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This book is devoted to the study of optimal control problems arising in forest management, an important and fascinating topic in mathematical economics studied by many researchers over the years. The volume studies the forest management problem by analyzing a class of optimal control problems that contains it and showing the existence of optimal solutions over infinite horizon. It also studies the structure of approximate solutions on finite intervals and their turnpike properties, as well as the stability of the turnpike phenomenon and the structure of approximate solutions on finite intervals in the regions close to the end points. The book is intended for mathematicians interested in the optimization theory, optimal control and their applications to the economic theory.

Forest management --- Statistical methods. --- Mathematical optimization. --- Calculus of Variations and Optimal Control; Optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Calculus of variations. --- Isoperimetrical problems --- Variations, Calculus of

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This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research.

Differential equations, Elliptic. --- Partial differential equations. --- Functional analysis. --- Integral equations. --- Calculus of variations. --- Mathematical physics. --- Partial Differential Equations. --- Functional Analysis. --- Integral Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematical Applications in the Physical Sciences. --- Physical mathematics --- Physics --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Equations, Integral --- Functional equations --- Functional analysis --- Functional calculus --- Calculus of variations --- Integral equations --- Partial differential equations --- Mathematics

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This book provides a comprehensive study of turnpike phenomenon arising in optimal control theory. The focus is on individual (non-generic) turnpike results which are both mathematically significant and have numerous applications in engineering and economic theory. All results obtained in the book are new. New approaches, techniques, and methods are rigorously presented and utilize research from finite-dimensional variational problems and discrete-time optimal control problems to find the necessary conditions for the turnpike phenomenon in infinite dimensional spaces. The semigroup approach is employed in the discussion as well as PDE descriptions of continuous-time dynamics. The main results on sufficient and necessary conditions for the turnpike property are completely proved and the numerous illustrative examples support the material for the broad spectrum of experts. Mathematicians interested in the calculus of variations, optimal control and in applied functional analysis will find this book a useful guide to the turnpike phenomenon in infinite dimensional spaces. Experts in economic and engineering modeling as well as graduate students will also benefit from the developed techniques and obtained results.

Control theory. --- Mathematical optimization. --- Differential equations, partial. --- Functional analysis. --- Group theory. --- Calculus of Variations and Optimal Control; Optimization. --- Partial Differential Equations. --- Functional Analysis. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Partial differential equations --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Calculus of variations. --- Partial differential equations. --- Isoperimetrical problems --- Variations, Calculus of

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The aim of this book is to present results related to Kato's famous inequality for bounded linear operators on complex Hilbert spaces obtained by the author in a sequence of recent research papers. As Linear Operator Theory in Hilbert spaces plays a central role in contemporary mathematics, with numerous applications in fields including Partial Differential Equations, Approximation Theory, Optimization Theory, and Numerical Analysis, the volume is intended for use by both researchers in various fields and postgraduate students and scientists applying inequalities in their specific areas. For the sake of completeness, all the results presented are completely proved and the original references where they have been firstly obtained are mentioned.

Hilbert space. --- Banach spaces --- Hyperspace --- Inner product spaces --- Functional analysis. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations

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This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.

Computer science --- Computational Mathematics and Numerical Analysis. --- Mathematics. --- Computer mathematics --- Electronic data processing --- Mathematics --- Variational inequalities (Mathematics) --- Inequalities, Variational (Mathematics) --- Calculus of variations --- Differential inequalities --- Computer mathematics.