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2012
The goal of this chapter is a more complete study of linear transformations of a complex or real vector space to itself, including the investigation of nondiagonalizable transformations. The Jordan normal forms for complex and real vector spaces are established.
Igor R. Shafarevich, Alexey O. Remizov
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The goal of this chapter is a more complete study of linear transformations of a complex or real vector space to itself, including the investigation of nondiagonalizable transformations. The Jordan normal forms for complex and real vector spaces are established.
Igor R. Shafarevich, Alexey O. Remizov
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29th Annual IEEE/NASA Software Engineering Workshop, 2006
Because of their strong economic impact, complexity and maintainability are among the most widely used terms in software engineering. But, they are also among the most weakly understood. A multitude of software metrics attempts to analyze complexity and a proliferation of different definitions of maintainability can be found in text books and corporate
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Because of their strong economic impact, complexity and maintainability are among the most widely used terms in software engineering. But, they are also among the most weakly understood. A multitude of software metrics attempts to analyze complexity and a proliferation of different definitions of maintainability can be found in text books and corporate
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2004
The normal forms discussed in this chapter are based on XOR and EQU as output connectives. The XOR-normal form is obscurely ascribed to Reed and Muller. Yet, as it seems to have been first considered and discussed systematically by Shegalkin [1927] I feel it a matter of fairness to call it and its dual a Shegalkin normal form.
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The normal forms discussed in this chapter are based on XOR and EQU as output connectives. The XOR-normal form is obscurely ascribed to Reed and Muller. Yet, as it seems to have been first considered and discussed systematically by Shegalkin [1927] I feel it a matter of fairness to call it and its dual a Shegalkin normal form.
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2004
Given a classical Hamiltonian function having an absolute minimum, we consider the problem of describing in the semiclassical limit the lowest part of the spectrum of the corresponding quantum operator. To this end we present an extension of the classical Birkhoff normal form to the semiclassical context and we use it to deduce spectral information on ...
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Given a classical Hamiltonian function having an absolute minimum, we consider the problem of describing in the semiclassical limit the lowest part of the spectrum of the corresponding quantum operator. To this end we present an extension of the classical Birkhoff normal form to the semiclassical context and we use it to deduce spectral information on ...
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2003
Consider a smooth (real or complex) matrix-valued function A(e) of a (real) small parameter e, having formal power series $$ A\left( \varepsilon \right)\, \sim \,{A_{{0\,}}} + \varepsilon {A_1} + {\varepsilon^2}{A_2} + .... $$ (3.1.1) How do the eigenvectors (or generalized eigenvectors) and eigenvalues of such a matrix vary with e?
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Consider a smooth (real or complex) matrix-valued function A(e) of a (real) small parameter e, having formal power series $$ A\left( \varepsilon \right)\, \sim \,{A_{{0\,}}} + \varepsilon {A_1} + {\varepsilon^2}{A_2} + .... $$ (3.1.1) How do the eigenvectors (or generalized eigenvectors) and eigenvalues of such a matrix vary with e?
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2000
Abstract We continue to study the Hamiltonian equation (5.1) near an invariant manifold T 2n = Ф0(R × T n which possesses the properties 1-5 as in Section 5.1.
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Abstract We continue to study the Hamiltonian equation (5.1) near an invariant manifold T 2n = Ф0(R × T n which possesses the properties 1-5 as in Section 5.1.
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