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Τι (ποιος) είναι Pfaffian forms - ορισμός
DIFFERENTIAL FORM OF DEGREE ONE; SECTION OF COTANGENT BUNDLE
1-form; One form; Pfaffian form; 1-forms; One-form
Contrapuntal Forms (Hepworth)
.jpg?width=200 "''Contrapuntal Forms'', in Harlow in 2016")
SCULPTURE BY BARBARA HEPWORTH
Contrapunctal Forms (sculpture); Contrapuntal Forms (sculpture)
Contrapuntal Forms (BH 165) is a stone sculpture by Barbara Hepworth, one of her first public commissions, made in 1950–51 for the Festival of Britain and installed outside the Dome of Discovery on South Bank, London. It was one of two Hepworth commissions for the festival: the other was an abstract rotating sculpture, Turning Forms (BH 166).
One-form
In linear algebra, a one-form on a vector space is the same as a linear functional on the space. The usage of one-form in this context usually distinguishes the one-forms from higher-degree multilinear functionals on the space.
Pfaffian function
Pfaffian chain; Noetherian chain; Noetherian function
In mathematics, Pfaffian functions are a certain class of functions whose derivative can be written in terms of the original function. They were originally introduced by Askold Khovanskii in the 1970s, but are named after German mathematician Johann Pfaff.
Βικιπαίδεια
One-form (differential geometry)
In differential geometry, a one-form on a differentiable manifold is a smooth section of the cotangent bundle. Equivalently, a one-form on a manifold is a smooth mapping of the total space of the tangent bundle of to whose restriction to each fibre is a linear functional on the tangent space. Symbolically,
where is linear.Often one-forms are described locally, particularly in local coordinates. In a local coordinate system, a one-form is a linear combination of the differentials of the coordinates:
where the are smooth functions. From this perspective, a one-form has a covariant transformation law on passing from one coordinate system to another. Thus a one-form is an order 1 covariant tensor field.