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Real function on a Euclidean space whose value depends only on distance from the origin
In mathematics, a radial function is a real-valued function defined on a Euclidean space ℝn whose value at each point depends only on the distance between
Radial_function
Type of mathematical function
In mathematics a radial basis function (RBF) is a real-valued function φ {\textstyle \varphi } whose value depends only on the distance between the input
Radial_basis_function
Description of particle density in statistical mechanics
In statistical mechanics, the radial distribution function, (or pair correlation function) g ( r ) {\displaystyle g(r)} in a system of particles (atoms
Radial_distribution_function
Machine learning kernel function
In machine learning, the radial basis function kernel, or RBF kernel, is a popular kernel function used in various kernelized learning algorithms. In
Radial_basis_function_kernel
Type of artificial neural network
mathematical modeling, a radial basis function network is an artificial neural network that uses radial basis functions as activation functions. The output of the
Radial_basis_function_network
Method in approximation theory
Radial basis function (RBF) interpolation is an advanced method in approximation theory for constructing high-order accurate interpolants of unstructured
Radial basis function interpolation
Radial_basis_function_interpolation
Artificial neural network node function
common activation functions can be divided into three categories: ridge functions, radial functions and fold functions. An activation function f is saturating
Activation_function
In mathematics, a radially unbounded function is a function f : R n → R {\displaystyle f:\mathbb {R} ^{n}\rightarrow \mathbb {R} } for which ‖ x ‖ → ∞
Radially_unbounded_function
Mathematical formula
the integral of a function on Rn is related to the integral of the function over spherical shells: level sets of the radial function. The formula plays
Coarea_formula
Coordinates comprising a distance and an angle
reference to the usual codomain of the arctan function, is to allow for arbitrary nonzero real values of the radial component and restrict the polar angle to
Polar_coordinate_system
Special type of functions in mathematics
equation as in the case of the radial wave function. However, the range of the variable is different: in the radial wave function, ξ ≥ 1 {\displaystyle \xi
Prolate spheroidal wave function
Prolate_spheroidal_wave_function
Mathematical description of quantum state
coordinates, and the wave function can be separated into functions of each coordinate, Ψnℓm(r,θ,ϕ)=R(r)Yℓm(θ,ϕ) where R are radial functions and Ym ℓ(θ, φ) are
Wave_function
Astronomic function
the masses of the components. The binary mass function follows from Kepler's third law when the radial velocity of one binary component is known. Kepler's
Binary_mass_function
Mathematical transform that expresses a function of time as a function of frequency
Bessel function of the first kind with order n + 2k − 2/2. When k = 0 this gives a useful formula for the Fourier transform of a radial function. This
Fourier_transform
Function describing an electron in an atom
the function that depends on distance r from the nucleus has radial nodes and decays as e−αr. The Slater-type orbital (STO) is a form without radial nodes
Atomic_orbital
hyperplane u⊥. Equivalently, the radial function of the intersection body IK is the Funk transform of the radial function of K. Intersection bodies were
Projection_body
Element of a basis for a function space
In mathematics, a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as
Basis_function
Family of solutions to related differential equations
Bessel functions are a class of special functions that commonly appear in problems involving wave motion, heat conduction, and other physical phenomena
Bessel_function
Eigenvalue problem for the Laplace operator
radial component R has the form R=γJn(ρ), where the Bessel function Jn(ρ) satisfies Bessel's equation z2Jn″+zJn′+(z2−n2)Jn=0, and z = k r. The radial
Helmholtz_equation
Special type of functions in mathematics
can be written as the product of a radial spheroidal wave function Rmn(−ic,iξ) and an angular spheroidal wave function Smn(−ic,η) by eimφ. Here c=kd/2,
Oblate spheroidal wave function
Oblate_spheroidal_wave_function
Materials simulation software
(m=−l,…,−1) of complex spherical harmonics, with l an implicit function of the radial function index j. The first line of code of the actual FHI-aims code
FHI-aims
Differential equation for the description of waves or standing wave
component that is a trigonometric function of the polar angle θ, multiplied by a Bessel function (of integer order) of the radial component. Further details
Wave_equation
Equation in solid state physics
a radial function P(r)/r and a spherical harmonic with an angular quantum number ℓ, namely ψ=(1/r)P(r)Sℓ(θ,ϕ). The equation for the radial function was
Hartree_equations
Polynomial sequence
φ)=Rnm(ρ)sin(mφ) and are odd function over the azimuthal angle φ. Here, ρ is the radial distance 0≤ρ≤1, and Rnm are the radial polynomials defined below
Zernike_polynomials
In physics, solution to Schrödinger equation
e. with respect to the angular basis) to obtain angle-independent radial functions w ℓ ( η , ρ ) {\displaystyle w_{\ell }(\eta ,\rho )} . Here ρ = k r
Coulomb_wave_function
Type of electric motor
A radial flux motor generates flux perpendicular to the axis of rotation. By contrast, an axial flux motor generates flux parallel to the axis. The features
Radial_flux_motor
provides motor function to the muscles in the posterior compartment of the forearm, which is mostly the extensor muscles of the hand. The radial nerve arises
Deep_branch_of_radial_nerve
Method in physics
atom nucleus α. An LAPW basis function is thus a plane wave in the IR and a linear combination of the radial functions ul,α(rα,El,α) and u˙l,α(rα,El,α)
Linearized augmented-plane-wave method
Linearized_augmented-plane-wave_method
Mathematical function
patterns in the feature space. Bell-shaped function Cauchy distribution Normal distribution Radial basis function kernel Squires, G. L. (2001-08-30). Practical
Gaussian_function
software package which uses density functional theory with a numerical radial function basis set to calculate the electronic properties of molecules, clusters
DMol3
Velocity of an object as the rate of distance change between the object and a point
the resulting radial-velocity amplitude allows the calculation of the lower bound on a planet's mass using the binary mass function. Radial velocity methods
Radial_velocity
Numerical method
the angular equation, we are left with the following equation of the radial function R(r): ddr(r2dRdr)−2mr2ℏ2(V(r)−E)R(r)=l(l+1)R(r). This equation can
Numerov's_method
Method for nonparametric multiple regression
to interpret Alternate smoothers, such as the radial function, harmonic function and additive function, have been suggested and their performances vary
Projection_pursuit_regression
Pictorial representation of the behavior of subatomic particles
exercise reproduces the standard formula for polar integration of a radial function: ∫f(r)dxdy=2π∫f(x)xdx In the path-integral for a nonabelian gauge field
Feynman_diagram
Bipolar-shaped progenitor cells of all neurons in the cerebral cortex and some glia
thinking, radial glia have been implicated as important mediators of brain evolution. The best characterized and first widely accepted function of radial glia
Radial_glial_cell
Compression of the radial nerve in the upper arm
of Form and Function. McGraw Hill. p. 496. ISBN 978-0-07-337825-1. "Cubital and Radial Tunnel Syndrome". Retrieved 4 December 2011. "Radial Tunnel Syndrome"
Radial_tunnel_syndrome
Radiation description framework
Note that the radial function hℓ(1)(kr) can be simplified in the far field limit 1/r≪1. hℓ(1)(kr)=(−i)ℓ+1eikrkr+𝒪(1/r2) Thus the radial dependence of
Multipole_radiation
Integral transform
R d {\displaystyle K\subset \mathbb {R} ^{d}} be a star body with radial function ρ K ( x ) = max { t : t x ∈ K } , {\displaystyle \rho _{K}({\boldsymbol
Funk_transform
scattering behaves according to a point spread function (PSF) that gives energy as a radial function of distance from the point that the electron beam
Proximity effect (electron beam lithography)
Proximity_effect_(electron_beam_lithography)
Nerve in the human body that supplies the posterior portion of the upper limb
The radial nerve is a nerve in the human body that supplies the posterior portion of the upper limb. It innervates the medial and lateral heads of the
Radial_nerve
Function used in signal processing
two-dimensional window function is shared by its two-dimensional Fourier transform. The difference between the separable and radial forms is akin to the
Window_function
Generalized function whose value is zero everywhere except at zero
= η1 to have an integrable radially symmetric decreasing rearrangement. Saichev & Woyczyński 1997, §1.1 The "delta function" as viewed by a physicist and
Dirac_delta_function
Structure in undulipodium
importance of the radial spoke in the proper function of these organelles, its structure and mode of action remain poorly understood. Radial spokes are T-shaped
Radial_spoke
Medical condition
to the carpus, radial deviation may be reinforced if forearm muscles are functioning poorly or have abnormal insertions. Although radial longitudinal deficiency
Radial_dysplasia
Description of a quantum-mechanical system
convenient. Thus, ψ(r,θ,φ)=R(r) Yℓm(θ,φ)=R(r) Θ(θ) Φ(φ), where R are radial functions and Ylm(θ,φ) are spherical harmonics of degree ℓ and order m. This
Schrödinger_equation
Representation theory
Harish-Chandra. The Plancherel theorem gives the eigenfunction expansion of radial functions for the Laplacian operator on the associated symmetric space X; it
Plancherel theorem for spherical functions
Plancherel_theorem_for_spherical_functions
Distribution of distances between pairs of particles in a given volume
f {\displaystyle f} . Of special practical importance is the radial distribution function, which is independent of orientation. It is a major descriptor
Pair_distribution_function
Bone embedded within a tendon or muscle, functioning as a biomechanical advantage
Although many carnivores have radial sesamoid bones, the giant panda and red panda independently evolved to have an enlarged radial sesamoid bone. This evolution
Sesamoid_bone
Smooth and compactly supported function
xn)=Ψ(x1)Ψ(x2)⋯Ψ(xn). A radially symmetric bump function in n variables can be formed by taking the function Ψn:ℝn→ℝ defined by Ψn(𝐱)=Ψ(|𝐱|). This function is supported
Bump_function
Radio antenna feature
engineering, radial has three distinct meanings, all referring to lines which radiate from (or intersect at) a radio antenna. Ground system radial wires When
Radial_(radio)
Function in harmonic analysis on groups
the zonal hyperbolic functions ψ correspond to radial functions that are eigenfunctions of the Laplacian. But in terms of the radial coordinate r, the Laplacian
Zonal_spherical_function
Concept in mathematical analysis
the unique radial and radially nonincreasing function, whose strict sublevel sets are open and have the same measure as those of the function u {\displaystyle
Pólya–Szegő_inequality
Function used in quantum chemistry
Angular-dependent derivatives of the spherical harmonics don't depend on the radial function and have to be evaluated separately. The fundamental mathematical properties
Slater-type_orbital
Coordinates comprising two distances and an angle
perpendicular to the longitudinal axis are called radial lines. The distance from the axis may be called the radial distance or radius, while the angular coordinate
Cylindrical_coordinate_system
Measure of a system's order
correlation function in an elemental liquid or a solid (often called a Radial distribution function or a pair correlation function). Correlation functions between
Correlation function (statistical mechanics)
Correlation_function_(statistical_mechanics)
transform (FRFT) Hankel transform: related to the Fourier Transform of radial functions. Fourier–Bros–Iagolnitzer transform Linear canonical transform For
List of Fourier-related transforms
List_of_Fourier-related_transforms
Equation in statistical mechanics
for the radial distribution function. The approximation is named after Jerome K. Percus and George J. Yevick. The direct correlation function represents
Percus–Yevick_approximation
Approximating an arbitrary function with a well-behaved one
theory Fitness approximation Kriging Least squares (function approximation) Radial basis function network Lakemeyer, Gerhard; Sklar, Elizabeth; Sorrenti
Function_approximation
Rate of change of velocity
in the opposite (or antiparallel) direction to the tangential velocity. Radial acceleration or normal acceleration (or centripetal acceleration during
Acceleration
Atoms with a single valence electron, so they behave like hydrogen
for a given state can be written using two radial functions and two angle functions. The radial functions depend on both the principal quantum number
Hydrogen-like_atom
Large blood vessel on upper limb
into the radial and ulnar arteries which run down the forearm. In some individuals, the bifurcation occurs much earlier and the ulnar and radial arteries
Brachial_artery
Concept in the analysis of dynamical systems
Lyapunov function, then the equilibrium is Lyapunov stable. If the Lyapunov-candidate-function V {\displaystyle V} is globally positive definite, radially unbounded
Lyapunov_function
Special mathematical functions defined on the surface of a sphere
extract a factor of radial dependence rℓ from the above-mentioned polynomial of degree ℓ; the remaining factor can be regarded as a function of the spherical
Spherical_harmonics
Method of measuring the extent of spatial localization of an electron
the radial distance from the nucleus; the ELF for radon has six clear maxima, whereas the electron density decreases monotonically and the radially weighted
Electron localization function
Electron_localization_function
Problem in convex geometry
is an intersection body. An intersection body is a star body whose radial function in a given direction u is the volume of the hyperplane section u⊥ ∩ K
Busemann–Petty_problem
Response of an optical system to a point source of light
lens axis, r is radial distance in the image plane, and wavenumber k = 2π/λ where λ = wavelength, then the argument of the function is: kr tan(Θmax)
Point_spread_function
Support-cells in the nervous system
eminence of the hypothalamus are a type of ependymal cell that descend from radial glia and line the base of the third ventricle. Drosophila melanogaster,
Glia
Speed and direction of a motion
radial velocity. The radial speed (or magnitude of the radial velocity) is the dot product of the velocity vector and the unit vector in the radial direction
Velocity
Mathematical operation
that functions with angular dependence in form of a hyperspherical harmonic retain it upon the multidimensional Fourier transform, while the radial part
Hankel_transform
Type of function
have orthogonality of both radial and angular parts. Walsh functions and Haar wavelets are examples of orthogonal functions with discrete ranges. Legendre
Orthogonal_functions
American mathematician
Pinsky, Mark A.; Stanton, Nancy K.; Trapa, Peter E. Fourier series of radial functions in several variables. J. Funct. Anal. 116 (1993), no. 1, 111–132. "Nancy
Nancy_K._Stanton
Number assigned to each electron shell in an atom
rules to the classical equations. The radial quantum number determines the number of nodes of the radial wave function R(r). In chemistry, values n = 1, 2
Principal_quantum_number
Topological set
X {\displaystyle A\subseteq X} of a linear space X {\displaystyle X} is radial at a given point a 0 ∈ A {\displaystyle a_{0}\in A} if for every x ∈ X {\displaystyle
Radial_set
Ligament of elbow
The radial collateral ligament (RCL), lateral collateral ligament (LCL), or external lateral ligament is a ligament in the elbow on the side of the radius
Radial collateral ligament of elbow joint
Radial_collateral_ligament_of_elbow_joint
Swedish physician researcher
(July 2007). "The quantitative relationship between longitudinal and radial function in left, right, and total heart pumping in humans". American Journal
Martin_Ugander
Describes the range of energies of an electron within the solid
and the narrow embedded TB d-bands. The radial functions of the atomic orbital part of the Wannier functions are most easily calculated by the use of
Electronic_band_structure
Method of hydrodynamics simulation
(link) Kostorz (2020). "A semi-analytical boundary integral method for radial functions with application to Smoothed Particle Hydrodynamics". Journal of Computational
Smoothed-particle hydrodynamics
Smoothed-particle_hydrodynamics
In machine learning, a Hyper basis function network, or HyperBF network, is a generalization of radial basis function (RBF) networks concept, where the
Hyper_basis_function_network
Medical condition
occur when either the radial nerve or part of the brachial plexus, containing various nerves that innervate sense and motor function to the arm and hand
Crutch_paralysis
Specifies a range of position-dependent colors
values, as opposed to linear. CSS and SVG both support linear gradients. A radial gradient is specified as a circle that has one color at the edge and another
Color_gradient
The radial arm maze was designed by Olton and Samuelson in 1976 to measure spatial learning and memory in rats. The original apparatus consists of eight
Radial_arm_maze
Coordinates comprising a distance and two angles
fundamental plane). The radial distance from the fixed point of origin is also called the radius, or radial line, or radial coordinate. The polar angle
Spherical_coordinate_system
Mathematical functions
In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied
Lemniscate_elliptic_functions
astrodynamics and celestial mechanics a radial trajectory is a Kepler orbit with zero angular momentum. Two objects in a radial trajectory move directly towards
Radial_trajectory
Differential operator in mathematics
if f(x)=F(r) is radial, then the angular term vanishes and Δf=F″(r)+N−1rF′(r)=1rN−1ddr(rN−1F′(r)). Thus every radial harmonic function on an annulus in
Laplace_operator
Knot that bounds an embedded disk in 4-space
position. This is useful because the critical points with respect to the radial function r carry geometrical meaning. At saddle points, trivial components are
Slice_knot
Measure of the fluid slip in the impeller of a compressor or a turbine
outlet flow in the same direction), slip is a very important phenomenon in radial impellers and is useful in determining the accurate estimation of work input
Slip_factor
Bone projection on the radius
The radial styloid process is a projection of bone on the lateral surface of the distal radius bone. The radial styloid process is found on the lateral
Radial_styloid_process
Flexor muscle in the upper arm
musculocutaneous nerve, and commonly also receives additional innervation from the radial nerve. The brachialis is the prime mover of elbow flexion generating about
Brachialis_muscle
Quantum mechanics concept for systems with central potentials, such as atoms
ϕ)=R(r)Yℓm(θ,ϕ).The differential equation which characterises the function R(r) is called the radial equation. The kinetic energy operator in spherical polar coordinates
Particle in a spherically symmetric potential
Particle_in_a_spherically_symmetric_potential
is dependent only on the distance from a nucleus. The choice of the radial function used to describe this electron density is arbitrary, granted that its
Multipole_density_formalism
Flow with periodic variations
velocity waves gets shifted towards the core.[citation needed] The Bessel function at its lower limit becomes limz→∞J0(z)=1−z24, which converges to the Hagen-Poiseuille
Pulsatile_flow
Indirect method for finding extrasolar planets and brown dwarfs
mass function. The Bayesian Kepler periodogram is a mathematical algorithm, used to detect single or multiple extrasolar planets from successive radial-velocity
Doppler_spectroscopy
Special function defined by an integral
flow in the Theis solution (called a well function) Radiative transfer in stellar and planetary atmospheres Radial diffusivity equation for transient or unsteady
Exponential_integral
Concept within complex analysis
is in Lp(T). The function F defined on the unit disk by F(reiθ) = (f ∗ Pr)(eiθ) is harmonic, and M f is the radial maximal function of F. When M f belongs
Hardy_space
Tool in multivariate statistical analysis
{\displaystyle \nu } is an integer, limiting values should be taken (see ). Radial basis function Genton, Marc G. (1 March 2002). "Classes of kernels for machine
Matérn_covariance_function
Special function occurring in problems possessing elliptic symmetry
solutions. Closely related are the modified Mathieu functions, also known as radial Mathieu functions, which are solutions of Mathieu's modified differential
Mathieu_function
Class of mathematical functions
complex plane containing the closed unit disc D(0, 1). The radial maximal function for the function φ (restricted to the unit disc) is defined on the unit
Subharmonic_function
Opening used to filter water in echinoderms
ducts that function in locomotion and feeding and respiration. Its main parts are the madreporite, the stone canal, the ring canal, the radial canals, the
Madreporite
The assessment of the regional function of the heart is a good tool for early detection of deterioration in certain parts of the heart wall before a cardiac
Regional function of the heart
Regional_function_of_the_heart
travel, tourism, insurance
RADIAL FUNCTION
RADIAL FUNCTION
Girl/Female
Arabic, French
Satisfied; Content
Girl/Female
Indian
Honesty, Just, Upright, Justice
Male
English
Variant spelling of English Gaddiel, GADIEL means "God is my fortune."Â
Boy/Male
Hindu, Indian
God's Kindness
Boy/Male
Sikh
King like incarnation of God in heaven
Surname or Lastname
English
English : habitational name from various places, for example either of the places named Radway (in Devon and Warwickshire), Reddaway or Roadway (both in Devon), all named from Old English rÄ“ad ‘red’ + waye ‘road’, ‘way’, or from Rodway in Somerset, in which the first element is from Old English rÄd ‘road’, ‘track’.
Girl/Female
Muslim
High, Sublime, Exquisite
Boy/Male
Muslim
Greenery
Girl/Female
Muslim
Content, Satisfied
Girl/Female
Muslim
Honesty, Just, Upright, Justice
Boy/Male
Sikh
Beauteous
Female
Serbian
(Радмила) Feminine form of Serbian Radmilo, RADMILA means "happy favor."
Girl/Female
Indian
Content, Satisfied
Boy/Male
Sikh
One on whom there is gods grace, Gods mercy
Boy/Male
Muslim
Brook, Rivulet
Girl/Female
Muslim
One who is full of shame
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
Girl/Female
Muslim
Leader, Pioneer
Girl/Female
Muslim
Veiled, Covered
Boy/Male
Hindu, Indian
Wife of Lord Krishna
RADIAL FUNCTION
RADIAL FUNCTION
RADIAL FUNCTION
RADIAL FUNCTION
RADIAL FUNCTION
RADIAL FUNCTION
RADIAL FUNCTION
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