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• Navier–Stokes equations
  $$\frac{\partial v}{\partial t} = − \star (v ∧ \star dv) + \frac{1}{2}d||v||^2 − dp + \mu d^∗dv. $$ $$\frac{\partial v}{\partial t} + \star (v ∧ \star dv) - \frac{1}{2}d||v||^2 = − dp + \mu d^∗dv. $$
  5 KB (742 words) - 03:32, 30 August 2012
• Calculus I, the discrete version
  *an edge $a=[x,x+h]$ corresponds to the node $a^\star=x+h/2$; and *a node $x$ corresponds to the edge $x^\star=[x-h/2,x+h/2]$. $\\$
  64 KB (11,521 words) - 19:48, 22 June 2017
• Rating votes
  ...r\quad \star\star\star\quad \star\star\star\star\quad \star\star\star\star\star\ .$$
  9 KB (1,553 words) - 06:12, 22 June 2016
• Triangulations
  ...n a simplicial complex $K$ and a vertex $A$ in $K$, the ''star''<!--\index{star}--> of $A$ in $K$ is the collection of all simplices in $K$ that contain $A The ''open star''<!--\index{open star}--> is the union of the insides of all these cells:
  30 KB (5,172 words) - 21:52, 26 November 2015
• Wave equation from Maxwell equations
  In terms of the [[Hodge duality|Hodge star operator]], the ''constitutive relations'' are: $$D=\varepsilon_0 \star E,$$
  4 KB (655 words) - 14:51, 13 July 2012
• Higher order votes
  ...r\quad \star\star\star\quad \star\star\star\star\quad \star\star\star\star\star\ .$$
  41 KB (6,942 words) - 05:04, 22 June 2016
• Discrete forms and cochains
  ...uad \star\star\star\quad \star\star\star\star\quad \star\star\star\star\star\ .$$
  34 KB (5,619 words) - 16:00, 30 November 2015
• Modeling with discrete exterior calculus
  ...{n}^{(i,j)})=-\frac{k}{4} \Big[ d_{x}(\star d_{x}(T_{n}^{(i-1,j)}))+d_{y}(\star d_{y}(T_{n}^{(i,j-1)})) \Big]\end{equation} where $d_{x}$ denotes an exterior derivative with respect to $x$ and $\star$ denotes the use of the Hodge Duality.
  31 KB (5,254 words) - 17:57, 21 July 2012
• Forms
  ...of $K$ is the set of $1$-chains over $R$ generated by the $1$-dimensional star of the vertex $A$: ...the edges adjacent to $A$, we can also think of all $1$-''chains'' in the star of $A$ as directions at $A$. They are subject to algebraic operations on ch
  13 KB (2,459 words) - 03:27, 25 June 2015
• Hodge duality of multivectors
  $$\star: \Lambda _k(V) \to \Lambda _{n-k}(V),$$ $$\star (p_{s(1)} \wedge p_{s(2)}\wedge ... \wedge p_{s(k)}):= (-1)^{\pi(s)}p_{s(k+
  3 KB (488 words) - 12:34, 14 August 2015
• Maxwell equations
  In terms of the [[Hodge duality|Hodge star operator]], the ''constitutive relations'' are: $$D=\varepsilon_0 \star E,$$
  6 KB (922 words) - 00:30, 9 April 2016
• ODEs
  ...K={\mathbb R}$ with the standard geometry: $|a|=1$ for all $a\in K,a\in K^\star$. for a given $a$. Here $r' '=\star d \star d r$, where $\star$ is the Hodge star operator of $K$.
  47 KB (8,415 words) - 15:46, 1 December 2015
• Topology Illustrated -- Index
  *[[Hodge star operator|Hodge star operator]] *[[open star|open star]]
  16 KB (1,773 words) - 00:41, 17 February 2016
• Maps of polyhedra
  ..., we realize that we are talking about $a$ and $f(a)$ located within the ''star'' of the corresponding vertex! Recall that given a complex $K$ and a vertex $A$ in $K$, the star<!--\index{star}--> of $A$ in $K$ is the collection of all cells in $K$ that contain $A$:
  51 KB (9,162 words) - 15:33, 1 December 2015
• Hodge dual
  ...- k)$-cochain is defined by its value on the [[Hodge duality|dual cell]] $\star a$ by $$\frac{1}{|\star a|}<\star \phi, \star a> = \frac{1}{|a|}<\phi, a>$$
  1,003 bytes (159 words) - 14:01, 27 July 2012
• Hodge duality of cubical forms
  Of course, the star operator is now extended to [[chains]] by [[linearity]]. With this arrangement we also ensure that we have $\star \star =Id$.
  7 KB (1,114 words) - 18:10, 27 August 2015
• Axioms of calculus
  ...we start with the set of all cells that contain $A$ called the (open) ''[[star]] of vertex'' $A$, Then the ''Hodge star operators'' are linear operators on the chain complexes:
  6 KB (1,124 words) - 14:17, 4 August 2013
• Manifolds
  ...erse may be ''curved''. For example, the observation that the light from a star passing the sun deviates from a straight line may be considered as evidence ...definition. First, by the above theorem, $K$ has to be a graph. Since the star of a vertex with more than one adjacent edge isn't homeomorphic to the open
  51 KB (8,919 words) - 01:58, 30 November 2015
• Codiffferential
  $$\delta = (-1)^{nk + n + 1}s\, {\star d\star} = (-1)^k\,{\star^{-1}d\star},$$
  382 bytes (57 words) - 03:15, 5 October 2012
• Convergence of the discrete to the continuous
  where $A_n$ is in the star of $A$ and $B_n$ is in the star of $B$ in $K_{nm}$, and where $A_n$ is in the star of $A$ and $B_n$ is in the star of $B$ in $K_{nm}$, and
  21 KB (3,664 words) - 02:02, 18 July 2018

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