Matrix Reimann-Hilbert Problems Related to Neutron Transport Theory

Burniston, E. E.; Siewert, C. E.; Silvennoinen, P.; Zweifel, P. F.

doi:10.13182/nse71-a19085

Cited by 15 publications

(7 citation statements)

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“…35) reduce to l+(u) and therefore (III. 43) as could have been obtained by the direct inversion of M 0 (n)IA=l.…”

Section: This Approach To Seeking Solutions To the Boltzmann Equationmentioning

confidence: 91%

Analytical calculations of neutron slowing down and transport in the constant-cross-section problem

Cacuci¹

1978

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“…35) reduce to l+(u) and therefore (III. 43) as could have been obtained by the direct inversion of M 0 (n)IA=l.…”

Section: This Approach To Seeking Solutions To the Boltzmann Equationmentioning

confidence: 91%

Analytical calculations of neutron slowing down and transport in the constant-cross-section problem

Cacuci¹

1978

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“…For example, an earlier proof of completeness of the eigensolutions (105) has been chal lenged (181), although further effort has verified completeness for a broad class of symmetric c-matrices (197). The difficulties are analogous to those encountered in Section III,C with the multiterm continuous-speed kernels.…”

Section: Multigroup Approximationmentioning

confidence: 98%

“…The separable kernel has been used to study the effects of oscilla ting sources in half-space or two-half-space geometry. In this case, however, no rigorous proof of half-range completeness has been found so no analog of expansion (118) is guaranteed (181). 6b.…”

Section: Continuous Speedmentioning

confidence: 99%

See 1 more Smart Citation

Singular Eigenfunction Expansions in Neutron Transport Theory

McCormíck

Kuščer

1973

Advances in Nuclear Science and Technology

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“…We might mention that numerous earlier investigations have been incomplete or have made assumptions in this respect. 8 …”

Section: Introductionmentioning

confidence: 99%

On Multigroup Transport Theory with a Degenerate Transfer Kernel

Silvennoinen

Zweifel

1972

Journal of Mathematical Physics

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The multigroup transport equation is studied in plane geometry assuming that the transfer kernel is representable in a degenerate form. The eigenvalue spectrum is analyzed and the associated eigensolutions are obtained in terms of generalized functions. Full-range orthogonality relation is demonstrated. The full-range completeness of the eigensolutions is established under rather general conditions. For the half-range completeness to hold, it is additionally required that the scattering kernel be self-adjoint and possesses reflection symmetry.

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Matrix Reimann-Hilbert Problems Related to Neutron Transport Theory

Cited by 15 publications

References 0 publications

Analytical calculations of neutron slowing down and transport in the constant-cross-section problem

Analytical calculations of neutron slowing down and transport in the constant-cross-section problem

Singular Eigenfunction Expansions in Neutron Transport Theory

On Multigroup Transport Theory with a Degenerate Transfer Kernel

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