... compact1
A locally compact group is always tacitly assumed to be a Hausdorff space. 
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... groups2
We assume that $G(\mathbb R)$ is a so-called split form. Without this assumption the formulation is more complicated. 
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... ``coupled''3
There is confusion here with the use of the word coupling by probabilists. 
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... (Pickard).4
These models are also popular in crystallography. 
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... vertical5
This used to be very realistic, but in modern oil recovery wells can be made at different angles. 
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