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Special type of functions in mathematics
In mathematics, prolate spheroidal wave functions (PSWFs) are eigenfunctions of the Laplacian in prolate spheroidal coordinates, adapted to boundary conditions
Prolate spheroidal wave function
Prolate_spheroidal_wave_function
Special type of functions in mathematics
applied mathematics, oblate spheroidal wave functions (like also prolate spheroidal wave functions and other related functions) are involved in the solution
Oblate spheroidal wave function
Oblate_spheroidal_wave_function
Math equation
S(t):=(1-t^{2})^{b/2}y(t)} , then S ( t ) {\displaystyle S(t)} is a prolate spheroidal wave function in the sense that it satisfies the equation ( 1 − t 2 ) d 2
Spheroidal_wave_equation
Surface formed by rotating an ellipse
semi-diameters. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a prolate spheroid, elongated like a rugby
Spheroid
Solutions of the Helmholtz equation
called oblate spheroidal wave functions if oblate spheroidal coordinates are used and prolate spheroidal wave functions if prolate spheroidal coordinates
Spheroidal_wave_function
Function used in signal processing
approximate closely the prolate spheroidal wave functions of order zero. Kaiser, James F. (Nov 1964). "A family of window functions having nearly ideal properties"
Window_function
Mathematical function
"Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions".
Slepian_function
American mathematician (1923–2007)
"Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty -- I" (PDF). BSTJ. Retrieved June 15, 2012. "Prolate Spheroidal Wave Functions, Fourier
David_Slepian
Solutions of Lamé's equation
corresponding calculations for Mathieu functions, and oblate spheroidal wave functions and prolate spheroidal wave functions). With the following boundary conditions
Lamé_function
Austrian-American mathematician (1927–2026)
Dolciani Award in 2020. Slepian, D.; Pollak, H. O. (1961). "Prolate spheroidal wave functions, Fourier analysis and uncertainty. I". The Bell System Technical
Henry_O._Pollak
Topics referred to by the same term
failure of the performance of a task Posterior spinal fusion Prolate spheroidal wave function Pounds per square foot, a measure of pressure; see also Pounds
PSF
Spectral density estimation technique
the Slepian functions or discrete prolate spheroidal sequences, after David Slepian (also known in literature as discrete prolate spheroidal sequences or
Multitaper
the nuclear force holding them together. The spatial extent of the prolate spheroid nucleon (and larger nuclides) is determined by root mean squared (RMS)
Shape_of_the_atomic_nucleus
Belgian geophysicist
Experiment, and to the theory of spatiospectral localization via prolate spheroidal wave functions. Simons is involved in the design of mobile marine instrumentation
Frederik_J._Simons
Quartic potential in quantum mechanics
corresponding results for Mathieu functions, Lamé functions, prolate spheroidal wave functions, oblate spheroidal wave functions and others). In field theory
Double-well_potential
Special function occurring in problems possessing elliptic symmetry
periodic differential equations, as for Lamé functions and prolate and oblate spheroidal wave functions. The asymptotic nature of the asymptotic solutions
Mathieu_function
Aspect of crystal optics
prolate spheroid touching the sphere at the poles, with an equatorial radius (extraordinary index) equal to the polar radius of the oblate spheroidal
Index_ellipsoid
Type of lens
Johannes; Osten, Wolfgang (20 July 2017). "Measuring aspheres quickly: tilted wave interferometry". Optical Engineering. 56 (11) 111713. doi:10.1117/1.OE.56
Aspheric_lens
Problem in physics and astronomy
fixed centers. It is well known that the Schrödinger wave equation is separable in prolate spheroidal coordinates and can be decoupled into two ordinary
Euler's_three-body_problem
Indian American academic (born 1954)
Vaidyanathan, "MIMO radar space-time adaptive processing using prolate spheroidal wave functions", IEEE Transactions on Signal Processing, Feb, 2008. https://ieeexplore
P._P._Vaidyanathan
Molecular ion
correlation). The wave equation (a partial differential equation) separates into two coupled ordinary differential equations when using prolate spheroidal coordinates
Dihydrogen_cation
History of research by Augustin-Jean Fresnel
assumption that the secondary waves are spherical for the ordinary refraction (which satisfies Snell's law) and spheroidal for the extraordinary refraction
Fresnel's_physical_optics
Plane curve
along its major axis to produce an ellipsoidal mirror (specifically, a prolate spheroid), this property holds for all rays out of the source. Alternatively
Ellipse
Change in sea level due to gravity
sufficiently deep ocean under the tidal force of a single deforming body is a prolate spheroid (essentially a three-dimensional oval) with major axis directed toward
Tide
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
History_of_metamaterials
Set of coordinates where the coordinate hypersurfaces all meet at right angles
general but still analytical orthogonal coordinate system is Similar Oblate Spheroidal (SOS) system, in which the transformation from the Cartesian coordinates
Orthogonal_coordinates
Team field sport
indicators of wind strength and direction. The football itself is a prolate spheroid leather ball, similar to the balls used in rugby or Australian rules
American_football
shock wave propagation within the explosive mass, this requires the pit to be a prolate spheroid, that is, roughly egg shaped. The shock wave first reaches
Nuclear_weapon_design
Order of reptiles (fossil)
drag of a simplified model of the body, that can be approached by a prolate spheroid, and the sustainable level of energy output by the muscles. A first
Plesiosaur
Particle motion in a non-uniform electric field due to dipole-field interactions
behavior of particles such as red blood cells (as oblate spheroids) or long thin tubes (as prolate ellipsoids) allowing the approximation of the dielectrophoretic
Dielectrophoresis
American mathematician (1929–1991)
1959). "On the theory of scalar diffusion and its application to the prolate spheroid". Annals of Physics. doi:10.1016/0003-4916(59)90083-1. hdl:2027.42/32464
Nicholas_D._Kazarinoff
Approximation in mathematics
Mathieu equation (best example), Lamé and ellipsoidal wave equations, oblate and prolate spheroidal wave equations, and equations with anharmonic potentials
Method of matched asymptotic expansions
Method_of_matched_asymptotic_expansions
Conserved physical quantity; rotational analogue of linear momentum
"What Do a Submarine, a Rocket and a Football Have in Common? Why the prolate spheroid is the shape for success" (Scientific American, November 8, 2010) Conservation
Angular_momentum
forces from the planet it orbits rather than flattened, resulting in a prolate spheroid shape where the equator is covered by an atmosphere but the poles rise
Extrasolar_planets_in_fiction
Method of encoding digital data on multiple carrier frequencies
Mecklenbrauker CF (Sep 2005). "Time-Variant Channel Estimation Using Discrete Prolate Spheroidal Sequences". IEEE Transactions on Signal Processing. 53 (9): 3597–3607
Orthogonal frequency-division multiplexing
Orthogonal_frequency-division_multiplexing
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PROLATE SPHEROIDAL-WAVE-FUNCTION
PROLATE SPHEROIDAL-WAVE-FUNCTION
PROLATE SPHEROIDAL-WAVE-FUNCTION
PROLATE SPHEROIDAL-WAVE-FUNCTION
PROLATE SPHEROIDAL-WAVE-FUNCTION
PROLATE SPHEROIDAL-WAVE-FUNCTION
PROLATE SPHEROIDAL-WAVE-FUNCTION
PROLATE SPHEROIDAL-WAVE-FUNCTION
PROLATE SPHEROIDAL-WAVE-FUNCTION
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