Papers I've written or co-authored, read in full below or downloaded as a PDF.
We introduce a method called Strict Steiner Symmetrization, an altered form of Steiner Symmetrization that fixes the number of vertices, to prove the Isoperimetric Inequality in \(\mathbb{R}^2\) via approximation by polygons. We establish that among all \(n\)-gon domains in the plane, the regular \(m\)-gon, \(m \geq n\), uniquely minimizes the isoperimetric ratio, and that the limit of this regular polygon (the circle) achieves equality in the isoperimetric inequality.
Mathematicians have conjectured that the simplexes are the polytopes that maximize the isotropic ratio among all convex bodies in \(\mathbb{R}^n\) (the Strong Slicing Conjecture). This has been established only in \(\mathbb{R}^2\), where the triangle is the unique maximizer. We use both theoretical and computational approaches to derive explicit formulas for the first and second derivatives of the isotropic ratio of a polytope in \(\mathbb{R}^2\) in terms of its vertices, aiming to provide a foundation for attacking the conjecture in higher dimensions.
China's fertility rate in 2025 is projected to be approximately 0.93 — meaning that, on average, each woman will bear fewer than one child over the course of her lifetime. This paper covers findings on marriage/fertility views among ages 20–50 in Guangzhou, China. Written entirely in Chinese.