A systematic study of the crystal structure of a layered iron oxypnictide LaFeAsO1-xHx as a function of pressure was performed using synchrotron X-ray diffraction. This compound exhibits a unique phase diagram of two superconducting phases and two parent phases. We established that the As-Fe-As angle of the FeAs4 tetrahedron widens on the application of pressure due to the interspace between th...

In this research, we aim to clarify the relationship between the structural distortion due to doping and the superconductivity existence in the FeAs4 structure. For this, we have prepared polycrystalline of NdFeAsO0.8F0.2, NdFeAs0.95Sb0.05O0.8F0.2 and Nd0.99Ca0.01FeAsO0.8F0.2 samples by one-step solid state reaction method. The structural and electrical properties of the samples were characteri...

Ca14FeAs11 is the first iron-containing representative of Ca14AlSb11 structure type and compound with isolated FeAs4 tetrahedra. It can be regarded as a salt-like containing [FeAs4]9− tetrahedra, linear [As3]7− units, As3− anions Ca2+ cations thus borderline between binary Fe−As intermetallics calcium arsenides. obtained by two-step high-temperature reaction, in which preformed FeAs alloy heate...

Three-dimensional Delaunay triangulations are the most common form of three-dimensional triangulations known, but they are not very suitable for tetrahedral nite element meshes because they tend to contain poorly-shaped sliver tetrahedra. In this paper, we present an algorithm for constructing improved-quality triangulations with respect to a tetrahedron shape measure. This algorithm uses combi...

We present an algorithm to test two tetrahedra for overlap. The algorithm is based on a dimension reduction technique that allows to apply the Separating Axis Theorem avoiding part of the computation needed to perform the Separating Axis Test. Source code is available online.

In this paper we prove that the surface of the regular truncated tetrahedron can be triangulated into 10 non-obtuse geodesic triangles, and also into 12 acute geodesic triangles. Furthermore, we show that both triangulations have minimal size.

We compute the asymptotical growth rate of a large family of Uq.sl2/ 6j –symbols and we interpret our results in geometric terms by relating them to volumes of hyperbolic truncated tetrahedra. We address a question which is strictly related with S Gukov’s generalized volume conjecture and deals with the case of hyperbolic links in connected sums of S S . We answer this question for the infinite...

Extending a similar result about triangles, we show that each Heronian tetrahedron may be positioned with integer coordinates. More generally, we show the following: if an integral distance set in R can be positioned with rational coordinates, then it can in fact be positioned with integer coordinates. The proof, which uses the arithmetic of quaternions, is tantamount to an algorithm.

We present a new characterisation of Goursat categories in terms of special kind of pushouts, that we call Goursat pushouts. This allows one to prove that, for a regular category, the Goursat property is actually equivalent to the validity of the denormalised 3-by-3 Lemma. Goursat pushouts are also useful to clarify, from a categorical perspective, the existence of the quaternary operations cha...