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  2. Character (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Character_(mathematics)

    A multiplicative character (or linear character, or simply character) on a group G is a group homomorphism from G to the multiplicative group of a field , usually the field of complex numbers. If G is any group, then the set Ch( G ) of these morphisms forms an abelian group under pointwise multiplication.

  3. Characterization (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Characterization_(mathematics)

    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 ...

  4. Non-Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Non-Euclidean_geometry

    The simplest of these is called elliptic geometry and it is considered a non-Euclidean geometry due to its lack of parallel lines. [12] By formulating the geometry in terms of a curvature tensor, Riemann allowed non-Euclidean geometry to apply to higher dimensions. Beltrami (1868) was the first to apply Riemann's geometry to spaces of negative ...

  5. Glossary of algebraic geometry - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_algebraic_geometry

    An example for a non-local property is separatedness (see below for the definition). Any affine scheme is separated, therefore any scheme is locally separated. However, the affine pieces may glue together pathologically to yield a non-separated scheme.

  6. Nonmetal - Wikipedia

    en.wikipedia.org/wiki/Nonmetal

    Radon is the most metallic of the noble gases and begins to show some cationic behavior, which is unusual for a nonmetal; [96] and; In extreme conditions, just over half of nonmetallic elements can form homopolyatomic cations. [o] Examples of nonmetal-like properties occurring in metals are:

  7. Nonmetallic material - Wikipedia

    en.wikipedia.org/wiki/Nonmetallic_material

    Some textbooks use the term nonmetallic elements such as the Chemistry of the Non-Metals by Ralf Steudel, [25]: 4 which also uses the general definition in terms of conduction and the Fermi level. [ 25 ] : 154 The approach based upon the elements is often used in teaching to help students understand the periodic table of elements, [ 26 ...

  8. Noncommutative quantum field theory - Wikipedia

    en.wikipedia.org/wiki/Noncommutative_quantum...

    In mathematical physics, noncommutative quantum field theory (or quantum field theory on noncommutative spacetime) is an application of noncommutative mathematics to the spacetime of quantum field theory that is an outgrowth of noncommutative geometry and index theory in which the coordinate functions [1] are noncommutative.

  9. Metallic mean - Wikipedia

    en.wikipedia.org/wiki/Metallic_mean

    Since the inverse of a metallic mean is less than 1, this formula implies that the quotient of two consecutive elements of such a sequence tends to the metallic mean, when k tends to the infinity. For example, if n = 1 , {\displaystyle n=1,} S n {\displaystyle S_{n}} is the golden ratio .