|
gptkbp:instanceOf
|
differential operator
|
|
gptkbp:actsOn
|
vector fields
scalar fields
|
|
gptkbp:alsoKnownAs
|
gptkb:Laplace_operator
|
|
gptkbp:application
|
gptkb:heat_equation
gptkb:wave_equation
gptkb:Laplace's_equation
gptkb:Poisson's_equation
|
|
gptkbp:coordinates
|
gptkb:cylindrical_coordinates
gptkb:spherical_coordinates
Cartesian coordinates
|
|
gptkbp:defines
|
sum of second partial derivatives
|
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gptkbp:discreteVersion
|
gptkb:discrete_Laplacian
gptkb:graph_Laplacian
|
|
gptkbp:eigenfunctions
|
harmonic functions
|
|
gptkbp:field
|
gptkb:mathematics
physics
|
|
gptkbp:generalizes
|
gptkb:Laplace–Beltrami_operator
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Laplacian
|
|
gptkbp:namedAfter
|
gptkb:Pierre-Simon_Laplace
|
|
gptkbp:notation
|
div grad
Δ
∇²
|
|
gptkbp:property
|
gptkb:self-adjoint_operator
elliptic operator
linear operator
|
|
gptkbp:relatedTo
|
curl
divergence
gradient
|
|
gptkbp:spectrumOfActivity
|
eigenvalues
|
|
gptkbp:symbol
|
∇²
|
|
gptkbp:usedIn
|
gptkb:spectral_graph_theory
gptkb:machine_learning
gptkb:probability_theory
gptkb:signal_processing
gptkb:Riemannian_geometry
Brownian motion
computer vision
differential geometry
fluid dynamics
partial differential equations
quantum mechanics
stochastic processes
image processing
vector calculus
network analysis
potential theory
electrostatics
random walks
|
|
gptkbp:bfsParent
|
gptkb:Laplace_operator
gptkb:Bochner–Weitzenböck_formula
gptkb:Bochner_formula
gptkb:Bochner_identity
gptkb:Vektoranalysis
gptkb:Divergence
gptkb:Poisson's_equation
|
|
gptkbp:bfsLayer
|
6
|