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This book contains well-written monographs within the broad spectrum of applied mathematics, offering an interesting reading of some of the current trends and problems in this fascinating and critically important field of science to a broad category of researchers and practitioners. Recent developments in high-performance computing are radically changing the way we do numerics. As the size of problems is expected to grow very large in the future, the gap between fast and slow algorithms is growing rapidly. Novel classes of numerical methods with reduced computational complexity are therefore needed to make the rigorous numerical solution of difficult problems arising in an industrial setting more affordable. The book is structured in four distinct parts, according to the purpose and approaches used in the development of the contributions, ranging from optimization techniques to graph-oriented approaches and approximation theory, providing a good mix of both theory and practice.

Physical Sciences, Engineering and Technology --- Mathematics --- Applied Mathematics

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Polynomials are well known for their ability to improve their properties and for their applicability in the interdisciplinary fields of engineering and science. Many problems arising in engineering and physics are mathematically constructed by differential equations. Most of these problems can only be solved using special polynomials. Special polynomials and orthonormal polynomials provide a new way to analyze solutions of various equations often encountered in engineering and physical problems. In particular, special polynomials play a fundamental and important role in mathematics and applied mathematics. Until now, research on polynomials has been done in mathematics and applied mathematics only. This book is based on recent results in all areas related to polynomials. Divided into sections on theory and application, this book provides an overview of the current research in the field of polynomials. Topics include cyclotomic and Littlewood polynomials; Descartes' rule of signs; obtaining explicit formulas and identities for polynomials defined by generating functions; polynomials with symmetric zeros; numerical investigation on the structure of the zeros of the q-tangent polynomials; investigation and synthesis of robust polynomials in uncertainty on the basis of the root locus theory; pricing basket options by polynomial approximations; and orthogonal expansion in time domain method for solving Maxwell's equations using paralleling-in-order scheme.

Physical Sciences, Engineering and Technology --- Mathematics --- Algebra

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This book aims to provide information about Fourier transform to those needing to use infrared spectroscopy, by explaining the fundamental aspects of the Fourier transform, and techniques for analyzing infrared data obtained for a wide number of materials. It summarizes the theory, instrumentation, methodology, techniques and application of FTIR spectroscopy, and improves the performance and quality of FTIR spectrophotometers.

Physical Sciences, Engineering and Technology --- Mathematics --- Applied Mathematics --- Frequency Domain Representation

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Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Let us begin with the fractional calculus-fractal geometry relationship, which allows for modeling with extreme precision of phenomena such as diffusion in porous media with fractional partial differential equations in fractal objects. Where the order of the equation is the same as the fractal dimension, this allows us to make calculations with enormous precision in diffusion phenomena-particularly in the oil industry, for new spillage prevention. Main applications to industry, design of fractal antennas to receive all frequencies and that is used in all cell phones, spacecraft, radars, image processing, measure, porosity, turbulence, scattering theory. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book: ""Part I: Petroleum Industry and Numerical Analysis""; ""Part II: Fractal Antennas, Spacecraft, Radars, Image Processing, and Measure""; and ""Part III: Scattering Theory, Porosity, and Turbulence."" It's impossible to picture today's research without fractal analysis.

Physical Sciences, Engineering and Technology --- Mathematics --- Applied Mathematics --- Dynamical Systems Theory

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This book focuses on several key aspects of nonlinear systems including dynamic modeling, state estimation, and stability analysis. It is intended to provide a wide range of readers in applied mathematics and various engineering disciplines an excellent survey of recent studies of nonlinear systems. With its thirteen chapters, the book brings together important contributions from renowned international researchers to provide an excellent survey of recent studies of nonlinear systems. The first section consists of eight chapters that focus on nonlinear dynamic modeling and analysis techniques, while the next section is composed of five chapters that center on state estimation methods and stability analysis for nonlinear systems.

Physical Sciences, Engineering and Technology --- Mathematics --- Applied Mathematics --- Dynamical Systems Theory