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The Barnes Opening (sometimes called Gedult's Opening) is a chess opening where White opens with: . 1. f3. The opening is named after Thomas Wilson Barnes (1825–1874), an English player who had an impressive [1] eight wins over Paul Morphy, including one game where Barnes answered 1.e4 with 1...f6, known as the Barnes Defence.
In mathematics, a free module is a module that has a basis, that is, a generating set that is linearly independent. Every vector space is a free module, [ 1 ] but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules.
The Zukertort Opening is a chess opening named after Johannes Zukertort that begins with the move: . 1. Nf3. Sometimes the name "Réti Opening" is used for the opening move 1.Nf3, [1] although most sources define the Réti more narrowly as the sequence 1.Nf3 d5 2.c4.
This remained the standard [4] in mathematics until Kenneth E. Iverson introduced, in his 1962 book A Programming Language, the names "floor" and "ceiling" and the corresponding notations ⌊x⌋ and ⌈x⌉. [5] [6] (Iverson used square brackets for a different purpose, the Iverson bracket notation.) Both notations are now used in mathematics ...
Field homomorphisms are maps φ: E → F between two fields such that φ(e 1 + e 2) = φ(e 1) + φ(e 2), φ(e 1 e 2) = φ(e 1) φ(e 2), and φ(1 E) = 1 F, where e 1 and e 2 are arbitrary elements of E. All field homomorphisms are injective. [13] If φ is also surjective, it is called an isomorphism (or the fields E and F are called isomorphic).
The aim of these activities is to save control costs, that become redundant when employees act independently and in a self-motivated fashion. In the book Empowerment Takes More Than a Minute, the authors illustrate three keys that organizations can use to open the knowledge, experience, and motivation power that people already have. [7]
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules.
In mathematics, the free group F S over a given set S consists of all words that can be built from members of S, considering two words to be different unless their equality follows from the group axioms (e.g. st = suu −1 t but s ≠ t −1 for s,t,u ∈ S). The members of S are called generators of F S, and the number of generators is the ...