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Angular 2.0 was announced at the ng-Europe conference 22–23 October 2014. [16] On April 30, 2015, the Angular developers announced that Angular 2 moved from Alpha to Developer Preview. [17] Angular 2 moved to Beta in December 2015, [18] and the first release candidate was published in May 2016. [19] The final version was released on 14 ...
In the mathematical field of differential topology, the Lie bracket of vector fields, also known as the Jacobi–Lie bracket or the commutator of vector fields, is an operator that assigns to any two vector fields X and Y on a smooth manifold M a third vector field denoted [X, Y]. Conceptually, the Lie bracket [X, Y] is the derivative of Y ...
Pullback (differential geometry) Let be a smooth map between smooth manifolds and . Then there is an associated linear map from the space of 1-forms on (the linear space of sections of the cotangent bundle) to the space of 1-forms on . This linear map is known as the pullback (by ), and is frequently denoted by .
Angle brackets or chevrons were the earliest type of bracket to appear in written English. Erasmus coined the term lunula to refer to the round brackets or parentheses ( ) recalling the shape of the crescent moon (Latin: luna). [6] Most typewriters only had the left and right parentheses. Square brackets appeared with some teleprinters.
In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms f : X → Z and g : Y → Z with a common codomain. The pullback is written. P = X ×f, Z, g Y.
In mathematics, a volume form or top-dimensional form is a differential form of degree equal to the differentiable manifold dimension. Thus on a manifold of dimension , a volume form is an -form. It is an element of the space of sections of the line bundle , denoted as . A manifold admits a nowhere-vanishing volume form if and only if it is ...
Definition. The interior product is defined to be the contraction of a differential form with a vector field. Thus if is a vector field on the manifold then is the map which sends a -form to the -form defined by the property that for any vector fields. When is a scalar field (0-form), by convention. The interior product is the unique ...
In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold.Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a principal connection on the frame bundle – see affine connection.