scholarly journals Some New Characterizations of Symplectic Curve in 4-Dimensional Symplectic Space

2019 ◽  
pp. 331-334
Author(s):  
Mehmet Bektaş ◽  
Esra Çiçek Çetin
Keyword(s):  
Symplectic Space ◽  
Symplectic Curve

scholarly journals k-TYPE SLANT HELICES FOR SYMPLECTIC CURVE IN 4-DIMENSIONAL SYMPLECTIC SPACE

2020 ◽  
pp. 641
Author(s):  
Esra Cicek Cetin ◽  
Mehmet Bektaş
Keyword(s):  
Differential Equations ◽  
Symplectic Space ◽  
Slant Helix ◽  
Symplectic Curve

In this study, we have expressed the notion of $k$-type slant helix in $4$-symplectic space. Also, we have generated some differential equations for $k$-type slant helix of symplectic regular curves. 

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

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].

Chiral strings, topological branes, and a generalised Weyl-invariance

2019 ◽  
Vol 34 (06n07) ◽  
pp. 1950031 ◽  
Author(s):  
Alex S. Arvanitakis
Keyword(s):  
Field Theory ◽  
Sigma Model ◽  
Space Time ◽  
Symplectic Space ◽  
Topological Field Theory ◽  
Brst Operator ◽  
Weyl Invariance ◽  
Fixed Action ◽  
Twistor Strings ◽  
Topological Field

We introduce a sigma model Lagrangian generalising a number of new and old models which can be thought of as chiral, including the Schild string, ambitwistor strings, and the recently introduced tensionless AdS twistor strings. This “chiral sigma model” describes maps from a [Formula: see text]-brane worldvolume into a symplectic space and is manifestly invariant under diffeomorphisms as well as under a “generalised Weyl invariance” acting on space–time coordinates and worldvolume fields simultaneously. Construction of the Batalin–Vilkovisky master action leads to a BRST operator under which the gauge-fixed action is BRST-exact; we discuss whether this implies that the chiral brane sigma model defines a topological field theory.

SYMPLECTIC SPACE OR ORTHOGONAL SPACE OF n QUBITS

2011 ◽  
Vol 09 (06) ◽  
pp. 1449-1457
Author(s):  
JIAN-WEI XU
Keyword(s):  
Hilbert Space ◽  
Orthogonal Group ◽  
Symplectic Group ◽  
Orthonormal Basis ◽  
Mathematical Structure ◽  
Symplectic Space ◽  
Orthogonal Space ◽  
Spin Flip

In Hilbert space of n qubits, we introduce symplectic space (n odd) or orthogonal space (n even) via the spin-flip operator. Under this mathematical structure we discuss some properties of n qubits, including homomorphically mapping local operations of n qubits into symplectic group or orthogonal group, and proving that the generalized "magic basis" is just the biorthonormal basis (i.e. the orthonormal basis of both Hilbert space and the orthogonal space). Finally, a demonstrated example is given to discuss the application in physics of this mathematical structure.

Constructions of compressed sensing matrices based on the subspaces of symplectic space over finite fields

2015 ◽  
Vol 15 (02) ◽  
pp. 1650025 ◽  
Author(s):  
You Gao ◽  
Xiaojuan Zhang
Keyword(s):  
Compressed Sensing ◽  
Finite Fields ◽  
Symplectic Geometry ◽  
Symplectic Space ◽  
The Matrix ◽  
Compressed Sensing Matrices ◽  
Sensing Matrices

The paper provides two constructions of compressed sensing matrices using the subspaces of symplectic space and singular symplectic space over finite fields. Then we compare the matrices constructed in this paper with the matrix constructed by DeVore, and compare the two matrices based on symplectic geometry and singular symplectic geometry over finite fields.

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