homogeneous
Of the same kind; alike, similarOf the same kind; alike, similar.
» They want a linguistically homogeneous country.
Вони хочуть лінгвістично однорідну країну.
Meaning
17 senses(not comparable)Of the same kind; alike, similar.
homogen, gleichartig
одноро́дныйodnoródnyj, гомоге́нныйgomogénnyj, единообра́зныйjedinoobráznyj
all of the same or similar kind or nature
(not comparable)Having the same composition throughout; of uniform make-up.
(not comparable)In the same state of matter.
(not comparable)In any of several technical senses uniform; scalable; having its behavior or form determined by, or the same as, its behavior on or form at a smaller component (of its domain of definition, of itself, etc.).
Of polynomials, functions, equations, systems of equations, or linear maps:
(not comparable)Such that all its nonzero terms have the same degree.
The polynomial x²+5xy+y² is homogeneous of degree 2, because x², xy, and y² are all degree 2 monomials
(not comparable)Such that all the constant terms are zero.
(not comparable)Such that if each of f 's inputs are multiplied by the same scalar, f 's output is multiplied by the same scalar to some fixed power (called the degree of homogeneity or degree of f). (Formally and more generally, of a partial function f between vector spaces whose domain is a linear cone) Satisfying the equality f(s mathbf x)=sᵏᶠ(
(not comparable)The function f(x,y)#61;x²#43;x²ʸ#43;y² is not homogeneous on all of #92;mathbb#123;R#125;² because f(2,2)#61;16#92;neq 2ᵏ#42;3#61;2ᵏf(1,1) for any k, but f is homogeneous on the subspace of #92;mathbb#123;R#125;² spanned by (1,0) because f(#92;alphax,#92;alphay)#61;#92;alphax²#61;#92;alpha²f(x,y) for all (x,y)#92;in#92;operatorname#123;Span#125;#92;#123;(1,0)#92;#125;.
In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
(not comparable)Capable of being written in the form f(x,y) mathop dy=g(x,y) mathop dx where f and g are homogeneous functions of the same degree as each other.
(not comparable)Having its degree-zero term equal to zero; admitting the trivial solution.
(not comparable)Homogeneous as a function of the dependent variable and its derivatives.
In abstract algebra and geometry:
(not comparable)Belonging to one of the summands of the grading (if the ring is graded over the natural numbers and the element is in the kth summand, it is said to be homogeneous of degree k; if the ring is graded over a commutative monoid I, and the element is an element of the ith summand, it is said to be of grade i)
Examples
18 sentencesThey want a linguistically homogeneous country.
Вони хочуть лінгвістично однорідну країну.
Cambodia is ethnically homogeneous.
Камбоджа етнічно однорідна.
The country is becoming increasingly homogeneous.
This is a linguistically homogeneous region.
Kabylie's physical geography is relatively homogeneous.
Translations
7 languagesBy meaning 1
By meaning 1
Origin
From Medieval Latin homogeneus, from Ancient Greek ὁμογενής (homogenḗs, “of the same race,From Medieval Latin homogeneus, from Ancient Greek ὁμογενής (homogenḗs, “of the same race, family or kind”), from ὁμός (homós, “same”) + γένος (génos, “kind”). Compare homo- (“same”) and -ous (adjectival suffix).
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Synonyms
11 synonyms- all of the same or similar kind or nature:homogenous