In 1910 Herman Weyl published one of the most widely quoted papers of the 20th century in Analysis, which initiated the study of singular Sturm-Liouville problems. The work on the foundations of Quantum Mechanics in the 1920s and 1930s, including the proof of the spectral theorem for unbounded self-adjoint operators in Hilbert space by von Neumann and Stone, provided some of the motivation for the study of differential operators in Hilbert space with particular emphasis on self-adjoint operators and their spectrum. Since then the topic developed in several directions and many results and applications have been obtained. In this monograph the authors summarize some of these directions discussing self-adjoint, symmetric, and dissipative operators in Hilbert and Symplectic Geometry spaces. Part I of the book covers the theory of differential and quasi-differential expressions and equations, existence and uniqueness of solutions, continuous and differentiable dependence on initial data, adjoint expressions, the Lagrange Identity, minimal and maximal operators, etc. In Part II characterizations of the symmetric, self-adjoint, and dissipative boundary conditions are established. In particular, the authors prove the long standing Deficiency Index Conjecture. In Part III the symmetric and self-adjoint characterizations are extended to two-interval problems. These problems have solutions which have jump discontinuities in the interior of the underlying interval. These jumps may be infinite at singular interior points. Part IV is devoted to the construction of the regular Green's function. The construction presented differs from the usual one as found, for example, in the classical book by Coddington and Levinson.
Although recognized as an important component of all energy storage and conversion technologies, electrochemical supercapacitators (ES) still face development challenges in order to reach their full potential. A thorough examination of development in the technology during the past decade, Electrochemical Supercapacitors for Energy Storage and Delivery: Fundamentals and Applications provides a comprehensive introduction to the ES from technical and practical aspects and crystallization of the technology, detailing the basics of ES as well as its components and characterization techniques. The book illuminates the practical aspects of understanding and applying the technology within the industry and provides sufficient technical detail of newer materials being developed by experts in the field which may surface in the future. The book discusses the technical challenges and the practical limitations and their associated parameters in ES technology. It also covers the structure and options for device packaging and materials choices such as electrode materials, electrolyte, current collector, and sealants based on comparison of available data. Supplying an in depth understanding of the components, design, and characterization of electrochemical supercapacitors, the book has wide-ranging appeal to industry experts and those new to the field. It can be used as a reference to apply to current work and a resource to foster ideas for new devices that will further the technology as it becomes a larger part of main stream energy storage.
In 1910 Herman Weyl published one of the most widely quoted papers of the 20th century in Analysis, which initiated the study of singular Sturm-Liouville problems. The work on the foundations of Quantum Mechanics in the 1920s and 1930s, including the proof of the spectral theorem for unbounded self-adjoint operators in Hilbert space by von Neumann and Stone, provided some of the motivation for the study of differential operators in Hilbert space with particular emphasis on self-adjoint operators and their spectrum. Since then the topic developed in several directions and many results and applications have been obtained. In this monograph the authors summarize some of these directions discussing self-adjoint, symmetric, and dissipative operators in Hilbert and Symplectic Geometry spaces. Part I of the book covers the theory of differential and quasi-differential expressions and equations, existence and uniqueness of solutions, continuous and differentiable dependence on initial data, adjoint expressions, the Lagrange Identity, minimal and maximal operators, etc. In Part II characterizations of the symmetric, self-adjoint, and dissipative boundary conditions are established. In particular, the authors prove the long standing Deficiency Index Conjecture. In Part III the symmetric and self-adjoint characterizations are extended to two-interval problems. These problems have solutions which have jump discontinuities in the interior of the underlying interval. These jumps may be infinite at singular interior points. Part IV is devoted to the construction of the regular Green's function. The construction presented differs from the usual one as found, for example, in the classical book by Coddington and Levinson.
This guide covers the main aspects of quality and product control, from the fundamentals through the practical processes, to advanced topics such as artificial neurofuzzy network modelling, and the design of supervisory control systems and their potential application to the paper and board industry.
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