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Valve's logo. Valve is an American video game developer and publisher founded in 1996 by Gabe Newell and Mike Harrington. The company is based in Bellevue, Washington. [1] Valve's first game was Half-Life, a first-person shooter released in 1998. [2] It sold over nine million retail copies.
Aperture Desk Job has been compared Valve's previous tech demos, The Lab and Aperture Hand Lab. [2] [4] The game features the voices of Nate Bargatze as Grady, J. K. Simmons reprising his role as Cave Johnson from Portal 2, and Debra Wilson as the Prison Warden and Announcer. [1] [13] [14] The game was released for free on Steam on March 1 ...
Portal is a 2007 puzzle-platform game developed and published by Valve.It was originally released in a bundle, The Orange Box, for Windows, Xbox 360 and PlayStation 3, and has been since ported to other systems, including Mac OS X, Linux, Android (via Nvidia Shield), and Nintendo Switch.
Portal is a series of first-person puzzle-platform video games developed by Valve.Set in the Half-Life universe, the two main games in the series, Portal (2007) and Portal 2 (2011), center on a woman, Chell, forced to undergo a series of tests within the Aperture Science Enrichment Center by a malicious artificial intelligence, GLaDOS, that controls the facility.
Let :, (,) be a (left) group action of a Lie group on a smooth manifold ; it is called a Lie group action (or smooth action) if the map is differentiable. Equivalently, a Lie group action of G {\displaystyle G} on M {\displaystyle M} consists of a Lie group homomorphism G → D i f f ( M ) {\displaystyle G\to \mathrm {Diff} (M)} .
In the theory of smooth manifolds, a congruence is the set of integral curves defined by a nonvanishing vector field defined on the manifold. Congruences are an important concept in general relativity , and are also important in parts of Riemannian geometry .
In mathematics, particularly topology, an atlas is a concept used to describe a manifold. An atlas consists of individual charts that, roughly speaking, describe individual regions of the manifold. In general, the notion of atlas underlies the formal definition of a manifold and related structures such as vector bundles and other fiber bundles.
Recall that a topological manifold is a topological space which is locally homeomorphic to . Differentiable manifolds (also called smooth manifolds) generalize the notion of smoothness on in the following sense: a differentiable manifold is a topological manifold with a differentiable atlas, i.e. a collection of maps from open subsets of to the manifold which are used to "pull back" the ...