Preface

**Section 4 99**

**Chapter 7 101**

**Chapter 8 117**

**Chapter 9 135**

Complex Functional Transforms and Their Applications

on Wavelet Analysis

*by Peng Du, Haibao Hu and Xiao Huang*

*by Bessem Zitouna and Jaleleddine Ben Hadj Slama*

Nonlinear Waves for the Structured Media *by Vyacheslav Vakhnenko, Dmitri Vengrovich*

*and Alexandre Michtchenko*

**II**

Extracting Coherent Structures in Near-Wall Turbulence Based

An Efficient Approach Based on the Near-Field Technique to Solve EMI Problems: Application to an AC/DC Flyback Converter

Mathematical Fundamentals of a Diagnostic Method by Long

The complex analysis is known as the theory of functions of complex variables inside of the mathematical analysis having extensions in arithmetic and algebraic geometry, number theory, and other sophisticated theories as the Nevanlinna theory to the meromorphic functions study, the Morse theory and complex projective geometry, where this last arises from the hyperbolic geometry and their extensions. The present book is centered on the advances in holomorphicity, analyticity of complex functions of one or several variables, their integration and evaluation. From the point of view of their geometry, we discuss the conformal mappings of surfaces and complex Riemannian surfaces, considering their singularities and their treatment through diverse tools that offer the complex analysis theory. Also we focus on the topology relationships between geometrical manifolds considering the integration invariants and their cohomology. In addition, diverse applications in inverse problems and ill posed problems of complex functions in engineering fields will be important.

**Dr. Francisco Bulnes**

IINAMEI A. C. (Investigación Internacional Avanzada en Matemáticas e Ingeniería), Research Department in Mathematics and Engineering, TESCHA, Chalco, Mexico

> **Olga A. Hachay** Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russian Federation

Section 1

Introductory Section

**1**

## Section 1
