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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
- ...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
- 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
- ...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
- ...nitary. DFSs can also be characterized as a special class of [[Decoherence-free subspaces#Quantum error-correcting codes(QECCs)|quantum error correcting co ...iel A. |last1=Lidar |first2=K. Birgitta |last2=Whaley |chapter=Decoherence-Free Subspaces and Subsystems |title=Irreversible Quantum Dynamics |editor-first ...26 KB (3,943 words) - 10:16, 12 March 2024
- ...th>\Omega</math> which is not known at the outset of the problem is the '''free boundary'''. ...gion the temperature is greater than the melting point of ice, this domain will be occupied by liquid water instead. The boundary formed from the ice/liqui ...10 KB (1,611 words) - 19:04, 27 April 2024
- ...mplex''' (sometimes also called the '''complex of free factors''') is a [[free group]] counterpart of the notion of the [[curve complex]] of a finite type ...actor complex is known to be [[δ-hyperbolic space|Gromov-hyperbolic]]. The free factor complex plays a significant role in the study of large-scale geometr ...10 KB (1,519 words) - 20:13, 27 January 2024
- ...electron in the conduction band or a hole in the valence band, where it is free to move. In interband absorption, the carrier starts in a fixed, nonconduct In the simplest approximation, the [[Drude model]], free carrier absorption is proportional to the square of the wavelength. ...4 KB (691 words) - 01:17, 17 December 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
- 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
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