A generalized operational calculus developed from Fredholm operator theory

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

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Quantum Resonances: Line Profiles and Dynamics

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc20030529 ◽

2003 ◽

Vol 68 (3) ◽

pp. 529-553 ◽

Cited By ~ 3

Author(s):

Ivana Paidarová ◽

Philippe Durand

Keyword(s):

Hydrogen Atom ◽

Operator Theory ◽

Quantum Dynamics ◽

Line Profiles ◽

Static Electric Field ◽

Reversal Effect ◽

Quantum Resonances ◽

Energy Dependent ◽

Effective Hamiltonians

The wave operator theory of quantum dynamics is reviewed and applied to the study of line profiles and to the determination of the dynamics of interacting resonances. Energy-dependent and energy-independent effective Hamiltonians are investigated. The q-reversal effect in spectroscopy is interpreted in terms of interfering Fano profiles. The dynamics of an hydrogen atom subjected to a strong static electric field is revisited.

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Operator theory on quaternionic Hilbert spaces

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700045032 ◽

1972 ◽

Vol 7 (2) ◽

pp. 297-299

Author(s):

Neil Charles Powers

Keyword(s):

Hilbert Spaces ◽

Operator Theory

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The Supersonic Flow Past a Slender Ducted Body of Revolution with an Annular Intake

Aeronautical Quarterly ◽

10.1017/s0001925900000214 ◽

1950 ◽

Vol 1 (4) ◽

pp. 305-318

Author(s):

G. N. Ward

Keyword(s):

Supersonic Flow ◽

Velocity Potential ◽

Operational Calculus ◽

The Body ◽

Body Of Revolution ◽

Internal Flows ◽

Flow Past ◽

External Forces ◽

Internal Pressures ◽

Slender Body Of Revolution

SummaryThe approximate supersonic flow past a slender ducted body of revolution having an annular intake is determined by using the Heaviside operational calculus applied to the linearised equation for the velocity potential. It is assumed that the external and internal flows are independent. The pressures on the body are integrated to find the drag, lift and moment coefficients of the external forces. The lift and moment coefficients have the same values as for a slender body of revolution without an intake, but the formula for the drag has extra terms given in equations (32) and (56). Under extra assumptions, the lift force due to the internal pressures is estimated. The results are applicable to propulsive ducts working under the specified condition of no “ spill-over “ at the intake.

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