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The English word fomite, which has been in use since 1859, is a back-formation from the plural fomites (originally borrowed from the Latin plural fōmĭtēs [ˈfoːmɪteːs] of fōmĕs). [ 29 ] [ 30 ] Over time, the English-language pronunciation of the plural fomites changed from / ˈ f oʊ m ɪ t iː z / ) to / ˈ f oʊ m aɪ t s / , which ...
The Vector Map (VMAP), also called Vector Smart Map, is a vector-based collection of geographic information system (GIS) data about Earth at various levels of detail. Level 0 (low resolution) coverage is global and entirely in the public domain. Level 1 (global coverage at medium resolution) is only partly in the public domain.
A local isometry from one (pseudo-)Riemannian manifold to another is a map which pulls back the metric tensor on the second manifold to the metric tensor on the first. When such a map is also a diffeomorphism , such a map is called an isometry (or isometric isomorphism ), and provides a notion of isomorphism ("sameness") in the category Rm of ...
Vector tiles, tiled vectors or vectiles [1] are packets of geographic data, packaged into pre-defined roughly-square shaped "tiles" for transfer over the web. This is an emerging method for delivering styled web maps, combining certain benefits of pre-rendered raster map tiles with vector map data.
Nevertheless, one can make this difficulty precise, using the notion of a vector field along a map. A section of φ ∗ TN over M is called a vector field along φ . For example, if M is a submanifold of N and φ is the inclusion, then a vector field along φ is just a section of the tangent bundle of N along M ; in particular, a vector field ...
The transpose is a map ′ ′ and is defined for linear maps between any vector spaces and , without requiring any additional structure. The Hermitian adjoint maps Y → X {\displaystyle Y\to X} and is only defined for linear maps between Hilbert spaces, as it is defined in terms of the inner product on the Hilbert space.
T is one-to-one as a map of sets. ker T = {0 V} dim(ker T) = 0; T is monic or left-cancellable, which is to say, for any vector space U and any pair of linear maps R: U → V and S: U → V, the equation TR = TS implies R = S. T is left-invertible, which is to say there exists a linear map S: W → V such that ST is the identity map on V.
Vector fields are commonly used to create patterns in computer graphics. Here: abstract composition of curves following a vector field generated with OpenSimplex noise. A vector field for the movement of air on Earth will associate for every point on the surface of the Earth a vector with the wind speed and direction for that point.