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The extended base of a triangle (a particular case of an extended side) is the line that contains the base. When the triangle is obtuse and the base is chosen to be one of the sides adjacent to the obtuse angle , then the altitude dropped perpendicularly from the apex to the base intersects the extended base outside of the triangle.
For example, the Euclidean topology on the plane admits as a base the set of all open rectangles with horizontal and vertical sides, and a nonempty intersection of two such basic open sets is also a basic open set. But another base for the same topology is the collection of all open disks; and here the full (B2) condition is necessary.
The electric charge Q, third component of weak isospin T 3 (also called T z, I 3 or I z) and weak hypercharge Y W are related by = +, (or by the alternative convention Q = T 3 + Y W). The first convention, used in this article, is equivalent to the earlier Gell-Mann–Nishijima formula. It makes the hypercharge be twice the average charge of a ...
[1] [2] [3] For example, the standard basis for a Euclidean space is an orthonormal basis, where the relevant inner product is the dot product of vectors. The image of the standard basis under a rotation or reflection (or any orthogonal transformation ) is also orthonormal, and every orthonormal basis for R n {\displaystyle \mathbb {R} ^{n ...
The standard unit vector bases of c 0, and of ℓ p for 1 ≤ p < ∞, are monotone Schauder bases. In this unit vector basis { b n }, the vector b n in V = c 0 or in V = ℓ p is the scalar sequence [ b n , j ] j where all coordinates b n, j are 0, except the n th coordinate:
Metric spaces are also studied in their own right in metric geometry [2] and analysis on metric spaces. [ 3 ] Many of the basic notions of mathematical analysis , including balls , completeness , as well as uniform , Lipschitz , and Hölder continuity , can be defined in the setting of metric spaces.
Although the case for two bases, and for d + 1 bases is well studied, very little is known about uncertainty relations for mutually unbiased bases in other circumstances. [ 27 ] [ 28 ] When considering more than two, and less than d + 1 {\displaystyle d+1} bases it is known that large sets of mutually unbiased bases exist which exhibit very ...
The weak interaction is responsible for various forms of particle decay, such as beta decay. It is weak and short-range, due to the fact that the weak mediating particles, W and Z bosons, have mass. W bosons have electric charge and mediate interactions that change the particle type (referred to as flavor) and charge.
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