Xin-Min Zhang

Schur-convex functions and isoperimetric inequalities

In this paper, we establish some analytic inequalities for Schurconvex functions that are made of solutions of a second order nonlinear differential equation. We apply these analytic inequalities to obtain some geometric inequalities.

Bonnesen-style inequalities and pseudo-perimeters for polygons

In this paper, we establish some Bonnesen-style isoperimetric inequalities for plane polygons via an analytic isoperimetric inequality and an isoperimetric inequality in pseudo-perimeters of polygons.

Generalized power means and interpolating inequalities

In this paper, we introduce a multi-parameter family of generalized power means, and use their special properties to provide a new method of interpolating inequalities. We give a different refinement of an inequality of Ky Fan as a particular application of our method.

Analytic and geometric isoperimetric inequalities

We prove uncountably many new analytic and geometric isoperimetric inequalities associated with the solutions of second order ordinary differential equations.

Markov chains and dynamic geometry of polygons

In this paper we construct sequences of polygons from a given n-sided cyclic polygon by iterated procedures and study the limiting behaviors of these sequences in terms of nonnegative matrices and Markov chains.

SIERPIŃSKI PEDAL TRIANGLES

We generalize the construction of the ordinary Sierpinski triangle to obtain a two-parameter family of fractals we call Sierpinski pedal triangles. These fractals are obtained from a given triangle by recursively deleting the associated pedal triangles in a manner analogous to the construction of the ordinary Sierpinski triangle, but their fractal dimensions depend on the choice of the initial triangles. In this paper, we discuss the fractal dimensions of the Sierpinski pedal triangles and the related area ratio problem, and provide some computer-generated graphs of the fractals.