منابع مشابه
Complementary Extremum Principles for Isoperimetric Optimisation Problems
An isoperimetric problem of the calculus of variations is reviewed. An integral functional, dependent on a function u (x), its derivative u′ (x) and on the independent variable x, is minimised. The minimisation is subject to the isoperimetric constraint that the length of the integration interval remains constant. The well-known Euler equation of the fundamental problem of the calculus of varia...
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We revisit the concavity property of the thermodynamic entropy in order to formulate a general proof of the minimum energy principle as well as of other equivalent extremum principles that are valid for thermodynamic potentials and corresponding Massieu functions under different constraints. The current derivation aims at providing a coherent formal framework for such principles which may be al...
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The spectrum for the Dirac equation for a particle in a potential V (r) includes, in addition to any bound-state energies, a continuum from mc to ∞ and a continuum from −mc2 to −∞. This renders useless an application of Rayleigh-Ritz theory, where one estimates the energy of the lowest state. Various possibilities exist, including working with matrix elements of H (see ref.2 of [142]) or of 1/H...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1978
ISSN: 0022-247X
DOI: 10.1016/0022-247x(78)90138-5