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- [[File:Offset (union-of-balls) filtration.png|thumb|upright=1.2|The offset filtration at six scale parameters on a point cloud sampled from two circles of differ ...002-2885-2 |issn=0179-5376|doi-access=free }}</ref> Since then, the offset filtration has become a primary example in the study of computational topology and dat ...14 KB (1,984 words) - 06:37, 25 November 2024
- ...humb|400x400px|A set of three nested subcomplexes within the Vietoris–Rips filtration on a set of points in the Euclidean plane.]] ...su |date=2019-01-30 |title=SimBa: An Efficient Tool for Approximating Rips-filtration Persistence via Simplicial Batch Collapse |journal=ACM Journal of Experimen ...18 KB (2,638 words) - 22:15, 14 October 2024
- ...ation theory]], a '''Jantzen filtration''' is a [[Filtration_(mathematics)|filtration]] of a [[Verma module]] of a [[semisimple Lie algebra]], or a [[Weyl module ==Jantzen filtration for Verma modules== ...3 KB (346 words) - 07:43, 23 June 2022
- ...c subgroup]] for that point, the Moy–Prasad filtration can be viewed as a filtration of a parahoric subgroup of a reductive group. The chief application of the Moy–Prasad filtration is to the [[representation theory]] of ''p''-adic groups, where it can be u ...21 KB (3,701 words) - 08:46, 15 October 2024
- ...non-decreasingly.<ref name="Klenke191" /> If <math> \mathbb F </math> is a filtration, then <math> (\Omega, \mathcal A, \mathbb F, P) </math> is called a '''fil ...'σ''-algebra and <math> \mathbb F= (\mathcal F_n)_{n \in \N} </math> is a filtration. ...5 KB (742 words) - 14:51, 11 December 2024
Page text matches
- ...)</math> is a [[associated graded module|graded module associated]] to the filtration. ...1 KB (147 words) - 13:10, 21 July 2024
- ...non-decreasingly.<ref name="Klenke191" /> If <math> \mathbb F </math> is a filtration, then <math> (\Omega, \mathcal A, \mathbb F, P) </math> is called a '''fil ...'σ''-algebra and <math> \mathbb F= (\mathcal F_n)_{n \in \N} </math> is a filtration. ...5 KB (742 words) - 14:51, 11 December 2024
- ...ally free ''E'' on ''X'' admits a Jordan-Hölder [[filtration (mathematics)|filtration]] with stable [[subquotient]]s, i.e. ...''X'' and <math>E_i/E_{i-1}</math> are stable. Although the Jordan-Hölder filtration is not unique, the subquotients are, which means that <math>gr E = \bigoplu ...1 KB (158 words) - 22:01, 5 June 2023
- ...ation theory]], a '''Jantzen filtration''' is a [[Filtration_(mathematics)|filtration]] of a [[Verma module]] of a [[semisimple Lie algebra]], or a [[Weyl module ==Jantzen filtration for Verma modules== ...3 KB (346 words) - 07:43, 23 June 2022
- ...ctrofiltration''' is a method that combines [[Membrane technology|membrane filtration]] and [[electrophoresis]] in a dead-end process. ...r completely avoided by the application of [[electric field]], improving [[filtration]]’s performance and increasing selectivity in case of fractionation. This a ...7 KB (922 words) - 04:52, 14 June 2024
- :::[[File:HN Filtration in triangulated category.png|frameless|600px|left]]{{Clear}} ...tically imposing the existence of [[Stable vector bundle#Harder–Narasimhan filtration|Harder–Narasimhan filtrations]] on elements of the category <math>\mathcal{ ...6 KB (955 words) - 15:29, 3 September 2024
- ...ct to the [[filtration (probability theory)#Augmented filtration|augmented filtration]] <math>\mathcal{F}^B</math> generated by <math>B</math> ...3 KB (340 words) - 22:42, 14 June 2024
- ...0},\mathbb{P})</math> has [[strong Markov property]] with respect to the filtration <math>\{\mathcal{F}_{t^+}\}_{t\geq 0}</math>. ...2 KB (319 words) - 02:39, 10 July 2020
- ...v maximal inequality''' is a [[Maximal function|maximal inequality]] for [[filtration (mathematics)|filtrations]], named for mathematicians [[F. Michael Christ|M A '''continuous filtration''' of <math>(M,\mu)</math> is a family of measurable sets <math>\{A_\alpha\ ...4 KB (574 words) - 23:28, 25 June 2021
- ...[[Filtration (probability theory)|filtered]] probability space, where the filtration satisfies the [[usual conditions]] and <math>T\in (0,\infty)</math>. Let <m ...2 KB (310 words) - 05:58, 27 September 2024
- ...hat persist over multiple scale parameters in a [[Filtration (mathematics)|filtration]]. Whereas the classical <math>n^{th}</math> Betti number equals the rank o ...th> for some [[natural number]] <math>n</math>. This sequences defines a ''filtration'' on the complex <math>K</math>. ...6 KB (873 words) - 15:55, 28 October 2023
- ...ogether with a complete, descending <math> {\mathbb Q}</math>-vector space filtration <math> \{F_r L\}_{r\ge 1} </math>, such that: ...ra]]s, i.e., Hopf algebras ''H'' endowed with a [[filtration (mathematics)|filtration]] so that ''H'' is isomorphic to <math>\varprojlim H / F_n H</math>. The fu ...3 KB (442 words) - 12:47, 4 October 2021
- {{short description|On jumps of upper numbering filtration of the Galois group of a finite Galois extension}} ...sse–Arf theorem''' is a result concerning jumps of the [[upper numbering]] filtration of the [[Galois group]] of a finite [[Galois extension]]. A special case o ...5 KB (854 words) - 11:29, 26 April 2024
- ==Canonical filtration== ...4 KB (625 words) - 11:47, 26 July 2022
- ...ds on the past times of <math>X</math> but is independent of the [[natural filtration]] <math >\mathcal{F}^W</math> of the Brownian motion. This gives a weak sol ...nd <math>\{\mathcal{F}_t^{W}\} _{t\in \R_+}</math> be the natural Brownian filtration that satisfies the usual conditions, ...4 KB (562 words) - 12:13, 21 July 2024
- This effect is of importance in [[cross-flow filtration]] and especially in [[Kidney dialysis|dialysis]]. It is significant especia * Siegfried Ripperger, ''Berechnungsansätze zur Crossflow-Filtration'', Chemieingenieurtechnik, (1993) p. 533-540 {{doi|10.1002/cite.330650 ...3 KB (391 words) - 04:03, 4 August 2022
- ...ls]]. It is a multidimensional extension of the [[Offset Filtration|offset filtration]] that captures density information about the underlying data set by filter ...}}</ref> Note that when <math>k=1</math> is fixed we recover the [[Offset Filtration]]. ...5 KB (752 words) - 11:55, 21 March 2024
- ...the underlying data set. The subdivision bifiltration relies on a natural filtration of the [[barycentric subdivision]] of a [[simplicial complex]] by [[Flag (g ...as the ''subdivision filtration.'' Since the complexes in the subdivision filtration shrink as <math>k</math> increases, we can regard it as a [[functor]] <math ...9 KB (1,303 words) - 13:33, 28 February 2024
- ...ath> be a continuous local martingale with respect to a [[right-continuous filtration]] <math>(\mathcal{F}_t)_{t \ge 0}</math>. If <math>(\exp(M_t/2))_{t \ge 0}< ...1 KB (147 words) - 04:29, 13 March 2024
- ...'(''λ'') in '''C''' equipped with an increasing [[filtration (mathematics)|filtration]] ...4 KB (550 words) - 02:16, 25 April 2023