For some non-linear function, we can use its first Jacobian to create a linear system. Then, we can use that system to write the first order Taylor:

\begin{equation} y’ = \nabla F(crit)y \end{equation}

where \(crit\) are critical points.

Phase Portrait stability

• if all \(Re[\lambda] < 0\) of \(\qty(\nabla F)(p)\) then \(p\) is considered stable—that is, points initially near \(p\) will exponentially approach \(p\)

• if at least one \(Re[\lambda] > 0\) of \(\qty(\nabla F)(p)\) then \(p\) is considered unstable—that is, points initially near \(p\) will go somewhere else

linked files is a linked list: in every block, it stores the location of the next block; we don’t store files contiguously. We simply store a part of the file in a block, and a pointer to wherever the next block where the file is located is.

this solves the contiguous allocation’s fragmentation problem.

problems

• massive seek time to get all the blocks for a given file: data scattered
• random access of files (“find the middle”) is hard: can’t easily jump to an arbitrary location; we had to read the file from the start

https://www.reddit.com/r/emacs/comments/c22ff1/gtk_4_support_for_key_themes_does_not_affect/

https://planet.kde.org/david-edmundson-2023-03-22-fixing-wayland-xwayland-screen-casting/

• Using P2P to trade stocks in a darkpool
• Sweep across LiquidNet and send normall if not needed