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- ...feet, and [[water strider]]s to name a few. The majority of self-cleaning surfaces can be placed into three categories:<br> ...lf-cleaning [[nanoparticle]]s that can be incorporated into other material surfaces to allow them to self-clean.<ref>{{Cite journal|last1=Shen|first1=Weiguo|la ...50 KB (7,080 words) - 07:48, 19 May 2024
- '''Phenotypic response surfaces (PRS)''' is an [[artificial intelligence]]-guided [[personalized medicine]] Phenotypic response surfaces fit a parabolic surface to a set of drug doses and biomarker values based o ...14 KB (2,019 words) - 00:33, 16 March 2024
- In [[mathematics]], '''systolic inequalities for curves on surfaces''' were first studied by [[Charles Loewner]] in 1949<!-- That should be lis ...totic behavior for large genus <math>g</math> of the systole of hyperbolic surfaces reveals some interesting constants. Thus, [[Hurwitz surface]]s <math>\Sigm ...7 KB (1,022 words) - 10:17, 30 January 2024
- The '''calculus of moving surfaces''' ('''CMS''') <ref>Grinfeld, P. (2010). "Hamiltonian Dynamic Equations for [[Category:Calculus|Moving surfaces]] ...9 KB (1,360 words) - 23:07, 4 February 2025
- ...such as [[computer-aided design]] and [[computer-aided manufacturing]], '''surfaces''' are one way of representing objects. The other ways are [[Wire-frame mo ==Open and closed surfaces== ...10 KB (1,560 words) - 23:58, 18 January 2025
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- {{Short description|Smooth, connected 2D surfaces in fluid dynamics}} .... International journal of engineering science, 35(3), 197–209.</ref> Lamb surfaces are orthogonal to the [[Lamb vector]] <math>\boldsymbol{\omega}\times\mathb ...1 KB (159 words) - 15:48, 30 August 2023
- [[File:Saddle Tower Minimal Surfaces.png|thumb|Two periods of a 3-fold saddle tower.]] ...Math. 62 (1988) pp. 83–114.</ref><ref>H. Karcher, Construction of minimal surfaces, in "Surveys in Geometry", Univ. of Tokyo, 1989, and Lecture Notes No. 12, ...1 KB (172 words) - 21:51, 9 February 2025
- {{About|the minimal surface|the ruled surfaces|Catalan surface}} ...ed by [[Eugène Charles Catalan]] in 1855.<ref>Catalan, E. "Mémoire sur les surfaces dont les rayons de courbures en chaque point, sont égaux et les signes cont ...2 KB (233 words) - 07:09, 15 July 2020
- In mathematics, a '''Burniat surface''' is one of the [[surfaces of general type]] introduced by {{harvs|txt|last=Burniat|first=Pol|year=196 ...t3=Chris A.M. | last4=Van de Ven | first4=Antonius | title=Compact Complex Surfaces | publisher= Springer-Verlag, Berlin | series=Ergebnisse der Mathematik und ...1 KB (140 words) - 17:42, 23 June 2024
- ...Chen-Gackstatter-Thayer surfaces.png|thumb|The first nine Chen–Gackstatter surfaces.]] ...her-genus Chen–Gackstatter surfaces and the Weierstrass representation for surfaces of infinite genus|journal=Experiment. Math.|volume=4|issue=1|year=1995|page ...3 KB (383 words) - 03:09, 23 October 2022
- ...ines. The term "Segre surface" is also occasionally used for various other surfaces, such as a quadric in 3-dimensional projective space, or the hypersurface *{{Citation | last1=Segre | first1=Corrado | title=Etude des différentes surfaces du 4<sup>e</sup> ordre à conique double ou cuspidale (générale ou décomposé ...2 KB (216 words) - 05:08, 4 April 2021
- ...ra theorem, valid in algebraic geometry over the complex numbers, has such surfaces as counterexamples, and these can only exist in [[characteristic p|characte ...ud surfaces''' were introduced in {{harv|Lang|1983}}, and give examples of surfaces of general type with global vector fields. ...2 KB (258 words) - 06:05, 25 December 2023
- ...?PPN591417707</ref><ref>Eric A. Lord, and Alan L. Mackay, Periodic minimal surfaces of cubic symmetry, Current science, vol. 85, no. 3, 10 August 2003</ref> ...tallography of soft materials.<ref>AL Mackay, Flexicrystallography: curved surfaces in chemical structures, Current Science, 69:2 25 July 1995</ref> ...2 KB (293 words) - 09:44, 18 January 2025
- ...ich are in fact [[quartic curve]]s over {{tmath|\mathbb{C} }}, and quartic surfaces over {{tmath|\mathbb{R} }}. For instance, the [[Klein quartic]] is a ''real ==Special quartic surfaces== ...3 KB (408 words) - 20:28, 26 May 2022
- ...Châtelet (mathematician)| title=Points rationnels sur certaines courbes et surfaces cubiques | url=http://retro.seals.ch/digbib/view?rid=ensmat-001:1959:5::55 ...mr=2914907|pages=231–236|title=Failure of the Hasse principle for Châtelet surfaces in characteristic 2|url=https://jtnb.cedram.org/item?id=JTNB_2012__24_1_231 ...1 KB (200 words) - 21:57, 21 April 2022
- ==Aspheric surfaces== Optical surfaces with non-spherical profiles, such as the surfaces of [[aspheric lens]]es, are typically designed such that their sag is descr ...2 KB (293 words) - 04:06, 18 January 2025
- {{About|the ruled surfaces|the minimal surface|Catalan's minimal surface}} ...arametric equations]] of the Catalan surface are [http://www.mathcurve.com/surfaces/catalan/catalan.shtml] ...2 KB (305 words) - 20:02, 31 July 2024
- ...the circular surface.<ref>S. Izumiya, K. Saji, and N. Takeuchi, "Circular Surfaces", ''Advances in Geometry'', de Gruyter, Vol 7, 2007, 295–313.</ref> ...ar surfaces are an analogue of [[ruled surface]]s. In the case of circular surfaces the generators are circles; called the generating circles. In the case of r ...2 KB (279 words) - 21:59, 14 November 2018
- ...et]] family) of a [[minimal surface]] is a one-parameter family of minimal surfaces which share the same [[Weierstrass–Enneper parameterization|Weierstrass dat ...nimal Surfaces in Euclidean Space by Examples, in Global Theory of Minimal Surfaces: ...3 KB (424 words) - 12:45, 20 January 2025
- ...uclidean space]]. It is named after [[Edmond Bour]], whose work on minimal surfaces won him the 1861 mathematics prize of the French Academy of Sciences.<ref>{ ...ion]].<ref>Ulrich Dierkes, Stefan Hildebrandt, Friedrich Sauvigny, Minimal Surfaces, Volume 1. Springer 2010</ref> ...2 KB (324 words) - 18:51, 9 May 2023
- In mathematics, a '''Catanese surface''' is one of the [[surfaces of general type]] introduced by {{harvs|txt|last=Catanese|first=Fabrizio|au ...ere is a group of order 5 [[free group action|acting freely]] on all these surfaces, then the quotient ''Z'' of ''Y'' by this group of order 5 is a Catanese su ...2 KB (253 words) - 23:58, 10 September 2024
- Sarti has also found sextic, octic and dodectic nodal surfaces with high numbers of nodes and high degrees of symmetry. | title = Pencils of symmetric surfaces in <math>\mathbb{P}_3</math> ...2 KB (298 words) - 00:43, 22 May 2024
- ...ref>M. Elisa G. G. de Oliveira, Some New Examples of Nonorientable Minimal Surfaces, Proceedings of the American Mathematical Society, Vol. 98, No. 4, Dec., 19 ...-Wing Fung, Minimal Surfaces as Isotropic Curves in C3: Associated minimal surfaces and the Björling's problem. MIT BA Thesis. 2004 http://ocw.mit.edu/courses/ ...2 KB (315 words) - 17:16, 24 May 2024
- ...& Tibor Radó, World Scientific, 1992 (p. 239-240)</ref> It is a family of surfaces with one planar [[End (topology)|end]] and one [[Enneper surface]]-like sel ...1680/11/1/26 Erhan Güler and Ömer Kişi, ''(ζ−m, ζm)-Type Algebraic Minimal Surfaces in Three-Dimensional Euclidean Space''] ...2 KB (250 words) - 21:06, 6 January 2025
- ...n |last2=Larsson |title=Bonnet Transformation of Infinite Periodic Minimal Surfaces with Hexagonal Symmetry |journal=J. Chem. Soc. Faraday Trans. |year=1990 |v ...or=Adam G. Weyhaupt |title=Deformations of the gyroid and lidinoid minimal surfaces |journal=Pacific Journal of Mathematics |volume=235 |year=2008 |issue=1 |pa ...2 KB (323 words) - 11:38, 18 January 2023