15 citations · 114 across the 31 of their papers we have counts for
9 papers · 1 filter
A Polynomially Irreducible Functional Basis of Elasticity Tensors
Zhenyu Ming, Yannan Chen, Liqun Qi +1
Tensor function representation theory is an essential topic in both theoretical and applied mechanics. For the elasticity tensor, Olive, Kolev and Auffray (2017) proposed a minimal…
Tensor Norm, Cubic Power and Gelfand Limit
Liqun Qi, Shenglong Hu, Xinzhen Zhang +1
We establish two inequalities for the nuclear norm and the spectral norm of tensor products. The first inequality indicates that the nuclear norm of the square matrix is a matrix n…
Biquadratic Tensors, Biquadratic Decomposition and Norms of Biquadratic Tensors
Liqun Qi, Shenglong Hu, Xinzhen Zhang
Biquadratic tensors play a central role in many areas of science. Examples include elasticity tensor and Eshelby tensor in solid mechanics, and Riemann curvature tensor in relativi…
Spectral Norm and Nuclear Norm of a Third Order Tensor
Liqun Qi, Shenglong Hu
The spectral norm and the nuclear norm of a third order tensor play an important role in the tensor completion and recovery problem. We show that the spectral norm of a third order…
Generating Hypergraphs, Decomposability and Classification of Two-Step Nilpotent Lie Algebras
Shenglong Hu, Liqun Qi, Honglian Zhang
In 1973, Gauger proposed a generator-relation method and a duality theory for two-step nilpotent Lie algebras. Based upon these, he classified two-step nilpotent Lie algebras of di…
Nilpotent Decomposition of Solvable Lie Algebras
Liqun Qi
Semisimple Lie algebras have been completely classified by Cartan and Killing. The Levi theorem states that every finite dimensional Lie algebra is isomorphic to a semidirect sum o…