symplectic

UK /sɪmˈplɛktɪk/ US /sɪmˈplɛktɪk/
adj 5noun 2

Definitions

adj

1

Placed in or among, as if woven together.

2

Whose characteristic abelian subgroups are cyclic.

3

That is alternating and nondegenerate.

4

That is equipped with an alternating nondegenerate bilinear form.

5

Of or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form.

There exist interesting and unexplored relations between symplectic geometry and the theory of critical points of holomorphic functions.

1997, C. H. Cushman-de Vries (translator), Richard H. Cushman, Gijs M. Tuynman (translation editors), Jean-Marie Souriau, Structure of Dynamical Systems: A Symplectic View of Physics, Springer Science & Business Media (Birkhäuser).

noun

1

A symplectic bilinear form, manifold, geometry, etc.

The structure of stable symplectics on finite dimensional spaces has been studied by Krein [8], Gelfand & Lidskii [9], and Moser [10] in work of considerable practical importance.

2

A bone in the teleostean fishes that forms the lower ossification of the suspensorium, and which articulates below with the quadrate bone by which it is firmly held.

The symplectics (9) consist of a somewhat curved central triangular portion with the base upward, and anteriorly and posteriorly from this extends a wing-like process.

The symplectics (Fig. 8, sym) are thin slender bones placed vertically in between the quadrates and the hyomandibulars.

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