Related papers: Characterization of Pentagons Determined by Two X-…
Let $P$ be a planar $n$-gon with the sidelengths $a_1, \ldots, a_n$ and let us denote by $L=L(P)$ the corresponding planar polygonal linkage. We are concerned with the problem of finding conditions on the sidelengths $a_i$ which guarantee…
The power spectrum of the synchrotron radiation generated by the motion of a two-body charged system in an accelerator is derived in the framework of the Schwinger source theory. The final formula can be used to verify the Lorentz length…
Several characterizations of complex ellipsoids among convex bodies in Cn, in terms of their sections and projections are proved. Characterizing complex symmetry in similar terms is an important tool.
In this paper we study the attenuated $X$-ray transform of 2-tensors supported in strictly convex bounded subsets in the Euclidean plane. We characterize its range and reconstruct all possible 2-tensors yielding identical $X$-ray data. The…
A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combinatorial tilings of the sphere by geometrically congruent…
We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying…
Rutherford backscattering and particle induced x-ray emission have been utilized to precisely characterize targets used in nuclear fission experiments. The method allows for a fast and non destructive determination of target thickness,…
We show that the problem to decide whether two (convex) polytopes, given by their vertex-facet incidences, are combinatorially isomorphic is graph isomorphism complete, even for simple or simplicial polytopes. On the other hand, we give a…
For a number of basic experiments on two-photon intensity correlations it is pointed out that the results, which are usually explained in terms of the formalism of canonical field quantization, can also be explained in terms of quantum wave…
We present detailed calculations of the diffraction pattern of a powder of bundles of C$_{60}$ peapods. The influence of all pertinent structural parameters of the bundles on the diffraction diagram is discussed, which should lead to a…
Probabilities of measurement outcomes of two-particle entangled states give a physically transparent interpretation of the concurrence and of the I-concurrence as entanglement measures. The (I)-concurrence can thus be measured…
A complete classification of all finite bijective set-theoretic solutions $(S,s)$ to the Pentagon Equation is obtained. First, it is shown that every such solution determines a semigroup structure on the set $S$ that is the direct product…
We prove the following generalised empty pentagon theorem: for every integer $\ell \geq 2$, every sufficiently large set of points in the plane contains $\ell$ collinear points or an empty pentagon. As an application, we settle the next…
Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case…
Two qubits is the simplest system where the notions of separable and entangled states and entanglement witnesses first appear. We give a three dimensional geometric description of these notions. This description however carries no…
A fixed set of vertices in the plane may have multiple planar straight-line triangulations in which the degree of each vertex is the same. As such, the degree information does not completely determine the triangulation. We show that even if…
While present vertex technology cannot measure x_s much beyond 20, the Standard Model accomodates significantly larger x_s values. This note presents a method to determine very large x_s with present technology. The determination is based…
In 1995, Marjorie Rice discovered an interesting tiling by using convex pentagons. The authors discovered novel properties of the tilings of convex pentagon which Rice used in the discovery. As a result, many new convex pentagon tilings…
This paper discusses consistent flag bicolorings of maps and maniplexes, in their own right and as generalizations of orientations and pseudo-orientations. Furthermore, a related doubling concept is introduced, and relationships between…
Entangled two-photon spectroscopy is expected to provide advantages compared with classical protocols. It is achieved by coherently controlling the spectral properties of energy-entangled photons. We present here an experimental setup that…