Appendix A: Properties of EDS grids In this appendix, we characterize the dispersion of points, the number of points, and the degree of uniformity of the constructed EDS. Also, we discuss the relation of our results to recent mathematical literature. A.1 Dispersion of points in EDS grids We borrow the notion of dispersion from the literature on quasi-Monte Carlo optimization methods; see, for e...

We show that for every quasivariety K of relational structures there is a semilattice S with operators such that the lattice of quasiequational theories of K (the dual of the lattice of sub-quasivarieties of K) is isomorphic to Con(S,+, 0, F). As a consequence, new restrictions on the natural quasi-interior operator on lattices of quasi-equational theories are found. 1. Motivation and terminolo...

The bulk structure of the ?-Al5Fe2 intermetallic compound consists in an ordered framework pentagonal antiprims with composition Al2Fe inside which nearly continuous chains fractionally occupied Al sites exist. At low temperature, ordering these channel atoms can occur, leading to various superstructures. Although Al5Fe2 phase is technological importance being present protective coating for ste...

We present new methods for increasing the magnitude and uniformity of rotation of a Faraday rotator with a large clear aperture . We show theoretically and experimentally that the amount of rotation and the uniformity of rotation across the aperture can be simultaneously increased by introducing a small separation between adjacent, oppositely oriented magnets . Furthermore we show that the unif...

Let X be a smooth projective scheme of dimension d ≥ 1 over the field k, and let C be an indecomposable coherent sheaf on X . Then there is an Auslander-Reiten sequence in the category of quasi-coherent sheaves on X , 0 → (ΣC)⊗ ω −→ B −→ C → 0. Here ΣC is the (d−1)’st syzygy in a minimal injective resolution of C, and ω is the dualizing sheaf of X . 0. Introduction This note shows that Auslande...

We prove that every fragmentable linearly ordered compact space is almost totally disconnected. This combined with a result of Arvanitakis yields that every linearly ordered quasi Radon-Nikodým compact space is Radon-Nikodým, providing a new partial answer to the problem of continuous images of Radon-Nikodým compacta. It is an open problem posed by Namioka [8] whether the class of Radon-Nikodým...

We say that a family of graphs G = {Gn : n ≥ 1} is p-quasi-random, 0 < p < 1, if it shares typical properties of the random graph G(n, p); for a definition, see below. We denote by Q(p) the class of all graphs H for which e(Gn) ≥ (1 + o(1))p ( n 2 ) and the number of not necessarily induced labeled copies of H in Gn is at most (1 + o(1))pn imply that G is p-quasi-random. In this note, we show t...

We show that there exist bivariate proper quasi-copulas that do not induce a doubly stochastic signed measure on [0, 1]. We construct these quasi-copulas from the so-called proper quasitransformation square matrices.