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  2. Laplace operator - Wikipedia

    en.wikipedia.org/wiki/Laplace_operator

    The Laplace operator is named after the French mathematician Pierre-Simon de Laplace (1749–1827), who first applied the operator to the study of celestial mechanics: the Laplacian of the gravitational potential due to a given mass density distribution is a constant multiple of that density distribution.

  3. Laplace operators in differential geometry - Wikipedia

    en.wikipedia.org/wiki/Laplace_operators_in...

    The Hodge Laplacian, also known as the Laplace–de Rham operator, is a differential operator acting on differential forms. (Abstractly, it is a second order operator on each exterior power of the cotangent bundle.) This operator is defined on any manifold equipped with a Riemannian- or pseudo-Riemannian metric.

  4. List of Laplace transforms - Wikipedia

    en.wikipedia.org/wiki/List_of_Laplace_transforms

    The unilateral Laplace transform takes as input a function whose time domain is the non-negative reals, which is why all of the time domain functions in the table below are multiples of the Heaviside step function, u(t). The entries of the table that involve a time delay τ are required to be causal (meaning that τ > 0).

  5. Laplace transform - Wikipedia

    en.wikipedia.org/wiki/Laplace_transform

    The following table provides Laplace transforms for many common functions of a single variable. [31] [32] For definitions and explanations, see the Explanatory Notes at the end of the table. Because the Laplace transform is a linear operator, The Laplace transform of a sum is the sum of Laplace transforms of each term.

  6. Laplace–Beltrami operator - Wikipedia

    en.wikipedia.org/wiki/Laplace–Beltrami_operator

    Conversely, characterizes the Laplace–Beltrami operator completely, in the sense that it is the only operator with this property. As a consequence, the Laplace–Beltrami operator is negative and formally self-adjoint, meaning that for compactly supported functions f {\displaystyle f} and h {\displaystyle h} ,

  7. Laplace's equation - Wikipedia

    en.wikipedia.org/wiki/Laplace's_equation

    In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties.This is often written as = or =, where = = is the Laplace operator, [note 1] is the divergence operator (also symbolized "div"), is the gradient operator (also symbolized "grad"), and (,,) is a twice-differentiable real-valued function.

  8. Discrete Laplace operator - Wikipedia

    en.wikipedia.org/wiki/Discrete_Laplace_operator

    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 grid.For the case of a finite-dimensional graph (having a finite number of edges and vertices), the discrete Laplace operator is more commonly called the Laplacian matrix.

  9. Spectral shape analysis - Wikipedia

    en.wikipedia.org/wiki/Spectral_shape_analysis

    Spectral shape analysis relies on the spectrum (eigenvalues and/or eigenfunctions) of the Laplace–Beltrami operator to compare and analyze geometric shapes. Since the spectrum of the Laplace–Beltrami operator is invariant under isometries, it is well suited for the analysis or retrieval of non-rigid shapes, i.e. bendable objects such as humans, animals, plants, etc.