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Function with a multiplicative scaling behaviour
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_function
Type of ordinary differential equation
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
Homogeneous differential equation
Homogeneous_differential_equation
Used to define marginal product and to distinguish allocative efficiency
production function is homogeneous of degree one, it is sometimes called "linearly homogeneous". A linearly homogeneous production function with inputs
Production_function
Polynomial whose nonzero terms all have the same degree
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
Homogeneous_polynomial
Differential equation that is linear with respect to the unknown function
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
Linear_differential_equation
Linear map or polynomial function of degree one
Geometrically, the graph of the function must pass through the origin. Homogeneous function Nonlinear system Piecewise linear function Linear approximation Linear
Linear_function
Real function with secant line between points above the graph itself
Indeed, convex functions are exactly those that satisfies the hypothesis of Jensen's inequality. A first-order homogeneous function of two positive variables
Convex_function
Type of function in linear algebra
Unlike seminorms, a sublinear function does not have to be nonnegative-valued and also does not have to be absolutely homogeneous. Seminorms are themselves
Sublinear_function
Special mathematical functions defined on the surface of a sphere
introduced the name of "spherical harmonics" for these functions. The solid harmonics were homogeneous polynomial solutions R 3 → R {\displaystyle \mathbb
Spherical_harmonics
Probability distribution
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
Cauchy_distribution
Type of mathematical distribution
power functions, homogeneous distributions on R include the Dirac delta function and its derivatives. The Dirac delta function is homogeneous of degree
Homogeneous_distribution
Type of mathematical expression
the function that it defines: a constant term and a constant polynomial define constant functions.[citation needed] In fact, as a homogeneous function, it
Polynomial
Class of mathematical functions
meromorphic function with a pole of order 2 at each period λ {\displaystyle \lambda } in Λ {\displaystyle \Lambda } . ℘ {\displaystyle \wp } is a homogeneous function
Weierstrass_elliptic_function
Coordinate system used in projective geometry
In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcul, are
Homogeneous_coordinates
Generalized function whose value is zero everywhere except at zero
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
Dirac_delta_function
Expression in commutative algebra
specifically in algebraic combinatorics and commutative algebra, the complete homogeneous symmetric polynomials are a specific kind of symmetric polynomials. Every
Complete homogeneous symmetric polynomial
Complete_homogeneous_symmetric_polynomial
Type of random mathematical object
a (pseudo)-random number generating function capable of simulating Poisson random variables. For the homogeneous case with the constant λ {\textstyle
Poisson_point_process
Formulation of classical mechanics using momenta
{q}}})\end{aligned}}} This simplification is a result of Euler's homogeneous function theorem. Hence, the Hamiltonian becomes H = ∑ i = 1 n ( ∂ T ( q
Hamiltonian_mechanics
Method of solution to differential equations
of Green's functions in mathematics is to solve non-homogeneous boundary value problems. In modern theoretical physics, Green's functions are also usually
Green's_function
System where changes of output are not proportional to changes of input
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 ) =
Nonlinear_system
Uniformity of a material or system at every point
state of having identical cumulative distribution function or values". The definition of homogeneous strongly depends on the context used. For example
Homogeneity_(physics)
Energy contained within a system
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)
Internal_energy
Multivalued function in mathematics
In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse
Lambert_W_function
cube root of 1. Euler–Gompertz constant Euler's homogeneous function theorem – A homogeneous function is a linear combination of its partial derivatives
List of topics named after Leonhard Euler
List_of_topics_named_after_Leonhard_Euler
Order-preserving mathematical function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept
Monotonic_function
Binary relation over a set and itself
In mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian
Homogeneous_relation
Functional equation
Conjugate homogeneous additive map Homogeneous function – Function with a multiplicative scaling behaviour Minkowski functional – Function made from a
Cauchy's_functional_equation
Type of functional equation (mathematics)
partial differential equations. The unknown function u depends on two variables x and t or x and y. Homogeneous first-order linear partial differential equation:
Differential_equation
Notion in calculus
a function of several variables (for simplicity taken here as a vector argument). Then the n-th differential defined in this way is a homogeneous function
Differential_of_a_function
Mathematical function
according to the central limit theorem. Gaussian functions are the Green's function for the (homogeneous and isotropic) diffusion equation (and to the heat
Gaussian_function
Type of algebraic structure
called the homogeneous part of degree n {\displaystyle n} of I {\displaystyle I} . A homogeneous ideal is the direct sum of its homogeneous parts. If
Graded_ring
Change in a property of a mixture component with respect to amount
} 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
Partial_molar_property
Function spaces generalizing finite-dimensional p norm spaces
defines an absolutely homogeneous function for 0 < p < 1 ; {\displaystyle 0<p<1;} however, the resulting function does not define a norm, because
Lp_space
elementary symmetric functions ei and the complete homogeneous symmetric function hi for all i. It also sends each power sum symmetric function pi to (−1)i−1pi
Ring_of_symmetric_functions
Function made from a set
[0,\infty )} is continuous. A nonnegative sublinear function is a nonnegative homogeneous function f : X → [ 0 , ∞ ) {\textstyle f:X\to [0,\infty )} that
Minkowski_functional
Typically linear operator defined in terms of differentiation of functions
variable, the eigenspaces of Θ are the spaces of homogeneous functions. (Euler's homogeneous function theorem) In writing, following common mathematical
Differential_operator
Curve defined as zeros of polynomials
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
Algebraic_curve
Vector-valued function of multiple vectors, linear in each argument
its arguments is zero. Algebraic form Multilinear form Homogeneous polynomial Homogeneous function Tensors Lang, Serge (2005) [2002]. "XIII. Matrices and
Multilinear_map
Geometric transformation
2D computer graphics#Scaling Digital zoom Dilation (metric space) Homogeneous function Homothetic transformation Orthogonal coordinates Scalar (mathematics)
Scaling_(geometry)
Properties independent of system size, and proportional to system size
properties are homogeneous functions of degree 1 with respect to { A j } {\displaystyle \{A_{j}\}} .) It follows from Euler's homogeneous function theorem that
Intensive and extensive properties
Intensive_and_extensive_properties
Collection of random variables
single positive constant, then the process is called a homogeneous Poisson process. The homogeneous Poisson process is a member of important classes of stochastic
Stochastic_process
Topics referred to by the same term
ring Homogeneous equation (linear algebra): systems of linear equations with zero constant term Homogeneous function Homogeneous graph Homogeneous (large
Homogeneity_(disambiguation)
Topics referred to by the same term
scales from the fish Scale (disambiguation) Scaling function (disambiguation) Homogeneous function, used for scaling extensive properties in thermodynamic
Scaling
In mathematics, straight line touching a plane curve without crossing it
converting to homogeneous coordinates. Specifically, let the homogeneous equation of the curve be g(x, y, z) = 0 where g is a homogeneous function of degree
Tangent
Function specifying the behavior of a component in an electronic or control system
a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that models
Transfer_function
Microeconomic function
Marshallian demand correspondence of a continuous utility function is a homogeneous function with degree zero. This means that for every constant a > 0
Marshallian_demand_function
Partial differential equation describing the evolution of temperature in a region
the homogeneous Neumann boundary conditions ux(0, t) = 0. The Green's function number of this solution is X20. Problem on (0,∞) with homogeneous initial
Heat_equation
Differential equation containing derivatives with respect to only one variable
source term, leading to further classification. Homogeneous A linear differential equation is homogeneous if r ( x ) = 0 {\displaystyle r(x)=0} . In this
Ordinary differential equation
Ordinary_differential_equation
Features that do not change if length or energy scales are multiplied by a common factor
dimensions to the idea of a homogeneous polynomial, and more generally to a homogeneous function. Homogeneous functions are the natural denizens of projective
Scale_invariance
Drug enforcement leads to higher potency
p_{n},U)} , for i = 1 , … , n {\displaystyle i=1,\dots ,n} . For a homogeneous function f ( z 1 , … , z n , V ) {\displaystyle f(z_{1},\dots ,z_{n},V)} of
Iron_law_of_prohibition
Characteristic in consumer theory
are called homothetic if they can be represented by a utility function which is homogeneous of degree 1. For example, in an economy with two goods x , y
Homothetic_preferences
In mathematics, invariant of square matrices
appropriate function is not clear.[citation needed] These rules have several further consequences: The determinant is a homogeneous function, i.e., det
Determinant
Short exact sequence of sheaves on projective space
0-homogeneous function on V (again partially defined). We obtain 1-homogeneous vector fields by multiplying the Euler vector field by such functions. This
Euler_sequence
Mathematical function, denoted exp(x) or e^x
coefficients can be expressed in terms of exponential functions and, when they are not homogeneous, antiderivatives. This holds true also for systems of
Exponential_function
Polynomial with all terms of degree two
polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, 4 x 2 + 2 x y − 3 y 2 {\displaystyle 4x^{2}+2xy-3y^{2}}
Quadratic_form
Method for assigning values to integrals
is, however, well-defined if K {\displaystyle K} is a continuous homogeneous function of degree − n {\displaystyle -n} whose integral over any sphere centered
Cauchy_principal_value
Type of differential equation
distribution of a homogeneous solid is a harmonic function. It is usually a matter of straightforward computation to check whether or not a given function is harmonic
Partial_differential_equation
Type of functions, in mathematical analysis
analysis, a holonomic function is a smooth function of several variables that is a solution of a system of linear homogeneous differential equations
Holonomic_function
Mathematical transformation
It follows that if a function is homogeneous of degree r then its image under the Legendre transformation is a homogeneous function of degree s, where 1/r
Legendre_transformation
Concept in mathematics
gi's are regular functions on U. Since X is projective, each gi is a fraction of homogeneous elements of the same degree in the homogeneous coordinate ring
Morphism of algebraic varieties
Morphism_of_algebraic_varieties
Generalized scaling operation in geometry
In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and
Homothety
Family of functions to transform data
production function. The CES production function is a homogeneous function of degree one. When λ = 1, this produces the linear production function: Q = α
Power_transform
Distance from origin of tangent hyperplanes
positive homogeneous, convex, real valued function is the (convex) indicator function of a compact convex set. Many authors restrict the support function to
Support_function
Microeconomic concept
{\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
Returns_to_scale
Generalization of the concept of directional derivative
Gateaux differential defines a function d f x ( v ) : X → Y . {\displaystyle df_{x}(v):X\to Y.} This function is homogeneous in the sense that for all scalars
Gateaux_derivative
Mathematical function
that is, taking variables with repetition, one arrives at the complete homogeneous symmetric polynomials.) Given an integer partition (that is, a finite
Elementary symmetric polynomial
Elementary_symmetric_polynomial
Integral transform
Funk transform F maps smooth even homogeneous functions of degree −2 on R3\{0} to smooth even homogeneous functions of degree −1 on R3\{0}. The Funk-Radon
Funk_transform
Type of symmetric polynomials in mathematics
that generalize the elementary symmetric polynomials and the complete homogeneous symmetric polynomials. In representation theory they are the characters
Schur_polynomial
Mathematical definition of point elasticity
elasticity Elasticity (economics) Elasticity coefficient (biochemistry) Homogeneous function Logarithmic derivative The elasticity can also be defined if the
Elasticity_of_a_function
Method of solution for inhomogeneous ODEs
the homogeneous solution, it is necessary to multiply by a sufficiently large power of x in order to make the solution independent. If the function of
Method of undetermined coefficients
Method_of_undetermined_coefficients
Well-quasi-ordering of finite trees
application of the theorem gives the existence of a fast-growing TREE function. TREE(3) is one of the largest simply defined finite numbers, dwarfing
Kruskal's_tree_theorem
Equation in thermodynamics
The internal energy is thus a first-order homogenous function. Applying Euler's homogeneous function theorem, one finds the following relation: U = T S
Gibbs–Duhem_equation
Solutions of Legendre's differential equation
solutions can be expressed using hypergeometric functions. Since the differential equation is linear, homogeneous (the right hand side =zero) and of second
Legendre_function
Economic formula of productivity
productivity. When the model exponents sum to one, the production function is first-order homogeneous, which implies constant returns to scale—that is, if all
Cobb–Douglas production function
Cobb–Douglas_production_function
Description of particle density in statistical mechanics
) {\displaystyle \rho g(r)} . This simplified definition holds for a homogeneous and isotropic system. A more general case will be considered below. In
Radial_distribution_function
Mathematical transform that expresses a function of time as a function of frequency
takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output
Fourier_transform
Problem in hydrodynamics
configuration at all times of a homogeneous rotating fluid mass in which the motion, in an inertial frame, is a linear function of the coordinates. Dirichlet's
Dirichlet's ellipsoidal problem
Dirichlet's_ellipsoidal_problem
Scalar physical quantities representing system states
U(\{\alpha y_{i}\})=\alpha U(\{y_{i}\})} it follows from Euler's homogeneous function theorem that the internal energy can be written as: U ( { y i } )
Thermodynamic_potential
Formulation of classical mechanics
relation to solve for the coordinates. If the potential energy is a homogeneous function of the coordinates and independent of time, and all position vectors
Lagrangian_mechanics
Mechanical system whose constraints are independent of time
not vanish: T = T 2 . {\displaystyle T=T_{2}.} Kinetic energy is a homogeneous function of degree 2 in generalized velocities. As shown at right, a simple
Scleronomous
Existence and uniqueness of solutions to initial value problems
differential equations will possess a single stationary point y = 0. First, the homogeneous linear equation dy/dt = ay ( a < 0 {\displaystyle a<0} ), a stationary
Picard–Lindelöf_theorem
Polynomial with only one term
embeddings. Monomial representation Monomial matrix Homogeneous polynomial Homogeneous function Multilinear form Log-log plot Power law Sparse polynomial
Monomial
Tool in mathematical dimension theory
strongly related notions which measure the growth of the dimension of the homogeneous components of the algebra. These notions have been extended to filtered
Hilbert series and Hilbert polynomial
Hilbert_series_and_Hilbert_polynomial
see complete homogeneous symmetric polynomials. Representation theory Newton's identities Ian G. Macdonald (1979), Symmetric Functions and Hall Polynomials
Power sum symmetric polynomial
Power_sum_symmetric_polynomial
Two circular coil device which creates a homogeneous magnetic field
genuinely is nearly homogeneous between the coils. To understand the behavior of the field around the center point, we may define the function B ( x ) = B n
Helmholtz_coil
Functions in mathematics
mean-value property of the harmonic functions and its converse follows immediately observing that the non-homogeneous equation, for any 0 < s < r {\displaystyle
Harmonic_function
Several equations of degree 1 to be solved simultaneously
to a homogeneous system, then the vector sum u + v is also a solution to the system. If u is a vector representing a solution to a homogeneous system
System_of_linear_equations
Function that only depends on time
combinations of the homogeneous solutions and the forcing term. For example, f ( t ) {\displaystyle f(t)} is the forcing function in the nonhomogeneous
Forcing function (differential equations)
Forcing_function_(differential_equations)
Methods of calculating definite integrals
\int _{a}^{b}f(x)\,dx} to a given degree of accuracy. If f(x) is a smooth function integrated over a small number of dimensions, and the domain of integration
Numerical_integration
Mathematical operator
variable, the eigenspaces of θ are the spaces of homogeneous functions. (Euler's homogeneous function theorem) Difference operator Delta operator Elliptic
Theta_operator
Solution method for linear differential equations
calculation in quantum mechanics in which the wave function is recast as an exponential function, semiclassically expanded, and then either the amplitude
WKB_approximation
Technique for solving linear ordinary differential equations
(n−1)-th order equation for v {\displaystyle v} . Consider the general, homogeneous, second-order linear constant coefficient ordinary differential equation
Reduction_of_order
Emission spectrum with Lorentzian profile
inhomogeneous way. The homogeneous broadened emission line will have a Lorentzian profile (i.e. will be best fitted by a Lorentzian function), while the inhomogeneously
Spectral_broadening
Technique for expressing a polynomial in simpler fashion by using more variables
technique for expressing a homogeneous polynomial in a simpler fashion by adjoining more variables. Specifically, given a homogeneous polynomial, polarization
Polarization of an algebraic form
Polarization_of_an_algebraic_form
Determinant of the matrix of first derivatives of a set of functions
{\displaystyle n} linearly independent functions that are all solutions of the same monic n {\displaystyle n} th-order homogeneous-linear ordinary differential
Wronskian
Problem in convex geometry
intersection body if and only if the function 1/||x|| is a positive definite distribution, where ||x|| is the homogeneous function of degree 1 that is 1 on the
Busemann–Petty_problem
Integral of the Gaussian function, equal to sqrt(π)
also known as the Euler–Poisson integral, is the integral of the Gaussian function f ( x ) = e − x 2 {\displaystyle f(x)=e^{-x^{2}}} over the entire real
Gaussian_integral
Within the field of fluid dynamics, Homogeneous isotropic turbulence is an idealized version of the realistic turbulence, but amenable to analytical studies
Homogeneous isotropic turbulence
Homogeneous_isotropic_turbulence
Identity relating to differential equations
identity) is an equation that expresses the Wronskian of two solutions of a homogeneous second-order linear ordinary differential equation in terms of a coefficient
Abel's_identity
utility-maximizing rational agents can take the shape of any function that is continuous, homogeneous of degree zero, and in accord with Walras's law. This implies
Excess_demand_function
HOMOGENEOUS FUNCTION
HOMOGENEOUS FUNCTION
Male
Celtic
, great justiciary, or functionary.
Male
Egyptian
, a great functionary.
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Male
Egyptian
, an Egyptian functionary.
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Biblical
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Male
Egyptian
, the son of the functionary Heknofre.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, a high Egyptian functionary.
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Male
Egyptian
, Functionary of the Interior.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
HOMOGENEOUS FUNCTION
HOMOGENEOUS FUNCTION
Boy/Male
Indian, Telugu
Daring; Freedom-loving
Male
Czechoslovakian
, slave council man.
Girl/Female
Arabic, Muslim
Intelligent; Hidden Treasure
Male
English
Anglicized form of Hebrew Atsel, AZEL means "noble." In the bible, this is the name of a place near Jerusalem, and a descendant of Saul.
Boy/Male
Hebrew
Sympathy of God.
Boy/Male
American, Australian, British, Christian, English, German, Teutonic
Noble Friend; Elf Friend
Boy/Male
Gujarati, Hindu, Indian, Malayalam, Marathi, Oriya, Sanskrit, Sikh, Telugu
Conqueror of the Mind
Girl/Female
Tamil
Summit, Peak
Boy/Male
Indian, Punjabi, Sikh
King's Victory; Victory of Land
Boy/Male
Finnish
HOMOGENEOUS FUNCTION
HOMOGENEOUS FUNCTION
HOMOGENEOUS FUNCTION
HOMOGENEOUS FUNCTION
HOMOGENEOUS FUNCTION
n.
A medicinal substance made into a cohesive, homogeneous lump, of consistency suitable for making pills; as, blue mass.
n.
The condition of having homogonous flowers.
n.
The result of eliminating n variables between n homogeneous equations of any degree; -- called also resultant.
n.
The state or quality of being homogeneous in elements or first principles; likeness or identity of parts.
a.
Homogeneous.
a.
Holding the particles of a homogeneous body together; as, cohesive attraction; producing cohesion; as, a cohesive force.
a.
Having a resemblance in structure, due to descent from a common progenitor with subsequent modification; homogenetic; -- applied both to animals and plants. See Homoplastic.
a.
Homogenous; uniform.
n.
The eliminant of the n partial differentials of any homogenous function of n variables. See Eliminant.
n.
The very thin transparent and apparently homogeneous sheath which incloses a striated muscular fiber; the myolemma.
a.
Without a definite structure, or arrangement of parts; without organization; devoid of cells; homogeneous; as, a structureless membrane.
a.
Homogeneous.
n.
The mixing or blending of different elements, races, societies, etc.; also, the result of such combination or blending; a homogeneous union.
a.
Having all the flowers of a plant alike in respect to the stamens and pistils.
a.
Not discrete or separated; compact; homogenous.
n.
A mass formed by the union of homogeneous particles; -- in distinction from a compound, formed by the union of heterogeneous particles.
n.
That method of reproduction in which the successive generations are alike, the offspring, either animal or plant, running through the same cycle of existence as the parent; gamogenesis; -- opposed to heterogenesis.
a.
Of the same kind of nature; consisting of similar parts, or of elements of the like nature; -- opposed to heterogeneous; as, homogeneous particles, elements, or principles; homogeneous bodies.
a.
Possessing the same number of factors of a given kind; as, a homogeneous polynomial.
a.
Homogenous.