Eigenvalue Perturbation Research Articles

A Symmetrized Perturbation Procedure for the Transport Operator

A perturbation procedure based upon a symmetrized form of the linear transport operator is introduced. Results of the analytical perturbation theory are applied in establishing the existence of perturbation series for the operator and its eigenvalues. The proposed procedure is numerically implemented in reactor mathematics where eigenvalue perturbations are computed and the results compared with the pertinent exact values.

Perturbation of eigenvalues with an engineering application—A supplement

Perturbation of eigenvalues with an engineering application—A supplement

Perturbation of eigenvalues with an engineering application

Perturbation of eigenvalues with an engineering application

A Modified Short Kino Gun for Low Noise Operation†

ABSTRACT Results obtained from the eigenvalue perturbation method and Monte Carlo calculations are discussed. It is noted that the space-charge waves experience a growth during the latter part of the beam trajectory in the first half cycloid before the beam enters the interaction region. From the formula for the diocotron gain for a beam between two conducting planes, it is shown that diocotron gain is maximum when the beam is placed symmetrically with respect to the two conducting planes and is reduced to zero value when the beam position approaches either of the two conducting planes. Some further considerations for diocotron gain reduction are discussed. These results are in agreement with the experimental results. It is shown that the growth noticed in the earlier methods is essentially due to the diocotron gain during the latter part of the beam trajectory in the gun region. For low noise operation, a virtual elimination of the latter part of the gun region in the short Kino gun and a modified short ...

THE SOLUTION OF SOME PERTURBATION PROBLEMS FOR MATRICES AND SELFADJOINT OR NON-SELFADJOINT DIFFERENTIAL EQUATIONS I

CONTENTS Introduction Chapter 1. The perturbation of symmetric and non-symmetric matrices § 1. Introduction § 2. The perturbation of solutions of linear algebraic equations § 3. The perturbation of eigenvalues and eigenvectors Chapter 2. The perturbation of selfadjoint and non-selfadjoint boundary problems § 4. Perturbation without raising the order of the differential operator § 5. Perturbation by operators of higher order § 6. The case in which the limit problem is on the spectrum § 7. The perturbation of eigenvalues and eigenfunctions Appendix I. The perturbation of eigenvalues and eigenvectors (the general case) Appendix II. The convergence of the series for λε and vε Appendix III. The perturbation of boundary problems by means of differential operators of higher order (general boundary conditions) References