7 papers
Deriving Newton's Canonical Forms of Cubic Curves via the Center of Polynomials
Hua-Lin Huang, Lili Liao, Yu Ye +1
Existing classifications of real plane cubic curves rely on sophisticated tools and require a lengthy exposition. This paper provides a concise yet elementary treatment of this cla…
Direct Sum and Direct Product Decompositions of Multivariate Functions
Hua-Lin Huang, Yiming Liu, Jianhua Xiang +1
This paper addresses the problem of whether or not a vector-valued multivariate functions can be expressed as a sum or a product of vector-valued functions in disjoint sets of vari…
The Waring Problem of Harmonic Polynomials
Hua-Lin Huang, Yilun Tang, Yu Ye +1
This paper investigates the Waring problem of harmonic polynomials. By characterizing the annihilating ideal of a homogeneous harmonic polynomial, i.e., a real binary form that is…
Eigenvalues and equivalence classes of third-order symmetric tensors
Lishan Fang, Hua-Lin Huang, Shengyuan Ruan +2
This paper demonstrates that third-order real symmetric tensors cannot be classified up to equivalence by their eigenvalues only, thereby resolving a problem posed by Qi in 2006. B…
The Waring Problem of Complex Binary Forms
Hua-Lin Huang, Haoran Miao, Yu Ye
The Waring problem of forms concerns the expression of homogeneous multivariate polynomials as sums of powers of linear forms. This paper focuses on complex binary forms, and we so…
On the Classification of Finite Quasi-Quantum Groups over Abelian Groups
Hua-Lin Huang, Gongxiang Liu, Yuping Yang +1
Using a variety of methods developed in the theory of finite-dimensional quasi-Hopf algebras, we classify all finite-dimensional coradically graded pointed coquasi-Hopf algebras ov…
Harrison center and products of sums of powers
Hua-Lin Huang, Lili Liao, Huajun Lu +1
This paper is mainly concerned with identities like \[ (x_1^d + x_2^d + \cdots + x_r^d) (y_1^d + y_2^d + \cdots y_n^d) = z_1^d + z_2^d + \cdots + z_n^d \] where $x=(x_1, x_2…