www.youtube.com/watch?v=PbuiIhr0LVA 7 Different Types of Plastic and Their Uses by Orange Plastics Academy (2018) Does not mention packaging foams.
Sometimes systems of Diophantine equations are considered.
Problems generally involve finding integer solutions to the equations, notably determining if any solution exists, and if infinitely solutions exist.
The general problem is known to be undecidable: Hilbert's tenth problem.
The Pythagorean triples, and its generalization Fermat's last theorem, are the quintessential examples.
Ciro Santilli's eulogy: effortless effort
This is a term "invented" by Ciro Santilli to refer to quantum compilers that are able to convert non-specifically-quantum (functional, since there is no state in quantum software) programs into quantum circuit.
The term is made by adding "quantum" to the more "classical" concept of "high-level synthesis", which refers to software that converts an imperative program into register transfer level hardware, typicially for FPGA applications.
Metric created by IonQ.
In 2024 they started making tumblers illegal:
So why privacy coins weren't fully forbidden then?
Quantum field theory lecture by Tobias Osborne (2017) mentions that quantization is a guess.
For the discovery of green fluorescent protein.
When the process changes,
cr3
change to point to the page table of the new current process.This creates a problem: the TLB is now filled with a bunch of cached entries for the old process.
A simple and naive solution would be to completely invalidate the TLB whenever the
cr3
changes.However, this is would not be very efficient, because it often happens that we switch back to process 1 before process 2 has completely used up the entire TLB cache entries.
The solution for this is to use so called "Address Space Identifiers" (ASID) as mentioned in sources such as:
Basically, the OS assigns a different ASID for each process, and then TLB entries are automatically also tagged with that ASID. This way when the process makes an access, the TLB can determine if a hit is actually for the current process, or if it is an old address coincidence with another process.
The x86 also offers the
invlpg
instruction which explicitly invalidates a single TLB entry. Other architectures offer even more instructions to invalidated TLB entries, such as invalidating all entries on a given range.Ciro Santilli's sport of choice circa 2020, see also: Ciro Santilli's cycling.
Patches which were merged by Ciro himself on repositories which eh feels have large public visibility, e.g. those to which he has been given push permission.
Repositories to which Ciro gained push permission because of his contributions:
The key and central motivation for studying Lie groups and their Lie algebras appears to be to characterize symmetry in Lagrangian mechanics through Noether's theorem, just start from there.
Notably local symmetries appear to map to forces, and local means "around the identity", notably: local symmetries of the Lagrangian imply conserved currents.
More precisely: local symmetries of the Lagrangian imply conserved currents.
TODO Ciro Santilli really wants to understand what all the fuss is about:
Oh, there is a low dimensional classification! Ciro is a sucker for classification theorems! en.wikipedia.org/wiki/Classification_of_low-dimensional_real_Lie_algebras
The fact that there are elements arbitrarily close to the identity, which is only possible due to the group being continuous, is the key factor that simplifies the treatment of Lie groups, and follows the philosophy of continuous problems are simpler than discrete ones.
Bibliography:
- youtu.be/kpeP3ioiHcw?t=2655 "Particle Physics Topic 6: Lie Groups and Lie Algebras" by Alex Flournoy (2016). Good SO(3) explicit exponential expansion example. Then next lecture shows why SU(2) is the representation of SO(3). Next ones appear to eventually get to the physical usefulness of the thing, but I lost patience. Not too far out though.
- www.youtube.com/playlist?list=PLRlVmXqzHjURZO0fviJuyikvKlGS6rXrb "Lie Groups and Lie Algebras" playlist by XylyXylyX (2018). Tutorial with infinitely many hours
- www.staff.science.uu.nl/~hooft101/lectures/lieg07.pdf
- www.physics.drexel.edu/~bob/LieGroups.html
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