unique Green's function. Green's functions may be categorized, by the type of boundary conditions satisfied, by a Green's function number. Also, Green's functions...

Green's function number specifies the coordinate system and the type of boundary conditions that a Green's function satisfies. The Green's function number...

Multiscale Green's function (MSGF) is a generalized and extended version of the classical Green's function (GF) technique for solving mathematical equations...

kt}}}\exp \left(-{\frac {x^{2}}{4kt}}\right),} and the function g(x). (The Green's function number of the fundamental solution is X00.) Therefore, according...

foresee. True random number generators can be hardware random-number generators (HRNGs), wherein each generation is a function of the current value of...

the fields of probability, statistics, analytic number theory, and combinatorics. The gamma function can be seen as a solution to the interpolation problem...

In physics, the Green's function (or fundamental solution) for the Laplacian (or Laplace operator) in three variables is used to describe the response...

therefore, often called (causal) Green's functions (called "causal" to distinguish it from the elliptic Laplacian Green's function). In non-relativistic quantum...

the Green's functions used to solve inhomogeneous differential equations, to which they are loosely related. (Specifically, only two-point "Green's functions"...

then Green's theorem follows immediately for the region D. We can prove (1) easily for regions of type I, and (2) for regions of type II. Green's theorem...

Radó defined two functions related to the busy beaver game: the score function Σ(n) and the shifts function S(n). Both take a number of Turing machine...

many-body effects, one can resort to so-called Green's function methods. Indeed, knowledge of the Green's function of a system provides both ground (the total...

diffusion quantum Monte Carlo is a quantum Monte Carlo method that uses a Green's function to calculate low-lying energies of a quantum many-body Hamiltonian...

the Green's function describes the influence at (x′, y′, z′) of the data f and g. For the case of the interior of a sphere of radius a, the Green's function...

mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the...

number), a quadratic function c x 2 {\displaystyle cx^{2}} ( c {\displaystyle c} as a nonnegative real number) and an exponential function c e x {\displaystyle...

output another number. For example, if the doubling function is given the input three, then it outputs six, and if the squaring function is given the input...

complex distance from the origin. The associated Green's functions are referred as closed-form Green's functions. The method has also been extended for cylindrically-layered...

converse relation of the function f(w) = wew, where w is any complex number and ew is the exponential function. The function is named after Johann Lambert...

the eigenvalue, and f is the (eigen)function. When the equation is applied to waves, k is known as the wave number. The Helmholtz equation has a variety...

a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function. This implies...

linear response functions such as susceptibility, impulse response or impedance; see also transfer function. The concept of a Green's function or fundamental...

exponent to which a constant number e ≈ 2.718, the base, is raised. There are several other definitions of the exponential function, which are all equivalent...

practice, semigroups approximating the delta function arise as fundamental solutions or Green's functions to physically motivated elliptic or parabolic...

local lattice Green's function, one has to determine the hybridization function such that the corresponding impurity Green's function will coincide with...

This defines a function R [ X ] → C {\displaystyle \mathbb {R} [X]\to \mathbb {C} } This function is surjective since every complex number can be obtained...

complicated sums, according to the central limit theorem. Gaussian functions are the Green's function for the (homogeneous and isotropic) diffusion equation (and...

of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the...

requires the concept of a function. A function is a rule that, given one number, produces another number. An example is the function producing the x-th power...

obtain Laplace's equation. Poisson's equation may be solved using a Green's function: φ ( r ) = − ∭ f ( r ′ ) 4 π | r − r ′ | d 3 r ′ , {\displaystyle \varphi...