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Glite Dictionary
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Laplacian

Laplacian

1 9.9
About the Laplace operator used in math and physics
  • adjective
  • /ləˈplæs.i.ən/
  • Specialized
: laplaciano
  • To apply the Laplacian in calculations, one must understand its role in calculating curvature and diffusion processes.
  • Laplacian distribution

Examples

  • In physics, the concept of a Laplacian is crucial for solving partial differential equations involving second derivatives.

  • The pyramid transform can be implemented using Laplacian pyramid, contrast pyramid, gradient pyramid, and the morphological pyramid.

    Academic text (2016)

  • With the Laplacian operator defined as:

    Academic text (1995)

  • Apart from the incredibly fine-tuning required to make it happen, quantum uncertainty and the existence of chaotic systems that affect human life and biological evolution would prevent such a Laplacian mechanical prediction from working out.

    Academic text (2006)

  • The dithering technique based on the Laplacian model for AC coefficients is proposed in Ref. 5 to perform DCT histogram smoothing.

    Academic text (2017)

  • The behavior of wave functions can be described using the Laplacian operator to analyze quantum systems.

Surface Forms

Laplacian positive

Morphology

Laplacian = Laplace (semi-transparent) = Laplace + ian

Formally transparent as 'Laplace' + '-ian', but the meaning is specialized and requires knowledge of the mathematician/operator.

Etymology

Laplacian comes from the French mathematician Laplace and the ending -ian, which means 'related to'. Just like Newtonian means 'of Newton', Laplacian means 'of Laplace', so when something is Laplacian it is about Laplace's math tool that describes how things like heat or sound change in space.