Moment-sos Hierarchy, The: Lectures In Probability, Statistics, Computational Geometry, Control And Nonlinear Pdes

Moment-sos Hierarchy, The: Lectures In Probability, Statistics, Computational Geometry, Control And Nonlinear Pdes

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  • Author: Didier Henrion
  • Publisher: World Scientific
  • ISBN: 1786348551
  • Category : Mathematics
  • Languages : en
  • Pages : 248

The Moment-SOS hierarchy is a powerful methodology that is used to solve the Generalized Moment Problem (GMP) where the list of applications in various areas of Science and Engineering is almost endless. Initially designed for solving polynomial optimization problems (the simplest example of the GMP), it applies to solving any instance of the GMP whose description only involves semi-algebraic functions and sets. It consists of solving a sequence (a hierarchy) of convex relaxations of the initial problem, and each convex relaxation is a semidefinite program whose size increases in the hierarchy.The goal of this book is to describe in a unified and detailed manner how this methodology applies to solving various problems in different areas ranging from Optimization, Probability, Statistics, Signal Processing, Computational Geometry, Control, Optimal Control and Analysis of a certain class of nonlinear PDEs. For each application, this unconventional methodology differs from traditional approaches and provides an unusual viewpoint. Each chapter is devoted to a particular application, where the methodology is thoroughly described and illustrated on some appropriate examples.The exposition is kept at an appropriate level of detail to aid the different levels of readers not necessarily familiar with these tools, to better know and understand this methodology.


Differential Geometry (Sos)

Differential Geometry (Sos)

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  • Author: Lipschutz
  • Publisher:
  • ISBN: 9780070605008
  • Category :
  • Languages : en
  • Pages :


Differential Equations For Dummies

Differential Equations For Dummies

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  • Author: Steven Holzner
  • Publisher: John Wiley & Sons
  • ISBN: 0470178140
  • Category : Mathematics
  • Languages : en
  • Pages : 381

The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.


Differential Geometry

Differential Geometry

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  • Author: Martin M. Lipschutz
  • Publisher:
  • ISBN:
  • Category :
  • Languages : en
  • Pages : 269


Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory

Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory

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  • Author: Paul Gregory Goerss
  • Publisher: American Mathematical Soc.
  • ISBN: 0821832859
  • Category : Mathematics
  • Languages : en
  • Pages : 520

As part of its series of Emphasis Years in Mathematics, Northwestern University hosted an International Conference on Algebraic Topology. The purpose of the conference was to develop new connections between homotopy theory and other areas of mathematics. This proceedings volume grew out of that event. Topics discussed include algebraic geometry, cohomology of groups, algebraic $K$-theory, and $\mathbb{A 1$ homotopy theory. Among the contributors to the volume were Alejandro Adem,Ralph L. Cohen, Jean-Louis Loday, and many others. The book is suitable for graduate students and research mathematicians interested in homotopy theory and its relationship to other areas of mathematics.


Handbook of Antennas in Wireless Communications

Handbook of Antennas in Wireless Communications

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  • Author: Lal Chand Godara
  • Publisher: CRC Press
  • ISBN: 1351835920
  • Category : Technology & Engineering
  • Languages : en
  • Pages : 1043

The move toward worldwide wireless communications continues at a remarkable pace, and the antenna element of the technology is crucial to its success. With contributions from more than 30 international experts, the Handbook of Antennas in Wireless Communications brings together all of the latest research and results to provide engineering professionals and students with a one-stop reference on the theory, technologies, and applications for indoor, hand-held, mobile, and satellite systems. Beginning with an introduction to wireless communications systems, it offers an in-depth treatment of propagation prediction and fading channels. It then explores antenna technology with discussion of antenna design methods and the various antennas in current use or development for base stations, hand held devices, satellite communications, and shaping beams. The discussions then move to smart antennas and phased array technology, including details on array theory and beamforming techniques. Space diversity, direction-of-arrival estimation, source tracking, and blind source separation methods are addressed, as are the implementation of smart antennas and the results of field trials of systems using smart antennas implemented. Finally, the hot media topic of the safety of mobile phones receives due attention, including details of how the human body interacts with the electromagnetic fields of these devices. Its logical development and extensive range of diagrams, figures, and photographs make this handbook easy to follow and provide a clear understanding of design techniques and the performance of finished products. Its unique, comprehensive coverage written by top experts in their fields promises to make the Handbook of Antennas in Wireless Communications the standard reference for the field.


The Laplacian on a Riemannian Manifold

The Laplacian on a Riemannian Manifold

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  • Author: Steven Rosenberg
  • Publisher: Cambridge University Press
  • ISBN: 9780521468312
  • Category : Mathematics
  • Languages : en
  • Pages : 190

This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.


An Introduction to Extremal Kahler Metrics

An Introduction to Extremal Kahler Metrics

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  • Author: Gábor Székelyhidi
  • Publisher: American Mathematical Soc.
  • ISBN: 1470410478
  • Category : Mathematics
  • Languages : en
  • Pages : 210

A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for Riemann surfaces. Extremal metrics were introduced by Calabi as an attempt at finding a higher-dimensional generalization of this result, in the setting of Kähler geometry. This book gives an introduction to the study of extremal Kähler metrics and in particular to the conjectural picture relating the existence of extremal metrics on projective manifolds to the stability of the underlying manifold in the sense of algebraic geometry. The book addresses some of the basic ideas on both the analytic and the algebraic sides of this picture. An overview is given of much of the necessary background material, such as basic Kähler geometry, moment maps, and geometric invariant theory. Beyond the basic definitions and properties of extremal metrics, several highlights of the theory are discussed at a level accessible to graduate students: Yau's theorem on the existence of Kähler-Einstein metrics, the Bergman kernel expansion due to Tian, Donaldson's lower bound for the Calabi energy, and Arezzo-Pacard's existence theorem for constant scalar curvature Kähler metrics on blow-ups.


Semidefinite Optimization and Convex Algebraic Geometry

Semidefinite Optimization and Convex Algebraic Geometry

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  • Author: Grigoriy Blekherman
  • Publisher: SIAM
  • ISBN: 1611972280
  • Category : Mathematics
  • Languages : en
  • Pages : 487

An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.


Selected Works of Phillip A. Griffiths with Commentary

Selected Works of Phillip A. Griffiths with Commentary

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  • Author: Phillip Griffiths
  • Publisher: American Mathematical Soc.
  • ISBN: 9780821820872
  • Category : Mathematics
  • Languages : en
  • Pages : 816

Containing four parts such as Analytic Geometry, Algebraic Geometry, Variations of Hodge Structures, and Differential Systems that are organized according to the subject matter, this title provides the reader with a panoramic view of important and exciting mathematics during the second half of the 20th century.