homogeneous

形容词 adj.
中文释义
英 /ˌhɒm.ə(ʊ)ˈd͡ʒiː.nɪəs/|/ˌhəʊ.mə(ʊ)ˈd͡ʒiː.nɪəs/    美 /ˌhoʊ.moʊˈd͡ʒi.ni.əs/|/ˌhoʊ.mə-/|/-ˈd͡ʒɛ-/|/-njəs/|/həˈmɑ.d͡ʒə.nəs/

英文释义

形容词 adj.
  1. Of the same kind; alike, similar. not-comparable
  2. Having the same composition throughout; of uniform make-up. not-comparable
    — Their citizens were not of homogeneous origin, but were from all parts of Greece.
  3. In the same state of matter. not-comparable
  4. 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.). not-comparable
  5. 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:; Such that all its nonzero terms have the same degree. not-comparable
    — The polynomial x²+5xy+y² is homogeneous of degree 2, because x², xy, and y² are all degree 2 monomials
  6. 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:; Such that all the constant terms are zero. not-comparable
  7. 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:; 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
  8. 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;. not-comparable
  9. In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):; 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
  10. In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):; Having its degree-zero term equal to zero; admitting the trivial solution. not-comparable
  11. In ordinary differential equations (by analogy with the case for polynomial and functional homogeneity):; Homogeneous as a function of the dependent variable and its derivatives. not-comparable
  12. In abstract algebra and geometry:; 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) not-comparable
  13. In abstract algebra and geometry:; Which respects the grading of its domain and codomain. Formally: Satisfying f(V_j)⊆W_i+j for fixed i (called the degree or grade of f), V_j the jth component of the grading of f 's domain, W_k the kth component of the grading of f 's codomain, and + representing the monoid operation in I. not-comparable
  14. In abstract algebra and geometry:; Informally: Everywhere the same, uniform, in the sense that any point can be moved to any other (via the group action) while respecting the structure of the space. Formally: Such that the group action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful). not-comparable
  15. In abstract algebra and geometry:; Of or relating to homogeneous coordinates. not-comparable
  16. In miscellaneous other senses:; Informally: Determined by its restriction to the unit sphere. Formally: Such that, for all real t>0 and test functions ϕ( mathbf x), the equality S[t⁻ⁿϕ( mathbf x/t)]=t^(mS)[ϕ( mathbf x)] holds for some fixed real or complex m. not-comparable
  17. In miscellaneous other senses:; Holding between a set and itself; being an endorelation. not-comparable

词形变化

homogenous alternative

词汇关系

近义词
homogeneous invariable of a piece onefold samely uniform uniformal unmixed unvaried unvarying
反义词
heterogeneous inhomogeneous
下位词
connatural monolithic monotone steady unalloyed
衍生词
bihomogeneous dishomogeneous homogeneous broadening homogeneous catalysis homogeneous coordinate homogeneous equilibrium homogeneous function homogeneous ideal homogeneously homogeneous mixture homogeneousness homogeneous number homogeneous polynomial homogeneous radiation homogeneous society homogeneous space homogeneous system homogeneous width inhomogeneous nonhomogeneous prehomogeneous quasihomogeneous subhomogeneous superhomogeneous time-homogeneous Markovian type ultrahomogeneous unhomogeneous
相关词
homogeneity homogenesis homogenise homogenize homogeny

词源

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).
0 次浏览 数据来源: Wiktionary