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Polarization Patterns
Polarization or polarisation may refer to: Mathematics *Polarization of an Abelian variety, in the mathematics of complex manifolds *Polarization of an algebraic form, a technique for expressing a homogeneous polynomial in a simpler fashion by adjoining more variables *Polarization identity, expresses an inner product in terms of its associated norm *Polarization (Lie algebra) Physical sciences *Polarization (physics), the ability of waves to oscillate in more than one direction; polarization of light allows the glare-reducing effect of polarized sunglasses **Polarization (antenna), the state of polarization (in the above sense) of electromagnetic waves transmitted by or received by a radio antenna *Dielectric polarization, charge separation in insulating materials: **Polarization density, volume dielectric polarization **Dipolar polarization, orientation of permanent dipoles **Ionic polarization, displacement of ions in a crystal **Maxwell–Wagner–Sillars polarization, slow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abelian Variety
In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a smooth Algebraic variety#Projective variety, projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in algebraic geometry and indispensable tools for research on other topics in algebraic geometry and number theory. An abelian variety can be defined by equations having coefficients in any Field (mathematics), field; the variety is then said to be defined ''over'' that field. Historically the first abelian varieties to be studied were those defined over the field of complex numbers. Such abelian varieties turn out to be exactly those Complex torus, complex tori that can be holomorphic, holomorphically embedded into a complex projective space. Abelian varieties defined over algebraic number fields are a special case, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |