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1. |
Record Nr. |
UNINA9910787647303321 |
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Autore |
Sakhnovich Alexander |
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Titolo |
Inverse problems and nonlinear evolution equations : solutions, Darboux matrices and Weyl-Titchmarsh functions / / by Alexander Sakhnovich, Lev Sakhnovich, Inna Roitberg |
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Pubbl/distr/stampa |
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Berlin ; ; Boston : , : Walter de Gruyter GmbH & Co., KG, , [2013] |
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©2013 |
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Descrizione fisica |
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1 online resource (356 p.) |
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Collana |
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De Gruyter Studies in Mathematics ; ; 47 |
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Altri autori (Persone) |
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RoitbergInna |
SakhnovichL. A |
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Disciplina |
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Soggetti |
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Boundary value problems |
Darboux transformations |
Evolution equations, Nonlinear |
Functions |
Inverse problems (Differential equations) |
Matrices |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographies and index. |
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Nota di contenuto |
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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 |
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Sommario/riassunto |
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This book is based on the method of operator identities and related |
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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. |
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2. |
Record Nr. |
UNINA9910820869203321 |
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Autore |
Mitchell Thomas |
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Titolo |
Azure PowerShell quick start guide : deploy and manage Azure virtual machines with ease / / Thomas Mitchell |
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Pubbl/distr/stampa |
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Birmingham : , : Packt, , 2018 |
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Edizione |
[1st edition] |
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Descrizione fisica |
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1 online resource (118 pages) |
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Disciplina |
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Soggetti |
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Windows PowerShell (Computer program language) |
Cloud computing |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Sommario/riassunto |
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Leverage PowerShell to perform many day-to-day tasks in Microsoft Azure Key Features Deploy and manage Azure virtual machines with PowerShell commands. Get to grips with core concept of Azure PowerShell such as working with images and disks, custom script extension, high availability and more. Leverage hands-on projects to successfully apply what you learned through the course of this book. Book Description As an IT professional, it is important to keep up with cloud technologies and learn to manage those technologies. PowerShell is a critical tool that must be learned in order to effectively and more easily manage many Azure resources. This book is designed to teach you to leverage PowerShell to enable you to perform many day-to-day tasks in Microsoft Azure. Taking you through the basic tasks of installing Azure PowerShell and connecting to Azure, you will learn to properly connect to an Azure tenant with PowerShell. Next, you will dive into tasks such as deploying virtual machines with PowerShell, resizing them, and managing their power states with PowerShell. Then, you will learn how to complete more complex Azure tasks with PowerShell, such as deploying virtual machines from custom images, creating images from existing virtual machines, and creating and managing of data disks. Later, you will learn how to snapshot virtual machines, how to encrypt virtual machines, and how to leverage load |
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balancers to ensure high availability with PowerShell. By the end of this book, you will have developed dozens of PowerShell skills that are invaluable in the deployment and management of Azure virtual machines. What you will learn Manage virtual machines with PowerShell Resize a virtual machine with PowerShell Create OS disk snapshots via PowerShell Deploy new virtual machines from snapshots via PowerShell Provision and attach data disks to a virtual machine via PowerShell Load balance virtual machines with PowerShell Manage virtual machines with custom script extensions Who this book is for This book is intended for IT professionals who are responsible for managing Azure virtual machines. No prior PowerShell or Azure experience is needed. |
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