Homogeneous
31Homogeneous function — In mathematics, a homogeneous function is a function with multiplicative scaling behaviour: if the argument is multiplied by a factor, then the result is multiplied by some power of this factor.Formal definitionSuppose that f: V arr W qquadqquad… …
32Homogeneous polynomial — In mathematics, a homogeneous polynomial is a polynomial whose terms are monomials all having the same total degree; or are elements of the same dimension. For example, x^5 + 2 x^3 y^2 + 9 x^1 y^4 is a homogeneous polynomial of degree 5, in two… …
33Homogeneous charge compression ignition — Thermodynamics …
34Homogeneous (mathematics) — In mathematics, homogeneous may refer to:*Homogeneous polynomial, in algebra *Homogeneous function *Homogeneous equation, in particular: Homogeneous differential equation *Homogeneous system of linear equations, in linear algebra *Homogeneous… …
35Homogeneous coordinate ring — In algebraic geometry, the homogeneous coordinate ring R of an algebraic variety V given as a subvariety of projective space of a given dimension N is by definition the quotient ring R = K[X0, X1, X2, ..., XN]/I where I is the homogeneous ideal… …
36Homogeneous differential equation — A homogeneous differential equation has several distinct meanings.One meaning is that a first order ordinary differential equation is homogeneous if it has the form : frac{dy}{dx} = F(y/x).To solve such equations, one makes the change of… …
37Homogeneous broadening — If an optical emitter (e.g. an atom) shows homogeneous broadening, its linewidth is its natural linewidth (see spectral linewidth). In contrast, an inhomogeneously broadened emitter has a broader linewidth than the natural. Broadening in laser… …
38Homogeneous tree — In descriptive set theory, a tree over a product set Y imes Z is said to be homogeneous if there is a system of measures langlemu smid sin{}^{ …
39homogeneous reaction — ▪ chemical reaction any of a class of chemical reactions that occur in a single phase (gaseous, liquid, or solid), one of two broad classes of reactions homogeneous and heterogeneous based on the physical state of the substances present.… …
40homogeneous function — noun a) homogeneous polynomial b) the ratio of two homogeneous polynomials, such that the sum of the exponents in a term of the numerator is equal to the sum of the exponents in a term of the denominator …
