homogeneous

homogeneous englannista suomeksi

1. homogeeninen

1. samanlainen, homogeeninen

2. tasa-aineinen, homogeeninen

homogeneous englanniksi

1. Of the same kind; alike, similar.

2. Having the same composition throughout; of uniform make-up.

3. {{quote-text|en|year=1946|author=Bertrand Russell|title=History of Western Philosophy|section=I.25

4. In the same of matter.

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.).

6. (non-gloss)

7. Such that all its nonzero terms have the same degree.

''The polynomial x^2+5xy+y^2 is homogeneous of degree 2, because x^2, xy{{, and y^2 are all degree 2 monomials

8. Such that all the constant terms are zero.

9. 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). Satisfying the equality f(s\mathbf{x}) = s^kf(

11. 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.

12. Having its degree-zero term equal to zero; admitting the trivial solution.

13. Homogeneous as a function of the dependent variable and its derivatives.

14. (C) Belonging to one of the summands of the grading (''if the ring is graded over the numbers and the element is in the ''k''th 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 ''i''th summand, it is said to be ''of grade'' i'')

15. Which respects the grading of its domain and codomain. ''Formally:'' Satisfying f(V_j) \subseteq 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.

16. ''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 action is transitively and acts by automorphisms on the space (some authors also require that the action be faithful).

17. Of or relating to coordinates.

18. Holding between a set and itself; being an endorelation.