Contents



Preface

communications, economy and health, that is, Fourier transforms and the treatment of superconductivity under the vision of the electromagnetic properties of both type I and type II superconductors. We begin in Chapter 1, "On the Zap Integral Operators over Fourier Transforms," with the latest applications and mathematical properties of Fourier transforms like projection operators aimed at communications and electromagnetic emissions. The authors prove that under an appropriate space generated by the solutions of the generalized inhomogeneous Fredholm equation it is possible to operate in it with integral operators like those of the quantum mechanics theory, killing and creating solutions of homogeneous or inhomogeneous Fredholm equations, which can be used to improve communications and broadcasting by selecting the type of behavior we need. Chapter 2, "Quantum Fourier Operators and Their Application" revises the structure of the Quantum Fourier Operators (QFT) and its implementation putting these concepts in their proper perspective, the authors provide a brief overview of quantum computation and provide a permutation structure for putting the QFT in the context of universal computation. In Chapter 3, "A Fast Method for Numerical Realization of Fourier Tools," the author presents a new algorithm for fast summations of truncated Fourier series. Chapter 4, "Fourier Transform Infrared Spectroscopy of the Animal Tissues," examines how animal tissues are extensively used as scaffolds for tissue engineering and regenerative therapies. They are typically subjected to a decellularization process to obtain cell-free extracellular matrix (ECM) scaffolds. It is important to identify the chemical structure of the ECM scaffolds, and Fourier transform infrared spectroscopy (FTIR) appears to be the technique of choice. The chapter presents FTIR spectra of native and decellularized buffalo aortae, buffalo diaphragms, goat skin, and native bovine cortical bone. The transmittance peaks are that of organic collagen amide A, amide B, amide I, amide II, and amide III chemical functional groups in both native and decellularized aortae, diaphragms, and skin. In bone, the

3−, OH−

collagen amide A, amide B, amide I, amide II, and amide III chemical functional groups. In Chapter 5, "Medical Image Classification Using the Discriminant Power Analysis (DPA) of Discrete Cosine Transform (DCT) Coefficients," we see the relevance of medical imaging systems in medicine. These systems assist specialists in making the final decision about a patient's condition, and strongly help in early cancer detection. The classification of mammogram images represents a very important operation to identify whether breast cancer is benign or malignant. The authors propose a new computer-aided diagnostic (CAD) system composed of three steps. In the first step, the input image is pre-processed to remove the noise and artifacts and to separate the breast profile from the pectoral muscle. This operation is a difficult task that can affect the final decision. In the second step, we propose a features extraction method based on the discrete cosine transform (DCT), where the processed images of the breast profiles are transformed by the DCT where the part containing the highest energy value is selected. Then, in the features selection step, a new most discriminative power coefficients algorithm is proposed to select the most significant features. The obtained results show the effectiveness. In Chapter 6, "Path Integral Two Dimensional Models of P– and D–Wave Superconductors and Collective

in addition to organic

This book is devoted to some of the current fundamental tools on physics,

transmittance peaks are that of inorganic ν1, ν3 PO4
