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Adjoint Equations and Perturbation Algorithms in Nonlinear Problems

Adjoint Equations and Perturbation Algorithms in Nonlinear Problems

Guri I. Marchuk; Valeri I. Agoshkov; Victor P. Shutyaev

CRC Press
2020
nidottu
Sparked by demands inherent to the mathematical study of pollution, intensive industry, global warming, and the biosphere, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems is the first book ever to systematically present the theory of adjoint equations for nonlinear problems, as well as their application to perturbation algorithms. This new approach facilitates analysis of observational data, the application of adjoint equations to retrospective study of processes governed by imitation models, and the study of computer models themselves. Specifically, the book discusses: Principles for constructing adjoint operators in nonlinear problems Properties of adjoint operators and solvability conditions for adjoint equations Perturbation algorithms using the adjoint equations theory for nonlinear problems in transport theory, quasilinear motion, substance transfer, and nonlinear data assimilation Known results on adjoint equations and perturbation algorithms in nonlinear problemsThis groundbreaking text contains some results that have no analogs in the scientific literature, opening unbounded possibilities in construction and application of adjoint equations to nonlinear problems of mathematical physics.
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Adjoint Equations and Perturbation Algorithms in Nonlinear Problems

Adjoint Equations and Perturbation Algorithms in Nonlinear Problems

Guri I. Marchuk; Valeri I. Agoshkov; Victor P. Shutyaev

CRC Press Inc
1996
sidottu
Sparked by demands inherent to the mathematical study of pollution, intensive industry, global warming, and the biosphere, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems is the first book ever to systematically present the theory of adjoint equations for nonlinear problems, as well as their application to perturbation algorithms. This new approach facilitates analysis of observational data, the application of adjoint equations to retrospective study of processes governed by imitation models, and the study of computer models themselves. Specifically, the book discusses: Principles for constructing adjoint operators in nonlinear problems Properties of adjoint operators and solvability conditions for adjoint equations Perturbation algorithms using the adjoint equations theory for nonlinear problems in transport theory, quasilinear motion, substance transfer, and nonlinear data assimilation Known results on adjoint equations and perturbation algorithms in nonlinear problemsThis groundbreaking text contains some results that have no analogs in the scientific literature, opening unbounded possibilities in construction and application of adjoint equations to nonlinear problems of mathematical physics.
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Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces

Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces

Mikhail I. Kamenskii; Valeri V. Obukhovskii; Pietro Zecca

De Gruyter
2001
sidottu
The theory of set-valued maps and of differential inclusion is developed in recent years both as a field of his own and as an approach to control theory. The book deals with the theory of semilinear differential inclusions in infinite dimensional spaces. In this setting, problems of interest to applications do not suppose neither convexity of the map or compactness of the multi-operators. These assumption implies the development of the theory of measure of noncompactness and the construction of a degree theory for condensing mapping. Of particular interest is the approach to the case when the linear part is a generator of a condensing, strongly continuous semigroup. In this context, the existence of solutions for the Cauchy and periodic problems are proved as well as the topological properties of the solution sets. Examples of applications to the control of transmission line and to hybrid systems are presented.
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Convex and Set-Valued Analysis

Convex and Set-Valued Analysis

Aram V. Arutyunov; Valeri Obukhovskii

De Gruyter
2016
isokokoinen pokkari
This textbook is devoted to a compressed and self-contained exposition of two important parts of contemporary mathematics: convex and set-valued analysis. In the first part, properties of convex sets, the theory of separation, convex functions and their differentiability, properties of convex cones in finite- and infinite-dimensional spaces are discussed. The second part covers some important parts of set-valued analysis. There the properties of the Hausdorff metric and various continuity concepts of set-valued maps are considered. The great attention is paid also to measurable set-valued functions, continuous, Lipschitz and some special types of selections, fixed point and coincidence theorems, covering set-valued maps, topological degree theory and differential inclusions. Contents:PrefacePart I: Convex analysisConvex sets and their propertiesThe convex hull of a set. The interior of convex setsThe affine hull of sets. The relative interior of convex setsSeparation theorems for convex setsConvex functionsClosedness, boundedness, continuity, and Lipschitz property of convex functionsConjugate functionsSupport functionsDifferentiability of convex functions and the subdifferentialConvex conesA little more about convex cones in infinite-dimensional spacesA problem of linear programmingMore about convex sets and convex hullsPart II: Set-valued analysisIntroduction to the theory of topological and metric spacesThe Hausdorff metric and the distance between setsSome fine properties of the Hausdorff metricSet-valued maps. Upper semicontinuous and lower semicontinuous set-valued mapsA base of topology of the spaceHc(X)Measurable set-valued maps. Measurable selections and measurable choice theoremsThe superposition set-valued operatorThe Michael theorem and continuous selections. Lipschitz selections. Single-valued approximationsSpecial selections of set-valued mapsDifferential inclusionsFixed points and coincidences of maps in metric spacesStability of coincidence points and properties of covering mapsTopological degree and fixed points of set-valued maps in Banach spacesExistence results for differential inclusions via the fixed point methodNotationBibliographyIndex
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Holographic Interferometry in Experimental Mechanics

Holographic Interferometry in Experimental Mechanics

Yuri I. Ostrovsky; Valeri P. Shchepinov; Victor V. Yakovlev

Springer-Verlag Berlin and Heidelberg GmbH Co. K
2013
nidottu
This monograph deals with diverse applications of holographic interferome­ try in experimental solid mechanics. Holographic interferometry has experienced a development of twenty years. It has enjoyed success and suffered some disappointments mainly due to early overestimation of its potential. At present, development of holo­ graphic interferometry is progressing primarily as a technique for quantita­ tive measurements. This is what motivated us to write this book - to ana­ lyze the quantitative methods of holographic interferometry. The fringe patterns obtained in holographic interferometry are graphi­ cally descriptive. In the general case, however, because they contain infor­ mation on the total vectors of displacement for points on the surface of a stressed body, the interpretation of these interferograms is much more complicated than in typical conventional interferometry. In addition, the high sensitivity of the method imposes new requirements on the loading of the objects understudy. New approaches to designing loading fixtures are needed in many cases to ensure the desired loading conditions. The wealth of information obtained in holographic interferometry necessitates the use of modern computational mathematics. Therefore, practical implementation of the various methods of holographic interferometry must overcome sub­ stantial difficulties requiring adequate knowledge in diverse areas of science such as coherent optics, laser technology, mechanics, and applied mathe­ matics. Experimental methods play a significant role in solid mechanics.
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Fractured Porous Media

Fractured Porous Media

Pierre M. Adler; Jean-François Thovert; Valeri V. Mourzenko

Oxford University Press
2012
sidottu
This book provides a systematic treatment of the geometrical and transport properties of fractures, fracture networks, and fractured porous media. It is divided into two major parts. The first part deals with geometry of individual fractures and of fracture networks. The use of the dimensionless density rationalizes the results for the percolation threshold of the networks. It presents the crucial advantage of grouping the numerical data for various fracture shapes. The second part deals mainly with permeability under steady conditions of fractures, fracture networks, and fractured porous media. Again the results for various types of networks can be rationalized by means of the dimensionless density. A chapter is dedicated to two phase flow in fractured porous media.
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Wavelets in Neuroscience

Wavelets in Neuroscience

Alexander E. Hramov; Alexey A. Koronovskii; Valeri A. Makarov; Vladimir A. Maksimenko; Alexey N. Pavlov; Evgenia Sitnikova

Springer Nature Switzerland AG
2021
sidottu
This book illustrates how modern mathematical wavelet transform techniques offer fresh insights into the complex behavior of neural systems at different levels: from the microscopic dynamics of individual cells to the macroscopic behavior of large neural networks. It also demonstrates how and where wavelet-based mathematical tools can provide an advantage over classical approaches used in neuroscience. The authors well describe single neuron and populational neural recordings.This 2nd edition discusses novel areas and significant advances resulting from experimental techniques and computational approaches developed since 2015, and includes three new topics:• Detection of fEPSPs in multielectrode LFPs recordings.• Analysis of Visual Sensory Processing in the Brain and BCI for Human Attention Control;• Analysis and Real-time Classification of Motor-related EEG Patterns;The book is a valuable resource for neurophysiologists and physicists familiar with nonlinear dynamical systems and data processing, as well as for graduate students specializing in these and related areas.
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Wavelets in Neuroscience

Wavelets in Neuroscience

Alexander E. Hramov; Alexey A. Koronovskii; Valeri A. Makarov; Vladimir A. Maksimenko; Alexey N. Pavlov; Evgenia Sitnikova

Springer Nature Switzerland AG
2022
nidottu
This book illustrates how modern mathematical wavelet transform techniques offer fresh insights into the complex behavior of neural systems at different levels: from the microscopic dynamics of individual cells to the macroscopic behavior of large neural networks. It also demonstrates how and where wavelet-based mathematical tools can provide an advantage over classical approaches used in neuroscience. The authors well describe single neuron and populational neural recordings.This 2nd edition discusses novel areas and significant advances resulting from experimental techniques and computational approaches developed since 2015, and includes three new topics:• Detection of fEPSPs in multielectrode LFPs recordings.• Analysis of Visual Sensory Processing in the Brain and BCI for Human Attention Control;• Analysis and Real-time Classification of Motor-related EEG Patterns;The book is a valuable resource for neurophysiologists and physicists familiar with nonlinear dynamical systems and data processing, as well as for graduate students specializing in these and related areas.
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Wavelets in Neuroscience

Wavelets in Neuroscience

Alexander E. Hramov; Alexey A. Koronovskii; Valeri A. Makarov; Alexey N. Pavlov; Evgenia Sitnikova

Springer-Verlag Berlin and Heidelberg GmbH Co. K
2014
sidottu
This book examines theoretical and applied aspects of wavelet analysis in neurophysics, describing in detail different practical applications of the wavelet theory in the areas of neurodynamics and neurophysiology and providing a review of fundamental work that has been carried out in these fields over the last decade.Chapters 1 and 2 introduce and review the relevant foundations of neurophysics and wavelet theory, respectively, pointing on one hand to the various current challenges in neuroscience and introducing on the other the mathematical techniques of the wavelet transform in its two variants (discrete and continuous) as a powerful and versatile tool for investigating the relevant neuronal dynamics.Chapter 3 then analyzes results from examining individual neuron dynamics and intracellular processes. The principles for recognizing neuronal spikes from extracellular recordings and the advantages of using wavelets to address these issues are described and combined with approaches based on wavelet neural networks (chapter 4). The features of time-frequency organization of EEG signals are then extensively discussed, from theory to practical applications (chapters 5 and 6). Lastly, the technical details of automatic diagnostics and processing of EEG signals using wavelets are examined (chapter 7).The book will be a useful resource for neurophysiologists and physicists familiar with nonlinear dynamical systems and data processing, as well as for graduate students specializing in the corresponding areas.
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Wavelets in Neuroscience

Wavelets in Neuroscience

Alexander E. Hramov; Alexey A. Koronovskii; Valeri A. Makarov; Alexey N. Pavlov; Evgenia Sitnikova

Springer-Verlag Berlin and Heidelberg GmbH Co. K
2016
nidottu
This book examines theoretical and applied aspects of wavelet analysis in neurophysics, describing in detail different practical applications of the wavelet theory in the areas of neurodynamics and neurophysiology and providing a review of fundamental work that has been carried out in these fields over the last decade.Chapters 1 and 2 introduce and review the relevant foundations of neurophysics and wavelet theory, respectively, pointing on one hand to the various current challenges in neuroscience and introducing on the other the mathematical techniques of the wavelet transform in its two variants (discrete and continuous) as a powerful and versatile tool for investigating the relevant neuronal dynamics.Chapter 3 then analyzes results from examining individual neuron dynamics and intracellular processes. The principles for recognizing neuronal spikes from extracellular recordings and the advantages of using wavelets to address these issues are described and combined with approaches based on wavelet neural networks (chapter 4). The features of time-frequency organization of EEG signals are then extensively discussed, from theory to practical applications (chapters 5 and 6). Lastly, the technical details of automatic diagnostics and processing of EEG signals using wavelets are examined (chapter 7).The book will be a useful resource for neurophysiologists and physicists familiar with nonlinear dynamical systems and data processing, as well as for graduate students specializing in the corresponding areas.
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Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures

Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures

Leonid I. Manevitch; Agnessa Kovaleva; Valeri Smirnov; Yuli Starosvetsky

Springer Verlag, Singapore
2017
sidottu
This book suggests a new common approach to the study of resonance energy transport based on the recently developed concept of Limiting Phase Trajectories (LPTs), presenting applications of the approach to significant nonlinear problems from different fields of physics and mechanics. In order to highlight the novelty and perspectives of the developed approach, it places the LPT concept in the context of dynamical phenomena related to the energy transfer problems and applies the theory to numerous problems of practical importance. This approach leads to the conclusion that strongly nonstationary resonance processes in nonlinear oscillator arrays and nanostructures are characterized either by maximum possible energy exchange between the clusters of oscillators (coherence domains) or by maximum energy transfer from an external source of energy to the chain. The trajectories corresponding to these processes are referred to as LPTs. The development and the use of the LPTs concept are motivated by the fact that non-stationary processes in a broad variety of finite-dimensional physical models are beyond the well-known paradigm of nonlinear normal modes (NNMs), which is fully justified either for stationary processes or for nonstationary non-resonance processes described exactly or approximately by the combinations of the non-resonant normal modes. Thus, the role of LPTs in understanding and analyzing of intense resonance energy transfer is similar to the role of NNMs for the stationary processes. The book is a valuable resource for engineers needing to deal effectively with the problems arising in the fields of mechanical and physical applications, when the natural physical model is quite complicated. At the same time, the mathematical analysis means that it is of interest to researchers working on the theory and numerical investigation of nonlinear oscillations.
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Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures

Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures

Leonid I. Manevitch; Agnessa Kovaleva; Valeri Smirnov; Yuli Starosvetsky

Springer Verlag, Singapore
2019
nidottu
This book suggests a new common approach to the study of resonance energy transport based on the recently developed concept of Limiting Phase Trajectories (LPTs), presenting applications of the approach to significant nonlinear problems from different fields of physics and mechanics. In order to highlight the novelty and perspectives of the developed approach, it places the LPT concept in the context of dynamical phenomena related to the energy transfer problems and applies the theory to numerous problems of practical importance. This approach leads to the conclusion that strongly nonstationary resonance processes in nonlinear oscillator arrays and nanostructures are characterized either by maximum possible energy exchange between the clusters of oscillators (coherence domains) or by maximum energy transfer from an external source of energy to the chain. The trajectories corresponding to these processes are referred to as LPTs. The development and the use of the LPTs concept are motivated by the fact that non-stationary processes in a broad variety of finite-dimensional physical models are beyond the well-known paradigm of nonlinear normal modes (NNMs), which is fully justified either for stationary processes or for nonstationary non-resonance processes described exactly or approximately by the combinations of the non-resonant normal modes. Thus, the role of LPTs in understanding and analyzing of intense resonance energy transfer is similar to the role of NNMs for the stationary processes. The book is a valuable resource for engineers needing to deal effectively with the problems arising in the fields of mechanical and physical applications, when the natural physical model is quite complicated. At the same time, the mathematical analysis means that it is of interest to researchers working on the theory and numerical investigation of nonlinear oscillations.
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Valeria

Valeria

C a Watts

Ballads Bards Bookhouse
2021
pokkari
Rogue and Ranger are twin sisters who have inherited the family estate. Ventura is a warren of endless halls and passageways on grounds covered in hills, forests and quiet, sandy bays. It is a paradise.Or so they thought...Things have changed since Rogue and Ranger explored Ventura as children. From the moment they cross the threshold they are plagued by a dark presence, stalked by one who would claim Ventura's treasures for themselves.Ventura is hiding ancient secrets, and an evil seeks to claim them for itself. Rogue and Ranger are in a race against time to find the answers hidden in their family's history and when they do, it is more than they ever could have imagined.Romira Royce, their ancestor and powerful sorcerer, built far more than Ventura Estate. The worlds he created are in danger of being lost to the darkness overtaking the estate and the only way to stop it is to reunite the Heart of Ventura.But... it is pieces across the Venturan Universe.Join Rogue and Ranger on their journey through the worlds of Ventura, meeting all manner of creatures in their attempt to find the Guardians, those charged with the care of the Heart.sCan they reunite it in time to save their home?
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Valery and Poe

Valery and Poe

Lois Vines

New York University Press
1992
sidottu
Edgar Allen Poe's influence on the twentieth century French writer Paul Valery was profound, much more so than on Baudelaire and Mallarme. This book is the first comprehensive study of Poe's influence of Valery and is based on Valery's own concept of literary influence. Valery discovered in Poe's tales and literary essays a Drama of the intellect that was to inspire his Evening with Monsieur teste, Agathe, and Introduction to the method of Leonardo Da Vinci. Valery's poetics and approach to literary criticism have direct connections to Poe's Philosophy of Composition and Poetic Principle. Valery's only essay devoted to his American mentor, On Poe's Eureka, recognizes the importance of the cosmological poem in Valery's intellectual development. Eureka awakened in him an interest in science and mathematics that lasted a lifetime and inspired him to apply scientific analysis to literary genius, the first writer to place creative work on an analytical basis and explore the psychological aspects of literature.
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Valera in Dialogue/in Dialogue with Valera

Valera in Dialogue/in Dialogue with Valera

Thomas R. Franz

Peter Lang Publishing Inc
2000
sidottu
Juan Valera (1824-1905) was Spain's only realist with a lifelong insistence that narrative privilege invention over testimony. Throughout Valera's lengthy career, his novels engaged in a running esthetic debate with those of his chief rivals, Galdos and Alas. This debate, chronicled in the present work, led to many compromises and ultimately produced, in the twentieth-century fiction of Valle-Inclan and Unamuno, a novelistic form, also detailed here, that exhibited clear debts to Valera's catalytic influence."
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