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Characterization or characterisation is the representation of characters (persons, creatures, or other beings) ... Direct or explicit characterization
In mathematical logic, the Borel hierarchy is a stratification of the Borel algebra generated by the open subsets of a Polish space; elements of this algebra are called Borel sets.
A precursor to Brauer's induction theorem was Artin's induction theorem, which states that |G| times the trivial character of G is an integer combination of characters which are each induced from trivial characters of cyclic subgroups of G. Brauer's theorem removes the factor |G|, but at the expense of expanding the collection of subgroups used.
When θ is the trivial character of H, the induced character obtained is known as the permutation character of G (on the cosets of H). The general technique of character induction and later refinements found numerous applications in finite group theory and elsewhere in mathematics, in the hands of mathematicians such as Emil Artin , Richard ...
In mathematics, a characterization of an object is a set of conditions that, while possibly different from the definition of the object, is logically equivalent to it. [1] To say that "Property P characterizes object X " is to say that not only does X have property P , but that X is the only thing that has property P (i.e., P is a defining ...
When you create a character as perfect as Sherlock Holmes, as Arthur Conan Doyle did in 1887 — and not just a character but a whole situation, with a sidekick chronicler, Dr. Watson, a ...
Characterization 2 ⇒ characterization 5 [ edit ] In the sense of definition 2, the equation exp ( x + y ) = exp ( x ) exp ( y ) {\displaystyle \exp(x+y)=\exp(x)\exp(y)} follows from the term-by-term manipulation of power series justified by uniform convergence , and the resulting equality of coefficients is just the Binomial theorem .
In mathematics, a character group is the group of representations of an abelian group by complex-valued functions. These functions can be thought of as one-dimensional matrix representations and so are special cases of the group characters that arise in the related context of character theory .