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Hermitian Forms and Eigenvalue Bounds
Author(s) -
Warren F. W.
Publication year - 1978
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1978593249
Subject(s) - mathematics , eigenvalues and eigenvectors , mathematical analysis , inviscid flow , hermitian matrix , fourier series , quadratic equation , linear differential equation , radius , simple (philosophy) , differential equation , geometry , pure mathematics , physics , classical mechanics , philosophy , computer security , epistemology , quantum mechanics , computer science
A method of quadratic forms for eigenvalue bounds described in an earlier paper is developed and extended. In particular it is shown how restrictions upon eigenvalues may be found for a class of linear partial differential equations whose coefficients depend on one space variable and which are also periodic in time. An application is made to the problem of linear stability of periodic helical flows in a pipe. It is shown that the motion is stable if a criterion of the form is satisfied. Ω n ( r ) is the Fourier coefficient of the n th harmonic of the periodic angular velocity Ω( r ), and W n ( r ) is the corresponding coefficient of the axial velocity. b is the radius of the pipe, and R 0 is about 4.4. Stronger but less simple results are possible. Bounds for steady inviscid flows are also given.