相关论文: Structure factor for decorated Penrose tiling
A relaxed version of Gummelt's covering rules for the aperiodic decagon is considered, which produces certain random-tiling-type structures. These structures are precisely characterized, along with their relationships to various other…
Penrose tilings are the most famous aperiodic tilings, and they have been studied extensively. In particular, patterns composed with hexagons (H), boats (B) and stars (S) were soon exhibited and many physicists published on what they later…
We consider hierarchical structures such as Fibonacci sequences and Penrose tilings, and examine the consequences of different choices for the definition of isomorphism. In particular we discuss the role such a choice plays with regard to…
Tilings of a quadriculated annulus A are counted according to volume (in the formal variable q) and flux (in p). We consider algebraic properties of the resulting generating function Phi_A(p,q). For q = -1, the non-zero roots in p must be…
We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and…
The Fourier transform of the indicator function of arbitrary polygons and polyhedra is computed for complex wavevectors. Using the divergence theorem and Stokes' theorem, closed expressions are obtained. Apparent singularities, all…
Consider a regression or some regression-type model for a certain response variable where the linear predictor includes an ordered factor among the explanatory variables. The inclusion of a factor of this type can take place is a few…
For a large class of tilings, including those which are obtained by the generalized dual method from regular grids, it is shown that their algebra is stably isomorphic to a crossed product with $\Z^d$. Penrose tilings belong to this class.…
We investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric interpretations in the projective space over the split…
Factorization structures occur in toric differential and discrete geometry, and can be viewed in multiple ways, e.g., as objects determining substantial classes of explicit toric Sasaki and K\"ahler geometries, as special coordinates on…
The interior structure of arbitrary sets of quaternion units is analyzed using general methods of the theory of matrices. It is shown that the units are composed of quadratic combinations of fundamental objects having a dual mathematical…
We introduce the notion of quantum duplicates of an (associative, unital) algebra, motivated by the problem of constructing toy-models for quantizations of certain configuration spaces in quantum mechanics. The proposed (algebraic) model…
Unreplicated two-level factorial designs are often used in screening experiments to determine which factors out of a large plausible set are active. A theorem regarding the generalized word count pattern is stated and proved for…
Every isometry of a finite dimensional euclidean space is a product of reflections and the minimum length of a reflection factorization defines a metric on its full isometry group. In this article we identify the structure of intervals in…
Hyperuniformity is the study of stationary point processes with a sub-Poisson variance in a large window. In other words, counting the points of a hyperuniform point process that fall in a given large region yields a small-variance Monte…
We review recent results on hadron form factors and nucleon generalized parton distibutions obtained with dynamical lattice QCD simulations. We discuss lattice artifacts and open questions, and present the connection of lattice results to…
We examine the use of phenomenological form factors in tree level amplitudes for meson photoproduction. Two common recipes are shown to be fundamentally incorrect. An alternate form consistent with gauge invariance and crossing symmetry is…
The algebraic theory of third-order tensors under the $t$-product is naturally formulated over the complex field via Fourier block diagonalization. However, many applications require real-valued representations. In this paper, we…
Many signals in Nature, technology and experiment have a multi-component structure. By spectral decomposition and projection on the eigenvectors of a family of unitary operators, a robust method is developed to decompose a signals in its…
We present general techniques for constructing functorial factorizations appropriate for model structures that are not known to be cofibrantly generated. Our methods use "algebraic" characterizations of fibrations to produce factorizations…