Joint Invariants of Linear Symplectic Actions

We review computations of joint invariants on a linear symplectic space, discuss variations for an extension of group and space and relate this to other equivalence problems and approaches, most importantly to differential invariants.

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Lagrangian Curve Flows on Symplectic Spaces

Symmetry ◽

10.3390/sym13020298 ◽

2021 ◽

Vol 13 (2) ◽

pp. 298

Author(s):

Chuu-Lian Terng ◽

Zhiwei Wu

Keyword(s):

Soliton Solutions ◽

Differential Invariants ◽

Symplectic Space ◽

Hamiltonian Structures ◽

Linearly Independent ◽

Lagrangian Subspace ◽

Curve Flows ◽

Complete Set ◽

Smooth Map ◽

Darboux Transforms

A smooth map γ in the symplectic space R2n is Lagrangian if γ,γx,…, γx(2n−1) are linearly independent and the span of γ,γx,…,γx(n−1) is a Lagrangian subspace of R2n. In this paper, we (i) construct a complete set of differential invariants for Lagrangian curves in R2n with respect to the symplectic group Sp(2n), (ii) construct two hierarchies of commuting Hamiltonian Lagrangian curve flows of C-type and A-type, (iii) show that the differential invariants of solutions of Lagrangian curve flows of C-type and A-type are solutions of the Drinfeld-Sokolov’s C^n(1)-KdV flows and A^2n−1(2)-KdV flows respectively, (iv) construct Darboux transforms, Permutability formulas, and scaling transforms, and give an algorithm to construct explicit soliton solutions, (v) give bi-Hamiltonian structures and commuting conservation laws for these curve flows.

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An Approach to Proving Proof Obligation of Hybrid Event B Based on Differential Invariants

2017 IEEE 41st Annual Computer Software and Applications Conference (COMPSAC) ◽

10.1109/compsac.2017.52 ◽

2017 ◽

Author(s):

Jie Liu ◽

Jing Liu ◽

Miaomiao Zhang ◽

Haiying Sun ◽

Xiaohong Chen ◽

...

Keyword(s):

Differential Invariants ◽

Proof Obligation ◽

Hybrid Event

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Bounds on subspace codes based on totally isotropic subspace in symplectic spaces and extended symplectic spaces

Asian-European Journal of Mathematics ◽

10.1142/s1793557119500694 ◽

2019 ◽

Vol 12 (05) ◽

pp. 1950069

Author(s):

Mahdieh Hakimi Poroch

Keyword(s):

Sphere Packing ◽

Symplectic Space ◽

Isotropic Subspace ◽

Subspace Codes ◽

Singleton Bound ◽

Symplectic Spaces ◽

Isotropic Subspaces ◽

Totally Isotropic Subspace ◽

Totally Isotropic Subspaces

In this paper, we propose the Sphere-packing bound, Singleton bound and Gilbert–Varshamov bound on the subspace codes [Formula: see text] based on totally isotropic subspaces in symplectic space [Formula: see text] and on the subspace codes [Formula: see text] based on totally isotropic subspace in extended symplectic space [Formula: see text].

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