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formed by a chart and such a coordinate system is called a local coordinate system, coordinate chart, coordinate patch, coordinate map, or local frame. An...

automatic software updates via the Internet. Computer programs can often coordinate patches to update a target program. Automation simplifies the end-user's task –...

having y-coordinate zero in this patch). In AdS space time is periodic, and the universal cover has non-periodic time. The coordinate patch above covers...

In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be...

coordinate patches: subsets of the manifold which can be mapped into n-dimensional Euclidean space. See Manifold, Differentiable manifold, Coordinate...

other words, around almost every point, there is a coordinate patch on which a two-dimensional coordinate system is defined. For example, the surface of the...

other words, around almost every point, there is a coordinate patch on which a two-dimensional coordinate system is defined. For example, the surface of the...

compact support in a coordinate patch O ⊂ Ω ¯ {\displaystyle O\subset {\overline {\Omega }}} . First consider the case where the patch is disjoint from ∂...

measure zero is a set of measure zero, and the property of a subset of a coordinate patch having zero measure is invariant under diffeomorphism. There are many...

the integral of a function whose support is contained in a single coordinate patch of the manifold; then one uses a partition of unity to define the integral...

and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of...

the frame f = (X1, ..., Xn) at every point of the coordinate patch. If yi is a different coordinate system and Y 1 = ∂ ∂ y 1 , … , Y n = ∂ ∂ y n , {\displaystyle...

patches for their software products. It is widely referred to in this way by the industry. Microsoft formalized Patch Tuesday in October 2003. Patch Tuesday...

their corresponding projective spaces, and intersecting with an affine coordinate patch of P ( V ) {\displaystyle \mathbb {P} (V)} , we obtain an open subset...

equivalence of first order in terms of derivatives in an arbitrary coordinate patch. Then the differential of f at p is the set of all functions differentially...

affine coordinate system for CPn in the coordinate patch U 0 = { Z 0 ≠ 0 } {\displaystyle U_{0}=\{Z_{0}\neq 0\}} . One can develop an affine coordinate system...

other words, around almost every point, there is a coordinate patch on which a two-dimensional coordinate system is defined. For example, the surface of the...

e 0 . {\displaystyle X_{\gamma (0)}=e_{0}.} Note that in any given coordinate patch, (1) defines an ordinary differential equation, with the initial condition...

{\displaystyle \nu :[S:T]\mapsto [S^{3}:S^{2}T:ST^{2}:T^{3}].} In one coordinate patch of projective space, the map is simply the moment curve ν : x ↦ ( x...

bounding box of its control points in any given Cartesian coordinate system. The points in the patch corresponding to the corners of the deformed unit square...