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In geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors.The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product.
The triple product rule, known variously as the cyclic chain rule, cyclic relation, cyclical rule or Euler's chain rule, is a formula which relates partial ...
In abstract algebra, the triple product property is an identity satisfied in some groups. Let G {\displaystyle G} be a non-trivial group. Three nonempty subsets S , T , U ⊂ G {\displaystyle S,T,U\subset G} are said to have the triple product property in G {\displaystyle G} if for all elements s , s ′ ∈ S {\displaystyle s,s'\in S} , t , t ...
The triple product also has a minimum required value, and the name "Lawson criterion" may refer to this value. On August 8, 2021, researchers at Lawrence Livermore National Laboratory's National Ignition Facility in California confirmed to have produced the first-ever successful ignition of a nuclear fusion reaction surpassing the Lawson's ...
Triple product is a ternary operation on vectors. It may also mean: Jacobi triple product, an identity in number theory; Triple product rule, a calculus chain rule for three interdependent variables; Lawson criterion, the product in nuclear fusion; Triple product property, an abstract algebra identity satisfied in some groups
The Jacobi triple product identity is the Macdonald identity for the affine root system of type A 1, and is the Weyl denominator formula for the corresponding affine Kac–Moody algebra. Properties [ edit ]
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The pentagonal number theorem occurs as a special case of the Jacobi triple product. Q-series generalize Euler's function, which is closely related to the Dedekind eta function, and occurs in the study of modular forms.