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Exact solutions of the radial Schrödinger equation for some physical potentials

100%

Ikhdair S. , Sever R.

Open Physics

2007

tom 5

nr 4

516-527

By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrödinger equation for the pseudoharmonic and the Kratzer potentials in two dimensions. The bound-state solutions are easily calculated from this eigenfunction ansatz. The corresponding normalized wavefunctions are also obtained.

On controllability and observability of linear systems: multiple eigenvalue case

100%

Yaici M. , Belmehdi A.

Systems Science

2004

tom Vol. 30, no 2

11-20

This paper presents a method to verify the controllability and observability of linear multivariable systems with multiple modes using eigenprojectors or constituent matrices. Eigenprojectors are obtained by the partial fraction expansion of the numerator of the transfer function matrix of the system and the constituent matrices are obtained from the spectral decomposition of the state matrix. Eigenprojectors inform on the properties of the corresponding mode separately from the others, so controllability and observability of each mode are checked. A previous paper has dealt with linear systems with single eigenvalues, and the same method gave good results. Numerical examples are given to illustrate this method.

On the performance of high-gain residuals for detecting faults in a pipeline system

86%

Shields D. N.

Systems Science

2003

tom Vol. 29, nr 2

5-16

A theoretical class of nonlinear systems is considered. An n-dimensional pipeline system is examined, as an example system, for investigating the effectiveness of a high-gain observer-based residual for detecting faults. Detailed conditions are given for the investigation of residual effectiveness, such as selection of operating points, control inputs, sensor faults, component faults, fault positions and observer eigenvalues. Then, for various values of n, defined fault types and defined fault positions, the observer-residual performance is noted and characteristics are derived and compared. Qualitative and quantitative evidence in graphical and table form shows, in several ways, how the performance and effectiveness of observer-based residuals change as n, and system complexity, increases.

On the reconstruction of the current state of the linear difference-differential system with commensurable delays

72%

Khartouski V.

Systems Science

2003

tom Vol. 29, nr 4

55-67

In the present paper, we consider the problem of reconstruction of the current state of the difference-differential system with commensurable delays. The results obtained are used for the reconstruction of the current states of linear retarded partial parabolic differential equation.

Feedback and pole assignment of the second order singular distributed parameter control systems

58%

Ge Z. , Zhang B.

Systems Science

2003

tom Vol. 29, nr 4

19-27

Pole assignment for infinite many poles of the second order singular distributed parameter control system was discussed via functional analysis and operator theory in Hubert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This research is theoretically important for studying the stabilization and asymptotic stability of the second order singular distributed parameter control system.

Exact method of solution of torsional vibrations problem for discontinuous viscoelastic shaft with oscillators

58%

Cabański J.

Journal of Technical Physics

2001

tom Vol. 42, no 4

459-474

In this paper a generalized, exact method for solving the problems of torsional vibrations of a non-continuous viscoelastic shaft with oscillators has been presented. The oscillators are attached to the shaft by means of the viscoelastic constraints. The vibrations of this compound system are described by the set of conjugated, partial and ordinary differential equations. The separation of the variables in the complex Hilbert space, the obtained results from the analysis of the boundary-value problems and the proved generalized orthogonality of complex eigenvectors have been used to obtain the solution for free vibrations of the system at the arbitrary initial conditions. Finally, by applying the harmonic moment of the forced vibrations, the problem of the shaft has been solved. In the herein presented method, the operational generalized principles [6] have been applied.