Related papers: Construction of fullerenes
Let $R$ be an associative ring with unity $1$ and consider $k\in \mathbb{N}$ such that $1+1+..+1=k$ is invertible. Denote by $\omega$ an arbitrary kth root of unity in $R$ and let $UT^{(k)}_{\infty}(R)$ be the group of upper triangular…
We provide a general method for finding all natural operations on the Hochschild complex of E-algebras, where E is any algebraic structure encoded in a prop with multiplication, as for example the prop of Frobenius, commutative or…
Let $A$ be an artin algebra. The aim of this work is to describe the enlargements of an indecomposable complex in $\mathbf{C}_{n}(\mbox{proj} \,A)$, and to study the irreducible morphisms between them. Precisely, we prove that any…
A topological interlocking assembly consists of rigid blocks together with a fixed frame, such that any subset of blocks is kinematically constrained and therefore cannot be removed from the assembly. In this paper we pursue a modular…
Any endomorphism of a finitely generated free group naturally descends to an injective endomorphism of its stable quotient. In this paper, we prove a geometric incarnation of this phenomenon: namely, that every expanding irreducible train…
The join operad arises from the combinatorial study of the iterated join of simplices. We study a suitable simplicial version of this operad which includes the symmetries given by permutations of the factors of the join. From this…
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
Ouroboros functions have shown some interesting properties when subjected to conventional operations. The aim of this paper is to continue our investigation and prove some additional properties of these functions. Using algebraic methods,…
Collider processes with identified hadrons in the final state are widely studied in view of determining details of the proton structure and of understanding hadronization. Their theory description requires the introduction of fragmentation…
In this paper we use the Recursion Theorem to show the existence of various infinite sequences and sets. Our main result is that there is an increasing sequence e_0, e_1, e_2 .. such that W_{e_n}={e_{n+1}} for every n. Similarly, we prove…
We introduce a general definition of hybrid transforms for constructible functions. These are integral transforms combining Lebesgue integration and Euler calculus. Lebesgue integration gives access to well-studied kernels and to regularity…
We show that every irreducible integral Apollonian packing can be set in the Euclidean space so that all of its tangency spinors and all reduced coordinates and co-curvatures are integral. As a byproduct, we prove that in any integral…
In this paper we perform an explicit diagonalization of Hankel integral operators $ K^{(0)}, K^{(1)}, K^{(2)}, ... $ It turns out that each of these operators has a simple purely absolutely continuous spectrum filling in the interval $…
Let (k(n)) n=1,2,... be a strictly increasing sequence of positive integers . We consider a specific sequence of differential operators Tk(n),{\lambda} , n=1,2,... on the space of entire functions , that depend on the sequence (k(n))…
An $n$-tuple of operators $(V_1,...,V_n)$ acting on a Hilbert space $H$ is said to be isometric if the operator $[V_1\...\ V_n]:H^n\to H$ is an isometry. We prove a decomposition for an isometric tuple of operators that generalizes the…
We recover the holomorphic discrete series representations of $SU(1,n)$ as well as some unitary irreducible representations of $SU(n+1)$ by deformation of a minimal realization of $sl(n+1, {\mathbb C})$.
This paper discusses the question of how to recognize whether an operad is E_n (ie. equivalent to the little n-cubes operad). A construction is given which produces many new examples of E_n operads. This construction is developed in the…
We construct examples of Delone sets of the plane (that is, discrete subsets that are uniformly separated and coarsely dense) that are repetitive (each patch of the set appears in every large-enough ball) though non-rectifiable (i.e. non…
A stacking operation adds a $d$-simplex on top of a facet of a simplicial $d$-polytope while maintaining the convexity of the polytope. A stacked $d$-polytope is a polytope that is obtained from a $d$-simplex and a series of stacking…
We consider the problem of enumerating integer tetrahedra of fixed perimeter (sum of side-lengths) and/or diameter (maximum side-length), up to congruence. As we will see, this problem is considerably more difficult than the corresponding…