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- ...is unique. This is the Normal Form Theorem for the free groups and for the free product of groups. The proof here of the Normal Form Theorem follows the id ==Normal Form for Free Groups== ...6 KB (1,163 words) - 12:57, 7 November 2023
- In [[mathematics]], the '''free category''' or '''path category''' generated by a [[directed graph]] or [[q ...ith one vertex and one edge {{var|f}} from that object to itself, then the free category on {{var|Q}} has as arrows {{var|1}}, {{var|f}}, {{var|f}}∘{{var|f ...5 KB (739 words) - 11:28, 8 December 2024
- In [[abstract algebra|algebra]], a '''free presentation''' of a [[module (mathematics)|module]] ''M'' over a [[commuta Since ''f'' is a [[module homomorphism]] between [[free module]]s, it can be visualized as an (infinite) [[matrix (mathematics)|mat ...3 KB (546 words) - 03:35, 13 May 2024
- In mathematics, the '''free matroid''' over a given ground-set ''E'' is the [[matroid]] in which the in ...this matroid is the ground-set itself, ''E''. Among matroids on ''E'', the free matroid on ''E'' has the most independent sets, the highest rank, and the f ...2 KB (289 words) - 07:55, 1 February 2024
- ...nsor product]]s of their function algebras) is played by the notion of a [[free product]] of (non-commutative) probability spaces. ...ree central limit theorem; notions of [[free convolution]]; existence of [[free stochastic calculus]] and so on. ...4 KB (624 words) - 15:40, 27 October 2024
- {{For|the song|Free Loop (One Night Stand)}} ...d point. Formally, let <math>X</math> be a [[topological space]]. Then a free loop in <math>X</math> is an [[equivalence class]] of [[continuous function ...2 KB (263 words) - 22:38, 9 March 2024
- A '''coordinate-free''', or '''component-free''', treatment of a [[scientific theory]] or [[mathematical]] topic develops Coordinate-free treatments generally allow for simpler systems of equations and inherently ...4 KB (507 words) - 21:56, 1 January 2024
- ...m variables (see below; in the classical case, what would be the analog of free multiplicative convolution can be reduced to additive convolution by passin The notion of free convolution was introduced by [[Dan-Virgil Voiculescu]].<ref>Voiculescu, D. ...8 KB (1,158 words) - 08:09, 21 June 2023
- ...(non [[zero-divisor]]) of the ring. In other words, a module is ''torsion free'' if its [[torsion submodule]] contains only the zero element. ...ver integral domains and use this condition as the definition of a torsion-free module, but this does not work well over more general rings, for if the rin ...4 KB (672 words) - 14:20, 10 November 2024
- A '''free motion equation''' is a [[differential equation]] that describes a mechanic ...nomous mechanics]] on a configuration space <math>Q\to \mathbb R</math>, a free motion equation is defined as a second order [[non-autonomous system (mathe ...2 KB (326 words) - 20:00, 17 July 2022
- {{redirect-confuse|paradox of free choice|The Paradox of Choice{{!}}''The Paradox of Choice''}} '''Free choice''' is a phenomenon in natural language where a linguistic [[disjunct ...5 KB (727 words) - 13:57, 19 November 2024
- The '''free energy principle''' is a theoretical framework suggesting that the brain re | title = The anticipating brain is not a scientist: the free-energy principle from an ecological-enactive perspective ...51 KB (7,138 words) - 08:18, 9 February 2025
- A '''prior-free mechanism (PFM)''' is a [[mechanism design|mechanism]] in which the designe ...probability distribution]]. The seller's goal is to design an auction that will produce a reasonable profit even in worst-case scenarios. ...7 KB (1,038 words) - 16:27, 17 June 2023
- ...k=Yannís G. Kevrekidis |last2=Samaey |first2=G. |year=2009 |title=Equation-free multiscale computation: algorithms and applications |journal=Annual Review ..., brain modeling and neuronal systems are some typical examples. Equation-free modeling aims to use such microscale models to predict coarse macroscale em ...22 KB (3,154 words) - 23:23, 16 September 2023
- ...rred to as '''even-cycle-free graphs'''.<ref>{{citation |title=even-cycle--free graphs |url=https://www.graphclasses.org/classes/gc_706.html |access-date=2 ...dario-Berry|Chudnovsky|Havet|Reed|2008}} demonstrated that every even-hole-free graph contains a [[bisimplicial vertex]] (a vertex whose neighborhood is th ...7 KB (911 words) - 15:49, 18 December 2024
- {{for|the concept in physics |Free field}} In [[acoustics]], a '''free field''' is a situation or space in which no [[Reflection (physics)|sound r ...4 KB (551 words) - 03:32, 27 September 2023
- The '''inset''' shows beta decay of a free neutron as it is understood today; an electron and antineutrino are created ...cleus]], [[neutron]]s are (usually) stable particles. Outside the nucleus, free neutrons are unstable and have a [[mean lifetime]] of {{val|877.75|0.50|0.4 ...23 KB (3,067 words) - 16:30, 15 February 2025
- ...th affine [[complex curve]]. Because of the latter generalization, a quasi-free algebra can be thought of as signifying smoothness on a [[noncommutative sp ...ciative algebra over the complex numbers. Then ''A'' is said to be ''quasi-free'' if the following equivalent conditions are met:<ref name="definition">{{h ...5 KB (643 words) - 11:26, 13 August 2023
- ...thor3-link=Luis Nunes Vicente |year=2009 |title=Introduction to Derivative-Free Optimization |url=http://www.mat.uc.pt/~lnv/idfo/|accessdate=2014-01-18 |s In derivative-free optimization, various methods are employed to address these challenges usin ...5 KB (625 words) - 07:10, 20 April 2024
- ...stor, E. Vidal-Idiarte, A. Cid-Pastor, L. Martinez-Salamero, "Digital Loss-Free Resistor for power factor correction applications", Industrial Electronics ...ergy conversion.<ref name=singer1990/> It is possible to synthesize a Loss-Free Resistor (LFR) by the combination of a switched mode converter and a suitab ...7 KB (1,036 words) - 18:38, 10 November 2023
Page text matches
- ...is a [[module (mathematics)|module]] which is close to being [[free module|free]]. ...enerated module]] ''F'' over ''R'' such that <math> M \oplus F</math> is a free module. ...976 bytes (144 words) - 12:11, 18 June 2024
- {{For|the song|Free Loop (One Night Stand)}} ...d point. Formally, let <math>X</math> be a [[topological space]]. Then a free loop in <math>X</math> is an [[equivalence class]] of [[continuous function ...2 KB (263 words) - 22:38, 9 March 2024
- ...(non [[zero-divisor]]) of the ring. In other words, a module is ''torsion free'' if its [[torsion submodule]] contains only the zero element. ...ver integral domains and use this condition as the definition of a torsion-free module, but this does not work well over more general rings, for if the rin ...4 KB (672 words) - 14:20, 10 November 2024
- ...t-free languages|context-free]], just like the [[pumping lemma for context-free languages]]. It states that for every context-free language <math>L</math> there is a <math>c>0</math> such that for all <math ...2 KB (250 words) - 17:32, 18 September 2022
- ...hematicae |date=2010 |volume=472 |page=4|doi=10.4064/dm472-0-1 |doi-access=free }}</ref> | title = A characterization of free abelian groups ...2 KB (264 words) - 16:02, 22 September 2023
- ...as a locally free [[sheaf (mathematics)|sheaf]]. Every semistable locally free ''E'' on ''X'' admits a Jordan-Hölder [[filtration (mathematics)|filtration where <math>E_i</math> are locally free sheaves on ''X'' and <math>E_i/E_{i-1}</math> are stable. Although the Jord ...1 KB (158 words) - 22:01, 5 June 2023
- ...ated by ''GX'', the generators of some group ''X''; see [[Adjoint functors#Free groups]] ...571 bytes (80 words) - 00:43, 11 August 2023
- In mathematics, the '''free matroid''' over a given ground-set ''E'' is the [[matroid]] in which the in ...this matroid is the ground-set itself, ''E''. Among matroids on ''E'', the free matroid on ''E'' has the most independent sets, the highest rank, and the f ...2 KB (289 words) - 07:55, 1 February 2024
- ...]]) or [[free-free absorption]] (the absorption of light when scattering a free ion, also called [[bremsstrahlung]]).<ref>Phillips (1999), p. 92.</ref> It ...s form of the relation describes how changes in the density or temperature will affect the opacity. ...3 KB (415 words) - 01:32, 9 November 2024
- ...thinsp;''B''. The notion is a [[Ring theory|ring-theoretic]] analog of a [[free product]] of [[Group (mathematics)|groups]]. ...gory of commutative algebras|category of commutative ''R''-algebras]], the free product of two algebras (in that [[Category (mathematics)|category]]) is th ...2 KB (343 words) - 09:19, 20 July 2024
- ...nsor product]]s of their function algebras) is played by the notion of a [[free product]] of (non-commutative) probability spaces. ...ree central limit theorem; notions of [[free convolution]]; existence of [[free stochastic calculus]] and so on. ...4 KB (624 words) - 15:40, 27 October 2024
- ...h]], a [[block graph]], a [[split graph]], an [[interval graph]], a [[claw-free graph]], a 1-[[k-vertex-connected graph|vertex-connected graph]] and a 1-[[ == Bull-free graphs == ...4 KB (522 words) - 00:07, 17 October 2024
- A '''coordinate-free''', or '''component-free''', treatment of a [[scientific theory]] or [[mathematical]] topic develops Coordinate-free treatments generally allow for simpler systems of equations and inherently ...4 KB (507 words) - 21:56, 1 January 2024
- ...nt of the forgetful functor from the category of rings to '''Set'''; i.e., free module functor. Then <math>FU</math> defines a cotriple and the ''n''-th co ...re, <math>FU</math> defines a cotriple on the category of rings with ''F'' free ring functor and ''U'' forgetful. For a ring ''R'', one has: ...2 KB (297 words) - 08:42, 5 March 2024
- In [[abstract algebra|algebra]], a '''free presentation''' of a [[module (mathematics)|module]] ''M'' over a [[commuta Since ''f'' is a [[module homomorphism]] between [[free module]]s, it can be visualized as an (infinite) [[matrix (mathematics)|mat ...3 KB (546 words) - 03:35, 13 May 2024
- {{for|the concept in physics |Free field}} In [[acoustics]], a '''free field''' is a situation or space in which no [[Reflection (physics)|sound r ...4 KB (551 words) - 03:32, 27 September 2023
- | doi=10.1006/aima.1995.1032 | doi-access=free ...somorphic as a Hopf algebra to the [[universal enveloping algebra]] of the free Lie algebra on countably many variables. ...3 KB (425 words) - 08:35, 4 January 2024
- ...</math>-module <math>\mathcal{F}</math> and a [[locally free sheaf|locally free]] <math>\mathcal{O}_Y</math>-module <math>\mathcal{E}</math> of finite rank ...987 bytes (142 words) - 07:52, 22 April 2024
- |known_for=Coining the term [[free logic]] ...[[University of Salzburg]]. He has written extensively on the subject of [[free logic]], a term which he coined.<ref>{{Cite journal ...4 KB (510 words) - 13:42, 6 April 2024
- ...ry other partner at strictly less than 1/''n''. Formally, in a super-envy-free division of a resource ''C'' among ''n'' partners, each partner ''i'', with ...free|last1=Barbanel|first1=Julius B.}}</ref> He proved that a super-[[envy-free cake-cutting]] exists if-and-only-if the value measures of the ''n'' partne ...3 KB (494 words) - 18:10, 22 February 2022