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Definition. Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means ...
Under Chinese law, the use of geographic information in the People's Republic of China is restricted to entities that have special authorization from the administrative department for surveying and mapping under the State Council. [1] Consequences of the restriction include fines for unauthorized surveys, lack of geotagging information on many ...
A dot distribution map (or a dot density map or simply a dot map) is a type of thematic map that uses a point symbol to visualize the geographic distribution of a large number of related phenomena. Dot maps are a type of unit visualizations that rely on a visual scatter to show spatial patterns, especially variances in density.
A world map is a map of most or all of the surface of Earth. World maps, because of their scale, must deal with the problem of projection. Maps rendered in two dimensions by necessity distort the display of the three-dimensional surface of the Earth. While this is true of any map, these distortions reach extremes in a world map.
t. e. In continuum mechanics, the maximum distortion energy criterion (also von Mises yield criterion [1]) states that yielding of a ductile material begins when the second invariant of deviatoric stress reaches a critical value. [2] It is a part of plasticity theory that mostly applies to ductile materials, such as some metals.
The cylinder is an example of a developable surface. In mathematics, a developable surface (or torse: archaic) is a smooth surface with zero Gaussian curvature. That is, it is a surface that can be flattened onto a plane without distortion (i.e. it can be bent without stretching or compression). Conversely, it is a surface which can be made by ...
Miller projection with 1,000 km indicatrices of distortion. The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of , projected according to Mercator, and then the result is multiplied by to retain scale along the equator. [1] Hence:
The Jahn–Teller effect (JT effect or JTE) is an important mechanism of spontaneous symmetry breaking in molecular and solid-state systems which has far-reaching consequences in different fields, and is responsible for a variety of phenomena in spectroscopy, stereochemistry, crystal chemistry, molecular and solid-state physics, and materials science.
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