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Oscillation Theory for Difference and Functional Differential Equations, R.P. Agarwal; Said R. Grace; Donal O`Regan


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Автор: R.P. Agarwal; Said R. Grace; Donal O`Regan
Название:  Oscillation Theory for Difference and Functional Differential Equations
ISBN: 9789048154470
Издательство: Springer
Классификация: ISBN-10: 9048154472
Обложка/Формат: Paperback
Страницы: 338
Вес: 0.49 кг.
Дата издания: 06.12.2010
Язык: English
Размер: 234 x 156 x 18
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: This monograph is devoted to a rapidly developing area of research of the qualitative theory of difference and functional differential equations. In fact, in the last 25 years Oscillation Theory of difference and functional differential equations has attracted many researchers. This has resulted in hundreds of research papers in every major mathematical journal, and several books. In the first chapter of this monograph, we address oscillation of solutions to difference equations of various types. Here we also offer several new fundamental concepts such as oscillation around a point, oscillation around a sequence, regular oscillation, periodic oscillation, point-wise oscillation of several orthogonal polynomials, global oscillation of sequences of real- valued functions, oscillation in ordered sets, ( , R, )-oscillate, oscillation in linear spaces, oscillation in Archimedean spaces, and oscillation across a family. These concepts are explained through examples and supported by interesting results. In the second chapter we present recent results pertaining to the oscil- lation of n-th order functional differential equations with deviating argu- ments, and functional differential equations of neutral type. We mainly deal with integral criteria for oscillation. While several results of this chapter were originally formulated for more complicated and/or more general differ- ential equations, we discuss here a simplified version to elucidate the main ideas of the oscillation theory of functional differential equations. Further, from a large number of theorems presented in this chapter we have selected the proofs of only those results which we thought would best illustrate the various strategies and ideas involved.

Oscillation Theory for Difference and Functional Differential Equations

Автор: R.P. Agarwal; Said R. Grace; Donal O`Regan
Название: Oscillation Theory for Difference and Functional Differential Equations
ISBN: 0792362896 ISBN-13(EAN): 9780792362890
Издательство: Springer
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Цена: 111790.00 T
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Описание: This text reviews material from more than 300 publications on the oscillation theory of difference and functional differential equations of various types.

Oscillation Theory of Two-Term Differential Equations

Автор: Uri Elias
Название: Oscillation Theory of Two-Term Differential Equations
ISBN: 0792344472 ISBN-13(EAN): 9780792344476
Издательство: Springer
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Цена: 88500.00 T
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Описание: Deals with oscillation theory. This title considers the two-term linear differential equations Lny + p(x)y = 0, where Ln is a disconjugate operator of order n and p(x) has a fixed sign. It pays attention to the equation y(n) + p(x)y = 0.

Oscillation Theory of Two-Term Differential Equations

Автор: Uri Elias
Название: Oscillation Theory of Two-Term Differential Equations
ISBN: 9048148065 ISBN-13(EAN): 9789048148066
Издательство: Springer
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Цена: 130390.00 T
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Описание: The other restricts its area of interest to certain families of equations and studies in maximal details phenomena which characterize only those equations. Among them we find third and fourth order equations, self adjoint equations, etc.

Oscillators and Oscillator Systems

Автор: Jan R. Westra; Chris J.M. Verhoeven; Arthur H.M. v
Название: Oscillators and Oscillator Systems
ISBN: 0792386523 ISBN-13(EAN): 9780792386520
Издательство: Springer
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Цена: 156720.00 T
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Описание: In many electronic systems, such as telecommunication or measurement systems, oscillations play an essential role in the information processing. Oscillators and Oscillator Systems: Classification, Analysis and Synthesis takes a systematic approach to the design of high-performance oscillators and oscillator systems.

Oscillators and Oscillator Systems

Автор: Jan R. Westra; Chris J.M. Verhoeven; Arthur H.M. v
Название: Oscillators and Oscillator Systems
ISBN: 1441951105 ISBN-13(EAN): 9781441951106
Издательство: Springer
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Цена: 130590.00 T
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Описание: In many electronic systems, such as telecommunication or measurement systems, oscillations play an essential role in the information processing. Oscillators and Oscillator Systems: Classification, Analysis and Synthesis takes a systematic approach to the design of high-performance oscillators and oscillator systems.

Non-Oscillation Domains of Differential Equations with Two Parameters

Автор: Angelo B. Mingarelli; S. Gotskalk Halvorsen
Название: Non-Oscillation Domains of Differential Equations with Two Parameters
ISBN: 3540500782 ISBN-13(EAN): 9783540500780
Издательство: Springer
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Цена: 23280.00 T
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Описание: Offers an introduction to single linear differential equations (systems) with two parameters and extensions to difference equations and Stieltjes integral equations. This book is suitable for graduate students and researchers.

Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations

Автор: R.P. Agarwal; Said R. Grace; Donal O`Regan
Название: Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations
ISBN: 9048160952 ISBN-13(EAN): 9789048160952
Издательство: Springer
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Цена: 93160.00 T
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Frequency Methods in Oscillation Theory

Автор: G.A. Leonov; I.M. Burkin; A.I. Shepeljavyi
Название: Frequency Methods in Oscillation Theory
ISBN: 0792338960 ISBN-13(EAN): 9780792338963
Издательство: Springer
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Цена: 102480.00 T
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Описание: The linear theory of oscillations traditionally operates with frequency representa- tions based on the concepts of a transfer function and a frequency response. The universality of the critria of Nyquist and Mikhailov and the simplicity and obvi- ousness of the application of frequency and amplitude - frequency characteristics in analysing forced linear oscillations greatly encouraged the development of practi- cally important nonlinear theories based on various forms of the harmonic balance hypothesis 303]. Therefore mathematically rigorous frequency methods of investi- gating nonlinear systems, which appeared in the 60s, also began to influence many areas of nonlinear theory of oscillations. First in this sphere of influence was a wide range of problems connected with multidimensional analogues of the famous van der Pol equation describing auto- oscillations of generators of various radiotechnical devices. Such analogues have as a rule a unique unstable stationary point in the phase space and are Levinson dis- sipative. One of the pioneering works in this field, which started the investigation of a three-dimensional analogue of the van der Pol equation, was K. O. Friedrichs's paper 123]. The author suggested a scheme for constructing a positively invariant set homeomorphic to a torus, by means of which the existence of non-trivial periodic solutions was established. That scheme was then developed and improved for dif- ferent classes of multidimensional dynamical systems 131, 132, 297, 317, 334, 357, 358]. The method of Poincare mapping 12, 13, 17] in piecewise linear systems was another intensively developed direction.

Nonautonomous linear hamiltonian systems: oscillation, spectral theory and control

Автор: Johnson, Russell Obaya, Rafael Novo, Sylvia Nunez, Carmen Fabbri, Roberta
Название: Nonautonomous linear hamiltonian systems: oscillation, spectral theory and control
ISBN: 3319290231 ISBN-13(EAN): 9783319290232
Издательство: Springer
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Цена: 102480.00 T
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Описание: This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence.

Oscillation Theory

Автор: K. Kreith
Название: Oscillation Theory
ISBN: 3540062580 ISBN-13(EAN): 9783540062585
Издательство: Springer
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Цена: 23280.00 T
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Frequency Methods in Oscillation Theory

Автор: G.A. Leonov; I.M. Burkin; A.I. Shepeljavyi
Название: Frequency Methods in Oscillation Theory
ISBN: 9401065705 ISBN-13(EAN): 9789401065702
Издательство: Springer
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Цена: 102480.00 T
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Multimodal Oscillation-based Connectivity Theory

Автор: Palva
Название: Multimodal Oscillation-based Connectivity Theory
ISBN: 331932263X ISBN-13(EAN): 9783319322636
Издательство: Springer
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Цена: 113190.00 T
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Описание:

Systems-level neuronal mechanisms that coordinate the temporally, anatomically, and functionally distributed neuronal activity into coherent cognitive operations in the human brain have remained poorly understood. In humans, neuronal oscillations and synchronization can be recorded non-invasively with electro- and magnetoencephalography (EEG and MEG) that have excellent temporal resolution and an adequate spatial resolution when combined with source-reconstruction methods. In this book, leading authors in the field describe how recent methodological advances have paved the way to several major breakthroughs in the observations of large-scale synchrony from human non-invasive MEG data.
This volume also presents the caveats influencing analyses of synchronization. These include the non-homogeneous sensitivity of MEG to superficial cortical sources, and, most importantly, the multitude of consequences of linear mixing. Linear mixing is an immense confounder in the sensor-level analyses of synchronization, but is also present at the source level. Approaches that can be used to avoid or compensate for these issues are then discussed.
Thereafter, several authors take up a number of the functional roles that large-scale synchronization has in cognition. The authors assess how the spatio–temporal and –spectral organization and strength of both local and large-scale synchronized networks are associated with conscious sensory perception, visual working memory functions, and attention. These chapters summarize several lines of research showing how the strength of local and inter-areal oscillations in both cortical and subcortical brain structures is correlated with cognitive functions. Together these data suggest that synchronized neuronal oscillations may be a systems-level neuronal mechanism underlying the coordination of distributed processing in human cognition. In line with this argument, other authors go on to describe how oscillations and synchronization are altered in clinical populations, complementing the data presented on healthy subjects.
Importantly, this book includes chapters from authors using many different approaches to the analyses of neuronal oscillations, ranging from local oscillatory activities to the usage of graph theoretical tools in the analyses of synchronization. In this way the present volume provides a comprehensive view on the analyses and functional significance of neuronal oscillations in humans. This book is aimed at doctoral and post-doctoral students as well as research scientists in the fields of cognitive neuroscience, psychology, medicine, and neurosciences.


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