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36 relations: Academic Press, Angular momentum, Boundary value problem, Calculus of variations, Dirichlet energy, Dirichlet problem, Double-clad fiber, Drum, Eigenvalues and eigenvectors, Force, Hearing the shape of a drum, Helmholtz equation, Infimum and supremum, Journal of Modern Optics, Laplace operator, Laplace–Beltrami operator, Limit point, Manifold, Mathematical physics, Mathematics, Neumann boundary condition, Normal mode, Optical amplifier, Optical fiber, Optical Fiber Technology, Optics Communications, Paraxial approximation, Pond, Pressure, Rayleigh quotient, Smoothness, Sobolev space, Spectral geometry, Square-integrable function, Support (mathematics), Vibration.
Academic Press
Academic Press is an academic book publisher.
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Angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of linear momentum.
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Boundary value problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions.
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Calculus of variations
Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.
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Dirichlet energy
In mathematics, the Dirichlet energy is a measure of how variable a function is.
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Dirichlet problem
In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region.
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Double-clad fiber
Double-clad fiber (DCF) is a class of optical fiber with a structure consisting of three layers of optical material instead of the usual two.
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Drum
The drum is a member of the percussion group of musical instruments.
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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Force
In physics, a force is any interaction that, when unopposed, will change the motion of an object.
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Hearing the shape of a drum
To hear the shape of a drum is to infer information about the shape of the drumhead from the sound it makes, i.e., from the list of overtones, via the use of mathematical theory.
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Helmholtz equation
In mathematics & physics, the Helmholtz equation, named for Hermann von Helmholtz, is the partial differential equation where ∇2 is the Laplacian, k is the wavenumber, and A is the amplitude.
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Infimum and supremum
In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.
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Journal of Modern Optics
The Journal of Modern Optics is a peer-reviewed scientific journal that was established as Optica Acta in 1954.
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Laplace operator
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space.
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Laplace–Beltrami operator
In differential geometry, the Laplace operator, named after Pierre-Simon Laplace, can be generalized to operate on functions defined on surfaces in Euclidean space and, more generally, on Riemannian and pseudo-Riemannian manifolds.
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Limit point
In mathematics, a limit point (or cluster point or accumulation point) of a set S in a topological space X is a point x that can be "approximated" by points of S in the sense that every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Mathematical physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Neumann boundary condition
In mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann.
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Normal mode
A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation.
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Optical amplifier
An optical amplifier is a device that amplifies an optical signal directly, without the need to first convert it to an electrical signal.
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Optical fiber
An optical fiber or optical fibre is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair.
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Optical Fiber Technology
Optical Fiber Technology is a scientific journal that is published by Elsevier (formerly by Academic Press).
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Optics Communications
Optics Communications is a peer-reviewed rapid-publication scientific journal published by Elsevier.
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Paraxial approximation
In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system (such as a lens).
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Pond
A pond is a body of standing water, either natural or artificial, that is usually smaller than a lake.
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Pressure
Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
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Rayleigh quotient
In mathematics, for a given complex Hermitian matrix M and nonzero vector x, the Rayleigh quotient R(M, x), is defined as: For real matrices and vectors, the condition of being Hermitian reduces to that of being symmetric, and the conjugate transpose x^ to the usual transpose x'.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Sobolev space
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of ''Lp''-norms of the function itself and its derivatives up to a given order.
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Spectral geometry
Spectral geometry is a field in mathematics which concerns relationships between geometric structures of manifolds and spectra of canonically defined differential operators.
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Square-integrable function
In mathematics, a square-integrable function, also called a quadratically integrable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite.
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Support (mathematics)
In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.
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Vibration
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point.
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Dirichlet Laplacian, Dirichlet laplacian, Laplacian eigenvalue.
References
[1] https://en.wikipedia.org/wiki/Dirichlet_eigenvalue
