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Xiao-Yuan Wang

Publications and source records attributed to Xiao-Yuan Wang.

4 recordsLinked to original sources
arXiv2026

Harmonic K-quasiconformal Koebe functions: construction and application to Pavlovic's problem

We first construct the harmonic K-quasiconformal Koebe functions, filling a long-standing foundational gap in geometric function theory. This construction provides a unified parametric candidate extremal function framework for conformal mappings, quasiconformal mappings, and harmonic mappings, and we formulate related conjectures for the extremal theory of harmonic K-quasiconformal mappings. By combining this construction with Astala and Koskela's Hp-theory for quasiconformal mappings, we establish a sharp result concerning the optimal order of harmonic K-quasiconformal mappings with bounded Schwarzian norm in harmonic Hardy spaces. Motivated by the work of Chuaqui, Hernandez, and Martin [Math. Ann. 367, 1099-1122, 2017], this result gives a partial solution to Pavlovic's 2014 open problem on the embeddings of harmonic quasiconformal mappings into Hardy spaces, and outlines a path toward its complete solution.

math.CV↗
arXiv2023

A balanced Memristor-CMOS ternary logic family and its application

The design of balanced ternary digital logic circuits based on memristors and conventional CMOS devices is proposed. First, balanced ternary minimum gate TMIN, maximum gate TMAX and ternary inverters are systematically designed and verified by simulation, and then logic circuits such as ternary encoders, decoders and multiplexers are designed on this basis. Two different schemes are then used to realize the design of functional combinational logic circuits such as a balanced ternary half adder, multiplier, and numerical comparator. Finally, we report a series of comparisons and analyses of the two design schemes, which provide a reference for subsequent research and development of three-valued logic circuits.

eess.SP↗
arXiv2021

Some properties of certain close-to-convex harmonic mappings

In this paper, we determine the sharp estimates for Toeplitz determinants of a subclass of close-to-convex harmonic mappings. Moreover, we obtain an improved version of Bohr's inequalities for a subclass of close-to-convex harmonic mappings, whose analytic parts are Ma-Minda convex functions.

math.CV↗