Apolar

Definitions

  • Webster's Revised Unabridged Dictionary
    • a Apolar (Biol) Having no radiating processes; -- applied particularly to certain nerve cells.
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Century Dictionary and Cyclopedia
    • apolar Having no pole: in anatomy, applied to those nerve-cells which are not known to have, or are supposed not to have, any radiating process.
    • apolar In geometry, having no determinate polar.
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Etymology

Webster's Revised Unabridged Dictionary
Pref. a-, + polar,

Usage

In literature:

Apolar: without differentiated poles; without apparent radiating processes applied to cells.
"Explanation of Terms Used in Entomology" by John. B. Smith
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In science:

These varieties are studied via apolarity and syzygies.
Varieties of sums of powers
The apolar Artinian Gorenstein ring of a general cubic threefold 8.
Varieties of sums of powers
More generally we say that homogeneous forms f ∈ S and D ∈ T are apolar if f (D) = D(f ) = 0 (According to [Salmon 1885] the term was coined by Reye).
Varieties of sums of powers
In particular the socle of AF is 1-dimensional, and AF is indeed Gorenstein and is called the apolar Artinian Gorenstein ring of F ⊂ Pn .
Varieties of sums of powers
We call a subscheme Γ ⊂ ˇPn apolar to F , if the homogeneous ideal IΓ ⊂ F ⊥ ⊂ T .
Varieties of sums of powers
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