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Majorization and Inequalities among Complete Homogeneous Symmetric Functions
Jia Xu, Yong Yao
Inequalities among symmetric functions are fundamental in various branches of mathematics, thus motivating a systematic study of their structure. Majorization has been shown to cha…
A proof of Hilbert's theorem on ternary quartic forms with the ladder technique
Jia Xu, Yong Yao
This paper proposes a totally constructive approach for the proof of Hilbert's theorem on ternary quartic forms. The main contribution is the ladder technique, with which the Hilbe…
A Successive Resultant Projection for Cylindrical Algebraic Decomposition
Yong Yao, Jia Xu, Lu Yang
This note shows the equivalence of two projection operators which both can be used in cylindrical algebraic decomposition (CAD) . One is known as Brown's Projection (C. W. Brown (2…
A Majorization Order on Monomials and Termination of a Successive Difference Substitution Algorithm
Jia Xu, Yong Yao
We introduce a majorization order on monomials. With the help of this order, we derive a necessary condition on the positive termination of a general successive difference substitu…