This volume contains the proceedings of the workshop on Optimization Theory and Related Topics, held in memory of Dan Butnariu, from January 11-14, 2010, in Haifa, Israel. An active researcher in various fields of applied mathematics, Butnariu published over 80 papers. His extensive bibliography is included in this volume. The articles in this volume cover many different areas of Optimization Theory and its applications: maximal monotone operators, sensitivity estimates via Lyapunov functions, inverse Newton transforms, infinite-horizon Pontryagin principles, singular optimal control problems with state delays, descent methods for mixed variational inequalities, games on MV-algebras, ergodic convergence in subgradient optimization, applications to economics and technology planning, the exact penalty property in constrained optimization, nonsmooth inverse problems, Bregman distances, retraction methods in Banach spaces, and iterative methods for solving equilibrium problems. This volume will be of interest to both graduate students and research mathematicians.
At Les Houches in January 2015, experts in the field of particle trapping came together to discuss the fundamental physics of traps and the different types of applications. This textbook collates the lectures delivered there; the Second Winter School on Physics with Trapped Charged Particles.Taken as a whole, the book gives an overview of why traps for charged particles are important, how they work, their special features and limitations, and their application in areas such as precision measurements, mass spectrometry, optical clocks, plasma physics, antihydrogen creation, quantum simulation and quantum information processing. Chapters from various world experts include those on the basic properties of Penning traps, RF traps and particle accelerators, as well as those covering important practical aspects such as vacuum systems, detection techniques, and different types of particle cooling including laser cooling. Finally, individual chapters deal with the different areas of application listed above.Each chapter is complemented by fully worked problems, making Physics with Trapped Charged Particles perfect for advanced undergraduate and postgraduate students new to this topic.
This book is devoted to the development of geometrie methods for studying and revealing geometrie aspects of the theory of differential equations with quadratie right-hand sides (Riccati-type equations), which are closely related to the calculus of variations and optimal control theory. The book contains the following three parts, to each of which aseparate book could be devoted: 1. the classieal calculus of variations and the geometrie theory of the Riccati equation (Chaps. 1-5), 2. complex Riccati equations as flows on Cartan-Siegel homogeneity da mains (Chap. 6), and 3. the minimization problem for multiple integrals and Riccati partial dif ferential equations (Chaps. 7 and 8). Chapters 1-4 are mainly auxiliary. To make the presentation complete and self-contained, I here review the standard facts (needed in what folIows) from the calculus of variations, Lie groups and algebras, and the geometry of Grass mann and Lagrange-Grassmann manifolds. When choosing these facts, I pre fer to present not the most general but the simplest assertions. Moreover, I try to organize the presentation so that it is not obscured by formal and technical details and, at the same time, is sufficiently precise. Other chapters contain my results concerning the matrix double ratio, com plex Riccati equations, and also the Riccati partial differential equation, whieh the minimization problem for a multiple integral. arises in The book is based on a course of lectures given in the Department of Me and Mathematics of Moscow State University during several years."
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