Observability And Mathematics

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Observability and Mathematics

Author : Boris Khots
Publisher : CRC Press
ISBN 13 : 1000466272
Total Pages : 228 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Observability and Mathematics by : Boris Khots

Download or read book Observability and Mathematics written by Boris Khots and published by CRC Press. This book was released on 2021-11-10 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author approaches an old classic problem - the existence of solutions of Navier-Stokes equations. The main objective is to model and derive of equation of continuity, Euler equation of fluid motion, energy flux equation, Navier-Stokes equations from the observer point of view and solve classic problem for this interpretation of fluid motion laws. If we have a piece of metal or a volume of liquid, the idea impresses itself upon us that it is divisible without limit, that any part of it, however small, would again have the same properties. But, wherever the methods of research in the physics of matter were refined sufficiently, limits to divisibility were reached that are not due to the inadequacy of our experiments but to the nature of the subject matter. Observability in mathematics were developed by the author based on denial of infinity idea. He introduces observers into arithmetic, and arithmetic becomes dependent on observers. And after that the basic mathematical parts also become dependent on observers. This approach permits to reconsider the fluid motion laws, analyze them and get solutions of classic problems. Table of Contents 1. Introduction. 2. Observability and Arithmetic. 3. Observability and Vector Algebra. 4. Observability and Mathematical Analysis (Calculus). 5. Classic Fluid Mechanics equations and Observability. 6. Observability and Thermodynamical equations. 7. Observability and equation of continuity. 8. Observability and Euler equation of motion of the fluid. 9. Observability and energy flux and moment flux equations. 10. Observability and incompressible fluids. 11. Observability and Navier-Stokes equations. 12. Observability and Relativistic Fluid Mechanics. 13. Appendix: Review of publications of the Mathematics with Observers. 14. Glossary. Bibliography Index Biography Boris Khots, DrSci, lives in Iowa, USA, Independent Researcher. Alma Mater - Moscow State Lomonosov University, Department of Mathematics and Mechanics (mech-math). Creator of Observer’s Mathematics. Participant of more than 30 Mathematical international congresses, conferences. In particular, participated with presentation at International Congresses of Mathematicians on 1998 (Germany), 2002 (China), 2006 (Spain), 2010 (India), 2014 (South Korea). More than 150 mathematical books and papers.

Observability

Author : Agostino Martinelli
Publisher : SIAM
ISBN 13 : 1611976251
Total Pages : 277 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Observability by : Agostino Martinelli

Download or read book Observability written by Agostino Martinelli and published by SIAM. This book was released on 2020-08-24 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about nonlinear observability. It provides a modern theory of observability based on a new paradigm borrowed from theoretical physics and the mathematical foundation of that paradigm. In the case of observability, this framework takes into account the group of invariance that is inherent to the concept of observability, allowing the reader to reach an intuitive derivation of significant results in the literature of control theory. The book provides a complete theory of observability and, consequently, the analytical solution of some open problems in control theory. Notably, it presents the first general analytic solution of the nonlinear unknown input observability (nonlinear UIO), a very complex open problem studied in the 1960s. Based on this solution, the book provides examples with important applications for neuroscience, including a deep study of the integration of multiple sensory cues from the visual and vestibular systems for self-motion perception. Observability: A New Theory Based on the Group of Invariance is the only book focused solely on observability. It provides readers with many applications, mostly in robotics and autonomous navigation, as well as complex examples in the framework of vision-aided inertial navigation for aerial vehicles. For these applications, it also includes all the derivations needed to separate the observable part of the system from the unobservable, an analysis with practical importance for obtaining the basic equations for implementing any estimation scheme or for achieving a closed-form solution to the problem. This book is intended for researchers in robotics and automation, both in academia and in industry. Researchers in other engineering disciplines, such as information theory and mechanics, will also find the book useful.

Observability and Mathematics

Author : Boris Khots
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111399389
Total Pages : 261 pages
Book Rating : 4.1/5 (113 download)

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Book Synopsis Observability and Mathematics by : Boris Khots

Download or read book Observability and Mathematics written by Boris Khots and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-07-01 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories, but its mathematical foundation is still unclear. The ''mass gap'' property has been discovered by physicists from experiment, but it still has not been understood from a theoretical point of view. Proposed book describes author's approach to solution of this problem on base of Mathematics with Observers (removing from arithmetic infinity idea, taking into account Observers dependent ascending chain of embedded sets of finite decimal fractions with arithmetic operations locally coinciding with standard operations, and getting new calculus, diff geometry, etc), including interpretations of vector fields and differential forms, generalization of Yang-Mills equations, proof of mass gap existing, consideration the theory of matrix Lie groups and algebras, and this point of view gives the possibilities to make new approach and establish the existence of the Yang-Mills theory and a mass gap, Grand unified theories and Standard model of particle physics.

Observability and Mathematics

Author : Boris Khots
Publisher : de Gruyter
ISBN 13 : 9783111397351
Total Pages : 0 pages
Book Rating : 4.3/5 (973 download)

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Book Synopsis Observability and Mathematics by : Boris Khots

Download or read book Observability and Mathematics written by Boris Khots and published by de Gruyter. This book was released on 2024-07 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Yang-Mills theory is now the foundation of most of elementary particle theory, and its predictions have been tested at many experimental laboratories, but its mathematical foundation is still unclear. The ''mass gap'' property has been discovered by physicists from experiment, but it still has not been understood from a theoretical point of view. Proposed book describes author's approach to solution of this problem on base of Mathematics with Observers (removing from arithmetic infinity idea, taking into account Observers dependent ascending chain of embedded sets of finite decimal fractions with arithmetic operations locally coinciding with standard operations, and getting new calculus, diff geometry, etc), including interpretations of vector fields and differential forms, generalization of Yang-Mills equations, proof of mass gap existing, consideration the theory of matrix Lie groups and algebras, and this point of view gives the possibilities to make new approach and establish the existence of the Yang-Mills theory and a mass gap, Grand unified theories and Standard model of particle physics.

Controllability and Observability

Author : E Evangelisti
Publisher : Springer
ISBN 13 : 9783642110658
Total Pages : 298 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Controllability and Observability by : E Evangelisti

Download or read book Controllability and Observability written by E Evangelisti and published by Springer. This book was released on 2011-03-30 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: R.E. Kalman: Lectures on controllability and observability.- E. Kulikowski: Controllability and optimum contro.- A. Straszak: Supervisory controllabilityl.- L. Weiss: Lectures on controllability and observability.

Ensemble Observability of Dynamical Systems

Author : Shen-Shen Zeng
Publisher :
ISBN 13 : 9783832542801
Total Pages : 0 pages
Book Rating : 4.5/5 (428 download)

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Book Synopsis Ensemble Observability of Dynamical Systems by : Shen-Shen Zeng

Download or read book Ensemble Observability of Dynamical Systems written by Shen-Shen Zeng and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, the author introduces the concept of ensemble observability of dynamical systems and develop a theoretical framework in which this system property is characterized. An ensemble is a collection of nearly identical copies of one dynamical system, and it is said to be observable if the distribution of the nonidentical initial states can be reconstructed from observing the time evolution of a corresponding distribution of outputs. Similarly, a single dynamical system with output is said to be ensemble observable if a collection of copies of this system, with different initial states, is observable when considered as an ensemble. The consideration of ensemble observability is, in particular, motivated by recent efforts in the study of heterogeneous cell populations. Therein one aims to reconstruct a distribution of states within a population of cells, but is only given the time evolution of the distribution of certain measured quantities within the population. More generally, the motivation for introducing ensemble observability is rooted in the very concept of ensembles itself, in which a collection of individual systems may only be considered as a whole. A main result of this thesis illustrates a fundamental connection between the concept of ensemble observability and mathematical tomography problems. Another main result concerns a natural connection to polynomial systems, which is encountered in the course of a systems theoretic treatment of the ensemble observability problem through the consideration of moments of the distributions. The author also establishes a duality of both approaches for linear systems.

Controllability and Observability

Author : E. Evangelisti
Publisher : Springer Science & Business Media
ISBN 13 : 3642110630
Total Pages : 289 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Controllability and Observability by : E. Evangelisti

Download or read book Controllability and Observability written by E. Evangelisti and published by Springer Science & Business Media. This book was released on 2011-06-04 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: R.E. Kalman: Lectures on controllability and observability.- E. Kulikowski: Controllability and optimum contro.- A. Straszak: Supervisory controllabilityl.- L. Weiss: Lectures on controllability and observability.

Control of Degenerate and Singular Parabolic Equations

Author : Genni Fragnelli
Publisher : Springer Nature
ISBN 13 : 303069349X
Total Pages : 105 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Control of Degenerate and Singular Parabolic Equations by : Genni Fragnelli

Download or read book Control of Degenerate and Singular Parabolic Equations written by Genni Fragnelli and published by Springer Nature. This book was released on 2021-04-06 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects some basic results on the null controllability for degenerate and singular parabolic problems. It aims to provide postgraduate students and senior researchers with a useful text, where they can find the desired statements and the related bibliography. For these reasons, the authors will not give all the detailed proofs of the given theorems, but just some of them, in order to show the underlying strategy in this area.

Stochastic Systems: The Mathematics of Filtering and Identification and Applications

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9400985460
Total Pages : 655 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Stochastic Systems: The Mathematics of Filtering and Identification and Applications by : Michiel Hazewinkel

Download or read book Stochastic Systems: The Mathematics of Filtering and Identification and Applications written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last five years or so there has been an important renaissance in the area of (mathematical) modeling, identification and (stochastic) control. It was the purpose of the Advanced Study Institute of which the present volume constitutes the proceedings to review recent developments in this area with par ticular emphasis on identification and filtering and to do so in such a manner that the material is accessible to a wide variety of both embryo scientists and the various breeds of established researchers to whom identification, filtering, etc. are important (such as control engineers, time series analysts, econometricians, probabilists, mathematical geologists, and various kinds of pure and applied mathematicians; all of these were represented at the ASI). For these proceedings we have taken particular care to see to it that the material presented will be understandable for a quite diverse audience. To that end we have added a fifth tutorial section (besides the four presented at the meeting) and have also included an extensive introduction which explains in detail the main problem areas and themes of these proceedings and which outlines how the various contributions fit together to form a coherent, integrated whole. The prerequisites needed to understand the material in this volume are modest and most graduate students in e. g. mathematical systems theory, applied mathematics, econo metrics or control engineering will qualify.

Computation and Applied Mathematics

Author :
Publisher :
ISBN 13 :
Total Pages : 108 pages
Book Rating : 4./5 ( download)

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Book Synopsis Computation and Applied Mathematics by :

Download or read book Computation and Applied Mathematics written by and published by . This book was released on 1997 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations

Author : Genni Fragnelli
Publisher : American Mathematical Soc.
ISBN 13 : 1470419548
Total Pages : 83 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations by : Genni Fragnelli

Download or read book Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations written by Genni Fragnelli and published by American Mathematical Soc.. This book was released on 2016-06-21 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider a parabolic problem with degeneracy in the interior of the spatial domain, and they focus on observability results through Carleman estimates for the associated adjoint problem. The novelties of the present paper are two. First, the coefficient of the leading operator only belongs to a Sobolev space. Second, the degeneracy point is allowed to lie even in the interior of the control region, so that no previous result can be adapted to this situation; however, different cases can be handled, and new controllability results are established as a consequence.

Sobolev Spaces in Mathematics III

Author : Victor Isakov
Publisher : Springer Science & Business Media
ISBN 13 : 0387856528
Total Pages : 360 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Sobolev Spaces in Mathematics III by : Victor Isakov

Download or read book Sobolev Spaces in Mathematics III written by Victor Isakov and published by Springer Science & Business Media. This book was released on 2008-12-02 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, marking the centenary of S.L. Sobolev’s birth, presents the latest the results on some important problems of mathematical physics. The book contains two short biographical articles and unique archive photos of S. Sobolev.

Controllability and Observability for Quasilinear Hyperbolic Systems

Author : Daqian Li
Publisher : Amer Inst of Mathematical Sciences
ISBN 13 : 9787040241631
Total Pages : 222 pages
Book Rating : 4.2/5 (416 download)

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Book Synopsis Controllability and Observability for Quasilinear Hyperbolic Systems by : Daqian Li

Download or read book Controllability and Observability for Quasilinear Hyperbolic Systems written by Daqian Li and published by Amer Inst of Mathematical Sciences. This book was released on 2010 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Corrigendum and Improvements to “Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations” and Its Consequences

Download Corrigendum and Improvements to “Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations” and Its Consequences PDF Online Free

Author : Genni Fragnelli
Publisher : American Mathematical Society
ISBN 13 : 1470447878
Total Pages : 19 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Corrigendum and Improvements to “Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations” and Its Consequences by : Genni Fragnelli

Download or read book Corrigendum and Improvements to “Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations” and Its Consequences written by Genni Fragnelli and published by American Mathematical Society. This book was released on 2021-11-16 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Differential Geometry: The Interface between Pure and Applied Mathematics

Author : Mladen Luksic
Publisher : American Mathematical Soc.
ISBN 13 : 082185075X
Total Pages : 273 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Differential Geometry: The Interface between Pure and Applied Mathematics by : Mladen Luksic

Download or read book Differential Geometry: The Interface between Pure and Applied Mathematics written by Mladen Luksic and published by American Mathematical Soc.. This book was released on 1987 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Normally, mathematical research has been divided into 'pure' and 'applied', and only within the past decade has this distinction become blurred. However, differential geometry is one area of mathematics that has not made this distinction and has consistently played a vital role in both general areas. The papers in this volume represent the proceedings of a conference entitled 'Differential Geometry: The Interface Between Pure and Applied Mathematics', which was held in San Antonio, Texas, in April 1986. The purpose of the conference was to explore recent exciting applications and challenging classical problems in differential geometry. The papers represent a tremendous range of applications and techniques in such diverse areas as ordinary differential equations, Lie groups, algebra, numerical analysis and control theory.

Sixteenth International Conference Zaragoza-Pau on Mathematics and its Applications

Author : José Luis Gracia
Publisher : Prensas de la Universidad de Zaragoza
ISBN 13 : 8413407915
Total Pages : 228 pages
Book Rating : 4.4/5 (134 download)

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Book Synopsis Sixteenth International Conference Zaragoza-Pau on Mathematics and its Applications by : José Luis Gracia

Download or read book Sixteenth International Conference Zaragoza-Pau on Mathematics and its Applications written by José Luis Gracia and published by Prensas de la Universidad de Zaragoza. This book was released on 2024-02-08 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference Zaragoza-Pau on Mathematics and its Applications was organized by the Departamento de Matem.tica Aplicada, the Departamento de M.todos Estad.sticos and the Departamento de Matem.ticas, all of them from the Universidad de Zaragoza (Spain), and the Laboratoire de Math.matiques et de leurs Applications, from the Universit. de Pau et des Pays de l’Adour (France). This conference has been held every two years since 1989. The aim of this conference is to present recent advances in Applied Mathematics, Statistics and Pure Mathematics, putting special emphasis on subjects linked to petroleum engineering and environmental problems. The Sixteenth Conference took place in Jaca (Spain) from 7th to 9th September 2022. The official opening ceremony was graced by the presence of the Vice–Chancellor for Academic Policy of the University of Zaragoza, D. Jos. .ngel Castellanos G.mez, and Vice–Chancellor of the Research Commission of the University of Pau, Mme. Isabelle Baraille. During those three days, 111 mathematicians, coming from different universities, research institutes or the industrial sector, attended 8 plenary lectures, 69 contributed talks and a poster session with 7 posters. We note that in this edition there were 11 mini-symposia, five of them co-organized by colleagues from the Universidad de Zaragoza and the Universit. de Pau et des Pays de l’Adour.

Advanced Engineering Mathematics

Author : Lawrence Turyn
Publisher : CRC Press
ISBN 13 : 1482219395
Total Pages : 1455 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Advanced Engineering Mathematics by : Lawrence Turyn

Download or read book Advanced Engineering Mathematics written by Lawrence Turyn and published by CRC Press. This book was released on 2013-09-25 with total page 1455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with linear algebra and later expanding into calculus of variations, Advanced Engineering Mathematics provides accessible and comprehensive mathematical preparation for advanced undergraduate and beginning graduate students taking engineering courses. This book offers a review of standard mathematics coursework while effectively integrating science and engineering throughout the text. It explores the use of engineering applications, carefully explains links to engineering practice, and introduces the mathematical tools required for understanding and utilizing software packages. Provides comprehensive coverage of mathematics used by engineering students Combines stimulating examples with formal exposition and provides context for the mathematics presented Contains a wide variety of applications and homework problems Includes over 300 figures, more than 40 tables, and over 1500 equations Introduces useful MathematicaTM and MATLAB® procedures Presents faculty and student ancillaries, including an online student solutions manual, full solutions manual for instructors, and full-color figure sides for classroom presentations Advanced Engineering Mathematics covers ordinary and partial differential equations, matrix/linear algebra, Fourier series and transforms, and numerical methods. Examples include the singular value decomposition for matrices, least squares solutions, difference equations, the z-transform, Rayleigh methods for matrices and boundary value problems, the Galerkin method, numerical stability, splines, numerical linear algebra, curvilinear coordinates, calculus of variations, Liapunov functions, controllability, and conformal mapping. This text also serves as a good reference book for students seeking additional information. It incorporates Short Takes sections, describing more advanced topics to readers, and Learn More about It sections with direct references for readers wanting more in-depth information.