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Mathematics of Two-Dimensional Turbulence

Author: Sergei Kuksin

Publisher: Cambridge University Press

Published: 2012-09-20

Total Pages: 337

ISBN-13: 113957695X

This book is dedicated to the mathematical study of two-dimensional statistical hydrodynamics and turbulence, described by the 2D Navier–Stokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x) – proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces.

Mathematical Economics

Author: Vasily E. Tarasov

Publisher: MDPI

Published: 2020-06-03

Total Pages: 278

ISBN-13: 303936118X

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This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Author: Marc Fossorier

Publisher: Springer Science & Business Media

Published: 2006-02-03

Total Pages: 348

ISBN-13: 3540314237

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This book constitutes the refereed proceedings of the 16th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-16, held in Las Vegas, NV, USA in February 2006. The 25 revised full papers presented together with 7 invited papers were carefully reviewed and selected from 32 submissions. Among the subjects addressed are block codes; algebra and codes: rings, fields, and AG codes; cryptography; sequences; decoding algorithms; and algebra: constructions in algebra, Galois groups, differential algebra, and polynomials.

Solved Problems in Classical Mechanics

Author: O.L. de Lange

Publisher: Oxford University Press

Published: 2010-05-06

Total Pages: 608

ISBN-13: 0199582521

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simulated motion on a computer screen, and to study the effects of changing parameters. --

Leonhard Euler

Author: Robert E. Bradley

Publisher: Elsevier

Published: 2007-03-20

Total Pages: 543

ISBN-13: 0080471293

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The year 2007 marks the 300th anniversary of the birth of one of the Enlightenment’s most important mathematicians and scientists, Leonhard Euler. This volume is a collection of 24 essays by some of the world’s best Eulerian scholars from seven different countries about Euler, his life and his work. Some of the essays are historical, including much previously unknown information about Euler’s life, his activities in the St. Petersburg Academy, the influence of the Russian Princess Dashkova, and Euler’s philosophy. Others describe his influence on the subsequent growth of European mathematics and physics in the 19th century. Still others give technical details of Euler’s innovations in probability, number theory, geometry, analysis, astronomy, mechanics and other fields of mathematics and science. - Over 20 essays by some of the best historians of mathematics and science, including Ronald Calinger, Peter Hoffmann, Curtis Wilson, Kim Plofker, Victor Katz, Ruediger Thiele, David Richeson, Robin Wilson, Ivor Grattan-Guinness and Karin Reich- New details of Euler's life in two essays, one by Ronald Calinger and one he co-authored with Elena Polyakhova- New information on Euler's work in differential geometry, series, mechanics, and other important topics including his influence in the early 19th century

Linear Algebra

Author: Jin Ho Kwak

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 375

ISBN-13: 1475712006

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Linear algebra is one of the most important subjects in the study of science and engineering because of its widespread applications in social or natural science, computer science, physics, or economics. As one of the most useful courses in undergraduate mathematics, it has provided essential tools for industrial scientists. The basic concepts of linear algebra are vector spaces, linear transformations, matrices and determinants, and they serve as an abstract language for stating ideas and solving problems. This book is based on the lectures delivered several years in a sophomore level linear algebra course designed for science and engineering students. The primary purpose of this book is to give a careful presentation of the basic concepts of linear algebra as a coherent part of mathematics, and to illustrate its power and usefulness through applications to other disciplines. We have tried to emphasize the computational skills along with the mathematical abstractions, which have also an integrity and beauty of their own. The book includes a variety of interesting applications with many examples not only to help students understand new concepts but also to practice wide applications of the subject to such areas as differential equations, statistics, geometry, and physics. Some of those applications may not be central to the mathematical development and may be omitted or selected in a syllabus at the discretion of the instructor.

Selected Works of Wen-Tsun Wu

Author: Wen-tsun Wu

Publisher: World Scientific

Published: 2008

Total Pages: 477

ISBN-13: 9812791086

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This important book presents all the major works of Professor Wen-Tsun Wu, a widely respected Chinese mathematician who has made great contributions in the fields of topology and computer mathematics throughout his research career. The book covers Wu's papers from 1948 to 2005 and provides a comprehensive overview of his major achievements in algebraic topology, computer mathematics, and history of ancient Chinese mathematics. In algebraic topology, he discovered Wu classes and Wu formulas for Stiefel-Whitney classes of sphere bundles or differential manifolds, established an imbedding theory with an application to the layout problem of integrated circuits, and introduced the I*-functors which turned the "rational homotopy theory" created by D Sullivan into algorithmic form. In computer mathematics, he discovered Wu's method of mechanical theorem proving by means of computers, which has been applied to prove and even discover on the computers hundreds of non-trivial theorems in various kinds of elementary and differential geometries. He also discovered a new effective method of polynomial equations solving, which has been used to solve problems raised from the fields of robotics and mechanisms, CAGD, computer vision, theoretic physics, celestial mechanics, and chemical equilibrium computation.

Digital Signal Processing with Matlab Examples, Volume 2

Author: Jose Maria Giron-Sierra

Publisher: Springer

Published: 2016-12-02

Total Pages: 913

ISBN-13: 9811025371

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This is the second volume in a trilogy on modern Signal Processing. The three books provide a concise exposition of signal processing topics, and a guide to support individual practical exploration based on MATLAB programs. This second book focuses on recent developments in response to the demands of new digital technologies. It is divided into two parts: the first part includes four chapters on the decomposition and recovery of signals, with special emphasis on images. In turn, the second part includes three chapters and addresses important data-based actions, such as adaptive filtering, experimental modeling, and classification.

Applied Business Statistics 5e

Author: Trevor Wegner

Publisher:

Published: 2020

Total Pages: 570

ISBN-13: 9781485130499

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Applied Business Statistics 5e is an introductory and intermediate Statistics text for students of Management. Its business applications-oriented approach aims to teach Management students how statistics (or data analytics) can be used as a valuable decision-support tool in any discipline of management practice.

Raising Goats For Dummies

Author: Cheryl K. Smith

Publisher: John Wiley & Sons

Published: 2010-01-28

Total Pages: 360

ISBN-13: 0470633808

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Learn to raise goats and start reaping the benefits of owning these fun and useful animals Raising goats is a major part of human life (and survival) around the world. The movement has increased in popularity in recent years as consumers embrace a more sustainable lifestyle, reject commercialism, move to organic food options, and raise concerns about industrial agriculture practices. Raising Goats For Dummies provides you with an introduction to all aspects of owning, caring for, and the day-to-day benefits of raising goats. Breaks down the complicated process of choosing and purchasing the right goat breed to meet your needs and getting facilities for your goat set up. Provides in-depth information on proper grooming, handling, feeding, and milking Covers the basics of goat health and nutrition Offers tips and advice for using your goat to produce milk, meat, fiber, and more You'll quickly understand what makes these useful and delightful creatures so popular and gain the knowledge and skills to properly care for and utilize their many offerings with help from Raising Goats For Dummies.