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For example, the statement "an integer's prime factorization is unique up to ordering" is a concise way to say that any two lists of prime factors of a given integer are equivalent with respect to the relation R that relates two lists if one can be obtained by reordering (permuting) the other
from the top result below
https://en.wikipedia.org/wiki/Up_to
For example, the statement "an integer's prime factorization is unique up to ordering" is a concise way to say that any two lists of prime factors of a given integer are equivalent with respect to the relation R that relates two lists if one can be obtained by reordering (permuting) the other
https://en.wikipedia.org/wiki/Wedderburn%E2%80%93Artin_theorem
}
Here we used right modules because R ≅ E n d ( R R ) {\displaystyle R\cong \mathrm {End} (R_{R})} ; if we used left modules R {\displaystyle R} would be isomorphic to the opposite algebra of E n d ( R R ) {\displaystyle \mathrm {End} ({}_{R}R)} , but the proof would still go through
https://writtenhorror.com/game-review-a-twisted-place/
We descend deeper into the twisted place, though one can question if this place exists and it’s not the mind of our protagonist visualized
https://en-academic.com/dic.nsf/enwiki/28835
Approximation
If the distribution of the likelihood ratio corresponding to a particular null and alternative hypothesis can be explicitly determined then it can directly be used to form decision regions (to accept/reject the null hypothesis)
https://arxiv.org/html/2205.01882v5
5 Proof of Lemma 3
B Proof of Theorem 1-(ii) and Proposition 2
B
https://en.wikipedia.org/wiki/Double_centralizer_theorem
theorem can refer to any one of several similar results
https://arxiv.org/html/2407.00419v1
If we make no assumptions about the target population, we can do little more than attempt to mimic observed behavior as closely as possible, reducing the problem to one of imitation learning
https://news.ycombinator.com/item?id=49686380
After being frustrated with outdated & inaccurate data Claude used when I was trying to do some property research, I thought it'd be cool to build an MCP that can provide accurate property data
https://arxiv.org/html/2407.00575v3
Even worse, the manager would need to collect the parameters periodically if they are time-varying, and then solve the large-scale optimization problem again
https://blog.sigfpe.com/2005/05/dual-photography-part-ii.html?showComment=1122942660000
Like in the original paper you can extract more information per frame if you can make assumptions about the spatial coherence of the image
https://www.skills.google/focuses/1843?locale=he&parent=catalog
If you wanted to send a file from Cloud Storage, you would replace content with gcsContentUri and give it a value of the text file's uri in Cloud Storage
https://en.wikibooks.org/wiki/Abstract_Algebra/Ideals
Lemma: An ideal I {\displaystyle I} is proper if and only if 1 ∉ I {\displaystyle 1\notin I}
https://gowers.wordpress.com/2026/08/12/what-sort-of-maths-are-llms-good-at/
If they were, then their big speed advantage over us would mean that there would be much more of a flood of results
https://www.judegomila.com/posts/riemann-lambda-0.1787854
Nobody can prove that yet, but its known ceiling can be lowered, and this is my computer-assisted proof taking it from 0
https://terrytao.wordpress.com/2026/08/12/a-digestion-of-the-proof-of-sendovs-conjecture/
If one ignores the errors, one can show that these conditions are only simultaneously feasible if and all the vanish, but the argument was somewhat subtle (I had to proceed by inspecting the second Fourier coefficient of (1))
https://publishing.cdlib.org/ucpressebooks/view?docId=ft0z09n7m0
The Leigh Brackett interview was originally published as "Grab What You Can Get: The Screenwriter as Journeyman Plumber" in the August–September 1976 issue of Films in Review
https://wordtype.org/of/computing
computing can be used as a verb in the sense of "<missing sense definition>"
computing can be used as a noun in the sense of "The process or act of calculation" or "Action of using (a) computer(s)
https://github.com/optsuite/optlib
Our GitHub web page corresponding to this work can be found at here
https://saladtheory.github.io/
Well-Mixed
A salad must be a mixture of foods such that a typical person would not notice a difference if the relative position and orientation of its ingredients were randomized
https://math-ai-org.github.io/mathcode/
Theorem Library
Every proved theorem is auto-named, stored, and made importable so the prover and planner can reuse it
https://blog.sigfpe.com/2012/02/lawvere-theories-made-bit-easier.html?showComment=1328648551388
Even if we don't get code we can immediately use, we still get a good way to think about and analyse effects
https://en.wiktionary.org/wiki/auki
I think I can do it quickly, but the exact schedule is still up in the air
https://www.gsk-3inhibitor.com/2017/11/10/Dynein_assembly_factor_3/
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https://pure.knaw.nl/portal/en/publications/herpublicatie-1-lemma-6/
2013
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https://www-archiv.fdm.uni-hamburg.de/b-online/delta/grass/www/dilophot.htm
Awns 1, or 3; median, or median and lateral (if the lobes are considered awn-tipped); the median different in form from the laterals (if laterals are considered present); from a sinus; geniculate; hairless, or hairy; much longer than the body of the lemma; entered by several veins; deciduous (seemingly, in D
https://universaldependencies.org/treebanks/sga_dipsgg/sga_dipsgg-pos-ADJ.html
ambiguous types:
Morphology
The form / lemma ratio of ADJ is 1
https://en.wiktionary.org/wiki/banians
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https://en.wiktionary.org/wiki/colapsaste
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https://www-archiv.fdm.uni-hamburg.de/b-online/delta/grass/www/dasyochl.htm
Awns 1; median; from a sinus; non-geniculate; hairless; much shorter than the body of the lemma to about as long as the body of the lemma; entered by one vein
Sites: en.wikipedia.org (3) · arxiv.org (3) · blog.sigfpe.com (2) · writtenhorror.com (1)