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Elementary mapping of disease occurrences in space and time simultaneously revealed the geographic extent of spread throughout the territory.
Pixel-based EDX elementary mapping highlighted the distribution of Se and Cd (Additional file 2: Figure S2B and D, respectively), which exactly corresponded to the ultrastructural shape of QDs (Additional file 2: Figure S2C).
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With a pair of binoculars and some elementary map skills, it's hard to miss.
Mary, a nondriver, referred to herself as the navigator, although her sense of direction and her elementary map reading were no better than mine.
The key techniques used also relate to closures of joint similarity orbits of matrices and elementary maps on B(H).
Thus for a semigroup G which is finitely generated by such elementary maps, we get (J(G)={0}).
We say that e is an elementary embedding of A into B if e is an elementary map and its domain is the whole domain of A. As the name implies, elementary embeddings are always embeddings.
We say that (X,<) is an indiscernible sequence in A if for every natural number n, and all elements a1,…,an,b 1,…,b n of A such that a1 < … < an and b1 < … < bn, the map taking each ai to the corresponding bi is an elementary map.
Such maps are built with combinations of sets of elementary self-maps which can be expansive or non-expansive and the last ones can be contractive (including the case of strict contractions).
The composite self-map generating the trajectory solution sequence from initial conditions is defined with sets of elementary self-maps being associated with distinct active parameterizations which are switched through time by switching rules which guarantee the fulfilment of the suitable properties.
Both constructions still lead to matroids if X is a subset of edges of G. Relation of the first construction to elementary strong maps (if G is planar) and representability properties of the matroids arising from these constructions are also presented.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com