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# ''R'' has no [[dense submodule|dense]] right ideals except ''R'' itself. *{{citation |last=Faith |first=Carl |title=Rings and things and a fine array of twentieth century associative algebra |series=Mathemati ...

...e claims in this paragraph, each sentence in this paragraph should have at least one source.|date=November 2022}} ...e claims in this paragraph, each sentence in this paragraph should have at least one source.|date=November 2022}} ...

...roperties'' ("bad things don't happen") and ''liveness properties'' ("good things do happen").<ref name="Lamport1977">{{Cite journal * The safety property prohibits these "bad things": executions that start in a state satisfying <math>P</math> and terminate ...

This sketch glosses over some things, such as how to handle fixed points. It turns out that more mappings and mo ...the points of the plane (other than the origin) can be divided into two [[dense set]]s which we may call ''A'' and ''B''. If the ''A'' points of a given po ...

...athematician [[Guillermo Martínez (writer)|Guillermo Martínez]], Borges at least had a knowledge of mathematics at the level of first courses in [[algebra]] ...ena''), he deals with another form of infinity; one whose elements are a [[dense set]], that is, for any two elements, we can always find another between th ...

which (among other things) allows for <math>X</math> to be endowed with the subspace topology induced ...er} {}^t F = \{ 0 \}</math>) if and only if the range of <math>F</math> is dense in <math>\left(W, \sigma\left(W, Z, c\right)\right).</math>{{sfn|Narici|Bec ...

Other times these programmers apply the [[rule of least power]]—they deliberately use a computer language that is not quite fully T ...a computer with a million small parts, each with two states, would have at least 2^1,000,000 possible states:{{sfn|Minsky|1967|p=25}} ...

...{{EquationNote|9}}) is very complicated, and averaging further complicates things. ...bom | first1=O. | last2=Taloni | first2=A. | title=On single-file and less dense processes | journal=EPL (Europhysics Letters) | publisher=IOP Publishing | ...

...n switching between a filter on a space <math>X</math> and a filter on a [[dense subspace]] <math>S \subseteq X.</math>{{sfn|Howes|1995|pp=83-92}} The {{em|[[supremum]]}} or {{em|[[least upper bound]]}} of <math>\mathbb{F} \text{ in } \operatorname{DualIdeals}(X ...

...lts (proposed structure is shown to the right). In organopolysilazanes, at least one organic substituent is bound to the silicon atom. The amount and type o ...is relatively high because of changing commercial availability among other things. Nevertheless, for some applications, polysilazanes proved to be competitiv ...

...imize interactions with the solvent. This leads to a much more clumped and dense polymer deposited onto the surface. These cores, once created, can be used for things such as [[drug delivery]] and [[microreactor]]s. For drug delivery, the pol ...

...when capital ''X'' is also the name of the random variable, and other like things, need to get cleaned up.|date=March 2020}} ...e widely used [[radial basis function]] kernels), then with probability at least <math>1-\delta </math>:<ref name="SongThesis" /> ...

...obability on real weights with better runtime have been developed, one for dense data,<ref>{{cite arXiv ...blished that a min-wise independent family of permutations must include at least ...

...n constituents, and the mixing, placement and curing methods employed. All things being equal, concrete with a lower water-cement (cementitious) ratio makes ...vapor out of concrete due to sufficiently high heating rate or adequately dense pore structure, a large pore pressure can cause spalling. At the same time, ...

...that the physiology of the human [[retina]] is such that there must be at least 477 pixels per inch in a pixelated display for the pixels to become imperce <blockquote>The sort of rich, data-dense information design espoused by [[Edward Tufte]] can now not only be made on ...

...o One Told It |url=https://www.scientificamerican.com/article/how-ai-knows-things-no-one-told-it/ |access-date=17 May 2023 |website=[[Scientific American]] | [[File:RAG schema.svg|thumb|Two-phase process of document retrieval using dense [[Word embedding|embeddings]] and LLM for answer formulation]] ...

...tive barrier; it allows some things to pass through but stops others. Such things may be [[molecule]]s, [[ion]]s, or other small particles. Membranes can be ...the membrane which leads to a reduction in use at same application and the least preferred action is a disposal and landfilling <ref>{{cite journal |last1=L ...

...ast2=José Cocero |first2=María|isbn=9780471238966 }}</ref> It behaves as a dense gas with a dissolving power equivalent to that of organic solvents of low [ ...oi-access=free }}</ref><ref>{{Cite web |date=2005 |title=The Drive to Make Things Happen |url=https://vrchemistry.chem.ox.ac.uk/potential/text/solutions3.htm ...

...flow become strained.<ref>Gladwell, M. 2000. The Tipping Point: How Little things Can Make A Big Difference. United States of America, Little Brown.</ref> ...ies involvement in the relationship. Strong ties are often found in highly dense groups of nodes who share many similarities and connections within the grou ...

...nd [[Cygnus A]] at the same frequencies. This established magnetars as, at least, one ultimate source of fast radio bursts,<ref name="AT-20201104">{{cite ne ...rce inside the Milky Way galaxy<ref name=nature15769>{{cite journal |title=Dense magnetized plasma associated with a fast radio burst |journal=Nature |date= ...