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The existence of the exponential map is one of the primary reasons that Lie algebras are a useful tool for studying Lie groups. The ordinary exponential function of mathematical analysis is a special case of the exponential map when G {\displaystyle G} is the multiplicative group of positive real numbers (whose Lie algebra is the additive group ...
exponential map (Lie theory) from a Lie algebra to a Lie group, More generally, in a manifold with an affine connection, (), where is a geodesic with initial velocity X, is sometimes also called the exponential map. The above two are special cases of this with respect to appropriate affine connections.
However, cartographic propaganda is widely successful because maps are often presented as a miniature model of reality, and it is a rare occurrence that a map is referred to as a distorted model, which sometimes can "lie" and contain items that are completely different from reality. [4]
Interstate 495 (I-495) is an auxiliary Interstate Highway in southeastern New York state. It is jointly maintained by the New York State Department of Transportation (NYSDOT), the New York City Department of Transportation (NYCDOT), MTA Bridges and Tunnels (TBTA), and the Port Authority of New York and New Jersey (PANYNJ).
How to Lie with Maps is a nonfiction book written by Mark Monmonier detailing issues with cartographic representation and targeted at the general public. [1] [2] [3] First published in 1991 by the University of Chicago Press, it explores the various ways in which maps can be manipulated and how these distortions influence the general public's perceptions and understanding of the world. [1]
This glossary of geography terms is a list of definitions of terms and concepts used in geography and related fields, including Earth science, oceanography, cartography, and human geography, as well as those describing spatial dimension, topographical features, natural resources, and the collection, analysis, and visualization of geographic ...
If is a Lie group with Lie algebra , then we have the exponential map from to , written as X ↦ e X , X ∈ g . {\displaystyle X\mapsto e^{X},\quad X\in {\mathfrak {g}}.} If G {\displaystyle G} is a matrix Lie group, the expression e X {\displaystyle e^{X}} can be computed by the usual power series for the exponential.
The light but non-white background color enables the use of white as a map symbol (the county boundary across the center). Also note the central box showing the location of a separate detail inset map. In addition to the map itself, there are various elements that are included in the map layout. The following are common elements of a map layout ...