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A Boolean algebra can be interpreted either as a special kind of ring (a Boolean ring) or a special kind of distributive lattice (a Boolean lattice). Each interpretation is responsible for different distributive laws in the Boolean algebra. Similar structures without distributive laws are near-rings and near-fields instead of rings and division ...
In algebra, the distribution algebra (,) of a p-adic Lie group G is the K-algebra of K-valued distributions on G. (See the reference for a more precise definition.) (See the reference for a more precise definition.)
In algebraic geometry, given a linear algebraic group G over a field k, a distribution on it is a linear functional [] satisfying some support condition. A convolution of distributions is again a distribution and thus they form the Hopf algebra on G , denoted by Dist( G ), which contains the Lie algebra Lie( G ) associated to G .
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011.
The support of the distribution associated with the Dirac measure at a point is the set {}. [12] If the support of a test function does not intersect the support of a distribution T then = A distribution T is 0 if and
The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations .
An expectation E on an algebra A of random variables is a normalized, positive linear functional. What this means is that E[k] = k where k is a constant; E[X * X] ≥ 0 for all random variables X; E[X + Y] = E[X] + E[Y] for all random variables X and Y; and; E[kX] = kE[X] if k is a constant. One may generalize this setup, allowing the algebra ...
In mathematics, a Colombeau algebra is an algebra of a certain kind containing the space of Schwartz distributions.While in classical distribution theory a general multiplication of distributions is not possible, Colombeau algebras provide a rigorous framework for this.
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