codifferential

名词 n.
中文释义

英文释义

名词 n.
  1. The projected differential of an extensor field.
    — In the language of differential geometry, the incompressible inviscid Euler equations can be written in vorticity-vector potential form as #92;begin#123;matrix#125;#92;partial#95;t#92;omega#43;#123;#92;mathcalL#125;#95;u#92;omegaamp;#61;0#92;#92;uamp;#61;#92;delta#92;tilde#92;eta#123;-1#125;#92;Delta#123;-1#125;#92;omega#92;end#123;matrix#125; where #92;omega is the vorticity 2-form, #123;#92;mathcalL#125;#95;u denotes the Lie derivative with respect to the velocity field u, #92;Delta is the Hodge Laplacian, #92;delta is the codifferential (the negative of the divergence operator), and #92;tilde#92;eta#123;-1#125; is the canonical map from 2-forms to 2-vector fields induced by the Euclidean metric #92;eta.
  2. the formal adjoint of the exterior derivative; a differential-geometric version of the divergence operator; the exterior derivative sandwiched between two Hodge star operators with some additional factor(s) that take(s) care of the sign; the Hermitian conjugate of the exterior derivative under the inner product for k-form fields over some manifold M: (α,β)=∫_Mα∧⋆β, so that (α,dβ)=(δα,β).
    — One important concept is the introduction of codifferential operator

词形变化

codifferentials plural

词源

Etymology tree
Proto-Indo-European *ḱe?
Proto-Indo-European *ḱóm
Proto-Italic *kom
Proto-Italic *kom-
Latin con-
Latin co-der.
English co-
Proto-Indo-European *dwóh₁
Proto-Indo-European *d(w)is-
Proto-Italic *dis-
Latin dis-
Proto-Indo-European *bʰer-
Proto-Indo-European *bʰéreti
Proto-Italic *ferō
Latin ferō
Latin differō
Latin differēns
Proto-Indo-European *-yós
Proto-Italic *-ios
Old Latin -ios
Latin -ius
Latin -ia
Latin differentia
Proto-Indo-European *h₂el-der.?
Proto-Italic *-ālis
Latin -ālis
Latin differentiālislbor.
English differential
English codifferential
From co- + differential.
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