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This monograph discusses the issues of stability and the control of impulsive systems on hybrid time domains, with systems presented on discrete-time domains, continuous-time domains, and hybrid-time domains (time scales). Research on impulsive systems has recently attracted increased interest around the globe, and significant progress has been made in the theory and application of these systems. This book introduces recent developments in impulsive systems and fundamentals of various types of differential and difference equations. It also covers studies in stability related to time delays and other various control applications on the different impulsive systems. In addition to the analyses presented on dynamical systems that are with or without delays or impulses, this book concludes with possible future directions pertaining to this research.

Differentiable dynamical systems. --- Systems theory. --- Dynamical Systems and Ergodic Theory. --- Systems Theory, Control. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Dynamics. --- Ergodic theory. --- System theory. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Systems, Theory of --- Systems science --- Science --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Philosophy

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This book is aimed toward graduate students and researchers in mathematics, physics and engineering interested in the latest developments in analytic inequalities, Hilbert-Type and Hardy-Type integral inequalities, and their applications. Theories, methods, and techniques of real analysis and functional analysis are applied to equivalent formulations of Hilbert-type inequalities, Hardy-type integral inequalities as well as their parameterized reverses. Special cases of these integral inequalities across an entire plane are considered and explained. Operator expressions with the norm and some particular analytic inequalities are detailed through several lemmas and theorems to provide an extensive account of inequalities and operators. .

Operator theory. --- Differentiable dynamical systems. --- Mathematics. --- Numerical analysis. --- Operator Theory. --- Dynamical Systems and Ergodic Theory. --- Real Functions. --- Numerical Analysis. --- Mathematical analysis --- Math --- Science --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Functional analysis --- Integral inequalities. --- Inequalities (Mathematics) --- Dynamics. --- Ergodic theory. --- Functions of real variables. --- Real variables --- Functions of complex variables --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics

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This book contains the proceedings of the Seventh National Conference of the Italian Systems Society. The title, Systemics of Incompleteness and Quasi-Systems, aims to underline the need for Systemics and Systems Science to deal with the concepts of incompleteness and quasiness. Classical models of Systemics are intended to represent comprehensive aspects of phenomena and processes. They consider the phenomena in their temporal and spatial completeness. In these cases, possible incompleteness in the modelling is assumed to have a provisional or practical nature, which is still under study, and because there is no theoretical reason why the modelling cannot be complete. In principle, this is a matter of non-complex phenomena, to be considered using the concepts of the First Systemics. When dealing with emergence, there are phenomena which must be modelled by systems having multiple models, depending on the aspects being taken into consideration. Here, incompleteness in the modelling is intrinsic, theoretically relating changes in properties, structures, and status of system. Rather than consider the same system parametrically changing over time, we consider sequences of systems coherently. We consider contexts and processes for which modelling is incomplete, being related to only some properties, as well as those for which such modelling is theoretically incomplete—as in the case of processes of emergence and for approaches considered by the Second Systemics. In this regard, we consider here the generic concept of quasi explicating such incompleteness. The concept of quasi is used in various disciplines including quasi-crystals, quasi-particles, quasi-electric fields, and quasi-periodicity. In general, the concept of quasiness for systems concerns their continuous structural changes which are always meta-stable, waiting for events to collapse over other configurations and possible forms of stability; whose equivalence depends on the type of phenomenon under study. Interest in the concept of quasiness is not related to its meaning of rough approximation, but because it indicates an incompleteness which is structurally sufficient to accommodate processes of emergence and sustain coherence or generate new, equivalent or non-equivalent, levels. The conference was devoted to identifying, discussing and understanding possible interrelationships of theoretical disciplinary improvements, recognised as having prospective fundamental roles for a new Quasi-Systemics. The latter should be able to deal with problems related to complexity in more general and realistic ways, when a system is not always a system and not always the same system. In this context, the inter-disciplinarity should consist, for instance, of a constructionist, incomplete, non-ideological, multiple, contradiction-tolerant, Systemics, always in progress, and in its turn, emergent.

System theory. --- System analysis. --- Social systems. --- Differentiable dynamical systems. --- Operations research. --- Systems theory. --- Dynamical Systems and Ergodic Theory. --- Operations Research/Decision Theory. --- Systems Theory, Control. --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Dynamics. --- Ergodic theory. --- Decision making. --- Systems, Theory of --- Systems science --- Science --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Philosophy --- Decision making

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This book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations. This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.

Distribution (Probability theory. --- Numerical analysis. --- Differentiable dynamical systems. --- Differential equations, partial. --- Probability Theory and Stochastic Processes. --- Numerical Analysis. --- Dynamical Systems and Ergodic Theory. --- Partial Differential Equations. --- Partial differential equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Mathematical analysis --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Stochastic differential equations. --- Fokker-Planck equation --- Probabilities. --- Dynamics. --- Ergodic theory. --- Partial differential equations. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

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This book is devoted to Prof. Juan J. Nieto, on the occasion of his 60th birthday. Juan José Nieto Roig (born 1958, A Coruña) is a Spanish mathematician, who has been a Professor of Mathematical Analysis at the University of Santiago de Compostela since 1991. His most influential contributions to date are in the area of differential equations. Nieto received his degree in Mathematics from the University of Santiago de Compostela in 1980. He was then awarded a Fulbright scholarship and moved to the University of Texas at Arlington where he worked with Professor V. Lakshmikantham. He received his Ph.D. in Mathematics from the University of Santiago de Compostela in 1983. Nieto's work may be considered to fall within the ambit of differential equations, and his research interests include fractional calculus, fuzzy equations and epidemiological models. He is one of the world’s most cited mathematicians according to Web of Knowledge, and appears in the Thompson Reuters Highly Cited Researchers list. Nieto has also occupied different positions at the University of Santiago de Compostela, such as Dean of Mathematics and Director of the Mathematical Institute. He has also served as an editor for various mathematical journals, and was the editor-in-chief of the journal Nonlinear Analysis: Real World Applications from 2009 to 2012. In 2016, Nieto was admitted as a Fellow of the Royal Galician Academy of Sciences. This book consists of contributions presented at the International Conference on Nonlinear Analysis and Boundary Value Problems, held in Santiago de Compostela, Spain, 4th-7th September 2018. Covering a variety of topics linked to Nieto’s scientific work, ranging from differential, difference and fractional equations to epidemiological models and dynamical systems and their applications, it is primarily intended for researchers involved in nonlinear analysis and boundary value problems in a broad sense. .

Differential Equations. --- Differential equations, partial. --- Functional equations. --- Differentiable dynamical systems. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Difference and Functional Equations. --- Dynamical Systems and Ergodic Theory. --- Mathematical and Computational Biology. --- Mathematical Applications in the Physical Sciences. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Partial differential equations --- 517.91 Differential equations --- Equations, Functional --- Functional analysis --- Boundary value problems --- Differential equations. --- Partial differential equations. --- Difference equations. --- Dynamics. --- Ergodic theory. --- Biomathematics. --- Mathematical physics. --- Physical mathematics --- Physics --- Biology --- Mathematics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Calculus of differences --- Differences, Calculus of --- Equations, Difference