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Physics Letters A, ISSN 0375-9601, 02/2019, Volume 383, Issue 8, pp. 707 - 717
Characterization of the multipartite mixed state entanglement is still a challenging problem. This is due to the fact that the entanglement for the mixed... 
Genuine multipartite concurrence | Polynomial invariant of degree 2 | Multipartite entanglement | PHYSICS, MULTIDISCIPLINARY
Journal Article
Quantum Information Processing, ISSN 1570-0755, 8/2019, Volume 18, Issue 8, pp. 1 - 7
Journal Article
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica, ISSN 1024-7696, 2015, Volume 79, Issue 3, pp. 14 - 34
Journal Article
Journal of Algebra, ISSN 0021-8693, 12/2017, Volume 492, pp. 157 - 184
Let be an elementary abelian -group of order . Let be a faithful indecomposable representation of with dimension 2 over a field of characteristic , and let... 
Elementary abelian p-groups | Invariant theory | Symmetric powers | Modular representation theory | Relative stable module category | MATHEMATICS | CYCLIC GROUP | PRIME-ORDER | POLYNOMIAL INVARIANTS | RINGS
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 07/2016, Volume 207, pp. 232 - 240
The -invariant polynomial subspaces play a crucial role in ideal interpolation. In this paper, we analyze the structure of a second-degree -invariant... 
Ideal interpolation | [formula omitted]-invariant polynomial subspace | Discrete approximation problem | D-invariant polynomial subspace | MATHEMATICS | LIMITS
Journal Article
Journal of the European Mathematical Society, ISSN 1435-9855, 2016, Volume 18, Issue 3, pp. 657 - 680
We study the degree 3 cohomological invariants with coefficients in Q/Z(2) of a semi-simple group over an arbitrary field. A list of all invariants of adjoint... 
Semisimple groups | Torsors | Classifying space | Cohomological invariants | MATHEMATICS | MATHEMATICS, APPLIED | classifying space | cohomological invariants | torsors
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 02/2012, Volume 45, Issue 6, pp. 065302 - 17
We give explicit index-free formulae for all the degree 6 (and also degree 4 and 2) algebraically independent local unitary invariant polynomials for... 
PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | MULTIPARTICLE ENTANGLEMENT | Illustrations | Polynomials | Algebra | Mathematical analysis | Invariants
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 04/2013, Volume 46, Issue 13, pp. 1 - 9
We give a practical, necessary and sufficient condition for two pure n-qubit states to be stochastic local operations and classical communication (SLOCC)... 
CLASSIFICATION | ENTANGLEMENT MONOTONES | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | GEOMETRY | Construction | Equivalence | Mathematical analysis | Classification | Determinants | Qubits (quantum computing) | Polynomials | Stochasticity | Invariants
Journal Article
Quantum Information and Computation, ISSN 1533-7146, 11/2010, Volume 10, Issue 11-12, pp. 1018 - 1028
We show that for even n qubits, n-tangle is the square of the SLOCC polynomial invariant of degree 2. We find that the n-tangle is not the residual... 
3-tangle | Residual entanglement | SLOCC polynomial invariants | N-tangle of even n qubits | n-tangle of even n qubits | STATES | residual entanglement | LOCAL INVARIANTS | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 3/2019, Volume 366, Issue 3, pp. 927 - 979
The concept and the construction of modular graph functions are generalized from genus-one to higher genus surfaces. The integrand of the four-graviton... 
Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | SPACE | 2-LOOP SUPERSTRINGS | PHYSICS, MATHEMATICAL | KAWAZUMI-ZHANG | High Energy Physics - Theory
Journal Article
Electronic Journal of Qualitative Theory of Differential Equations, ISSN 1417-3875, 2015, Volume 2015, Issue 55, pp. 1 - 15
We study the existence and non-existence of periodic orbits and limit cycles for planar polynomial differential systems of degree n having n real invariant... 
Polynomial vector fields | Periodic orbits | Limit cycles | Invariant straight lines | Polynomial differential systems | MATHEMATICS | MATHEMATICS, APPLIED | periodic orbits | polynomial vector fields | polynomial differential systems | ALGEBRAIC-CURVES | invariant straight lines | limit cycles
Journal Article
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 09/2004, Volume 13, Issue 6, pp. 719 - 735
The transforms of two oriented parallel strands to a k-half twist of two strands are called tk-move and $\bar{t}_k$ -move respectively depending on the... 
Vassiliev invariants | move | Twist sequence | Conway polynomial | Δ-move | Jones polynomial | Knots | MATHEMATICS | Delta-move | knots | t(k)-move | twist sequence | KNOT POLYNOMIALS
Journal Article
Canadian Journal of Mathematics, ISSN 0008-414X, 02/2016, Volume 68, Issue 1, pp. 3 - 23
AbstractIn this paper, we extend the definition of the SL(2,ℂ) Casson invariant to arbitrary knots K in integral homology 3-spheres and relate it to the... 
3-manifolds | A-polynomial | Casson invariant | Character variety | Knots
Journal Article
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, ISSN 0008-414X, 02/2016, Volume 68, Issue 1, pp. 3 - 23
In this paper, we extend the definition of the SL(2, C) Casson invariant to arbitrary knots K in integral homology 3-spheres and relate it to the m-degree of... 
3-manifolds | MATHEMATICS | A-polynomial | REPRESENTATIONS | CHARACTER VARIETIES | character variety | Casson invariant | knots | SURGERIES
Journal Article
JOURNAL OF ALGEBRA, ISSN 0021-8693, 06/2018, Volume 503, pp. 590 - 603
Given a rank n irreducible finite reflection group W, the W-invariant polynomial functions defined in R-n can be written as polynomials of n algebraically... 
Finite reflection groups | Harmonic functions | SYSTEM | MATHEMATICS | FINITE | Basic invariant polynomials | Basic invariants | SETS | MEAN-VALUE PROBLEMS
Journal Article
Bulletin des sciences mathématiques, ISSN 0007-4497, 09/2013, Volume 137, Issue 6, pp. 746 - 774
The quadrics here considered are the nine real quadrics: parabolic cylinder, elliptic cylinder, hyperbolic cylinder, cone, hyperboloid of one sheet, hyperbolic... 
Polynomial vector fields | Invariant quadrics | Invariant conics | Extactic polynomial | MATHEMATICS, APPLIED | INTEGRABILITY | MULTIPLICITY | LINES
Journal Article
Algebra Colloquium, ISSN 1005-3867, 03/2014, Volume 21, Issue 1, pp. 95 - 116
We use computer algebra to determine the Lie invariants of degree <= 12 in the free Lie algebra on two generators corresponding to the natural representation... 
Hermite normal form | representation theory | free Lie algebras | LLL algorithm | invariant Lie polynomials | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | RINGS
Journal Article
Journal of Algebra, ISSN 0021-8693, 06/2018, Volume 503, pp. 590 - 603
Given a rank irreducible finite reflection group , the -invariant polynomial functions defined in can be written as polynomials of algebraically independent... 
Finite reflection groups | Harmonic functions | Basic invariant polynomials | Basic invariants
Journal Article
Physical Review A - Atomic, Molecular, and Optical Physics, ISSN 1050-2947, 2003, Volume 67, Issue 4, pp. 423031 - 423035
We describe explicitly the algebra of polynomial functions on the Hilbert space of four-qubit states that are invariant under the group SL(2,C)(4) of... 
PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | OPTICS | Physics - Quantum Physics | Computation and Language | Computer Science | HILBERT SPACE | POLYNOMIALS | DATA TRANSMISSION | INFORMATION THEORY | ALGEBRA | ATOMIC AND MOLECULAR PHYSICS | SL GROUPS | QUANTUM MECHANICS
Journal Article
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