# Viability, Invariance and Applications

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## Viability Invariance and Applications

Author | : Ovidiu Carja,Mihai Necula,Ioan I. Vrabie |

Publsiher | : Elsevier |

Total Pages | : 356 |

Release | : 2007-07-18 |

ISBN 10 | : 9780080521664 |

ISBN 13 | : 0080521665 |

Language | : EN, FR, DE, ES & NL |

**Viability Invariance and Applications Book Review:**

The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time. The book includes the most important necessary and sufficient conditions for viability starting with Nagumo’s Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts. New concepts for multi-functions as the classical tangent vectors for functions Provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions Clarifying examples, illustrations and numerous problems, completely and carefully solved Illustrates the applications from theory into practice Very clear and elegant style

## Analele tiin ifice Ale Universit ii Al I Cuza Din Ia i

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2008 |

ISBN 10 | : |

ISBN 13 | : UCBK:C083615252 |

Language | : EN, FR, DE, ES & NL |

**Analele tiin ifice Ale Universit ii Al I Cuza Din Ia i Book Review:**

## System Modeling and Optimization

Author | : Christian Pötzsche,Clemens Heuberger,Barbara Kaltenbacher,Franz Rendl |

Publsiher | : Springer |

Total Pages | : 361 |

Release | : 2014-11-27 |

ISBN 10 | : 3662455048 |

ISBN 13 | : 9783662455043 |

Language | : EN, FR, DE, ES & NL |

**System Modeling and Optimization Book Review:**

This book is a collection of thoroughly refereed papers presented at the 26th IFIP TC 7 Conference on System Modeling and Optimization, held in Klagenfurt, Austria, in September 2013. The 34 revised papers were carefully selected from numerous submissions. They cover the latest progress in a wide range of topics such as optimal control of ordinary and partial differential equations, modeling and simulation, inverse problems, nonlinear, discrete, and stochastic optimization as well as industrial applications.

## Value Functions in Control Systems and Differential Games

Author | : Sławomir Plaskacz |

Publsiher | : Unknown |

Total Pages | : 119 |

Release | : 2003 |

ISBN 10 | : |

ISBN 13 | : UOM:39015069296039 |

Language | : EN, FR, DE, ES & NL |

**Value Functions in Control Systems and Differential Games Book Review:**

## Mathematical Analysis and Applications

Author | : V. Rădulescu,Vicentiu D. Radulescu,Constantin Niculescu (P.) |

Publsiher | : American Institute of Physics |

Total Pages | : 167 |

Release | : 2006-05-25 |

ISBN 10 | : |

ISBN 13 | : UOM:39015064105078 |

Language | : EN, FR, DE, ES & NL |

**Mathematical Analysis and Applications Book Review:**

This book comprises the proceedings of the International Conference on Mathematical Analysis and Applications, held in Craiova, Romania, 23-24 September 2005. The peer-reviewed papers presented here cover a range of topics at the interface between mathematical physics, numerical analysis, optimal control, and calculus of variations. The coverage includes nonlinear analysis and partial differential equations as well as classical mathematical analysis and dynamical systems.

## Viability Theory

Author | : Jean-Pierre Aubin,Alexandre M. Bayen,Patrick Saint-Pierre |

Publsiher | : Springer Science & Business Media |

Total Pages | : 803 |

Release | : 2011-07-13 |

ISBN 10 | : 9783642166846 |

ISBN 13 | : 3642166849 |

Language | : EN, FR, DE, ES & NL |

**Viability Theory Book Review:**

Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning fields that have traditionally developed in isolation. The purpose of this book is to present an initiation to applications of viability theory, explaining and motivating the main concepts and illustrating them with numerous numerical examples taken from various fields.

## Journal of analysis and its application

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2004 |

ISBN 10 | : |

ISBN 13 | : UOM:39015059084411 |

Language | : EN, FR, DE, ES & NL |

**Journal of analysis and its application Book Review:**

## Pure Mathematics and Applications

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2002 |

ISBN 10 | : |

ISBN 13 | : UOM:39015057387071 |

Language | : EN, FR, DE, ES & NL |

**Pure Mathematics and Applications Book Review:**

## Differential Equations

Author | : Ioan I Vrabie |

Publsiher | : World Scientific Publishing Company |

Total Pages | : 528 |

Release | : 2016-05-30 |

ISBN 10 | : 981474980X |

ISBN 13 | : 9789814749800 |

Language | : EN, FR, DE, ES & NL |

**Differential Equations Book Review:**

This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem. In addition, it contains simple introductions to some topics which are not usually included in classical textbooks: the exponential formula, conservation laws, generalized solutions, Caratheodory solutions, differential inclusions, variational inequalities, viability, invariance, and gradient systems. In this new edition, some typos have been corrected and two new topics have been added: Delay differential equations and differential equations subjected to nonlocal initial conditions. The bibliography has also been updated and expanded.

## SIAM Journal on Control and Optimization

Author | : Society for Industrial and Applied Mathematics |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2002 |

ISBN 10 | : |

ISBN 13 | : UCSD:31822020344586 |

Language | : EN, FR, DE, ES & NL |

**SIAM Journal on Control and Optimization Book Review:**

## Dynamic Systems and Applications

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2001 |

ISBN 10 | : |

ISBN 13 | : UOM:39015053954189 |

Language | : EN, FR, DE, ES & NL |

**Dynamic Systems and Applications Book Review:**

## Applicationes Mathematicae

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 1996 |

ISBN 10 | : |

ISBN 13 | : UOM:39015049363750 |

Language | : EN, FR, DE, ES & NL |

**Applicationes Mathematicae Book Review:**

## Acta arithmetica

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 1936 |

ISBN 10 | : |

ISBN 13 | : UCSD:31822023349400 |

Language | : EN, FR, DE, ES & NL |

**Acta arithmetica Book Review:**

## Discussiones Mathematicae

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 1995 |

ISBN 10 | : |

ISBN 13 | : UOM:39015049071668 |

Language | : EN, FR, DE, ES & NL |

**Discussiones Mathematicae Book Review:**

## Differential Equations an Introduction to Basic Concepts Third Edition

Author | : Ioan I. Vrabie |

Publsiher | : World Scientific Publishing Company |

Total Pages | : 528 |

Release | : 2016-05-30 |

ISBN 10 | : 9789814759205 |

ISBN 13 | : 9814759201 |

Language | : EN, FR, DE, ES & NL |

**Differential Equations an Introduction to Basic Concepts Third Edition Book Review:**

This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem. In addition, it contains simple introductions to some topics which are not usually included in classical textbooks: the exponential formula, conservation laws, generalized solutions, Caratheodory solutions, differential inclusions, variational inequalities, viability, invariance, and gradient systems.In this new edition, some typos have been corrected and two new topics have been added: Delay differential equations and differential equations subjected to nonlocal initial conditions. The bibliography has also been updated and expanded.

## Mathematical Reviews

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2008 |

ISBN 10 | : |

ISBN 13 | : UOM:39015082440754 |

Language | : EN, FR, DE, ES & NL |

**Mathematical Reviews Book Review:**

## Viability and Resilience of Complex Systems

Author | : Guillaume Deffuant,Nigel Gilbert |

Publsiher | : Springer |

Total Pages | : 224 |

Release | : 2011-08-03 |

ISBN 10 | : 3642204236 |

ISBN 13 | : 9783642204234 |

Language | : EN, FR, DE, ES & NL |

**Viability and Resilience of Complex Systems Book Review:**

One common characteristics of a complex system is its ability to withstand major disturbances and the capacity to rebuild itself. Understanding how such systems demonstrate resilience by absorbing or recovering from major external perturbations requires both quantitative foundations and a multidisciplinary view on the topic. This book demonstrates how new methods can be used to identify the actions favouring the recovery from perturbations. Examples discussed include bacterial biofilms resisting detachment, grassland savannahs recovering from fire, the dynamics of language competition and Internet social networking sites overcoming vandalism. The reader is taken through an introduction to the idea of resilience and viability and shown the mathematical basis of the techniques used to analyse systems. The idea of individual or agent-based modelling of complex systems is introduced and related to analytically tractable approximations of such models. A set of case studies illustrates the use of the techniques in real applications, and the final section describes how one can use new and elaborate software tools for carrying out the necessary calculations. The book is intended for a general scientific audience of readers from the natural and social sciences, yet requires some mathematics to gain a full understanding of the more theoretical chapters. It is an essential point of reference for those interested in the practical application of the concepts of resilience and viability

## Consistency Problems for Heath Jarrow Morton Interest Rate Models

Author | : Damir Filipovic |

Publsiher | : Springer |

Total Pages | : 138 |

Release | : 2004-11-02 |

ISBN 10 | : 354044548X |

ISBN 13 | : 9783540445487 |

Language | : EN, FR, DE, ES & NL |

**Consistency Problems for Heath Jarrow Morton Interest Rate Models Book Review:**

Bond markets differ in one fundamental aspect from standard stock markets. While the latter are built up to a finite number of trade assets, the underlying basis of a bond market is the entire term structure of interest rates: an infinite-dimensional variable which is not directly observable. On the empirical side, this necessitates curve-fitting methods for the daily estimation of the term structure. Pricing models, on the other hand, are usually built upon stochastic factors representing the term structure in a finite-dimensional state space. Written for readers with knowledge in mathematical finance (in particular interest rate theory) and elementary stochastic analysis, this research monograph has threefold aims: to bring together estimation methods and factor models for interest rates, to provide appropriate consistency conditions and to explore some important examples.

## Differential Games and Applications

Author | : Tamer S. Başar,Tamer Başar,Pierre Bernhard |

Publsiher | : Unknown |

Total Pages | : 201 |

Release | : 1989 |

ISBN 10 | : |

ISBN 13 | : UOM:39015012051796 |

Language | : EN, FR, DE, ES & NL |

**Differential Games and Applications Book Review:**

This volume contains fifteen articles on the topic of differential and dynamic games, focusing on both theory and applications. It covers a variety of areas and presents recent developments on topics of current interest. It should be useful to researchers in differential and dynamic games, systems and control, operations research and mathematical economics.

## Nonlinear Dynamics and Controls

Author | : Anil K. Bajaj,Navaratnam Sri Namachchivaya,Matthew A. Franchek |

Publsiher | : Amer Society of Mechanical |

Total Pages | : 239 |

Release | : 1996 |

ISBN 10 | : |

ISBN 13 | : UOM:39015040642434 |

Language | : EN, FR, DE, ES & NL |

**Nonlinear Dynamics and Controls Book Review:**

Proceedings of the November 1996 symposium. Contains 35 papers related to theoretical, experimental, and computational aspects of dynamics, vibration, and control of nonlinear mechanical and structural systems. The papers are divided according to the symposium's seven technical sessions: analytical