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Author: Yongxiang Huang
Publisher:
ISBN:
Category :
Languages : en
Pages : 238
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Book Description
La décomposition modale empirique (Empirical Mode Decomposition - EMD) ou la Transformation de Hilbert Huang (HHT) est une nouvelle méthode d'analyse temps-fréquence qui est particulièrement adaptée pour des séries temporelles non-linéaires et non stationnaires. Nous avons obtenu comme résultat le fait que la méthode EMD correspond à un banc de filtre dyadique (ou quasi-dyadique) pour la turbulence pleinement développée. Pour caractériser les propriétés intermittentes d'une série temporelle invariante d'échelle, nous avons généralisé l'analyse spectrale de Hilbert-Huang classique à des moments d'ordre arbitraires, pour effectuer ce que nous avons appelé " analyse spectrale de Hilbert d'ordre arbitraire ". Ceci fournit un nouveau cadre pour analyser l'invariance d'échelle directement dans un espace amplitude-fréquence. Nous validons tout d'abord la méthode en analysant des séries temporelles de mouvement Brownien fractionnaire, et en analysant des séries temporelles multifractales synthétiques. Nous comparons les résultats obtenus avec la nouvelle méthode, à l'analyse classique utilisant les fonctions de structure : nous trouvons numériquement que la méthodologie utilisant l'approche de Hilbert fournit un estimateur plus précis pour le paramètre d'intermittence. Nous appliquons ensuite cette méthodologie Hilbert-Huang à une base de données de turbulence homogène et localement isotrope, pour caractériser les propriétés multifractales invariantes d'échelle de séries temporelles de vitesse. Finalement nous appliquons la nouvelle méthodologie à des données environnementales : des débits de rivière, et des données de turbulence marine dans la zone de surf.
Author: Yongxiang Huang
Publisher:
ISBN:
Category :
Languages : en
Pages : 238
Get Book Here
Book Description
La décomposition modale empirique (Empirical Mode Decomposition - EMD) ou la Transformation de Hilbert Huang (HHT) est une nouvelle méthode d'analyse temps-fréquence qui est particulièrement adaptée pour des séries temporelles non-linéaires et non stationnaires. Nous avons obtenu comme résultat le fait que la méthode EMD correspond à un banc de filtre dyadique (ou quasi-dyadique) pour la turbulence pleinement développée. Pour caractériser les propriétés intermittentes d'une série temporelle invariante d'échelle, nous avons généralisé l'analyse spectrale de Hilbert-Huang classique à des moments d'ordre arbitraires, pour effectuer ce que nous avons appelé " analyse spectrale de Hilbert d'ordre arbitraire ". Ceci fournit un nouveau cadre pour analyser l'invariance d'échelle directement dans un espace amplitude-fréquence. Nous validons tout d'abord la méthode en analysant des séries temporelles de mouvement Brownien fractionnaire, et en analysant des séries temporelles multifractales synthétiques. Nous comparons les résultats obtenus avec la nouvelle méthode, à l'analyse classique utilisant les fonctions de structure : nous trouvons numériquement que la méthodologie utilisant l'approche de Hilbert fournit un estimateur plus précis pour le paramètre d'intermittence. Nous appliquons ensuite cette méthodologie Hilbert-Huang à une base de données de turbulence homogène et localement isotrope, pour caractériser les propriétés multifractales invariantes d'échelle de séries temporelles de vitesse. Finalement nous appliquons la nouvelle méthodologie à des données environnementales : des débits de rivière, et des données de turbulence marine dans la zone de surf.
Author: Adarsh S
Publisher: CRC Press
ISBN: 1000346641
Category : Mathematics
Languages : en
Pages : 182
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Book Description
Accurate prediction of hydrological variables is essential for efficient water resources planning and management. Proper understanding of the characteristics of the time series may help in improving the simulation and forecasting accuracy of hydrological variables. This book presents a detailed description and application of multiscale time-frequency characterization tool for the spectral analysis of hydrological time series. It presents spectral analysis methods for hydrological applications through a wide variety of illustrative case studies including Wavelet transforms, Hilbert Huang Transform and their extensions.
Author: Fedor S. Rofe-Beketov
Publisher: World Scientific
ISBN: 9812562761
Category : Science
Languages : en
Pages : 463
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Book Description
- Detailed bibliographical comments and some open questions are given after each chapter - Indicates connections between the content of the book and many other topics in mathematics and physics - Open questions are formulated and commented with the intention to attract attention of young mathematicians
Author: Kurt Otto Friedrichs
Publisher:
ISBN: 9781258449834
Category :
Languages : en
Pages : 218
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Book Description
The Present Lectures Intend To Provide An Introduction To The Spectral Analysis Of Self-Joint Operators Within The Framework Of Hilbert Space Theory. The Guiding Notion In This Approach Is That Of Spectral Representation. At The Same Time The Notion Of Function Of An Operator Is Emphasized. The Definition Of Hilbert Space: In Mathematics, A Hilbert Space Is A Real Or Complex Vector Space With A Positive-Definite Hermitian Form, That Is Complete Under Its Norm. Thus It Is An Inner Product Space, Which Means That It Has Notions Of Distance And Of Angle (Especially The Notion Of Orthogonality Or Perpendicularity). The Completeness Requirement Ensures That For Infinite Dimensional Hilbert Spaces The Limits Exist When Expected, Which Facilitates Various Definitions From Calculus. A Typical Example Of A Hilbert Space Is The Space Of Square Summable Sequences. Hilbert Spaces Allow Simple Geometric Concepts, Like Projection And Change Of Basis To Be Applied To Infinite Dimensional Spaces, Such As Function Spaces. They Provide A Context With Which To Formalize And Generalize The Concepts Of The Fourier Series In Terms Of Arbitrary Orthogonal Polynomials And Of The Fourier Transform, Which Are Central Concepts From Functional Analysis. Hilbert Spaces Are Of Crucial Importance In The Mathematical Formulation Of Quantum Mechanics.
Author: Fedor S. Rofe-Beketov
Publisher: World Scientific
ISBN: 9812703454
Category : Mathematics
Languages : en
Pages : 466
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Book Description
This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic SchrAdinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals). The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators."
Author: Norden E Huang
Publisher: World Scientific
ISBN: 981450825X
Category : Mathematics
Languages : en
Pages : 399
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Book Description
This book is written for scientists and engineers who use HHT (Hilbert-Huang Transform) to analyze data from nonlinear and non-stationary processes. It can be treated as a HHT user manual and a source of reference for HHT applications. The book contains the basic principle and method of HHT and various application examples, ranging from the correction of satellite orbit drifting to detection of failure of highway bridges.The thirteen chapters of the first edition are based on the presentations made at a mini-symposium at the Society for Industrial and Applied Mathematics in 2003. Some outstanding mathematical research problems regarding HHT development are discussed in the first three chapters. The three new chapters of the second edition reflect the latest HHT development, including ensemble empirical mode decomposition (EEMD) and modified EMD.The book also provides a platform for researchers to develop the HHT method further and to identify more applications.
Author: Christophe Cheverry
Publisher: Springer Nature
ISBN: 3030674622
Category : Mathematics
Languages : en
Pages : 258
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Book Description
This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience, the authors present topics in a progressive manner so that each chapter builds on the ones preceding. Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book. Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader. A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. PhD students and researchers will also find this volume to be of interest, particularly the research directions provided in later chapters.
Author: Gilbert Helmberg
Publisher: Elsevier
ISBN: 1483164179
Category : Science
Languages : en
Pages : 362
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Book Description
North-Holland Series in Applied Mathematics and Mechanics, Volume 6: Introduction to Spectral Theory in Hilbert Space focuses on the mechanics, principles, and approaches involved in spectral theory in Hilbert space. The publication first elaborates on the concept and specific geometry of Hilbert space and bounded linear operators. Discussions focus on projection and adjoint operators, bilinear forms, bounded linear mappings, isomorphisms, orthogonal subspaces, base, subspaces, finite dimensional Euclidean space, and normed linear spaces. The text then takes a look at the general theory of linear operators and spectral analysis of compact linear operators, including spectral decomposition of a compact selfadjoint operator, weakly convergent sequences, spectrum of a compact linear operator, and eigenvalues of a linear operator. The manuscript ponders on the spectral analysis of bounded linear operators and unbounded selfadjoint operators. Topics include spectral decomposition of an unbounded selfadjoint operator and bounded normal operator, functions of a unitary operator, step functions of a bounded selfadjoint operator, polynomials in a bounded operator, and order relation for bounded selfadjoint operators. The publication is a valuable source of data for mathematicians and researchers interested in spectral theory in Hilbert space.
Author: D. E. Edmunds
Publisher: Springer
ISBN: 3030021254
Category : Mathematics
Languages : en
Pages : 324
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Book Description
This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature. Starting with the basics of elliptic operators and their naturally associated function spaces, the authors then proceed to cover various related topics of current and continuing importance. Particular attention is given to the characterisation of self-adjoint extensions of symmetric operators acting in a Hilbert space and, for elliptic operators, the realisation of such extensions in terms of boundary conditions. A good deal of material not previously available in book form, such as the treatment of the Schauder estimates, is included. Requiring only basic knowledge of measure theory and functional analysis, the book is accessible to graduate students and will be of interest to all researchers in partial differential equations. The reader will value its self-contained, thorough and unified presentation of the modern theory of elliptic operators.
Author: Michael Hölling
Publisher: Springer Science & Business
ISBN: 364254696X
Category : Technology & Engineering
Languages : en
Pages : 207
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Book Description
This book presents the results of the seminar “Wind Energy and the Impact of Turbulence on the Conversion Process” which was supported from three societies, namely the EUROMech, EAWE and ERCOFATC and took place in Oldenburg, Germany in spring 2012. The seminar was one of the first scientific meetings devoted to the common topic of wind energy and basic turbulence. The established community of researchers working on the challenging puzzle of turbulence for decades met the quite young community of researchers, who face the upcoming challenges in the fast growing field of wind energy applications. From the fluid mechanical point of view, wind turbines are large machines operating in the fully turbulent atmospheric boundary layer. In particular they are facing small-scale turbulent inflow conditions. It is one of the central puzzles in basic turbulence research to achieve a fundamental understanding of the peculiarities of small-scale turbulence. This book helps to better understand the resulting aerodynamics around the wind turbine’s blades and the forces transmitted into the machinery in this context of puzzling inflow conditions. This is a big challenge due to the multi-scale properties of the incoming wind field ranging from local flow conditions on the profile up to the interaction of wake flows in wind farms.
