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Shapes and Geometries
Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.
Boundaries, Interfaces, and Transitions
Nine papers bring together geometric tools developed in distant areas of mathematics, mechanics, and physics, for application in the design, identification, and control of technological processes. The articles discuss topics such as: the transition to turbulence via turbulent bursts; intrinsic differential geometric methods in the asymptotic analysis of linear thin shells; local theory of shape analysis via distance functions; shape memory; dendrites, fingers, interfaces, and free boundaries; superconductivity; front propagation; hysteresis; and dynamic metastability and singular perturbations. Annotation copyrighted by Book News, Inc., Portland, OR
Introduction to Optimization and Hadamard Semidifferential Calculus, Second Edition
This second edition provides an enhanced exposition of the long-overlooked Hadamard semidifferential calculus, first introduced in the 1920s by mathematicians Jacques Hadamard and Maurice René Fréchet. Hadamard semidifferential calculus is possibly the largest family of nondifferentiable functions that retains all the features of classical differential calculus, including the chain rule, making it a natural framework for initiating a large audience of undergraduates and non-mathematicians into the world of nondifferentiable optimization. Introduction to Optimization and Hadamard Semidifferential Calculus, Second Edition builds upon its prior editions foundations in Hadamard semidifferent...
Optimal Control of Coupled Systems of Partial Differential Equations
Contains contributions originating from the 'Conference on Optimal Control of Coupled Systems of Partial Differential Equations', held at the 'Mathematisches Forschungsinstitut Oberwolfach' in March 2008. This work covers a range of topics such as controllability, optimality systems, model-reduction techniques, and fluid-structure interactions.
Optimal Control of Partial Differential Equations
The application of PDE-based control theory and the corresponding numerical algorithms to industrial problems have become increasingly important in recent years. This volume offers a wide spectrum of aspects of the discipline, and is of interest to mathematicians and scientists working in the field.
Design of Delay-Based Controllers for Linear Time-Invariant Systems
This book provides the mathematical foundations needed for designing practical controllers for linear time-invariant systems. The authors accomplish this by incorporating intentional time delays into measurements with the goal of achieving anticipation capabilities, reduction in noise sensitivity, and a fast response. The benefits of these types of delay-based controllers have long been recognized, but designing them based on an analytical approach became possible only recently. Design of Delay-Based Controllers for Linear Time-Invariant Systems provides a thorough survey of the field and the details of the analytical approaches needed to design delay-based controllers. In addition, readers ...
Partial Differential Equations
As a satellite conference of the 1998 International Mathematical Congress and part of the celebration of the 650th anniversary of Charles University, the Partial Differential Equations Theory and Numerical Solution conference was held in Prague in August, 1998. With its rich scientific program, the conference provided an opportunity for almost 200 participants to gather and discuss emerging directions and recent developments in partial differential equations (PDEs). This volume comprises the Proceedings of that conference. In it, leading specialists in partial differential equations, calculus of variations, and numerical analysis present up-to-date results, applications, and advances in nume...
Control of Coupled Partial Differential Equations
The international Conference on Optimal Control of Coupled Systems of partial Differential Equations was held at the Mathematisches Forschungs institut Oberwolfach from April, 17 to 23, 2005. The applications discussed during the conference includes the optimization and control of quantum mechanical systems.
Stochastic Processes, Estimation, and Control
Uncertainty and risk are integral to engineering because real systems have inherent ambiguities that arise naturally or due to our inability to model complex physics. The authors discuss probability theory, stochastic processes, estimation, and stochastic control strategies and show how probability can be used to model uncertainty in control and estimation problems. The material is practical and rich in research opportunities.
The Shapes of Things
Many things around us have properties that depend on their shape--for example, the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function (in the calculus sense) with respect to a "shape variable." This approach, which is useful for understanding mathematical models containing geometric partial differential equations (PDEs), allows readers to obtain formulas for geometric quantities (such as curvature) that are clearer than those usually offered in differential geometry texts. Readers will learn how to compute sensitivities with respect to geometry by developing basic calculus tools on surfaces and combining them with the calculus of variations. Several applications that utilize shape derivatives and many illustrations that help build intuition are included.
