Optimal control of a two-parameter system in a Hilbert space

1999 ◽  
Vol 97 (2) ◽  
pp. 3908-3916
Author(s):  
I. V. Gaishun ◽  
M. P. Dymkov
Keyword(s):  
Optimal Control ◽  
Hilbert Space ◽  
Parameter System ◽  
Two Parameter

A two-parameter eigenvalue problem involving complex potentials

1990 ◽  
Vol 116 (1-2) ◽  
pp. 177-191
Author(s):  
M. Faierman
Keyword(s):  
Hilbert Space ◽  
Eigenvalue Problem ◽  
Differential Equations ◽  
Complex Potentials ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Parameter System ◽  
Complete Set ◽  
Necessary And Sufficient ◽  
Two Parameter

SynopsisWe consider a two-parameter system of ordinary differential equations of the second order involving complex potentials and show that, unlike the case of real potentials, the eigenfunctions of the system do not necessarily form a complete set in the usual Hilbert space associated with the problem. We also give a necessary and sufficient condition for the eigenfunctions to be complete. Finally, we establish some results concerning the eigenvalues of the system.

Some results of the Barbier-Chalonge-Divan system of stellar classification

1966 ◽  
Vol 24 ◽  
pp. 77-90 ◽  
Author(s):  
D. Chalonge
Keyword(s):  
Early Type ◽  
Parameter System ◽  
Early Type Stars ◽  
Two Parameter

Several years ago a three-parameter system of stellar classification has been proposed (1, 2), for the early-type stars (O-G): it was an improvement on the two-parameter system described by Barbier and Chalonge (3).

scholarly journals The Hilbert Space of Double Fourier Coefficients for an Abstract Wiener Space

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 389
Author(s):  
Jeong-Gyoo Kim
Keyword(s):  
Hilbert Space ◽  
Fourier Series ◽  
Fourier Coefficients ◽  
Double Sequence ◽  
Intermediate Stage ◽  
Wiener Space ◽  
Abstract Wiener Space ◽  
Abstract Space ◽  
Double Sequences ◽  
Two Parameter

Fourier series is a well-established subject and widely applied in various fields. However, there is much less work on double Fourier coefficients in relation to spaces of general double sequences. We understand the space of double Fourier coefficients as an abstract space of sequences and examine relationships to spaces of general double sequences: p-power summable sequences for p = 1, 2, and the Hilbert space of double sequences. Using uniform convergence in the sense of a Cesàro mean, we verify the inclusion relationships between the four spaces of double sequences; they are nested as proper subsets. The completions of two spaces of them are found to be identical and equal to the largest one. We prove that the two-parameter Wiener space is isomorphic to the space of Cesàro means associated with double Fourier coefficients. Furthermore, we establish that the Hilbert space of double sequence is an abstract Wiener space. We think that the relationships of sequence spaces verified at an intermediate stage in this paper will provide a basis for the structures of those spaces and expect to be developed further as in the spaces of single-indexed sequences.

Optimale Steuerung eines Systems mit verteilten Parametern am Beispiel eines Tiefofens / Optimal control of a distributed parameter system applied to a metallurgical Furnace

1974 ◽  
Vol 22 (11) ◽  
Author(s):  
D. Franke
Keyword(s):  
Optimal Control ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Wird Eine ◽  
Parameter System ◽  
Metallurgical Furnace ◽  
Mathematisches Modell

Der Beitrag behandelt am Beispiel eines Tiefofens die Anwendung der Optimierungstheorie für Systeme mit verteilten Parametern. Als mathematisches Modell wird die Wärmeleitungsdifferentialgleichung zugrunde gelegt.Die Minimierung eines quadratischen Güte-Index bei beschränkter Stellgröße führt nach A. G. Butkovskiy auf eine nichtlineare Integralgleichung für die optimale Steuerfunktion. Zur Lösung dieser Integralgleichung wird eine hybride Rechenschaltung vorgestellt. Anhand eines Zahlenbeispiels werden Rechnerergebnisse mitgeteilt und diskutiert.

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