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Testing whether a differentiable map is a diffeomorphism can be made locally under some mild restrictions. This is the Hadamard-Caccioppoli theorem: [1] If , are connected open subsets of such that is simply connected, a differentiable map : is a diffeomorphism if it is proper and if the differential: is bijective (and hence a linear isomorphism) at each point in .
A fork of CraftBukkit, called Spigot which was backward compatible with plugins started to be developed. In 2012, Spigot released a server software, called BungeeCord, made to link many servers together via a proxy "linking" server. BungeeCord had a separate plugin API from Spigot where Spigot plugins could work side by side.
An infinitesimal Lie algebra action () is injective if and only if the corresponding global Lie group action is free. This follows from the fact that the kernel of d e σ x : g → T x M {\displaystyle \mathrm {d} _{e}\sigma _{x}\colon {\mathfrak {g}}\to T_{x}M} is the Lie algebra g x ⊆ g {\displaystyle {\mathfrak {g}}_{x}\subseteq {\mathfrak ...
While many fast-food joints claim they serve “real” chicken, some still rely on antibiotic-laden, factory-farmed mystery meat. Here are 7 chains that actually use high-quality, real chicken.
Leonardo DiCaprio and Kate Winslet still remain close pals, even nearly 30 years after Titanic!. On Tuesday, Nov. 19, DiCaprio, who celebrated his 50th birthday on Nov. 11, posed with Winslet, 49 ...
The NBA has upgraded a foul committed by Draymond Green on Zach Edey to a Flagrant 1 after reviewing the play.. The foul in question occurred midway through the third quarter of Friday's 123–118 ...
The 9K111 Fagot (Russian: Фагот; "bassoon") is a second-generation tube-launched semi-automatic command to line of sight (SACLOS) wire-guided anti-tank missile system of the Soviet Union for use from ground or vehicle mounts.
Performed by Frank Oz (1976–2000), Eric Jacobson (2001–present); A temperamental diva pig who is the Muppets' break-out and "authentic superstar". [1]: 28 Until 2015, she was the romantic significant other of Kermit.