Download or read book Polynomials Dynamics and Choice written by Scott Crass and published by CRC Press. This book was released on 2022-08-23 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Polynomials Dynamics and Choice written by Scott Crass and published by CRC Press. This book was released on 2022-08-23 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computational Methods for the Study of Dynamic Economies written by European Economic Association. Summer School and published by Oxford University Press. This book was released on 1999-03-04 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together leading contributors in the field of macroeconomics who explain how to implement the computational techniques needed to solve dynamic economics models. The contributors cover a broad range of techniques.
Download or read book Sliding Mode Control In Engineering written by Wilfrid Perruquetti and published by CRC Press. This book was released on 2002-01-29 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Symmetric Functions and Hall Polynomials written by Ian Grant Macdonald and published by Oxford University Press. This book was released on 1998 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reissued classic text is the acclaimed second edition of Professor Ian Macdonald's groundbreaking monograph on symmetric functions and Hall polynomials. The first edition was published in 1979, before being significantly expanded into the present edition in 1995. This text is widely regarded as the best source of information on Hall polynomials and what have come to be known as Macdonald polynomials, central to a number of key developments in mathematics and mathematical physics in the 21st century Macdonald polynomials gave rise to the subject of double affine Hecke algebras (or Cherednik algebras) important in representation theory. String theorists use Macdonald polynomials to attack the so-called AGT conjectures. Macdonald polynomials have been recently used to construct knot invariants. They are also a central tool for a theory of integrable stochastic models that have found a number of applications in probability, such as random matrices, directed polymers in random media, driven lattice gases, and so on. Macdonald polynomials have become a part of basic material that a researcher simply must know if (s)he wants to work in one of the above domains, ensuring this new edition will appeal to a very broad mathematical audience. Featuring a new foreword by Professor Richard Stanley of MIT.
Download or read book Analytic Theory of Polynomials written by Qazi Ibadur Rahman and published by Oxford University Press. This book was released on 2002 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents easy to understand proofs of same of the most difficult results about polynomials demonstrated by means of applications
Download or read book Dynamics of Polyatomic Van der Waals Complexes written by Nadine Halberstadt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This publication is the Proceedings of the NATO Advanced Research Workshop (ARW) on the Dynamics of Polyatomic Van der Waals Molecules held at the Chateau de Bonas, Castera-Verduzan, France, from August 21 through August 26, 1989. Van der Waals complexes provide important model problems for understanding energy transfer and dissipation. These processes can be described in great detail for Van der Waals complexes, and the insight gained from such studies can be applied to more complicated chemical problems that are not amenable to detailed study. The workshop concentrated on the current questions and future prospects for extend ing our highly detailed knowledge of triatomic Van der Waals molecule dynamics to polyatomic molecules and clusters (one molecule surrounded by several, or up to sev eral tens of, atoms). Both experimental and theoretical studies were discussed, with particular emphasis on the dynamical behavior of dissociation as observed in the dis tributions of quantum states of the dissociation product molecules. The discussion of theoretical approaches covered the range from complete ab initio studies with a rig orous quantum mechanical treatment of the dynamics to the empirical determination of potential energy surfaces and a classical mechanical treatment of the dynamics. Time independent, time dependent and statistical approaches were considered. The workshop brought together experts from different fields which, we hope, benefited from their mutual interaction around the central theme of the Dynamics of Van der Waals complexes.
Download or read book Handbook of Fluid Dynamics written by Richard W. Johnson and published by CRC Press. This book was released on 2016-04-06 with total page 1544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Fluid Dynamics offers balanced coverage of the three traditional areas of fluid dynamics—theoretical, computational, and experimental—complete with valuable appendices presenting the mathematics of fluid dynamics, tables of dimensionless numbers, and tables of the properties of gases and vapors. Each chapter introduces a different fluid dynamics topic, discusses the pertinent issues, outlines proven techniques for addressing those issues, and supplies useful references for further research. Covering all major aspects of classical and modern fluid dynamics, this fully updated Second Edition: Reflects the latest fluid dynamics research and engineering applications Includes new sections on emerging fields, most notably micro- and nanofluidics Surveys the range of numerical and computational methods used in fluid dynamics analysis and design Expands the scope of a number of contemporary topics by incorporating new experimental methods, more numerical approaches, and additional areas for the application of fluid dynamics Handbook of Fluid Dynamics, Second Edition provides an indispensable resource for professionals entering the field of fluid dynamics. The book also enables experts specialized in areas outside fluid dynamics to become familiar with the field.
Download or read book Polynomials written by Cheon Seoung Ryoo and published by BoD – Books on Demand. This book was released on 2019-05-02 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polynomials are well known for their ability to improve their properties and for their applicability in the interdisciplinary fields of engineering and science. Many problems arising in engineering and physics are mathematically constructed by differential equations. Most of these problems can only be solved using special polynomials. Special polynomials and orthonormal polynomials provide a new way to analyze solutions of various equations often encountered in engineering and physical problems. In particular, special polynomials play a fundamental and important role in mathematics and applied mathematics. Until now, research on polynomials has been done in mathematics and applied mathematics only. This book is based on recent results in all areas related to polynomials. Divided into sections on theory and application, this book provides an overview of the current research in the field of polynomials. Topics include cyclotomic and Littlewood polynomials; Descartes' rule of signs; obtaining explicit formulas and identities for polynomials defined by generating functions; polynomials with symmetric zeros; numerical investigation on the structure of the zeros of the q-tangent polynomials; investigation and synthesis of robust polynomials in uncertainty on the basis of the root locus theory; pricing basket options by polynomial approximations; and orthogonal expansion in time domain method for solving Maxwell's equations using paralleling-in-order scheme.
Download or read book Orthogonal Polynomials on the Unit Circle Spectral theory written by Barry Simon and published by American Mathematical Soc.. This book was released on 2005 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. This book discusses topics such as asymptotics of Toeplitz determinants (Szego's theorems), and limit theorems for the density of the zeros of orthogonal polynomials.
Download or read book Polynomial Chaos Methods for Hyperbolic Partial Differential Equations written by Mass Per Pettersson and published by Springer. This book was released on 2015-03-10 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dimension and one uncertain parameter as its extension is conceptually straightforward. The numerical methods designed guarantee that the solutions to the uncertainty quantification systems will converge as the mesh size goes to zero. Examples from computational fluid dynamics are presented together with numerical methods suitable for the problem at hand: stable high-order finite-difference methods based on summation-by-parts operators for smooth problems, and robust shock-capturing methods for highly nonlinear problems. Academics and graduate students interested in computational fluid dynamics and uncertainty quantification will find this book of interest. Readers are expected to be familiar with the fundamentals of numerical analysis. Some background in stochastic methods is useful but notnecessary.
Download or read book Feedback Control of Dynamic Bipedal Robot Locomotion written by Eric R. Westervelt and published by CRC Press. This book was released on 2018-10-03 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bipedal locomotion is among the most difficult challenges in control engineering. Most books treat the subject from a quasi-static perspective, overlooking the hybrid nature of bipedal mechanics. Feedback Control of Dynamic Bipedal Robot Locomotion is the first book to present a comprehensive and mathematically sound treatment of feedback design for achieving stable, agile, and efficient locomotion in bipedal robots. In this unique and groundbreaking treatise, expert authors lead you systematically through every step of the process, including: Mathematical modeling of walking and running gaits in planar robots Analysis of periodic orbits in hybrid systems Design and analysis of feedback systems for achieving stable periodic motions Algorithms for synthesizing feedback controllers Detailed simulation examples Experimental implementations on two bipedal test beds The elegance of the authors' approach is evident in the marriage of control theory and mechanics, uniting control-based presentation and mathematical custom with a mechanics-based approach to the problem and computational rendering. Concrete examples and numerous illustrations complement and clarify the mathematical discussion. A supporting Web site offers links to videos of several experiments along with MATLAB® code for several of the models. This one-of-a-kind book builds a solid understanding of the theoretical and practical aspects of truly dynamic locomotion in planar bipedal robots.
Download or read book Advances in Nonlinear Dynamics Volume I written by Walter Lacarbonara and published by Springer Nature. This book was released on with total page 719 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book XVA written by Andrew Green and published by John Wiley & Sons. This book was released on 2015-10-23 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Heights of Polynomials and Entropy in Algebraic Dynamics written by Graham Everest and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this book is the theory of heights as they appear in various guises. This includes a large body of results on Mahlers measure of the height of a polynomial. The authors'approach is very down to earth as they cover the rationals, assuming no prior knowledge of elliptic curves. The chapters include examples and particular computations, with all special calculation included so as to be self-contained. The authors devote space to discussing Mahlers measure and to giving some convincing and original examples to explain this phenomenon. XXXXXXX NEUER TEXT The main theme of this book is the theory of heights as it appears in various guises. To this §End.txt.Int.:, it examines the results of Mahlers measure of the height of a polynomial, which have never before appeared in book form. The authors take a down-to-earth approach that includes convincing and original examples. The book uncovers new and interesting connections between number theory and dynamics and will be interesting to researchers in both number theory and nonlinear dynamics.
Download or read book Control Theory for Engineers written by Brigitte d'Andréa-Novel and published by Springer Science & Business Media. This book was released on 2013-05-09 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control Theory is at the heart of information and communication technologies of complex systems. It can contribute to meeting the energy and environmental challenges we are facing. The textbook is organized in the way an engineer classically proceeds to solve a control problem, that is, elaboration of a mathematical model capturing the process behavior, analysis of this model and design of a control to achieve the desired objectives. It is divided into three Parts. The first part of the text addresses modeling aspects through state space and input-output representations. The notion of the internal state of a system (for example mechanical, thermal or electrical), as well as its description using a finite number of variables, is also emphasized. The second part is devoted to the stability analysis of an equilibrium point. The authors present classical tools for stability analysis, such as linearization techniques and Lyapunov functions. Central to Control Theory are the notions of feedback and of closed-loop, and the third part of the textbook describes the linear control synthesis in a continuous and discrete-time framework and also in a probabilistic context. Quadratic optimization and Kalman filtering are presented, as well as the polynomial representation, a convenient approach to reject perturbations on the system without making the control law more complex. Throughout the text, different examples are developed, both in the chapters and in the exercises.
Download or read book Helicopter Aerodynamics and Dynamics written by North Atlantic Treaty Organization. Advisory Group for Aerospace Research and Development. Fluid Dynamics Panel and published by . This book was released on 1973 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt:
