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Quick ViewThis book studies the methods for solving non-linear, partial differential equations that have physical meaning, and soliton theory with applications. Specific descriptions on the formation mechanism of soliton solutions of non-linear, partial differential equations are given, and some methods for solving this kind of solution such as the Inverse Scattering Transform method, Backlund Transformation method,…
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Quick ViewThis book focuses on the theory and applications of quaternions. Chapter One collects some old problems on lattice orders and directed partial orders on complex numbers and quaternions, and summarizes recent development in answering those questions. Chapter Two discusses spin 1 particles with anomalous magnetic moments in the external uniform electric field. Chapter Three examines…
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Quick ViewThis books provides new research on the theories and applications of complex systems. Chapter One reviews the process algebra approach to quantum electrodynamics. Chapter Two describes a specific aspect of complex systems and the fact that they may consist of established subsystems or components that originate from converging industries. Chapter Three examines the development of…
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Quick ViewThis book presents an introduction to the theory of nonlinear integral equations on time scales. Many population discrete models such as the logistic model, the Ricker model, the Beverton-Holt model, Leslie-Gower competition model and others can be investigated using nonlinear integral equations on the set of the natural numbers. This book contains different analytical and…
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Quick ViewChapter One addresses the importance of weighted linear regression in fitting straight lines. In Chapter Two, the authors cover the homocedastic condition, i.e. variance of y’s independent of x, errors of y’s accumulative, the heterocedastic case, i.e. variance or standard deviation proportional to x values, respectively, and orthogonal regression (error in both axes). The chapter…
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Quick ViewThe theory of hypernumbers and extrafunctions is further development in distribution theory inspired by contemporary physics and influenced by problems in mathematical physics. It makes more functions differentiable and provides new kinds of derivatives and hyperderivatives aimed at solving more differential and operator equations than ever before possible. In the book, extrafunctions are extended to…
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Quick ViewThis book has two volumes and consists of forty-four chapters, which are divided into five sections: (i) Mathematical treatment of non-linear problems, including the differential equations, numerical methods, algorithms and solutions; (ii) theoretical and computational studies dedicated to the physics and chemistry of advanced materials, nanostructured and fractal systems; (iii) articles dedicated to non-linear processes…
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Quick ViewThe book has two volumes and consists of forty-four chapters, which are divided into five sections: (i) Mathematical treatment of non-linear problems, including the differential equations, numerical methods, algorithms and solutions; (ii) theoretical and computational studies dedicated to the physics and chemistry of advanced materials, nanostructured systems and fractal systems; (iii) articles dedicated to non-linear…
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Quick ViewIn recent times, polynomial chaos expansion has emerged as a dominant technique to determine the response uncertainties of a system by propagating the uncertainties of the inputs. In this regard, the opening chapter of Uncertainty Quantification: Advances in Research and Applications, an intrusive approach called Galerkin Projection as well as non-intrusive approaches (such as pseudo-spectral…
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Quick ViewThis self-contained book provides the reader with a comprehensive presentation of recent investigations on operator theory over non-Archimedean Banach and Hilbert spaces. This includes, non-archimedean valued fields, bounded and unbounded linear operators, bilinear forms, functions of linear operators and one-paramter families of bounded linear operators on free branch spaces.
For titles published prior to 2016, please click here.
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