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This book is prepared as a combination of the manuscripts submitted by respected mathematicians and scientists around the world. As an editor, I truly enjoyed reading each manuscript. Not only will the methods and explanations help you to understand more about graph theory, but I also hope you will find it joyful to discover ways that you can apply graph theory in your scientific field. I believe the book can be read from the beginning to the end at once. However, the book can also be used as a reference guide in order to turn back to it when it is needed. I have to mention that this book assumes the reader to have a basic knowledge about graph theory. The very basics of the theory and terms are not explained at the beginner level. I hope this book will support many applied and research scientists from different scientific fields.

Physical Sciences, Engineering and Technology --- Mathematics --- Discrete Mathematics --- Graph Theory

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This book is an introduction to the mathematical analysis of Bayesian decision-making when the state of the problem is unknown but further data about it can be obtained. The objective of such analysis is to determine the optimal decision or solution that is logically consistent with the preferences of the decision-maker, that can be analyzed using numerical utilities or criteria with the probabilities assigned to the possible state of the problem, such that these probabilities are updated by gathering new information.

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

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This book presents examples of modern optimization algorithms. The focus is on a clear understanding of underlying studied problems, understanding described algorithms by a broad range of scientists and providing (computational) examples that a reader can easily repeat.

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

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Modeling and simulating biological and physical systems are nowadays active branches of science. The diversity and complexity of behaviors and patterns present in the natural world have their reciprocity in life systems. Bifurcations, solitons and fractals are some of these ubiquitous structures that can be indistinctively identified in many models with the most diverse applications, from microtubules with an essential role in the maintenance and the shaping of cells, to the nano/microscale structure in disordered systems determined with small-angle scattering techniques. This book collects several works in this direction, giving an overview of some models and theories, which are useful for the study and analysis of complex biological and physical systems. It can provide a good guidance for physicists with interest in biology, applied research scientists and postgraduate students.

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

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The editor has incorporated contributions from a diverse group of leading researchers in the field of differential equations. This book aims to provide an overview of the current knowledge in the field of differential equations. The main subject areas are divided into general theory and applications. These include fixed point approach to solution existence of differential equations, existence theory of differential equations of arbitrary order, topological methods in the theory of ordinary differential equations, impulsive fractional differential equations with finite delay and integral boundary conditions, an extension of Massera's theorem for n-dimensional stochastic differential equations, phase portraits of cubic dynamic systems in a Poincare circle, differential equations arising from the three-variable Hermite polynomials and computation of their zeros and reproducing kernel method for differential equations. Applications include local discontinuous Galerkin method for nonlinear Ginzburg-Landau equation, general function method in transport boundary value problems of theory of elasticity and solution of nonlinear partial differential equations by new Laplace variational iteration method. Existence/uniqueness theory of differential equations is presented in this book with applications that will be of benefit to mathematicians, applied mathematicians and researchers in the field. The book is written primarily for those who have some knowledge of differential equations and mathematical analysis. The authors of each section bring a strong emphasis on theoretical foundations to the book.

Physical Sciences, Engineering and Technology --- Mathematics --- Analysis & Calculus