Diffraction of weighted lattice subsets
نویسنده
چکیده
A Dirac comb of point measures in Euclidean space with bounded complex weights that is supported on a lattice Γ inherits certain general properties from the lattice structure. In particular, its autocorrelation admits a factorization into a continuous function and the uniform lattice Dirac comb, and its diffraction measure is periodic, with the dual lattice Γ ∗ as lattice of periods. This statement remains true in the setting of a locally compact Abelian group that is also σ-compact.
منابع مشابه
representation theorems of $L-$subsets and $L-$families on complete residuated lattice
In this paper, our purpose is twofold. Firstly, the tensor andresiduum operations on $L-$nested systems are introduced under thecondition of complete residuated lattice. Then we show that$L-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. Thus the new representation theorem of$L-$subsets on complete re...
متن کاملMODULARITY OF AJMAL FOR THE LATTICES OF FUZZY IDEALS OF A RING
In this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring R. These fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. Using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...
متن کاملON THE SYSTEM OF LEVEL-ELEMENTS INDUCED BY AN L-SUBSET
This paper focuses on the relationship between an $L$-subset and the system of level-elements induced by it, where the underlying lattice $L$ is a complete residuated lattice and the domain set of $L$-subset is an $L$-partially ordered set $(X,P)$. Firstly, we obtain the sufficient and necessary condition that an $L$-subset is represented by its system of level-elements. Then, a new representat...
متن کاملX-ray diffraction peak profile analysis of maraged Fe-Ni-Mn steels
X-ray diffraction peak profile analysis was used to identify changes in the lattice distortions during isothermal aging of Fe-10Ni-7Mn (wt. %) maraging steel. Integral peak breadths were analyzed using classical Williamson-Hall equation taking the elastic anisotropy into account. It was found that substantial lattice distortions rise during precipitation hardening which depend strongly on the s...
متن کامل