In mathematics, a homogeneous function is a function of several variables such that the following holds: If each of the function's arguments is multiplied...

homogeneous, because the sum of exponents does not match from term to term. The function defined by a homogeneous polynomial is always a homogeneous function...

members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives. In the case of linear...

production function is homogeneous of degree one, it is sometimes called "linearly homogeneous". A linearly homogeneous production function with inputs...

Geometrically, the graph of the function must pass through the origin. Homogeneous function Nonlinear system Piecewise linear function Linear approximation Linear...

the function that it defines: a constant term and a constant polynomial define constant functions.[citation needed] In fact, as a homogeneous function, it...

cube root of 1. Euler–Gompertz constant Euler's homogeneous function theorem – A homogeneous function is a linear combination of its partial derivatives...

Indeed, convex functions are exactly those that satisfies the hypothesis of Jensen's inequality. A first-order homogeneous function of two positive variables...

In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcul, are...

state of having identical cumulative distribution function or values". The definition of homogeneous strongly depends on the context used. For example...

non-constant function. If the constant term is the zero function, then the differential equation is said to be homogeneous, as it is a homogeneous polynomial...

of Leibniz Homogeneous space for a Lie group G, or more general transformation group Homogeneous function Homogeneous polynomial Homogeneous equation (linear...

functions with x 0 ( t ) {\displaystyle x_{0}(t)} a homogeneous function of degree one and γ ( t ) {\displaystyle \gamma (t)} a positive homogeneous function...

power functions, homogeneous distributions on R include the Dirac delta function and its derivatives. The Dirac delta function is homogeneous of degree...

Marshallian demand correspondence of a continuous utility function is a homogeneous function with degree zero. This means that for every constant a > 0...

projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane curve can be...

} By Euler's second theorem for homogeneous functions, Z i ¯ {\displaystyle {\bar {Z_{i}}}} is a homogeneous function of degree 0 (i.e., Z i ¯ {\displaystyle...

specifically in algebraic combinatorics and commutative algebra, the complete homogeneous symmetric polynomials are a specific kind of symmetric polynomials. Every...

properties are homogeneous functions of degree 1 with respect to { A j } {\displaystyle \{A_{j}\}} .) It follows from Euler's homogeneous function theorem that...

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept...

{q}}})\end{aligned}}} This simplification is a result of Euler's homogeneous function theorem. Hence, the Hamiltonian becomes H = ∑ i = 1 n ( ∂ T ( q ...

are called homothetic if they can be represented by a utility function which is homogeneous of degree 1.: 146  For example, in an economy with two goods...

delta function is an even distribution (symmetry), in the sense that δ ( − x ) = δ ( x ) {\displaystyle \delta (-x)=\delta (x)} which is homogeneous of degree...

introduced the name of "spherical harmonics" for these functions. The solid harmonics were homogeneous polynomial solutions R 3 → R {\displaystyle \mathbb...

a (pseudo)-random number generating function capable of simulating Poisson random variables. For the homogeneous case with the constant λ {\textstyle...

The equation is called homogeneous if C = 0 {\displaystyle C=0} and f ( x ) {\displaystyle f(x)} is a homogeneous function. The definition f ( x ) =...

variable, the eigenspaces of Θ are the spaces of homogeneous functions. (Euler's homogeneous function theorem) In writing, following common mathematical...

constant. It is easily seen that U {\displaystyle U} is a linearly homogeneous function of the three variables (that is, it is extensive in these variables)...

{\displaystyle \ F(aK,aL)=aF(K,L)} . In this case, the function F {\displaystyle F} is homogeneous of degree 1. Decreasing returns to scale if (for any...

scales from the fish Scale (disambiguation) Scaling function (disambiguation) Homogeneous function, used for scaling extensive properties in thermodynamic...