The Resource Discrete and continuous models in the theory of networks, Fatihcan M. Atay, Pavel B. Kurasov, Delio Mugnolo, editors
Discrete and continuous models in the theory of networks, Fatihcan M. Atay, Pavel B. Kurasov, Delio Mugnolo, editors
Resource Information
The item Discrete and continuous models in the theory of networks, Fatihcan M. Atay, Pavel B. Kurasov, Delio Mugnolo, editors represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Discrete and continuous models in the theory of networks, Fatihcan M. Atay, Pavel B. Kurasov, Delio Mugnolo, editors represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 This book contains contributions from the participants of the research group hosted by the ZiF  Center for Interdisciplinary Research at the University of Bielefeld during the period 20132017 as well as from the conclusive conference organized at Bielefeld in December 2017. The contributions consist of original research papers: they mirror the scientific developments fostered by this research program or the stateoftheart results presented during the conclusive conference. The volume covers current research in the areas of operator theory and dynamical systems on networks and their applications, indicating possible future directions. The book will be interesting to researchers focusing on the mathematical theory of networks; it is unique as, for the first time, continuous network models  a subject that has been blooming in the last twenty years  are studied alongside more classical and discrete ones. Thus, instead of two different worlds often growing independently without much intercommunication, a new path is set, breaking with the tradition. The fruitful and beneficial exchange of ideas and results of both communities is reflected in this book
 Language
 eng
 Extent
 1 online resource
 Contents

 Intro  Preface  Contents  Stability Matters for ReactionDiffusionEquations on Metric Graphs Under the AntiKirchhoff Vertex Condition  1 Metric Graphs  2 Stationary Solutions  3 Stability  4 Nonlinearities Vanishing at 0  5 Constant Nonlinearities  6 Odd Nonlinearities  7 Loops  References  ManyParticle Quantum Graphs: A Review  1 Introduction  2 Preliminaries  2.1 OneParticle Quantum Graphs  2.2 ManyParticle Kinematics  3 Singular Pair Interactions  3.1 VertexInduced Singular Interactions  3.2 Contact Interactions
 3.3 A LiebLiniger Model on Graphs  4 BoseEinstein Condensation  4.1 Free Bosons  4.2 Interacting Bosons  5 Exactly Solvable ManyParticle Quantum Graphs  6 ManyParticle Models on a Quantum Wire  6.1 The Model Without HardWall Binding Potential  6.2 The Model with a HardWall Binding Potential  6.3 Random Singular Pair Interactions  6.4 The Condensation of Electron Pairs in a Quantum Wire  6.5 The Impact of Surface Defects on a Condensate of Electrons  References  Deterministic and Stochastic MeanField SIRS Models on Heterogeneous Networks  1 Introduction
 2 The Deterministic Model  3 The Critical Threshold  3.1 Computing the MetaStable State  3.2 The Heterogeneous Case  4 Simulations for the Deterministic Heterogeneous Case  5 Stochastic SIRS Model  6 Conclusion  References  Kreĭn Formula and Convergence of Hamiltonians with Scaled Potentials in Dimension One  1 Introduction  2 Main Result  3 Kreĭn resolvent Formula  3.1 Operators in the Outer Space  3.2 Operators in the Inner Space  3.3 Operator in the Full Space  4 Limit of R(z)  4.1 Limiting Hamiltonian: Generic Case  4.2 Limiting Hamiltonian: Nongeneric Case
 4 The Asymptotic Expansion of the Regularized Trace of the Heat Kernel  Appendix 1: Notations  Appendix 2: Integral Identities for the K0Macdonald Function  2.1 A Converse Watson Lemma  References  Modeling Dynamic Coupling in Social Interactions  1 Introduction  2 Coupling and Information Exchange  3 Dynamic Exchanges and Coupling in Sensorimotor Synchronisation  4 Quantifying Interactive Coupling  5 Applying Dynamic Timecourse Models to Sensorimotor Synchronisation Data  5.1 Nature of the Partner  5.2 Nature of the Information Being Exchanged
 Isbn
 9783030440978
 Label
 Discrete and continuous models in the theory of networks
 Title
 Discrete and continuous models in the theory of networks
 Statement of responsibility
 Fatihcan M. Atay, Pavel B. Kurasov, Delio Mugnolo, editors
 Language
 eng
 Summary
 This book contains contributions from the participants of the research group hosted by the ZiF  Center for Interdisciplinary Research at the University of Bielefeld during the period 20132017 as well as from the conclusive conference organized at Bielefeld in December 2017. The contributions consist of original research papers: they mirror the scientific developments fostered by this research program or the stateoftheart results presented during the conclusive conference. The volume covers current research in the areas of operator theory and dynamical systems on networks and their applications, indicating possible future directions. The book will be interesting to researchers focusing on the mathematical theory of networks; it is unique as, for the first time, continuous network models  a subject that has been blooming in the last twenty years  are studied alongside more classical and discrete ones. Thus, instead of two different worlds often growing independently without much intercommunication, a new path is set, breaking with the tradition. The fruitful and beneficial exchange of ideas and results of both communities is reflected in this book
 Cataloging source
 YDX
 Dewey number
 511/.5
 Index
 no index present
 LC call number
 QA166
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName

 Atay, Fatihcan M
 Kurasov, P
 Mugnolo, Delio
 Series statement
 Operator theory, advances and applications
 Series volume
 281
 http://library.link/vocab/subjectName

 Graph theory
 Mathematical analysis
 Ergodic theory
 Label
 Discrete and continuous models in the theory of networks, Fatihcan M. Atay, Pavel B. Kurasov, Delio Mugnolo, editors
 Bibliography note
 References  Ground States of the L2Critical NLS Equation with Localized Nonlinearity on a Tadpole Graph  1 Introduction  2 Setting and Main Results  3 Preliminaries and Compactness  4 Proof of Theorem 2.1  References  An Asymptotic Expansion of the Trace of the Heat Kernel of a Singular Twoparticle Contact Interaction in Onedimension  1 Introduction  2 Preliminaries  3 The Resolvent Kernel  3.1 Trace Class Property of the Regularized Resolvent  3.2 An Asymptotic Analysis of the Trace of the Regularized Resolvent
 Contents

 Intro  Preface  Contents  Stability Matters for ReactionDiffusionEquations on Metric Graphs Under the AntiKirchhoff Vertex Condition  1 Metric Graphs  2 Stationary Solutions  3 Stability  4 Nonlinearities Vanishing at 0  5 Constant Nonlinearities  6 Odd Nonlinearities  7 Loops  References  ManyParticle Quantum Graphs: A Review  1 Introduction  2 Preliminaries  2.1 OneParticle Quantum Graphs  2.2 ManyParticle Kinematics  3 Singular Pair Interactions  3.1 VertexInduced Singular Interactions  3.2 Contact Interactions
 3.3 A LiebLiniger Model on Graphs  4 BoseEinstein Condensation  4.1 Free Bosons  4.2 Interacting Bosons  5 Exactly Solvable ManyParticle Quantum Graphs  6 ManyParticle Models on a Quantum Wire  6.1 The Model Without HardWall Binding Potential  6.2 The Model with a HardWall Binding Potential  6.3 Random Singular Pair Interactions  6.4 The Condensation of Electron Pairs in a Quantum Wire  6.5 The Impact of Surface Defects on a Condensate of Electrons  References  Deterministic and Stochastic MeanField SIRS Models on Heterogeneous Networks  1 Introduction
 2 The Deterministic Model  3 The Critical Threshold  3.1 Computing the MetaStable State  3.2 The Heterogeneous Case  4 Simulations for the Deterministic Heterogeneous Case  5 Stochastic SIRS Model  6 Conclusion  References  Kreĭn Formula and Convergence of Hamiltonians with Scaled Potentials in Dimension One  1 Introduction  2 Main Result  3 Kreĭn resolvent Formula  3.1 Operators in the Outer Space  3.2 Operators in the Inner Space  3.3 Operator in the Full Space  4 Limit of R(z)  4.1 Limiting Hamiltonian: Generic Case  4.2 Limiting Hamiltonian: Nongeneric Case
 4 The Asymptotic Expansion of the Regularized Trace of the Heat Kernel  Appendix 1: Notations  Appendix 2: Integral Identities for the K0Macdonald Function  2.1 A Converse Watson Lemma  References  Modeling Dynamic Coupling in Social Interactions  1 Introduction  2 Coupling and Information Exchange  3 Dynamic Exchanges and Coupling in Sensorimotor Synchronisation  4 Quantifying Interactive Coupling  5 Applying Dynamic Timecourse Models to Sensorimotor Synchronisation Data  5.1 Nature of the Partner  5.2 Nature of the Information Being Exchanged
 Dimensions
 unknown
 Extent
 1 online resource
 Form of item
 online
 Isbn
 9783030440978
 Other control number

 10.1007/9783030440978
 10.1007/978303044
 Specific material designation
 remote
 System control number

 on1193327647
 (OCoLC)1193327647
 Label
 Discrete and continuous models in the theory of networks, Fatihcan M. Atay, Pavel B. Kurasov, Delio Mugnolo, editors
 Bibliography note
 References  Ground States of the L2Critical NLS Equation with Localized Nonlinearity on a Tadpole Graph  1 Introduction  2 Setting and Main Results  3 Preliminaries and Compactness  4 Proof of Theorem 2.1  References  An Asymptotic Expansion of the Trace of the Heat Kernel of a Singular Twoparticle Contact Interaction in Onedimension  1 Introduction  2 Preliminaries  3 The Resolvent Kernel  3.1 Trace Class Property of the Regularized Resolvent  3.2 An Asymptotic Analysis of the Trace of the Regularized Resolvent
 Contents

 Intro  Preface  Contents  Stability Matters for ReactionDiffusionEquations on Metric Graphs Under the AntiKirchhoff Vertex Condition  1 Metric Graphs  2 Stationary Solutions  3 Stability  4 Nonlinearities Vanishing at 0  5 Constant Nonlinearities  6 Odd Nonlinearities  7 Loops  References  ManyParticle Quantum Graphs: A Review  1 Introduction  2 Preliminaries  2.1 OneParticle Quantum Graphs  2.2 ManyParticle Kinematics  3 Singular Pair Interactions  3.1 VertexInduced Singular Interactions  3.2 Contact Interactions
 3.3 A LiebLiniger Model on Graphs  4 BoseEinstein Condensation  4.1 Free Bosons  4.2 Interacting Bosons  5 Exactly Solvable ManyParticle Quantum Graphs  6 ManyParticle Models on a Quantum Wire  6.1 The Model Without HardWall Binding Potential  6.2 The Model with a HardWall Binding Potential  6.3 Random Singular Pair Interactions  6.4 The Condensation of Electron Pairs in a Quantum Wire  6.5 The Impact of Surface Defects on a Condensate of Electrons  References  Deterministic and Stochastic MeanField SIRS Models on Heterogeneous Networks  1 Introduction
 2 The Deterministic Model  3 The Critical Threshold  3.1 Computing the MetaStable State  3.2 The Heterogeneous Case  4 Simulations for the Deterministic Heterogeneous Case  5 Stochastic SIRS Model  6 Conclusion  References  Kreĭn Formula and Convergence of Hamiltonians with Scaled Potentials in Dimension One  1 Introduction  2 Main Result  3 Kreĭn resolvent Formula  3.1 Operators in the Outer Space  3.2 Operators in the Inner Space  3.3 Operator in the Full Space  4 Limit of R(z)  4.1 Limiting Hamiltonian: Generic Case  4.2 Limiting Hamiltonian: Nongeneric Case
 4 The Asymptotic Expansion of the Regularized Trace of the Heat Kernel  Appendix 1: Notations  Appendix 2: Integral Identities for the K0Macdonald Function  2.1 A Converse Watson Lemma  References  Modeling Dynamic Coupling in Social Interactions  1 Introduction  2 Coupling and Information Exchange  3 Dynamic Exchanges and Coupling in Sensorimotor Synchronisation  4 Quantifying Interactive Coupling  5 Applying Dynamic Timecourse Models to Sensorimotor Synchronisation Data  5.1 Nature of the Partner  5.2 Nature of the Information Being Exchanged
 Dimensions
 unknown
 Extent
 1 online resource
 Form of item
 online
 Isbn
 9783030440978
 Other control number

 10.1007/9783030440978
 10.1007/978303044
 Specific material designation
 remote
 System control number

 on1193327647
 (OCoLC)1193327647
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