Global Behavior of Nonlinear Difference Equations of Higher Order with Applications (Mathematics and Its Applications)

Book Description

This volume presents a systematic study of the global behaviour of solutions of nonlinear scalar difference equations of order greater than one. Of particular interest are aspects such as global asymptotic stability, periodicity, permanence and persistence, and also semicycles of solutions. As well as exposing the reader to the very frontiers of the subject, important open problems are also formulated.
The book has six chapters. Chapter 1 presents an introduction to the subject and deals with preliminaries. Chapter 2 considers global stability results. Chapter 3 is devoted to rational recursive structures. Chapter 4 describes various applications. The topic of Chapter 5 is periodic cycles, and Chapter 6 discusses a number of open problems and conjectures involving interesting types of difference equations. Each chapter includes notes and references. The volume concludes with three appendices, a comprehensive bibliography, and name and subject indices.
For graduate students and researchers whose work involves difference and differential equations.

Applied Nonlinear Time Series Analysis: Applications in Physics, Physiology and Finance (World Scientific Series on Nonlinear Science Series a)

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Applied Nonlinear Time Series Analysis: Applications in Physics, Physiology and Finance (World Scientific Series on Nonlinear Science Series a)
Michael Small
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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ASIN: 981256117X

Variational Methods for Potential Operator Equations: With Applications to Nonlinear Elliptic Equations (De Gruyter Studies in Mathematics)

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Variational Methods for Potential Operator Equations: With Applications to Nonlinear Elliptic Equations (De Gruyter Studies in Mathematics)
Jan Chabrowski
Manufacturer: Walter de Gruyter
ProductGroup: Book
Binding: Hardcover

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ASIN: 311015269X

Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems (Ergebnisse der Mathematik und ihrer Grenzgebiete. ... / A Series of Modern Surveys in Mathematics)

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Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems (Ergebnisse der Mathematik und ihrer Grenzgebiete. ... / A Series of Modern Surveys in Mathematics)
Michael Struwe
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540664793

Book Description

Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radó. The book gives a concise introduction to variational methods and presents an overview of areas of current research in the field. The third edition gives a survey on new developments in the field. References have been updated and a small number of mistakes have been rectified.

Nonlinear Regression Analysis and Its Applications (Wiley Series in Probability and Statistics)

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Great book about a complex subject.
watch out
excellent and practical text on nonlinear regression

Nonlinear Regression Analysis and Its Applications (Wiley Series in Probability and Statistics)
Douglas M. Bates , and Donald G. Watts
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Paperback

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ASIN: 0470139005

Book Description

A balanced presentation of the theoretical, practical, and computational aspects of nonlinear regression. This book provides background material on linear regression, including a geometrical development for linear and nonlinear least squares. The authors employ real data sets throughout, and their extensive use of geometric constructs and continuing examples makes the progression of ideas appear very natural. The book also includes pseudocode for computing algorithms.

Customer Reviews:

Great book about a complex subject........2006-10-02

I am a non-statistics graduate student, but I needed to learn this material for my thesis project. Nonlinear regression is definitely an advanced topic, but with only one class in matrix algebra and a year of calculus, I was able to understand and follow along. Many sections I had to re-read a few times, but they do make sense. I don't expect that this topic could be any more simply put at this level of detail. Bonus: Bates is an author of the nls function in R. All the terminology in this book matches the terminolgy in the function parameters.

watch out.......2003-10-02

If you are looking for some general guidelines into non-linear regression this is NOT for you. This is way over basic if not over intermediate bordering on super advanced non-linear regression discussion. The beginner and fairly knowledgeable person that is looking for some basic insight into non-linear work should stay away from this. A long way from this!

excellent and practical text on nonlinear regression.......2001-04-21

Along with Gallant's book on nonlinear regression this book is one of the best. It is on an intermediate level and assumes some knowledge of linear regression. Notable unique aspects of the book are (1) good use of geometry, (2) discussion of derivative free methods, (3) use of profile likelihood and profile t plots and (4) measures of degree of nonlinearity of the problem. The authors also provide many real world applications directly from their consulting experience.

Book Description

With the discovery of type-II superconductivity by Abrikosov, the prediction of vortex lattices, and their experimental observation, quantized vortices have become a central object of study in superconductivity, superfluidity, and Bose--Einstein condensation. This book presents the mathematics of superconducting vortices in the framework of the acclaimed two-dimensional Ginzburg-Landau model, with or without magnetic field, and in the limit of a large Ginzburg-Landau parameter, kappa.

This text presents complete and mathematically rigorous versions of both results either already known by physicists or applied mathematicians, or entirely new. It begins by introducing mathematical tools such as the vortex balls construction and Jacobian estimates. Among the applications presented are: the determination of the vortex densities and vortex locations for energy minimizers in a wide range of regimes of applied fields, the precise expansion of the so-called first critical field in a bounded domain, the existence of branches of solutions with given numbers of vortices, and the derivation of a criticality condition for vortex densities of non-minimizing solutions. Thus, this book retraces in an almost entirely self-contained way many results that are scattered in series of articles, while containing a number of previously unpublished results as well.

The book also provides a list of open problems and a guide to the increasingly diverse mathematical literature on Ginzburg--Landau related topics. It will benefit both pure and applied mathematicians, physicists, and graduate students having either an introductory or an advanced knowledge of the subject.

Modelling and Control of Mini-Flying Machines (Advances in Industrial Control)

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Modelling and Control of Mini-Flying Machines (Advances in Industrial Control)
Pedro Castillo , Rogelio Lozano , and Alejandro E. Dzul
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Accessories:

ASIN: 1852339578

Book Description

Problems in the motion control of aircraft are of perennial interest to the control engineer as they tend to be of complex and nonlinear nature.

Modelling and Control of Mini-Flying Machines is an exposition of models developed for various types of mini-aircraft:

planar Vertical Take-off and Landing aircraft;
helicopters;
quadrotor mini-rotorcraft;
other fixed-wing aircraft;
blimps;

for each of which it propounds:

detailed models derived from Euler-Lagrange methods;
appropriate nonlinear control strategies and convergence properties;
real-time experimental comparisons of the performance of control algorithms;
review of the principal sensors, on-board electronics, real-time architecture and communications systems for mini-flying machine control, including discussion of their performance;
detailed explanation of the use of the Kalman filter to flying machine localization.

To researchers and students in nonlinear control and its applications Modelling and Control of Mini-Flying Machines provides valuable insights to the application of real-time nonlinear techniques in an always challenging area.

Nonlinear Time Series Analysis: Methods and Applications (Nonlinear Time Series and Chaos)

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Passion
Extremely disappointing.
Dramatic, chaotic and yet analytic.

Nonlinear Time Series Analysis: Methods and Applications (Nonlinear Time Series and Chaos)
Cees Diks
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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Customer Reviews:

Passion.......2001-03-02

Of course there are many books dealing with the relationship between non-linear time series and chaos. It resembles the situation where one has to choose among two women that you both love, but after spending a weekend without passion with one of them, you know where to go for. After reading the book by Diks, and comparing it to related work, I can only come to the conclusion that it stands out. The book is clear, well written, and obviously relevant to theorists working in such divergent fields as statistics, finance, and physics. To each professor supervising a Ph.D. student I would therefore like to say: put it on the required reading list and if necessary use to force to make them on the subjects discussed by Diks.

Extremely disappointing........2001-02-26

This is not my first book about nonlinear time series and chaos theory and really i'm just wondering how it get published. I'm trying to find something positive to say but i cannot. I cannot recall what i did learn from it: just one thing, testing for reversibility. Ok, that's rather short for a book, a paper would have been sufficient, and less costly. I've just wasted my money on this. In addition, i'm not the kind of reviewer who is used to give 1 star to a good book, it has to be very bad to get that.

Rather go to Kantz or Abarbanel for useful books on nonlinear time series analysis...

Dramatic, chaotic and yet analytic........2000-05-04

Seldomly I have read a book on this subject which was so clear and well written. Diks turns out to be a captivating writer, who does not scare away from truth, equations, or Greek letters. I'm waiting for part 2, to see how the story ends.

Nonlinear Analysis (Series in Mathematical Analysis and Applications)

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Nonlinear Analysis (Series in Mathematical Analysis and Applications)
Leszek Gasinski , and Nikolaos S. Papageorgiou
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 1584884843

Book Description

Nonlinear analysis is a broad, interdisciplinary field characterized by a remarkable mixture of analysis, topology, and applications. Its concepts and techniques provide the tools for developing more realistic and accurate models for a variety of phenomena encountered in fields ranging from engineering and chemistry to economics and biology. This volume focuses on topics in nonlinear analysis pertinent to the theory of boundary value problems and their application in areas such as control theory and the calculus of variations. It complements the many other books on nonlinear analysis by addressing topics previously discussed fully only in scattered research papers. These include recent results on critical point theory, nonlinear differential operators, and related regularity and comparison principles. The rich variety of topics, both theoretical and applied, make Nonlinear Analysis useful to anyone, whether graduate student or researcher, working in analysis or its applications in optimal control, theoretical mechanics, or dynamical systems. An appendix contains all of the background material needed, and a detailed bibliography forms a guide for further study.

Variational Methods in Shape Optimization Problems (Progress in Nonlinear Differential Equations and Their Applications)

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Variational Methods in Shape Optimization Problems (Progress in Nonlinear Differential Equations and Their Applications)
Dorin Bucur , and Giuseppe Buttazzo
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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ASIN: 0817643591

Book Description

The study of shape optimization problems encompasses a wide spectrum of academic research with numerous applications to the real world. In this work these problems are treated from both the classical and modern perspectives and target a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems.

Key topics and features:

* Presents foundational introduction to shape optimization theory

* Studies certain classical problems: the isoperimetric problem and the Newton problem involving the best aerodynamical shape, and optimization problems over classes of convex domains

* Treats optimal control problems under a general scheme, giving a topological framework, a survey of "gamma"-convergence, and problems governed by ODE

* Examines shape optimization problems with Dirichlet and Neumann conditions on the free boundary, along with the existence of classical solutions

* Studies optimization problems for obstacles and eigenvalues of elliptic operators

* Poses several open problems for further research

* Substantial bibliography and index

Driven by good examples and illustrations and requiring only a standard knowledge in the calculus of variations, differential equations, and functional analysis, the book can serve as a text for a graduate course in computational methods of optimal design and optimization, as well as an excellent reference for applied mathematicians addressing functional shape optimization problems.

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