Polynomials Dynamics And Choice
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Polynomials Dynamics And Choice
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Author : Scott Crass
language : en
Publisher: CRC Press
Release Date : 2022-08-23
Polynomials Dynamics And Choice written by Scott Crass and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-23 with Mathematics categories.
Working out solutions to polynomial equations is a mathematical problem that dates from antiquity. Galois developed a theory in which the obstacle to solving a polynomial equation is an associated collection of symmetries. Obtaining a root requires "breaking" that symmetry. When the degree of an equation is at least five, Galois Theory established that there is no formula for the solutions like those found in lower degree cases. However, this negative result doesn't mean that the practice of equation-solving ends. In a recent breakthrough, Doyle and McMullen devised a solution to the fifth-degree equation that uses geometry, algebra, and dynamics to exploit icosahedral symmetry. Polynomials, Dynamics, and Choice: The Price We Pay for Symmetry is organized in two parts, the first of which develops an account of polynomial symmetry that relies on considerations of algebra and geometry. The second explores beyond polynomials to spaces consisting of choices ranging from mundane decisions to evolutionary algorithms that search for optimal outcomes. The two algorithms in Part I provide frameworks that capture structural issues that can arise in deliberative settings. While decision-making has been approached in mathematical terms, the novelty here is in the use of equation-solving algorithms to illuminate such problems. Features Treats the topic—familiar to many—of solving polynomial equations in a way that’s dramatically different from what they saw in school Accessible to a general audience with limited mathematical background Abundant diagrams and graphics.
Polynomial Approximation For Data Driven System Analysis And Control Of Nonlinear Systems
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Author : Tim Martin
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2024-12-15
Polynomial Approximation For Data Driven System Analysis And Control Of Nonlinear Systems written by Tim Martin and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-15 with Technology & Engineering categories.
This thesis presents data-driven methods for nonlinear systems, enabling the verification of system-theoretical properties and the design of state feedbacks based on measured trajectories. Despite noisy data, the developed methods provide rigorous guarantees and leverage convex optimization. Classical control techniques require a mathematical model of the system dynamics, which derivation from first principles often demands expert knowledge or is time-consuming. In contrast, data-based control methods determine system properties and controllers from system trajectories. Whereas recent developments address linear systems, dynamical systems are generally nonlinear in practice. Therefore, this thesis first introduces a data-based system representation for unknown polynomial systems to determine dissipativity and integral quadratic constraints via sum-of-squares optimization. The second part of the thesis establishes a polynomial representation of nonlinear systems based on polynomial interpolation. Due to the unknown interpolation polynomial, a set of polynomials containing the actual interpolation polynomial is deduced from noisy data. This set, along with a polynomial bound on the approximation error, forms the basis for determining dissipativity properties and designing state feedbacks with stability guarantees utilizing robust control techniques and sum-of-squares relaxation.
Computational Methods For The Study Of Dynamic Economies
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Author : Ramon Marimon
language : en
Publisher: OUP Oxford
Release Date : 1999-03-04
Computational Methods For The Study Of Dynamic Economies written by Ramon Marimon and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-03-04 with Business & Economics categories.
Macroeconomics increasingly uses stochastic dynamic general equilibrium models to understand theoretical and policy issues. Unless very strong assumptions are made, understanding the properties of particular models requires solving the model using a computer. This volume brings together leading contributors in the field who explain in detail how to implement the computational techniques needed to solve dynamic economics models. A broad spread of techniques are covered, and their application in a wide range of subjects discussed. The book provides the basics of a toolkit which researchers and graduate students can use to solve and analyse their own theoretical models.
Xva
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Author : Andrew Green
language : en
Publisher: John Wiley & Sons
Release Date : 2015-10-23
Xva written by Andrew Green and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-23 with Business & Economics categories.
Thorough, accessible coverage of the key issues inXVA XVA – Credit, Funding and Capital ValuationAdjustments provides specialists and non-specialists alikewith an up-to-date and comprehensive treatment of Credit, Debit,Funding, Capital and Margin Valuation Adjustment (CVA, DVA, FVA,KVA and MVA), including modelling frameworks as well as broader ITengineering challenges. Written by an industry expert, this booknavigates you through the complexities of XVA, discussing in detailthe very latest developments in valuation adjustments including theimpact of regulatory capital and margin requirements arising fromCCPs and bilateral initial margin. The book presents a unified approach to modelling valuationadjustments including credit risk, funding and regulatory effects.The practical implementation of XVA models using Monte Carlotechniques is also central to the book. You'll also find thoroughcoverage of how XVA sensitivities can be accurately measured, thetechnological challenges presented by XVA, the use of gridcomputing on CPU and GPU platforms, the management of data, and howthe regulatory framework introduced under Basel III presentsmassive implications for the finance industry. Explores how XVA models have developed in the aftermath of thecredit crisis The only text to focus on the XVA adjustments rather than thebroader topic of counterparty risk. Covers regulatory change since the credit crisis includingBasel III and the impact regulation has had on the pricing ofderivatives. Covers the very latest valuation adjustments, KVA and MVA. The author is a regular speaker and trainer at industry events,including WBS training, Marcus Evans, ICBI, Infoline and RISK If you're a quantitative analyst, trader, banking manager, riskmanager, finance and audit professional, academic or studentlooking to expand your knowledge of XVA, this book has youcovered.
Sliding Mode Control In Engineering
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Author : Wilfrid Perruquetti
language : en
Publisher: CRC Press
Release Date : 2002-01-29
Sliding Mode Control In Engineering written by Wilfrid Perruquetti and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-29 with Technology & Engineering categories.
Provides comprehensive coverage of the most recent developments in the theory of non-Archimedean pseudo-differential equations and its application to stochastics and mathematical physics--offering current methods of construction for stochastic processes in the field of p-adic numbers and related structures. Develops a new theory for parabolic equat
Laminational Models For Some Spaces Of Polynomials Of Any Degree
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Author : Alexander Blokh
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Laminational Models For Some Spaces Of Polynomials Of Any Degree written by Alexander Blokh and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.
The so-called 'pinched disk' model of the Mandelbrot set is due to A. Douady, J. H. Hubbard, and W. P. Thurston. It can be described in the language of geodesic laminations.
Advances In Nonlinear Dynamics Volume I
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Author : Walter Lacarbonara
language : en
Publisher: Springer Nature
Release Date : 2024-05-11
Advances In Nonlinear Dynamics Volume I written by Walter Lacarbonara and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-11 with Technology & Engineering categories.
This volume aims to present the latest advancements in experimental, analytical, and numerical methodologies aimed at exploring the nonlinear dynamics of diverse systems across varying length and time scales. It delves into the following topics: Methodologies for nonlinear dynamic analysis (harmonic balance, asymptotic techniques, enhanced time integration) Data-driven dynamics, machine learning techniques Exploration of bifurcations and nonsmooth systems Nonlinear phenomena in mechanical systems and structures Experimental dynamics, system identification, and monitoring techniques Fluid-structure interaction Dynamics of multibody systems Turning processes, rotating systems, and systems with time delays
Nonlinear And Global Analysis
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Author : Felix E. Browder
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Nonlinear And Global Analysis written by Felix E. Browder and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This volume contains a number of research-expository articles that appeared in the Bulletin of the AMS between 1979 and 1984 and that address the general area of nonlinear functional analysis and global analysis and their applications. The central theme concerns qualitative methods in the study of nonlinear problems arising in applied mathematics, mathematical physics, and geometry. Since these articles first appeared, the methods and ideas they describe have been applied in an ever-widening array of applications. Readers will find this collection useful, as it brings together a range of influential papers by some of the leading researchers in the field.
Information And Communication Technologies And Sustainable Development
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Author : Stanislav Dovgyi
language : en
Publisher: Springer Nature
Release Date : 2023-11-17
Information And Communication Technologies And Sustainable Development written by Stanislav Dovgyi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-17 with Computers categories.
The book highlights the most important research areas in ICT, their impact on e-society, environment sustainable development, namely analytics, security, geoinformation systems, and mathematical modeling. The studies contain a discussion on artificial intelligence in various spheres of society, practical implementation of the IoT, geoinformation systems, and remote sensing of the earth. The book focuses on improving services providing, system architecture for SDN, forecasting social and environment sustainable development based on global information space, a new approach to radio electronics systems for the novel cloud infrastructure implementation. The results are used for novel systems and to promote new approaches for e-societies. The book offers a valuable resource for specialists of R&D organizations, the management of state administration who are involved in sustainable society development, professors, university lecturers, Ph.D. students, and bachelor and master degree students.
Controlling Chaos And Bifurcations In Engineering Systems
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Author : Guanrong Chen
language : en
Publisher: CRC Press
Release Date : 1999-09-28
Controlling Chaos And Bifurcations In Engineering Systems written by Guanrong Chen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-28 with Technology & Engineering categories.
Over the last two decades, chaos in engineering systems has moved from being simply a curious phenomenon to one with real, practical significance and utility. Engineers, scientists, and mathematicians have similarly advanced from the passive role of analyzing chaos to their present, active role of controlling chaos-control directed not only at suppression, but also at exploiting its enormous potential. We now stand at the threshold of major advances in the control and synchronization of chaos for new applications across the range of engineering disciplines. Controlling Chaos and Bifurcations in Engineering Systems provides a state-of-the-art survey of the control-and anti-control-of chaos in dynamical systems. Internationally known experts in the field join forces in this volume to form this tutorial-style combination of overview and technical report on the latest advances in the theory and applications of chaos control. They detail various approaches to control and show how designers can use chaos to create a wider variety of properties and greater flexibility in the design process. Chaos control promises to have a major impact on novel time- and energy-critical engineering applications. Within this volume, readers will find many challenging problems-yet unsolved-regarding both the fundamental theory and potential applications of chaos control and anti-control. Controlling Chaos and Bifurcations in Engineering Systems will bring readers up-to-date on recent development in the field and help open the door to new advances.