相关论文: Pure point diffraction and cut and project schemes…

Quasiperiodic arrangements of the constitutive materials in composites result in effective properties with very unusual electromagnetic and elastic properties. The paper discusses the cut-and-projection method that is used to characterize…

We discuss how the diffraction theory of a single translation bounded measure or a family of such measures can be understood within the framework of unitary group representations. This allows us to prove an orthogonality feature of measures…

We define spherical diffraction measures for a wide class of weighted point sets in commutative spaces, i.e. proper homogeneous spaces associated with Gelfand pairs. In the case of the hyperbolic plane we can interpret the spherical…

The logarithmic slope of the diffractive structure function is a potential observable scanning the hard and soft contributions in diffraction, allowing to disentangle the QCD dynamics. We report our calculations concerning this quantity, in…

We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is…

This paper investigates the properties of trajectories in harmonic oscillator systems equipped with a point, absolutely continuous, or singular measure. As demonstrated in [30], infinite-dimensional linear flows of countable oscillator…

We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of "chaoticity". The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the…

We study projective functions. We prove that projective functions generalise lower and upper-semianalytic ones while being stable by composition and difference. We show that the class of projective functions is closed under sums,…

In this paper, we prove that given a cut-and-project scheme $(G, H, \mathcal{L})$ and a compact window $W \subseteq H$, the natural projection gives a bijection between the Fourier transformable measures on $G \times H$ supported inside the…

A homomorphism from a completely metrizable topological group into a free product of groups whose image is not contained in a factor of the free product is shown to be continuous with respect to the discrete topology on the range. In…

In this paper, we study the number of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms defined on $3-$torus with compact center leaves. Assuming the existence of a periodic leaf with Morse-Smale dynamics we prove…

The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…

We study continuous, equality knapsack problems with uniform separable, non-convex objective functions that are continuous, antisymmetric about a point, and have concave and convex regions. For example, this model captures a simple…

The classic middle-thirds Cantor set leads to a singular continuous measure via a distribution function that is know as the Devil's staircase. The support of the Cantor measure is a set of zero Lebesgue measure. Here, we discuss a class of…

Consider a topological dynamical system where the group is abelian and the topologies are locally compact and second-countable. Given an invariant measure for this system, we show that if its dynamical spectrum is contained in some Borel…

This paper studies the measure-preserving homeomorphisms on compact groups and proposes new methods for constructing measure-preserving homeomorphisms on direct products of compact groups and non-commutative compact groups. On the direct…

We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are…

We give a heuristic method to solve explicitly for an absolutely continuous invariant measure for a piecewise differentiable, expanding map of a compact subset $I$ of Euclidean space $R^d$. The method consists of constructing a skew product…

In a recent paper, Lenz and Moody (arXiv:1111.3617) presented a method for constructing families of real solutions to the inverse problem for a given pure point diffraction measure. Applying their technique and discussing some possible…

This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, is a…