated Si clusters as building blocks for constructing highly magnetic materials. In contrast to the known…
Previous work done in collaboration with David Brink is reviewed in the light of the recent observation of new charmonium-like resonances which can be interpreted as tetraquarks. In the framework of a schematic quark model the spectrum of…
Given a compact oriented triangulated $3$-manifold we find a non-trivial condition satisfied by certain labelings of the tetrahedra by elements of an arbitrary abelian group which we call angle structures. Smoothness of the manifold is used…
We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in descriptive set theoretic (topological) sense and in measure…
The notions of holomorphic symplectic structures and hypercomplex structures on Courant algebroids are introduced and then proved to be equivalent. These generalize hypercomplex triples and holomorphic symplectic 2-forms on manifolds…
The use of double groupoids and their associated double Lie algebroids and characteristic distributions is proposed for the description and analysis of continuous media that carry two different constitutive or geometric structures. Various…
We locate putative global minima for (C_60)_N clusters modelled by the potential of Pacheco and Prates-Ramalho up to N=105. These minima are based on icosahedral packing up to N=15, but above this size the lowest-energy structures are…
We provide a procedure for generating the irreducible representations of crystallography groups in any dimension. We also furnish a strategy to investigate the topology of the unitary dual of a crystallography group using sequences of…
We demonstrate the construction of several families of flexible polyhedra by extending Bricard octahedra to form larger composite flexible polyhedra. These flexible polyhedra are of genus 0 and 1, have dihedral angles that are non-constant…
The homogenization of a metamaterial made of a collection of scatterers periodically disposed is studied from three different points of view. Specifically tools for multiple scattering theory, functional analysis, differential geometry and…
Recently introduced composition operator for credal sets is an analogy of such operators in probability, possibility, evidence and valuation-based systems theories. It was designed to construct multidimensional models (in the framework of…
We introduce the notion of an ordered face structure. The ordered face structures to many-to-one computads are like positive face structures to positive-to-one computads. This allow us to give an explicit combinatorial description of…
Metal superhydrides, known for their high hydrogen content and polyhedral hydrogen cages, are promising candidates for high-temperature superconductivity. Recent research has emphasized "chemical pre-compression," enabling hydrogen…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
We show that mixtures comprised of multicomponent systems typically are much more structurally complex than the sum of their parts; sometimes, infinitely more complex. We contrast this with the more familiar notion of statistical mixtures,…
The chain of algebraic geometry constructions permits to transfer from the minimal surface with zero instability index, and from the lattice over the ring of cyclotomic integers to the tetra-block helix. The tetra-block is the 7-vertex…
A general construction yielding infinitely many families of $D(m^2)$-triples of triangular numbers is presented. Moreover, each triple obtained from this construction contains the same triangular number $T_n$.