In mathematics, the "'discrete Laplace operator "'is an analog of the continuous Laplace operator, defined so that it has meaning on a discrete grid.
32.
Most edge-detection algorithms are sensitive to noise; the 2-D Laplacian filter, built from a discretization of the Laplace operator, is highly sensitive to noisy environments.
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Where \ nabla ^ 2 is the Laplace operator, p is the acoustic pressure ( the local deviation from the ambient pressure ), and where c is the speed of sound.
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The hypotheses of G�rding's inequality are easy to verify for the Laplace operator ?, so there exist constants " C " and " G " e " 0
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In mathematical analysis, one often studies solution to partial differential equations, an important example of which is harmonic analysis, where one studies harmonic functions : the kernel of the Laplace operator.
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I believe this is more or less solvable when only a finite number of the a _ n aren't zero; e . g . the discrete Laplace operator is a famous special case.
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The delta function has only radial dependence, so the Laplace operator ( a . k . a . scalar Laplacian ) in the spherical coordinate system simplifies to ( see del in cylindrical and spherical coordinates)
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In one class of finite element methods, boundary-value problems for differential equations involving the Hodge-Laplace operator may need to be solved on topologically nontrivial domains, for example, in electromagnetic simulations.
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This fact plays a role in the study of the Dirichlet problem, and in the fact that there exists an orthonormal basis of consisting of eigenvectors of the Laplace operator ( with Dirichlet boundary condition ).
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Above, the generator ( and hence characteristic operator ) of Brownian motion on "'R " "'n " was calculated to be ��, where ? denotes the Laplace operator.
