Explicit solutions of coupled linear systems

2004 ◽  
pp. 253-258
Keyword(s):  
Linear Systems ◽  
Explicit Solutions

INTEGRATING SUPER-LIOUVILLE SYSTEM WITHOUT INTEGRATION

2000 ◽  
Vol 15 (09) ◽  
pp. 617-628 ◽  
Author(s):  
YI ZHEN ◽  
LIU ZHAO ◽  
ZHANYING YANG
Keyword(s):  
Linear Systems ◽  
Liouville Equation ◽  
Field Theories ◽  
Explicit Solutions

Explicit solutions of super-Liouville equation are obtained by the use of a super-extension of the so-called Drinfeld–Sokolov construction. Such solutions can be proved to be local and super-periodic using earlier results of Toppan on exchange algebras based on super-Drinfeld–Sokolov linear systems and of Babelon et al. on the proof of locality and periodicity of ordinary Toda field theories.

scholarly journals Solution of linear fractional order systems with variable coefficients

2020 ◽  
Vol 23 (3) ◽  
pp. 753-763
Author(s):  
Ivan Matychyn ◽  
Viktoriia Onyshchenko
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Initial Value Problem ◽  
Transition Matrix ◽  
State Transition ◽  
Variable Coefficients ◽  
Explicit Solutions ◽  
Fractional Order Systems ◽  
Initial Value ◽  
Theoretical Results

AbstractThe paper deals with the initial value problem for linear systems of FDEs with variable coefficients involving Riemann–Liouville derivatives. The technique of the generalized Peano–Baker series is used to obtain the state-transition matrix. Explicit solutions are derived both in the homogeneous and inhomogeneous case. The theoretical results are supported by an example.

scholarly journals Drazin-Star and Star-Drazin Inverses of Bounded Finite Potent Operators on Hilbert Spaces

2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Fernando Pablos Romo
Keyword(s):  
Linear Systems ◽  
Hilbert Spaces ◽  
Explicit Solutions ◽  
Finite Complex ◽  
Complex Matrix ◽  
Infinite Linear Systems ◽  
Infinite Linear

AbstractThe aim of this work is to extend to bounded finite potent endomorphisms on arbitrary Hilbert spaces the notions of the Drazin-Star and the Star-Drazin of matrices that have been recently introduced by D. Mosić. The existence, structure and main properties of these operators are given. In particular, we obtain new properties of the Drazin-Star and the Star-Drazin of a finite complex matrix. Moreover, the explicit solutions of some infinite linear systems on Hilbert spaces from the Drazin-Star inverse of a bounded finite potent endomorphism are studied.

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