homogeneous

adjectiveB2

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Tính từ

adjective

Comparative

homogenous

1.
(not comparable)Of the same kind; alike, similar.
2.
(not comparable)Having the same composition throughout; of uniform make-up.
3.
(not comparable)(chemistry) In the same state of matter.
4.
(not comparable)(mathematics) 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.).
5.
(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;.
6.
In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):
7.
In abstract algebra and geometry:
8.
In miscellaneous other senses:

Từ liên quan

Trái nghĩa

heterogeneousinhomogeneous

Cùng gốc / liên quan

dishomogeneousquasihomogeneoushomogeneous functiontime-homogeneous Markovian typehomogeneous polynomialhomogeneous mixturehomogeneouslyhomogeneous spaceinhomogeneoushomogeneousnesshomogeneous numbernonhomogeneousbihomogeneoushomogeneous catalysisprehomogeneoussubhomogeneoussuperhomogeneousultrahomogeneousunhomogeneoushomogeneous broadening

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Nguồn gốc từ

From homogeneus, from Ancient Greek ὁμογενής (of the same race, family or kind), from ὁμός (same) + γένος (kind). Compare homo- (same) and -ous.