In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean...
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In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean...
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In mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete...
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=\nabla \cdot \nabla =\nabla ^{2}} is the Laplace operator, ∇ ⋅ {\displaystyle \nabla \cdot } is the divergence operator (also symbolized "div"), ∇ {\displaystyle...
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partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined by the condition that...
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In mathematics, the Laplace transform, named after Pierre-Simon Laplace (/ləˈplɑːs/), is an integral transform that converts a function of a real variable...
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The discrete Laplace operator Δ h u {\displaystyle \Delta _{h}u} depends on the dimension n {\displaystyle n} . In 1D the Laplace operator is approximated...
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Pierre-Simon, Marquis de Laplace (/ləˈplɑːs/; French: [pjɛʁ simɔ̃ laplas]; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work...
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Biharmonic equation (redirect from Bi-Laplace operator)
\nabla ^{4}} , which is the fourth power of the del operator and the square of the Laplacian operator ∇ 2 {\displaystyle \nabla ^{2}} (or Δ {\displaystyle...
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the Green's function (or fundamental solution) for the Laplacian (or Laplace operator) in three variables is used to describe the response of a particular...
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Laplacian matrix (redirect from Laplace matrix)
Named after Pierre-Simon Laplace, the graph Laplacian matrix can be viewed as a matrix form of the negative discrete Laplace operator on a graph approximating...
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tensors of rank 0), the connection Laplacian is often called the Laplace–Beltrami operator. It is defined as the trace of the second covariant derivative:...
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Feature extraction Discrete Laplace operator Prewitt operator Irwin Sobel, 2014, History and Definition of the Sobel Operator K. Engel (2006). Real-time...
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mathematics, the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the linear partial differential equation: ∇ 2 f...
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, {\displaystyle \Delta _{0}\log f=-Kf^{2},} where ∆0 is the flat Laplace operator Δ 0 = ∂ 2 ∂ x 2 + ∂ 2 ∂ y 2 = 4 ∂ ∂ z ∂ ∂ z ¯ . {\displaystyle \Delta...
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sometimes quabla operator (cf. nabla symbol) is the Laplace operator of Minkowski space. The operator is named after French mathematician and physicist...
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be realized as the codifferential opposite to the gradient operator, and the Laplace operator on a function is the divergence of its gradient. An important...
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Del squared may refer to: Laplace operator, a differential operator often denoted by the symbol ∇2 Hessian matrix, sometimes denoted by ∇2 Aitken's delta-squared...
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discrete operators on graphs which are analogous to differential operators in calculus, such as graph Laplacians (or discrete Laplace operators) as discrete...
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differential equation. In applications to the physical sciences, operators such as the Laplace operator play a major role in setting up and solving partial differential...
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P-Laplacian (redirect from P-Laplace operator)
p-Laplace operator, is a quasilinear elliptic partial differential operator of 2nd order. It is a nonlinear generalization of the Laplace operator, where...
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Hamiltonian (quantum mechanics) (redirect from Hamiltonian Operator)
\nabla ^{2}} . In three dimensions using Cartesian coordinates the Laplace operator is ∇ 2 = ∂ 2 ∂ x 2 + ∂ 2 ∂ y 2 + ∂ 2 ∂ z 2 {\displaystyle \nabla ^{2}={\frac...
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Discrete calculus (category Linear operators in calculus)
corresponding multiplication is graded-commutative. See references. The Laplace operator Δ f {\displaystyle \Delta f} of a function f {\displaystyle f} at a...
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bounded. This operator is in fact a compact operator. The compact operators form an important class of bounded operators. The Laplace operator Δ : H 2 ( R...
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down quarks. alt-J (Δ), a British indie band Laplace operator (Δ), a differential operator Increment operator (∆) Symmetric difference, in mathematics, the...
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Inequality. (See talk on the article). As a simple example, consider the Laplace operator Δ. More specifically, suppose that one wishes to solve, for f ∈ L2(Ω)...
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Spectral shape analysis (section Laplace)
eigenfunctions) of the Laplace–Beltrami operator to compare and analyze geometric shapes. Since the spectrum of the Laplace–Beltrami operator is invariant under...
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Infinity Laplacian (redirect from Infinity Laplace operator)
mathematics, the infinity Laplace (or L ∞ {\displaystyle L^{\infty }} -Laplace) operator is a 2nd-order partial differential operator, commonly abbreviated...
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Ja. (1980), "The second term of the spectral asymptotics for a Laplace–Beltrami operator on manifolds with boundary", Funktsional. Anal. I Prilozhen, 14...
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Del (redirect from Nabla operator)
an operator that takes scalar to a scalar. It can be extended to operate on a vector, by separately operating on each of its components. The Laplace operator...
21 KB (3,846 words) - 05:41, 26 May 2024