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Formally, a rational map: between two varieties is an equivalence class of pairs (,) in which is a morphism of varieties from a non-empty open set to , and two such pairs (,) and (′ ′, ′) are considered equivalent if and ′ ′ coincide on the intersection ′ (this is, in particular, vacuously true if the intersection is empty, but since is assumed irreducible, this is impossible).
Concept mapping and mind mapping software is used to create diagrams of relationships between concepts, ideas, or other pieces of information. It has been suggested that the mind mapping technique can improve learning and study efficiency up to 15% over conventional note-taking. [1]
An introduction explaining the style objectives and the most convenient way to create a such map. A color summary table with two (up-to-date) map examples. The naming convention for upload, and other advice like the scale or the legend. An up-to-date SVG template. Further details on history, limits, and possible expansions. A gallery of examples.
A concept map or conceptual diagram is a diagram that depicts suggested relationships between concepts. [1] Concept maps may be used by instructional designers , engineers , technical writers , and others to organize and structure knowledge .
For example, Spec k[x] and Spec k(x) and have the same function field (namely, k(x)) but there is no rational map from the former to the latter. However, it is true that any inclusion of function fields of algebraic varieties induces a dominant rational map (see morphism of algebraic varieties#Properties .)
For example, the conic x 2 + y 2 + z 2 = 0 in P 2 over the real numbers R is uniruled but not ruled. (The associated curve over the complex numbers C is isomorphic to P 1 and hence is ruled.) In the positive direction, every uniruled variety of dimension at most 2 over an algebraically closed field of characteristic zero is ruled.
Map Time domain Space domain Number of space dimensions Number of parameters Also known as 3-cells CNN system: continuous: real: 3: 2D Lorenz system [1] discrete: real: 2: 1: Euler method approximation to (non-chaotic) ODE. 2D Rational chaotic map [2] discrete: rational: 2: 2: ACT chaotic attractor [3] continuous: real: 3: Aizawa chaotic ...
An example is given by the map from the affine plane A 2 to the conical singularity x 2 + y 2 = z 2 taking (X,Y) to (2XY, X 2 − Y 2, X 2 + Y 2). The XY -plane is already nonsingular so should not be changed by resolution, and any resolution of the conical singularity factorizes through the minimal resolution given by blowing up the singular ...