An Introduction to Complex Analysis is a textbook focusing on the fundamental theories and methods of complex analysis. Guided by the core logic of “from basic construction to in-depth application,” it systematically presents the key concepts and structure of the discipline. The book helps readers shift their perspective from the real number field to the complex number field, master the essential ideas and tools for studying complex functions, and build a solid foundation for further study in advanced complex analysis and related interdisciplinary fields such as physics, engineering, and mathematical physics.

Divided into seven chapters, the book features a clear and coherent content framework. It strikes a balance between theoretical rigor and practical learning: each key concept is introduced with precise definitions and intuitive explanations; important theorems are accompanied by detailed proofs; and targeted exercises at the end of each chapter help reinforce understanding.

While maintaining academic depth, the text remains accessible to beginners by avoiding excessive technical complexity. This book is ideal as an introductory textbook for junior undergraduate students majoring in mathematics. It also serves as a valuable reference for students in physics, electronics, and engineering, as well as for researchers in related fields interested in the core theories and practical applications of complex analysis.

This book presents in-depth research on positive parameters of hierarchical models under Stein’s loss function and proposes a novel empirical Bayesian estimation method. By integrating Stein’s loss function with empirical Bayesian estimation, the book tackles key challenges in estimating positive parameters that traditional methods struggle to address. It provides numerical simulations for each hierarchical model from at least four perspectives and analyzes extensive real-world data to empirically validate the effectiveness of the proposed method. The findings demonstrate that the MLE method outperforms the moment method in terms of consistency, goodness-of-fit, Bayes estimators, and PESLs.

The book is intended for graduate students, teachers, and researchers in statistics, particularly those interested in empirical Bayes analysis, positive parameters, hierarchical models and mixture distributions, Stein’s loss function, and other loss functions.

A Theory on Optimal Factorial Designs presents a rigorous and unified treatment of factorial design theory, centered on the general minimum lower-order confounding (GMC) criterion.

It develops the theoretical foundations of the GMC criterion and demonstrates its wide-ranging applications to two-level, blocked, split-plot, compromise, robust parameter, and s-level designs, as well as to orthogonal arrays.

Experimental design and analysis is a cornerstone of mathematical statistics, with extensive applications in agriculture, engineering, medicine, and the social sciences. Among established methodologies, factorial designs remain one of the most powerful and efficient tools for investigating systems involving multiple factors.

The GMC criterion provides a principled framework for selecting optimal factorial designs by rigorously quantifying and minimizing confounding among factor effects. This work delivers both theoretical insights and practical methodological guidance, making it a valuable reference for researchers and graduate students in statistics and allied disciplines.