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- ...n [[differential geometry]] and [[geometric topology]], the '''Milnor–Wood inequality''' is an obstruction to endow circle bundles over surfaces with a flat stru == The inequality == ...2 KB (347 words) - 08:50, 15 October 2024
- ...quant-ph/0610146].</ref> as an optimal refinement of Mark Fannes' original inequality, which was published in 1973.<ref name=":0">M. Fannes, [https://doi.org/10. == Statement of inequality == ...4 KB (569 words) - 10:05, 29 August 2024
- In [[quantum chemistry]] and [[physics]], the '''Lieb–Oxford inequality''' provides a lower bound for the indirect part of the [[Coulomb energy]] o ...nsity functional theory]] and plays a role in the proof of [[Lieb–Thirring inequality#The stability of matter|stability of matter]]. ...13 KB (1,877 words) - 21:45, 25 February 2025
- In mathematics, the '''Askey–Gasper inequality''' is an inequality for [[Jacobi polynomial]]s proved by {{harvs|txt| first=Richard| last=Askey In this form, with {{mvar|α}} a non-negative integer, the inequality was used by [[Louis de Branges]] in his proof of the [[de Branges's theorem ...4 KB (509 words) - 00:20, 10 January 2025
- In mathematics, the '''max–min inequality''' is as follows: ...n Z} g(z) \leq h(w) </math> holds for all <math>w \in W </math>. From this inequality, we also see that <math>\sup_{z \in Z} g(z) </math> is a lower bound on <ma ...2 KB (432 words) - 23:18, 18 August 2024
- ...ield of [[mathematical analysis]], an '''interpolation inequality''' is an inequality of the form ...math>, including [[Hölder's inequality|Hölder's Inequality]] and [[Young's inequality for convolutions]] which are also presented below. ...7 KB (1,098 words) - 01:14, 27 January 2025
- ...is not much larger than <math>A</math>. A slightly weaker version of this inequality was originally proven and published by Helmut Plünnecke (1970).<ref name=Pl ...ter published a simpler proof of the current, more general, version of the inequality. ...15 KB (2,856 words) - 08:52, 19 January 2023
- {{Short description|Inequality on the coefficients of the exponential of a power series}} In mathematics, the '''Lebedev–Milin inequality''' is any of several inequalities for the coefficients of the exponential o ...3 KB (413 words) - 19:54, 7 July 2024
- ...n the domain must actually be a ball. In the case of <math>n=2</math>, the inequality essentially states that among all drums of equal area, the circular drum (u ...equality holds in any [[Riemannian manifold]] in which the [[isoperimetric inequality]] holds.<ref>{{Cite book|url=http://worldcat.org/oclc/1106800772|title=Eige ...2 KB (249 words) - 17:53, 22 December 2024
- ...conjecture of [[John Ringrose]]. It is an extension of the [[Grothendieck inequality]]. *[[Haagerup-Pisier inequality]] ...2 KB (235 words) - 09:24, 18 August 2023
- The '''Bohr–Favard inequality''' is an inequality appearing in a problem of [[Harald Bohr]]<ref name="bohr1935theoreme">{{Cit ...of the integral of an almost-periodic function. The ultimate form of this inequality was given by [[Jean Favard]];<ref name="favard1937meilleurs">{{Cite journal ...2 KB (334 words) - 09:02, 3 August 2023
- {{Short description|Inequality which involves a linear function}} ...a [[linear function]]. A linear inequality contains one of the symbols of inequality:<ref>{{harvnb|Miller|Heeren|1986|loc=p. 355}}</ref> ...7 KB (1,101 words) - 03:21, 22 February 2025
- ...2006 |chapter=The Clausius–Duhem Inequality, an Interesting and Productive Inequality |title=Nonsmooth Mechanics and Analysis |series=Advances in mechanics and m This inequality is a statement concerning the irreversibility of natural processes, especia ...10 KB (1,470 words) - 02:41, 29 October 2023
- ...'Kunita–Watanabe inequality''' is a generalization of the [[Cauchy–Schwarz inequality]] to integrals of [[stochastic processes]]. ...2 KB (210 words) - 10:01, 3 April 2023
- In mathematics, the '''Bhatia–Davis inequality''', named after [[Rajendra Bhatia]] and [[Chandler Davis]], is an [[upper b Then the Bhatia–Davis inequality states: ...4 KB (572 words) - 04:17, 13 March 2024
- In [[Mathematics]], the '''Mashreghi–Ransford inequality''' is a bound on the growth rate of certain [[sequences]]. It is named aft {{DEFAULTSORT:Mashreghi-Ransford inequality}} ...2 KB (269 words) - 09:41, 3 January 2023
- ...happening simultaneously by their pairwise dependence. Informally Janson's inequality involves taking a sample of many independent random [[binary data|binary va Then the Janson inequality is: ...4 KB (588 words) - 12:42, 3 December 2024
- ...arvtxt|Kallman|Rota|1970}}, is a generalization of the [[Landau–Kolmogorov inequality]] to [[Banach spaces]]. It states that | contribution = On the inequality <math>\Vert f^{\prime} \Vert^{2}\leqq4\Vert f\Vert\cdot\Vert f''\Vert</math ...898 bytes (108 words) - 17:00, 15 July 2017
- In [[mathematics]], the '''Whitney inequality''' gives an upper bound for the error of best approximation of a function b ...>W(k)</math> is the smallest value of <math>W_k</math> for which the above inequality holds. The theorem is particularly useful when applied on intervals of smal ...6 KB (1,060 words) - 01:18, 12 January 2025
- In [[differential geometry]] the '''Hitchin–Thorpe inequality''' is a relation which restricts the topology of [[4-manifold]]s that carry == Statement of the Hitchin–Thorpe inequality == ...6 KB (847 words) - 18:47, 29 January 2024
Page text matches
- ...arvtxt|Kallman|Rota|1970}}, is a generalization of the [[Landau–Kolmogorov inequality]] to [[Banach spaces]]. It states that | contribution = On the inequality <math>\Vert f^{\prime} \Vert^{2}\leqq4\Vert f\Vert\cdot\Vert f''\Vert</math ...898 bytes (108 words) - 17:00, 15 July 2017
- ...n the domain must actually be a ball. In the case of <math>n=2</math>, the inequality essentially states that among all drums of equal area, the circular drum (u ...equality holds in any [[Riemannian manifold]] in which the [[isoperimetric inequality]] holds.<ref>{{Cite book|url=http://worldcat.org/oclc/1106800772|title=Eige ...2 KB (249 words) - 17:53, 22 December 2024
- ...lts that share the common name of the '''Ky Fan inequality'''. The Ky Fan inequality presented here is used in [[game theory]] to investigate the existence of a Another [[Ky Fan inequality]] is an [[inequality (mathematics)|inequality]] involving the [[geometric mean]] and [[arithmetic mean]] of two sets of [ ...1 KB (185 words) - 19:10, 5 July 2022
- {{Short description|Probabilistic inequality}} ...[supermartingale]] exceeds a certain value. The [[inequality (mathematics)|inequality]] is named after [[Jean Ville]], who proved it in 1939.<ref>{{cite thesis ...2 KB (202 words) - 04:45, 13 March 2024
- {{distinguish|Hadamard's inequality}} ...Hermite]] and [[Jacques Hadamard]] and sometimes also called '''Hadamard's inequality''', states that if a function ''f'' : [''a'', ''b''] →& ...2 KB (276 words) - 23:07, 6 February 2025
- {{Short description|Inequality for the number of extensions of partial orders to linear orders}} ...for the number of [[linear extension]]s of finite [[partial order]]s. The inequality was conjectured by [[Ivan Rival]] and Bill Sands in 1981. It was proved by ...2 KB (297 words) - 20:39, 19 March 2023
- '''Aristarchus's inequality''' (after the Greek [[Ancient Greek astronomy|astronomer]] and [[Greek math === Proof of the first inequality === ...3 KB (506 words) - 05:30, 11 February 2025
- In [[mathematics]], '''Mahler's inequality''', named after [[Kurt Mahler]], states that the [[geometric mean]] of the By the [[inequality of arithmetic and geometric means]], we have: ...1 KB (208 words) - 05:09, 16 October 2022
- In mathematics, the '''Fekete–Szegő inequality''' is an inequality for the coefficients of [[univalent function|univalent]] [[analytic functio The Fekete–Szegő inequality states that if ...1 KB (151 words) - 03:44, 17 April 2024
- [[File:Jordan inequality.svg|thumb|upright=1.2|<math>\frac{2}{\pi}x\leq \sin(x) \leq x\text{ for }x [[File:Jordans inequality.svg|thumb|upright=1.2|[[unit circle]] with angle x and a second circle with ...2 KB (309 words) - 20:34, 8 July 2023
- ...he [[Weyl equidistribution estimate]]. Loosely stated, the van der Corput inequality asserts that if a [[unit vector]] <math>v</math> in an [[inner product spac ==Statement of the inequality== ...3 KB (535 words) - 10:36, 18 March 2021
- ...conjecture of [[John Ringrose]]. It is an extension of the [[Grothendieck inequality]]. *[[Haagerup-Pisier inequality]] ...2 KB (235 words) - 09:24, 18 August 2023
- '''Abhyankar's inequality''' is an inequality involving extensions of [[valued field]]s in [[algebra]], introduced by {{h Abhyankar's inequality states that for an extension ''K''/''k'' of [[valued field]]s, the [[transc ...1,009 bytes (128 words) - 19:50, 12 September 2024
- ...anu.pdf "Concentration-of-measure inequalities" by Gábor Lugosi]</ref> The inequality states that, for <math>\lambda > 0,</math> Applying the Cantelli inequality to <math>-X</math> gives a bound on the lower tail, ...4 KB (597 words) - 17:48, 9 September 2024
- ...equality]]. It is an important lemma in the proof of the [[Plünnecke-Ruzsa inequality]]. <!-- The referenced article on the Plünnecke-Ruzsa inequality is currently a draft and has been submitted concurrently with this one. --> ...5 KB (944 words) - 18:29, 8 December 2024
- The '''Bohr–Favard inequality''' is an inequality appearing in a problem of [[Harald Bohr]]<ref name="bohr1935theoreme">{{Cit ...of the integral of an almost-periodic function. The ultimate form of this inequality was given by [[Jean Favard]];<ref name="favard1937meilleurs">{{Cite journal ...2 KB (334 words) - 09:02, 3 August 2023
- {{short description|Correlation-type inequality for four functions on a finite distributive lattice}} ...swede|Daykin|1978}}, also known as the '''four functions theorem''' (or '''inequality'''), ...3 KB (396 words) - 17:04, 16 August 2023
- ...anonical [[Gaussian measure]]. It generalizes the [[Gaussian isoperimetric inequality]]. ...quality on the discrete cube, and an elementary proof of the isoperimetric inequality in Gauss space|volume=25|journal=The Annals of Probability|number=1|publish ...3 KB (367 words) - 20:31, 3 February 2024
- In [[mathematics]], the '''three spheres inequality''' bounds the <math>L^2</math> norm of a [[harmonic function]] on a given [ == Statement of the three spheres inequality == ...1 KB (203 words) - 09:19, 5 February 2024
- In [[mathematical analysis]], the '''Young's inequality for integral operators''', is a bound on the <math>L^p\to L^q</math> [[oper ...y) = h (x - y) </math>, then the inequality becomes [[Young's convolution inequality]]. ...1 KB (228 words) - 01:39, 29 February 2020