A Turing machine that simulates another Turing machine/input pair that has been encoded as a string.
The concept is fundamental to state several key results in computer science, notably the halting problem.
Yes, Sheldon he has separate American and British English versions of pages!!!
For example, Kross bicycle (2017) had a Schwalbe tyre with markings:When inflated, the tires were about 3.5cm wide as measured with a ruler.
And the Mavic A319 rim had markings:
622x19C
In this:
- ISO (Etrto): 42-622. So:
- 42 is the inner rim width. The actual inflated tire is going to be even wider.
- 622 is the bead seat diameter. The actual inflated tire is going to be even wider.
- imperial: 28 x 1.60
- French: 700x40C:
- meaning of the "C" asked at: bicycles.stackexchange.com/questions/16190/what-does-the-c-in-bicycle-tire-size-mean
Besides being useful in engineering, it was very important historically from a "development of mathematics point of view", e.g. it was the initial motivation for the Fourier series.
Some interesting properties:
- TODO confirm: for a fixed boundary condition that does not depend on time, the solutions always approaches one specific equilibrium function.This is in contrast notably with the wave equation, which can oscillate forever.
- TODO: for a given point, can the temperature go down and then up, or is it always monotonic with time?
- information propagates instantly to infinitely far. Again in contrast to the wave equation, where information propagates at wave speed.
Sample numerical solutions:
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