Homometric point sets and inverse problems
نویسندگان
چکیده
منابع مشابه
Homometric Point Sets and Inverse Problems
The inverse problem of diffraction theory in essence amounts to the reconstruction of the atomic positions of a solid from its diffraction image. From a mathematical perspective, this is a notoriously difficult problem, even in the idealised situation of perfect diffraction from an infinite structure. Here, the problem is analysed via the autocorrelation measure of the underlying point set, whe...
متن کاملOn homometric sets in graphs
For a vertex set S ⊆ V (G) in a graph G, the distance multiset, D(S), is the multiset of pairwise distances between vertices of S in G. Two vertex sets are called homometric if their distance multisets are identical. For a graph G, the largest integer h, such that there are two disjoint homometric sets of order h in G, is denoted by h(G). We slightly improve the general bound on this parameter ...
متن کاملHomometric model sets and window covariograms
Two Delone sets are called homometric when they share the same autocorrelation or Patterson measure. A model set Λ within a given cut and project scheme is a Delone set that is defined through a window W in internal space. The autocorrelation measure of Λ is a pure point measure whose coefficients can be calculated via the so-called covariogram of W . Two windows with the same covariogram thus ...
متن کاملglobal results on some nonlinear partial differential equations for direct and inverse problems
در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Optimal change-point estimation in inverse problems
We develop a method of estimating change{points of a function in the case of indirect noisy observations. As two paradigmatic problems we consider de-convolution and errors-in-variables regression. We estimate the scalar products of our indirectly observed function with appropriate test functions, which are shifted over the interval of interest. An estimator of the change point is obtained by t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Zeitschrift für Kristallographie
سال: 2008
ISSN: 0044-2968
DOI: 10.1524/zkri.2008.1043