Observability And Mathematics

Author : Boris Khots
Publisher : CRC Press
Page : 228 pages
File Size : 40,9 Mb
Release : 2021-11-10
Category : Mathematics
ISBN : 9781000466270

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Observability and Mathematics by Boris Khots Pdf

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.

Author : Agostino Martinelli
Publisher : SIAM
Page : 277 pages
File Size : 49,6 Mb
Release : 2020-08-24
Category : Mathematics
ISBN : 9781611976250

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Observability by Agostino Martinelli Pdf

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.

Author : Boris Khots
Publisher : Walter de Gruyter GmbH & Co KG
Page : 261 pages
File Size : 42,9 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 9783111399386

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Observability and Mathematics by Boris Khots Pdf

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.

Author : Boris Khots
Publisher : de Gruyter
Page : 0 pages
File Size : 54,9 Mb
Release : 2024-07
Category : Computers
ISBN : 3111397351

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Observability and Mathematics by Boris Khots Pdf

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.

Author : E Evangelisti
Publisher : Springer
Page : 298 pages
File Size : 53,8 Mb
Release : 2011-03-30
Category : Electronic
ISBN : 3642110657

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Controllability and Observability by E Evangelisti Pdf

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.

Author : Shen-Shen Zeng
Publisher : Unknown
Page : 0 pages
File Size : 45,5 Mb
Release : 2016
Category : Differentiable dynamical systems
ISBN : 3832542809

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Ensemble Observability of Dynamical Systems by Shen-Shen Zeng Pdf

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.

Author : E. Evangelisti
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 54,6 Mb
Release : 2011-06-04
Category : Science
ISBN : 9783642110634

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Controllability and Observability by E. Evangelisti Pdf

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.

Author : Genni Fragnelli,Dimitri Mugnai
Publisher : Springer Nature
Page : 105 pages
File Size : 40,7 Mb
Release : 2021-04-06
Category : Mathematics
ISBN : 9783030693497

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Control of Degenerate and Singular Parabolic Equations by Genni Fragnelli,Dimitri Mugnai Pdf

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.

Author : Genni Fragnelli,Dimitri Mugnai
Publisher : American Mathematical Society
Page : 19 pages
File Size : 40,7 Mb
Release : 2021-11-16
Category : Mathematics
ISBN : 9781470447878

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

View the abstract.

Author : Daqian Li
Publisher : Amer Inst of Mathematical Sciences
Page : 222 pages
File Size : 40,5 Mb
Release : 2010
Category : Mathematics
ISBN : 7040241633

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Controllability and Observability for Quasilinear Hyperbolic Systems by Daqian Li Pdf

Author : Genni Fragnelli,Dimitri Mugnai
Publisher : American Mathematical Soc.
Page : 83 pages
File Size : 55,7 Mb
Release : 2016-06-21
Category : Carleman theorem
ISBN : 9781470419547

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Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations by Genni Fragnelli,Dimitri Mugnai Pdf

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.

Author : Victor Isakov
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 46,8 Mb
Release : 2008-12-02
Category : Mathematics
ISBN : 9780387856520

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Sobolev Spaces in Mathematics III by Victor Isakov Pdf

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.

Author : Mladen Luksic,Clyde Martin
Publisher : American Mathematical Soc.
Page : 273 pages
File Size : 43,5 Mb
Release : 1987
Category : Mathematics
ISBN : 9780821850756

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Differential Geometry: The Interface between Pure and Applied Mathematics by Mladen Luksic,Clyde Martin Pdf

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.

Author : José Luis Gracia,María Cruz López de Silanes,Manuel Palacios,Étienne Ahusborde,Chérif Amrouche,Gilles Carbou,Fabien Caubet
Publisher : Prensas de la Universidad de Zaragoza
Page : 228 pages
File Size : 54,8 Mb
Release : 2024-02-08
Category : Mathematics
ISBN : 9788413407913

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Sixteenth International Conference Zaragoza-Pau on Mathematics and its Applications by José Luis Gracia,María Cruz López de Silanes,Manuel Palacios,Étienne Ahusborde,Chérif Amrouche,Gilles Carbou,Fabien Caubet Pdf

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.

Author : Mike Hockney
Publisher : Magus Books
Page : 906 pages
File Size : 51,9 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 8210379456XXX

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The Mathmos by Mike Hockney Pdf

The universe is nothing like how it appears to us. So, what's it really like? What is it in itself? Neither our senses nor any experiments can reveal the ultimate truth of existence. Fortunately, one thing can: reason. We inhabit the Mathmos: the mathematical cosmos. This book reveals the compelling secrets of the hidden reality that we will never once "see", but we can surely know - thanks to mathematics. Do we live in a rational universe or a random universe? This is the choice between a mathematical universe and a scientific universe. The mathematical universe has a rational ultimate answer, the scientific universe does not. The scientific universe is magicked out of non-existence, as if out of a magician's top hat. Are you a member of the magicians' cult of science? Nothing is more alchemical than modern science. You can generate a cosmos out of randomness in nothingness, which is a much greater trick than merely manufacturing gold from lead.