Inverse problems of spectral analysis deal with the reconstruction of operators of the specified form in Hilbert or Banach spaces from certain of their spectral characteristics. An interest in spectral problems was initially inspired by quantum mechanics. The main inverse spectral problems have been solved already for Schrödinger operators and for their finite-difference analogues, Jacobi matrices. This book treats inverse problems in the theory of small oscillations of systems with finitely many degrees of freedom, which requires finding the potential energy of a system from the observations of its oscillations. Since oscillations are small, the potential energy is given by a positive definite quadratic form whose matrix is called the matrix of potential energy. Hence, the problem is to find a matrix belonging to the class of all positive definite matrices. This is the main difference between inverse problems studied in this book and the inverse problems for discrete analogues of the Schrödinger operators, where only the class of tridiagonal Hermitian matrices are considered.
Inverse problems of spectral analysis deal with the reconstruction of operators of the specified form in Hilbert or Banach spaces from certain of their spectral characteristics. An interest in spectral problems was initially inspired by quantum mechanics. The main inverse spectral problems have been solved already for Schrödinger operators and for their finite-difference analogues, Jacobi matrices. This book treats inverse problems in the theory of small oscillations of systems with finitely many degrees of freedom, which requires finding the potential energy of a system from the observations of its oscillations. Since oscillations are small, the potential energy is given by a positive definite quadratic form whose matrix is called the matrix of potential energy. Hence, the problem is to find a matrix belonging to the class of all positive definite matrices. This is the main difference between inverse problems studied in this book and the inverse problems for discrete analogues of the Schrödinger operators, where only the class of tridiagonal Hermitian matrices are considered.
Based on the premise that deconstruction and demystification are a necessary counterforce to 'shared myths', Tochon offers a provocative assessment of mass educational concepts and teacher education, proposing a rethinking of pedagogy in general.
The Catalan is a solid yet flexible chess opening system that is popular on all levels. Both amateurs and top-level strategists such as Vladimir Kramnik and Vishy Anand employ this opening to put a lot of unpleasant pressure on Black. In The Powerful Catalan grandmaster Victor Bologan presents a complete repertoire for White that covers all of Black’s responses. Also included are those variations where Black tries to steer the game into other openings like the Queen’s Indian or the Tarrasch Defence. The book is classically structured (starting with the rarest variations before moving on to the most popular ones) and contains original analysis of many recent tournament games. Bologan’s clearly formulated verbal explanations are essential for a good understanding of the strategic plans and the tactical themes of the Catalan. ,
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