Перевод и анализ слов искусственным интеллектом ChatGPT
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- этимология
normal derivation - перевод на русский
математика
нормальное дифференцирование
.png?width=200 "Figure 2: Weight (''W''), the frictional force (''F''<sub>''r''</sub>), and the normal force (''F''<sub>''n''</sub>) acting on a block. Weight is the product of mass (''m'') and the acceleration of gravity (''g'').")
математика
антидифференцирование
математика
инвариантная подгруппа
нормальный делитель
математика
делитель нормальный
математика
нормальная группа
общая лексика
вертикально направленная сила
нормальная сила
![A [[contour plot]] of <math>f(x, y)=x^2 + y^2</math>, showing the gradient vector in black, and the unit vector <math>\mathbf{u}</math> scaled by the directional derivative in the direction of <math>\mathbf{u}</math> in orange. The gradient vector is longer because the gradient points in the direction of greatest rate of increase of a function.](https://commons.wikimedia.org/wiki/Special:FilePath/Directional derivative contour plot.svg?width=200 "A [[contour plot]] of <math>f(x, y)=x^2 + y^2</math>, showing the gradient vector in black, and the unit vector <math>\mathbf{u}</math> scaled by the directional derivative in the direction of <math>\mathbf{u}</math> in orange. The gradient vector is longer because the gradient points in the direction of greatest rate of increase of a function.")
общая лексика
производная по нормали
Определение
Википедия
In mathematics, a derivation is a function on an algebra which generalizes certain features of the derivative operator. Specifically, given an algebra A over a ring or a field K, a K-derivation is a K-linear map D : A → A that satisfies Leibniz's law:
More generally, if M is an A-bimodule, a K-linear map D : A → M that satisfies the Leibniz law is also called a derivation. The collection of all K-derivations of A to itself is denoted by DerK(A). The collection of K-derivations of A into an A-module M is denoted by DerK(A, M).
Derivations occur in many different contexts in diverse areas of mathematics. The partial derivative with respect to a variable is an R-derivation on the algebra of real-valued differentiable functions on Rn. The Lie derivative with respect to a vector field is an R-derivation on the algebra of differentiable functions on a differentiable manifold; more generally it is a derivation on the tensor algebra of a manifold. It follows that the adjoint representation of a Lie algebra is a derivation on that algebra. The Pincherle derivative is an example of a derivation in abstract algebra. If the algebra A is noncommutative, then the commutator with respect to an element of the algebra A defines a linear endomorphism of A to itself, which is a derivation over K. That is,
where is the commutator with respect to . An algebra A equipped with a distinguished derivation d forms a differential algebra, and is itself a significant object of study in areas such as differential Galois theory.
