The prolate spheroidal wave functions are eigenfunctions of the Laplacian in prolate spheroidal coordinates, adapted to boundary conditions on certain ellipsoids of revolution (an ellipse rotated around its long axis, “cigar shape“). Related are the oblate spheroidal wave functions (“pancake shaped” ellipsoid).[1]
applied mathematics, oblate spheroidalwavefunctions (like also prolatespheroidalwavefunctions and other related functions) are involved in the solution...
S(t):=(1-t^{2})^{b/2}y(t)} , then S ( t ) {\displaystyle S(t)} is a prolatespheroidalwavefunction in the sense that it satisfies the equation ( 1 − t 2 ) d 2...
approximate closely the prolatespheroidalwavefunctions of order zero. Kaiser, James F. (Nov 1964). "A family of window functions having nearly ideal properties"...
foot, a measure of pressure; see also Pounds per square inch Prolatespheroidalwavefunction Pennsylvania Shakespeare Festival Phelps Stokes Fund Pittsfield...
Cambridge: Cambridge University Press, 1993. Slepian, D. (1978) "Prolatespheroidalwavefunctions, Fourier analysis, and uncertainty – V: The discrete case...
in the spectroscopic analysis of the quadrapole moments while the prolatespheroid shape of the nucleon arises from analysis of the intrinsic quadruple...
prolatespheroid touching the sphere at the poles, with an equatorial radius (extraordinary index) equal to the polar radius of the oblate spheroidal...
correlation). The wave equation (a partial differential equation) separates into two coupled ordinary differential equations when using prolatespheroidal coordinates...
be of varying geometric shape; spheres, discs, ellipsoids and prolate or oblate spheroids, and would be either isolated or set in a repeating pattern as...
Mathieu equation (best example), Lamé and ellipsoidal wave equations, oblate and prolatespheroidalwave equations, and equations with anharmonic potentials...
along its major axis to produce an ellipsoidal mirror (specifically, a prolatespheroid), this property holds for all rays out of the source. Alternatively...
sufficiently deep ocean under the tidal force of a single deforming body is a prolatespheroid (essentially a three-dimensional oval) with major axis directed toward...
behavior of particles such as red blood cells (as oblate spheroids) or long thin tubes (as prolate ellipsoids) allowing the approximation of the dielectrophoretic...
drag of a simplified model of the body, that can be approached by a prolatespheroid, and the sustainable level of energy output by the muscles. A first...
shock wave propagation within the explosive mass, this requires the pit to be a prolatespheroid, that is, roughly egg shaped. The shock wave first reaches...
"What Do a Submarine, a Rocket and a Football Have in Common? Why the prolatespheroid is the shape for success" (Scientific American, November 8, 2010) Conservation...
be chosen to match the symmetry of the problem. For example, the pressure wave due to an explosion far from the ground (or other barriers) depends on 3D...
Global Information