Inverse problems and nonlinear evolution equations : solutions, Darboux matrices and Weyl-Titchmarsh functions / / by Alexander Sakhnovich, Lev Sakhnovich, Inna Roitberg

• Record Nr.: UNINA9910462666203321
• Autore: Sakhnovich Alexander
• Pubbl/distr/stampa: Berlin ; ; Boston : , : Walter de Gruyter GmbH & Co., KG, , [2013]; ©2013
• Descrizione fisica: 1 online resource (356 p.)
• Collana: De Gruyter Studies in Mathematics ; ; 47
• Altri autori (Persone): RoitbergInna; SakhnovichL. A
• Disciplina: 515.357; 515/.357
• Soggetti: Boundary value problems; Darboux transformations; Evolution equations, Nonlinear; Functions; Inverse problems (Differential equations); Matrices; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographies and index.
• Nota di contenuto: Front matter -- Preface -- Notation -- Contents -- 0 Introduction -- 1 Preliminaries -- 2 Self-adjoint Dirac system: rectangular matrix potentials -- 3 Skew-self-adjoint Dirac system: rectangular matrix potentials -- 4 Linear system auxiliary to the nonlinear optics equation -- 5 Discrete systems -- 6 Integrable nonlinear equations -- 7 General GBDT theorems and explicit solutions of nonlinear equations -- 8 Some further results on inverse problems and generalized Bäcklund-Darboux transformation (GBDT) -- 9 Sliding inverse problems for radial Dirac and Schrödinger equations -- Appendices -- A General-type canonical system: pseudospectral and Weyl functions -- B Mathematical system theory -- C Krein's system -- D Operator identities corresponding to inverse problems -- E Some basic theorems -- Bibliography -- Index
• Sommario/riassunto: This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund-Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.

Transforming systems for parental depression and early childhood developmental delays : findings and lessons learned from the Helping Families Raise Healthy Children initiative / / Dana Schultz [and five others]

• Record Nr.: UNINA9910220096703321
• Autore: Schultz Dana (Dana J.)
• Pubbl/distr/stampa: Santa Monica, CA, : RAND Corporation, 2013; Santa Monica, CA : , : RAND Corporation, , 2013
• ISBN: 0-8330-7997-2; 0-8330-7999-9
• Descrizione fisica: 1 online resource (xxix, 166 pages) : illustrations
• Collana: Gale eBooks
• Disciplina: 362.3
• Soggetti: Developmental Disabilities - complications; Parenting - psychology; Caregivers - psychology; Community Mental Health Services; Depression - etiology; Parent-Child Relations; Parents of developmentally disabled children - Services for; Caregivers - Psychology; Depression, Mental
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Prepared for the Community Care Behavioral Health Organization."; "RAND Health."
• Nota di bibliografia: Includes bibliographical references (p. 159-166).
• Nota di contenuto: Cover; Title Page; Copyright; Preface; Contents; Figures; Tables; Summary; Abbreviations; Glossary; CHAPTER ONE: Introduction; Background on the Allegheny County Maternal and Child Health Care Collaborative; The Collaborative's Prior Work; Phase I: Planning Process, 2002-2004; Phase II: Pilot Testing, 2004-2006; Phase III: Maternal Depression Initiative, 2007-2010; The Broad Context for the Collaborative's Focus on Depression; Prevalence and Symptoms of Maternal Depression; Prevalence and Risk Factors of Maternal Depression for Low-Income Populations; Prevention and Intervention Effects for Women at Risk for DepressionLink Between Maternal Depression and Early Childhood Development; System Challenges to Addressing Maternal Depression; Maternal Depression Screening; Actions Taken Following Positive Screens; Engagement in Behavioral Health Treatment; The Need for a Cross-System Response to Maternal Depression in Allegheny County; The Helping Families Raise Healthy Children Initiative; Aims and Focus of the Initiative; Roles and Responsibilities of Key Stakeholder Groups; Strategies for Implementation; Initiative Timeline; Organization of This ReportCHAPTER TWO: Methods; The Initiative's Framework for System Change; Initiative Partners and Organization; Implementation Protocols and Procedures; Screening and Identification of At-Risk Families; Relationship-Based Service Coordination and Referrals; Engagement in Relationship-Based Services; Strategies to Support Initiative Implementation; Conducting Cross-System Provider Training; Supporting the Screening and Referral Processes; Convening a Learning Collaborative for Providers; Developing Community Partnerships; Assessing Progress to Inform Ongoing Implementation; Evaluation PlanData Collection for Process, Individual Outcome, and System Impact Measures; Data Collection Activities; Data Analysis; CHAPTER THREE: Results; Section A. Assessment of the Implementation Process: Screening and Identification, Referral, and Engagement in Services; Screening and Identification Results; Referral Results; Engagement-in-Services Results; Summary of the Process Measure Results; Section B. System Impact Results; Screening and Identification; Cross-System Networking and Referrals; Engagement in Services for At-Risk Families; Tracking Implementation Progress and Costs; Summary of Factors Driving System ChangeSection C. Individual-Level Outcome Results; Depression Screening; Parenting Stress; Health and Safety; Summary of the Individual Outcome Measure Results; Summary of the Results of the Overall Initiative; CHAPTER FOUR: Discussion; Lessons Learned; Screening and Identification; Referrals; Engagement in Services for At-Risk Families; Education, Training, and Support; Current Policy Context; Limitations; CHAPTER FIVE: Conclusions, Recommendations, and Next Steps; Sustainability of the Initiative's Components; Recommendations; Next Steps; APPENDIXES; A. Training Assessments
• Sommario/riassunto: The Helping Families Raise Healthy Children initiative addressed depression among parents of children with early childhood developmental delays, aligning the early intervention and behavioral health systems with a focus on relationship-based care. The initiative focused on identification of at-risk families, referral, and engagement in services that addressed the needs of parents and young children in the context of their relationship.