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- {{Other uses|Continuum (disambiguation){{!}}Continuum}} ...=Weisstein|first=Eric W.|title=Continuum|url=https://mathworld.wolfram.com/Continuum.html|access-date=2020-08-12|website=mathworld.wolfram.com|language=en}}</re ...2 KB (337 words) - 21:47, 11 March 2024
- ...d concepts and analysis techniques exist in these two types of percolation theory as well as the study of [[random graphs]] and [[random geometric graphs]]. ...7recent">{{cite journal|first=I.|last=Balberg|title=Recent developments in continuum percolation|journal=Philosophical Magazine B|volume=56|issue=6|pages=991–10 ...14 KB (1,994 words) - 20:00, 10 June 2024
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- {{Other uses|Continuum (disambiguation){{!}}Continuum}} ...=Weisstein|first=Eric W.|title=Continuum|url=https://mathworld.wolfram.com/Continuum.html|access-date=2020-08-12|website=mathworld.wolfram.com|language=en}}</re ...2 KB (337 words) - 21:47, 11 March 2024
- ...thesis|a weakened form]], <math>2^{\aleph_0}<2^{\aleph_1}</math>, of the [[Continuum Hypothesis]] (CH). It was discussed by [[Nikolai Luzin]] in 1935, althou ...109-110}} its falsity is also consistent since it is contradicted by the [[Continuum Hypothesis]], which follows from [[V=L]]. It is implied by [[Martin's Axio ...3 KB (463 words) - 21:13, 7 September 2024
- For [[statistics]] in [[probability theory]], the '''Boolean-Poisson model''' or simply '''Boolean model''' for a ran ...>C_\xi</math> and <math>A=\operatorname{E} (\Gamma).</math> The classical theory of [[stochastic geometry]] develops many further formulae. ...2 KB (330 words) - 10:59, 3 March 2023
- In [[set theory]], a branch of mathematics, the '''condensation lemma''' is a result about ...axiom of constructibility]] implies [[Continuum hypothesis#The generalized continuum hypothesis|GCH]]. ...2 KB (237 words) - 15:04, 15 November 2024
- ...oretic tree]] with properties that are incompatible with the [[generalized continuum hypothesis]]. It is named after [[Thomas Jech]] and [[Kenneth Kunen]], both A ''ω''<sub>1</sub>-tree is a [[Tree (set theory)|tree]] with [[cardinality]] <math>\aleph_1</math> and height ''ω''<sub>1</ ...2 KB (271 words) - 22:55, 29 January 2023
- ...th>2^{\aleph_0}<2^{\aleph_1}</math>, which is the negation of the [[second continuum hypothesis]].{{R|S2012|p=80}}{{R|K2012|at=Lecture 7}}{{R|CF2014|p=3616}} I ...This second assertion was [[Georg Cantor|Cantor]]'s original form of the [[Continuum Hypothesis]] (CH). Given the [[Axiom of Choice]], it is equivalent to the ...4 KB (491 words) - 17:40, 12 November 2024
- ==Continuum version== The discrete version can be proved from the continuum version through constructing <math>T:L^p(\mathbb{R},dx)\to L^q(N,\nu)</math ...4 KB (574 words) - 23:28, 25 June 2021
- {{Continuum mechanics|cTopic=[[Solid mechanics]]}} * [[Finite strain theory]] ...2 KB (268 words) - 11:44, 12 January 2024
- ...1962, [[Nathan Fine]] and [[Leonard Gillman]] proved that, assuming the [[continuum hypothesis]]: ...points is independent, in terms of [[Zermelo–Fraenkel set theory]], of the continuum hypothesis for a class of topological spaces that includes [[metric spaces] ...3 KB (365 words) - 02:58, 3 December 2023
- ...in a way that approaches the continuum formulation in the [[scaling limit|continuum limit]]. The class of fermions whose [[Dirac equation|Dirac operators]] sat ...citly violate [[Chirality (physics)|chiral symmetry]]. More precisely, the continuum chiral symmetry relation <math>D\gamma_5+\gamma_5 D=0</math> (where <math>D ...5 KB (614 words) - 13:10, 9 June 2023
- ...11083109X |issn=1540-3459|citeseerx=10.1.1.299.4261 }}</ref> In analogy to continuum phase-field models, where regions with ''u'' close to 0 or 1 are models for ...th>\Delta</math> is the [[Laplacian matrix|graph Laplacian]]. The ordinary continuum Allen–Cahn equation and the graph Allen–Cahn equation are natural counterpa ...4 KB (532 words) - 12:15, 25 October 2024
- ...torque is a function of local curvature. At a [[Timoshenko–Ehrenfest beam theory|more refined level]], the beam is a 2D body whose stress-tensor is a functi ...book|last1=Kline|first1=S.J.|year=2012|title=Similitude and Approximation Theory|edition=2012|publisher=Springer Science & Business Media|location=Berlin / ...8 KB (1,093 words) - 05:41, 18 February 2025
- ...A.A. Schekochihin. Astrophysical gyrokinetics: Basic equations and linear theory. ApJ, 651(1):590, 2006.</ref> The starting point is the [[Fokker–Planck equ ...Taylor and R.J. Hastie, Stability of general plasma equilibria - I formal theory. Plasma Phys. 10:479, 1968. ...8 KB (1,195 words) - 19:03, 23 February 2025
- ...anch of mathematics, the '''Burnett equations''' are a set of higher-order continuum equations for non-equilibrium flows and the transition regimes where the [[ {{continuum mechanics}} ...6 KB (765 words) - 20:09, 2 October 2024
- {{Short description|Set theory concept}} ...n them are [[mathematical proof|provable]], and constructing models of set theory for various [[consistency|consistent]] configurations of them. ...10 KB (1,598 words) - 07:02, 2 November 2024
- ...J. Brouwer]] (1918B), and was used to define the [[Continuum_(set_theory)|continuum]]. As his ideas were developed, the use of spreads became common in [[Intui [[Graph Theory|Graph theoretically]], one may think of a spread in terms of a [[Tree_(grap ...8 KB (1,221 words) - 21:23, 17 May 2023
- In [[mathematics|mathematical]] [[set theory]], '''Baumgartner's axiom (BA)''' can be one of three different [[axiom]]s ...th a combination of [[ZFC]], [[Martin's axiom]], and the negation of the [[continuum hypothesis]],<ref>{{citation|last=Baumgartner|first=James E.|doi=10.4064/fm ...4 KB (534 words) - 07:39, 7 November 2024
- {{Short description|Method for constructing models of set theory}} ...erated forcing can construct models where [[Martin's axiom]] holds and the continuum is any given regular cardinal. ...3 KB (486 words) - 03:26, 20 March 2023
- ...r Elastic Deformations'', Dover.</ref><ref>L. D. Landau, E. M. Lifshitz, ''Theory of Elasticity'', third edition</ref> ...surface. The quantity <math>\boldsymbol{F}</math> is the [[Finite strain theory#Deformation gradient tensor|deformation gradient tensor]], <math>J</math> i ...13 KB (1,923 words) - 03:07, 27 August 2023
- ...n other words, the endpoints of all stress vectors at a given point in the continuum body lie on the stress ellipsoid surface, i.e., the radius-vector from the | title = Theory of Elasticity ...4 KB (690 words) - 04:28, 14 February 2025