4 papers · 1 filter
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…
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…
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…