laplace operator sentence in Hindi
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- The infinitesimal generator ( and hence characteristic operator ) of a Brownian motion on "'R " "'n " is easily calculated to be ��, where ? denotes the Laplace operator.
- The fact that for arithmetic surfaces the arithmetic data determines the spectrum of the Laplace operator \ Delta was pointed out by M . F . Vign�ras and used by her to construct examples of isospectral compact hyperbolic surfaces.
- It is the generalisation of the Laplace operator in the sense that it is the differential operator which is invariant under the isometry group of the underlying space and it reduces to the Laplace operator if restricted to time independent functions.
- It is the generalisation of the Laplace operator in the sense that it is the differential operator which is invariant under the isometry group of the underlying space and it reduces to the Laplace operator if restricted to time independent functions.
- One use of integration by parts in operator theory is that it shows that the ( where " is the Laplace operator ) is a positive operator on ( see " L " " p " space ).
- In mathematics, the "'Laplace operator "'or "'Laplacian "'is a differential operator given by the divergence of the gradient of a cylindrical and spherical coordinates, the Laplacian also has a useful form.
- In various applications to physical problems, a function can be decomposed into physically meaningful eigenfunctions of a differential operator ( typically the Laplace operator ) : this forms the foundation for the spectral study of functions, in reference to the spectrum of the differential operator.
- Again the oscillatory part of the velocity vector is related to the velocity potential by " " ? " } }, while as before is the Laplace operator, and " " is the average speed of sound in the homogeneous medium.
- 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, where the operator gives a constant multiple of the mass density when it is applied to a given gravitational potential.
- In geometric topology, most commonly studied are Morse functions, which yield handlebody decompositions, while 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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