Sequence alignment is trying to match a DNA or amino acid sequence, even though the sequences might not be exactly the same, otherwise it would be a straight up string-search algorithm.

This is fundamental in bioinformatics for two reasons:

Transaction retries are inevitable, as some sQL isolation levels

Doesn't seem to have any simple built-in mechanism?

It is fun to see that some New Testament sources cite this Greek version rather than more ancient ones because they or their listeners would not understand the other original languages.

As per en.wikipedia.org/w/index.php?title=Semidirect_product&oldid=1040813965#Properties, unlike the Direct product, the semidirect product of two goups is neither unique, nor does it always exist, and there is no known algorithmic way way to tell if one exists or not.

This is because reaching the "output" of the semidirect produt of two groups requires extra non-obvious information that might not exist. This is because the semi-direct product is based on the product of group subsets. So you start with two small and completely independent groups, and it is not obvious how to join them up, i.e. how to define the group operation of the product group that is compatible with that of the two smaller input groups. Contrast this with the Direct product, where the composition is simple: just use the group operation of each group on either side.

Product of group subsets

So in other words, it is not a function like the Direct product. The semidiret product is therefore more like a property of three groups.

The semidirect product is more general than the direct product of groups when thinking about the group extension problem, because with the direct product of groups, both subgroups of the larger group are necessarily also normal (trivial projection group homomorphism on either side), while for the semidirect product, only one of them does.

Conversely, en.wikipedia.org/w/index.php?title=Semidirect_product&oldid=1040813965 explains that if $G=N⋊H$, and besides the implied requirement that N is normal, H is also normal, then $G=N\times H$.

Smallest example: $D_6=C_3⋊C_2$ where $D$ is a dihedral group and $C$ are cyclic groups. $C_3$ (the rotation) is a normal subgroup of $D_6$, but $C_2$ (the flip) is not.

Note that with the Direct product instead we get $C_6$ and not $D_6$, i.e. $C_3\times C_2=C_6$ as per the direct product of two cyclic groups of coprime order is another cyclic group.

TODO:

Bibliography: math.stackexchange.com/questions/1726939/is-this-intuition-for-the-semidirect-product-of-groups-correct

As mentioned at youtu.be/16BzIG0lrEs?t=397 from Video "Applied Materials by Asianometry (2021)", originally the companies fabs would make their own equipment. But eventually things got so complicated that it became worth it for separate companies to focus on equipment, which then then sell to the fabs.

When taking a penalty kick in soccer, the kicker must chose left or right.

And before he kicks, the goalkeeper must also decide left or right, because there is no time to see where the ball is going.

Because the kicker is right footed however, he kicker kicks better to one side than the other. So we have four probabilities:

The basis of 1970-20XX computers, gotta understand them I guess?

An example where SELECT FOR UPDATE is a good solution to an use case can be seen at: nodejs/sequelize/raw/parallel_select_and_update.js.

SELECT FOR UPDATE vs/together with the SQL transaction isolation level is commented at: stackoverflow.com/questions/10935850/when-to-use-select-for-update.

Tinker Tailor Soldier Spy:

Second quantization also appears to be useful not only for relativistic quantum mechanics, but also for condensed matter physics. The reason is that the basis idea is to use the number occupation basis. This basis is:

Bibliography: