The group of all transformations that preserve some bilinear form, notable examples:
- orthogonal group preserves the inner product
- unitary group preserves a Hermitian form
- Lorentz group preserves the Minkowski inner product
A young Ciro Santilli really liked this game, the way it makes you feel.
Extract certain pages of a PDF:
pdftk input.pdf cat 2-4 output out1.pdf
Course actually means "degree", not just one specific "course":
The course outline is given in a "handbook", a one or more PDF files that contain what people will learn and other practicalities. There is a full list of handbooks at: www.ox.ac.uk/students/academic/guidance/undergraduate/handbooks, but many of them are closed. The system is so closed that even the fucking course list is closed, e.g. all links at: www2.physics.ox.ac.uk/students/undergraduates are closed. Insane.
Canonical example: Euclidean space.
All possible repetitive crystal structures!
219 of them.
Specials sub case of the general linear group when the determinant equals exactly 1.
Of course, "Ciro Santilli" with quotes, since all of those are either taken directly from others, or had been previously formulated by others.
These have almost certainly been transferred to nuclear DNA in the course of evolution.
This isn't completely surprising, since when mitochondria die, their DNA is kind of left in the cell, so it is not hard to imagine how genes end up getting uptaken by the nucleus. This is suggested at Power, Sex, Suicide by Nick Lane (2006) page 196.
A limiting factor appears to be that you can't just past those genes in the nucleus, further mutations are necessary for mitochondrial protein import to work, apparenty some kind of tagging with extra amino acids.
However, you likely don't want to remove all genes from the mitochondria because mitochondria have DNA because they need to be controlled individually.
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