GF(4) Updated +Created
Ciro Santilli tried to add this example to Wikipedia, but it was reverted, so here we are, see also: Section "Deletionism on Wikipedia".
This is a good first example of a field of a finite field of non-prime order, this one is a prime power order instead.
, so one way to represent the elements of the field will be the to use the 4 polynomials of degree 1 over GF(2):
  • 0X + 0
  • 0X + 1
  • 1X + 0
  • 1X + 1
Note that we refer in this definition to anther field, but that is fine, because we only refer to fields of prime order such as GF(2), because we are dealing with prime powers only. And we have already defined fields of prime order easily previously with modular arithmetic.
Over GF(2), there is only one irreducible polynomial of degree 2:
Addition is defined element-wise with modular arithmetic modulo 2 as defined over GF(2), e.g.:
Multiplication is done modulo , which ensures that the result is also of degree 1.
For example first we do a regular multiplication:
Without modulo, that would not be one of the elements of the field anymore due to the !
So we take the modulo, we note that:
and by the definition of modulo:
which is the final result of the multiplication.
TODO show how taking a reducible polynomial for modulo fails. Presumably it is for a similar reason to why things fail for the prime case.
Good targets for amateur astronomy Updated +Created
Looking at most astronomical object through a Telescope is boring because you only see a white ball or point every time. Such targets would likely only be interesting with spectroscopy analysis.
There are however some objects that you can see the structure of even with an amateur telescope, and that makes them very exciting.
Some good ones:
git rebase moves commits one by one Updated +Created
In order to solve conflicts, you just have to understand what commit you are trying to move where.
E.g. if from:
5 master
|
4 7 my-feature HEAD
| |
3 6
|/
2
|
1
we do:
git rebase master
what happens step by step is first 6 is moved on top of 5:
6on5 HEAD
|
5 master
|
4                 7 my-feature
|                 |
3                 6
|                 |
2-----------------+
|
1
and then 7 is moved on top of the new 6:
7on5 HEAD
|
6on5
|
5 master
|
4                 7 my-feature
|                 |
3                 6
|                 |
2-----------------+
|
1
All good? so OK, let's move the my-feature to the new 7:
7on5 my-feature HEAD
|
6on5
|
5 master
|
4
|
3
|
2
|
1
SQL contiguous ranges Updated +Created
stackoverflow.com/questions/17046204/how-to-find-the-boundaries-of-groups-of-contiguous-sequential-numbers/17046749#17046749 just works, even in SQLite which supports all quoting types known to man including [] for compatibility with insane RDBMSs!
Here's a slightly saner version:
rm -f tmp.sqlite
sqlite3 tmp.sqlite "create table mytable (id integer primary key autoincrement, number integer, status integer)"
sqlite3 tmp.sqlite <<EOF
insert into mytable(number, status) values
  (100,0),
  (101,0),
  (102,0),
  (103,0),
  (104,1),
  (105,1),
  (106,0),
  (107,0),
  (1014,0),
  (1015,0),
  (1016,1),
  (1017,0)
EOF
sqlite3 tmp.sqlite <<EOF
SELECT
  MIN(id) AS "id",
  MIN(number) AS "from",
  MAX(number) AS "to"
FROM (
  SELECT ROW_NUMBER() OVER (ORDER BY number) - number AS grp, id, number
  FROM mytable
  WHERE status = 0
)
GROUP BY grp
ORDER BY MIN(number)
EOF
output:
1|100|103
7|106|107
9|1014|1015
12|1017|1017
To get only groups of length greater than 1:
sqlite3 tmp.sqlite <<EOF
SELECT "id", "from", "to", "to" - "from" + 1 as "len" FROM (
  SELECT
    MIN("id") AS "id",
    MIN(number) AS "from",
    MAX(number) AS "to"
  FROM (
    SELECT ROW_NUMBER() OVER (ORDER BY "number") - "number" AS "grp", "id", "number"
    FROM "mytable"
    WHERE "status" = 0
  )
  GROUP BY "grp"
  ORDER BY MIN("number")
) WHERE "len" > 1
EOF
Output:
1|100|103|4
7|106|107|2
9|1014|1015|2
Laurel and Hardy Updated +Created
Graph representation Updated +Created
Lebesgue integral Updated +Created
"More complex and general" integral. Matches the Riemann integral for "simple functions", but also works for some "funkier" functions that Riemann does not work for.
Ciro Santilli sometimes wonders how much someone can gain from learning this besides the beauty of mathematics, since we can hand-wave a Lebesgue integral on almost anything that is of practical use. The beauty is good reason enough though.
Last universal common ancestor Updated +Created
Latin Updated +Created
List of Nobel Prizes in Physiology and Medicine Updated +Created
LC oscillator Updated +Created
Lawrence Livermore National Laboratory Updated +Created
Founded partly due to the influence of Edward Teller who thought Los Alamos National Laboratory was not making good progress on thermonuclear weapons, large part of which was developed there.
Lattice gauge theory Updated +Created
LA-UR Updated +Created
Publicly released documents from the Los Alamos National Laboratory are marked with this identifier. This is for example the case of each video on ther YouTube channel: www.youtube.com/@LosAlamosNationalLab. E.g. Video "Historic, unique Manhattan Project footage from Los Alamos by Los Alamos National Lab" is marked with "LA-UR 11-4449".
www.osti.gov/biblio/1372821 contains "How to Get an LA-UR: Using RASSTI to Release Your Work" which is of interest: permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-17-26023. That document documents the acronym's expansion, plus it leaks some internal-only URLs such as lasearch.lanl.gov/oppie/service.
TODO is there somewhere you can search for the document for a given identifier? Some PDFs are listed at: sgp.fas.org/othergov/doe/lanl/index2b.html
Laughlin wavefunction Updated +Created
Lattice Microbes Updated +Created
GPU accelerated, simulates the Craig's minimized M. genitalium, JCVI-syn3A at a particle basis of some kind.
Lab head is the cutest-looking lady ever: chemistry.illinois.edu/zan, Zaida (Zan) Luthey-Schulten.
Google Quantum AI Updated +Created
Google's quantum hardware/software effort.
The "AI" part is just prerequisite buzzword of the AI boom era for any project and completely bullshit.
According to job postings such as: archive.ph/wip/Fdgsv their center is in Goleta, California, near Santa Barbara. Though Google tends to promote it more as Santa Barbara, see e.g. Daniel's t-shirt at Video "Building a quantum computer with superconducting qubits by Daniel Sank (2019)".
Video 1.
Control of transmon qubits using a cryogenic CMOS integrated circuit (QuantumCasts) by Google (2020)
Source. Fantastic video, good photos of the Google Quantum AI setup!
List of rocks Updated +Created

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