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Today, more sophisticated techniques are necessary for spectral analysis, reconstruction, restoration of signals, their digital and analogic processing, specialized signal diagnostics, and short intervals with occurrences that require greater speed and precision. As the frequency domain of the wavelet transform gets more detailed and considerably more specific in various applications, it necessitates specialized scholarly attention in its many forms and relationships with other transforms with special functions. For example, using the wavelet transform with special functions can prove valuable in creating and designing special signal filters or the interphase between reception-emission devices with specialized sensors for medical use. In quantum phenomena, its corresponding version of the wavelet transform is instrumental in the spectral study of particles and their correlation. Therefore, using specialists' and experts' views, this book delves into an exposition on spectral analysis, restoring, monitoring, and signal processing, as well as essential applications required in waveguides and for the improvement of medical images, proving the wavelet transform to be helpful in resolution analysis in time-frequency, with an emphasis on different methods of the calculus using FFT and DSTFT. This book has been divided into four sections covering all the abovementioned subjects.

Transformations (Mathematics) --- Wavelets (Mathematics)

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This book presents a review of various issues related to Lorentz symmetry breaking. Explicitly, we consider (i) motivations for introducing Lorentz symmetry breaking, (ii) classical aspects of Lorentz-breaking field theory models including typical forms of Lorentz-breaking additive terms, wave propagation in Lorentz-breaking theories, and mechanisms for breaking the Lorentz symmetry; (iii) quantum corrections in Lorentz-breaking theories, especially the possibilities for perturbation generating the most interesting Lorentz-breaking terms; (iv) correspondence between non-commutative field theories and Lorentz symmetry breaking; (v) supersymmetric Lorentz-breaking theories; and (vi) Lorentz symmetry breaking in a curved space-time. We close the book with the review of experimental studies of Lorentz symmetry breaking. The importance and relevance of these topics are explained, first, by studies of limits of applicability of the Lorentz symmetry, second, by searches of the possible extensions of the standard model, including the Lorentz-breaking ones, and need to study their properties, third, by the relation between Lorentz symmetry breaking with string theory, fourth, by the problem of formulating a consistent quantum gravity theory, so that various modified gravity models are to be examined.

Lorentz transformations. --- Special relativity (Physics) --- Transformations (Mathematics)

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Laplace transformation. --- Transformation, Laplace --- Calculus, Operational --- Differential equations --- Transformations (Mathematics)

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Laplace transformation. --- Transformation, Laplace --- Calculus, Operational --- Differential equations --- Transformations (Mathematics)

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Suitable as supplemental reading in courses in differential and integral calculus, numerical analysis, approximation theory and computer-aided geometric design. Relations of mathematical objects to each other are expressed by transformations. The repeated application of a transformation over and over again, i.e., its iteration leads to solution of equations, as in Newton's method for finding roots, or Picard's method for solving differential equations. This book studies a treasure trove of iterations, in number theory, analysis and geometry, and applied them to various problems, many of them taken from international and national Mathematical Olympiad competitions. Among topics treated are classical and not so classical inequalities, Sharkovskii's theorem, interpolation, Bernstein polynomials, BŽzier curves and surfaces, and splines. Most of the book requires only high school mathematics; the last part requires elementary calculus. This book would be an excellent supplement to courses in calculus, differential equations,, numerical analysis, approximation theory and computer-aided geometric design.

Iterative methods (Mathematics) --- Transformations (Mathematics) --- Algorithms --- Differential invariants --- Geometry, Differential --- Iteration (Mathematics) --- Numerical analysis --- Iterative methods (Mathematics). --- Transformations (Mathematics).