Relaxation lengths and non-negative solutions in neutron transport

Jan Kyncl; Ivo Marek

Aplikace matematiky (1977)

  • Volume: 22, Issue: 1, page 1-13
  • ISSN: 0862-7940

How to cite

top

Kyncl, Jan, and Marek, Ivo. "Relaxation lengths and non-negative solutions in neutron transport." Aplikace matematiky 22.1 (1977): 1-13. <http://eudml.org/doc/14988>.

@article{Kyncl1977,
author = {Kyncl, Jan, Marek, Ivo},
journal = {Aplikace matematiky},
keywords = {equation of neutron transport; fredholm theory; integro-partial differential equations; spectral theory; existence of nonnegative eigenfunctions; Equation of Neutron Transport; Fredholm Theory; Integro-Partial Differential Equations; Spectral Theory; Existence of Nonnegative Eigenfunctions},
language = {eng},
number = {1},
pages = {1-13},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Relaxation lengths and non-negative solutions in neutron transport},
url = {http://eudml.org/doc/14988},
volume = {22},
year = {1977},
}

TY - JOUR
AU - Kyncl, Jan
AU - Marek, Ivo
TI - Relaxation lengths and non-negative solutions in neutron transport
JO - Aplikace matematiky
PY - 1977
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 22
IS - 1
SP - 1
EP - 13
LA - eng
KW - equation of neutron transport; fredholm theory; integro-partial differential equations; spectral theory; existence of nonnegative eigenfunctions; Equation of Neutron Transport; Fredholm Theory; Integro-Partial Differential Equations; Spectral Theory; Existence of Nonnegative Eigenfunctions
UR - http://eudml.org/doc/14988
ER -

References

top
  1. M. Borysewicz J. Mika, Time behavior of thermal neutrons in moderator media, CNEN Documents CEC (68), 1 Bologna (1968). (1968) 
  2. K. M. Case, 10.1016/0003-4916(60)90060-9, Ann. Phys. 9 (1960), 1-23. (1960) Zbl0087.42301MR0109471DOI10.1016/0003-4916(60)90060-9
  3. C. Cercignani, 10.1016/0003-4916(66)90145-X, Ann. Phys. 40 (1966), 454 - 468. (1966) MR0219288DOI10.1016/0003-4916(66)90145-X
  4. B. Davison, Milne problem in a multiplying medium with a linearly anisotropic scattering, Canadian Report CRT 358 (1946). (1946) 
  5. B. Davison, Neutron Transport Theory, Oxford University Press, London 1957. (1957) Zbl0077.22505MR0095716
  6. J. J. Duderstadt, 10.1063/1.1664842, J. Math. Phys. 10 (1969), 266-276. (1969) MR0237159DOI10.1063/1.1664842
  7. N. Dunford J. T. Schwartz, Linear operators, Part I. Interscience Publ. New York 1957. (1957) 
  8. L. C. Gokhberg M. G. Krein, The basic propositions on defect numbers, root numbers and indices of linear operators, Usp. mat. nauk XII (1957), 43-118 (Russian). (1957) 
  9. H. Grad, Asymptotic theory of the Boltzmann equation, I. Proceedings of the Third Intern. Symp. Rarefied Gas Dynamics, Vol. I, Academic Press, New York -London, 1963, pp. 26-59. (1963) Zbl0115.45006MR0156656
  10. E. Hecke, Über die Integralgleichung der kinetischen Gastheorie, Math. Zeitschrift 12 (1922), 277-286. (1922) 
  11. S. Kaplan, Properties of the relaxation lengths in P L , double P L and angle-space synthetic approximations, Bull. Sci. Eng. 28 (1967), 456. (1967) 
  12. T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin-Heidelberg- New York 1966. (1966) Zbl0148.12601MR0203473
  13. M. G. Krein M. A. Rutman, Linear operators leawing invariant a cone in a Banach space, Usp. mat. Nauk III (1948), N 1, 3 - 95 (Russian), English translation in the Translations of the AMS, Vol. 26 (1952). (1948) MR0027128
  14. I. Kuščer N. Corngold, 10.1103/PhysRev.139.A981, Phys. Rev. 139 (1965), A981-990; 140 (1965), A85. (1965) DOI10.1103/PhysRev.139.A981
  15. I. Kuščer I. Vidav, 10.1016/0022-247X(69)90214-5, J. Math. Anal. Appl. 25 (1969), 80-92. (1969) DOI10.1016/0022-247X(69)90214-5
  16. I. Marek, 10.1137/0119060, SIAM J. Appl. Math. 19 (1970), 607-628. (1970) Zbl0219.47022MR0415405DOI10.1137/0119060
  17. I. Marek, On Fredholm points of compactly perturbed bounded linear operators, Acta Univ. Carol. - Mathematica et Physica Vol. 17, (1976) No. 1, 65 - 72. (1976) MR0423106
  18. I. Marek, On some spectral properties of Radon-Nikolskii operators and their generalizations, Comment. Math. Univ. Carol. 3, 1 (1962), 20-30. (1962) MR0144216
  19. J. Mika, 10.13182/NSE61-1, Nucl. Sd. Eng. 11 (1961), 415 - 427. (1961) DOI10.13182/NSE61-1
  20. B. Montagnini M. L. Demuru, 10.1016/0022-247X(65)90052-1, J. Math. Anal. Appl. 12 (1965), 49-57. (1965) MR0186322DOI10.1016/0022-247X(65)90052-1
  21. W. Rudin, Functional Analysis, McGraw-Hill Co. New York, 1973. (1973) Zbl0253.46001MR0365062
  22. I. Sawashima, On spectral properties of some positive operators, Natur. Sci. Rep. Ochanomizu Univ. 15 (1969), 55-66. (1969) MR0187096
  23. V. F. Turchin, Thermal Neutrons, Gosatomizdat, Moscow 1963 (Russian). (1963) 
  24. L. Van Hove, 10.1103/PhysRev.95.249, Phys. Rev. 95 (1954), 249. (1954) Zbl0056.44205MR0063964DOI10.1103/PhysRev.95.249
  25. A. M. Weinberg E. P. Wigner, The Physical Theory of Neutron Chain Reactors, Chicago University Press, Chicago 1958. (1958) MR0113336
  26. M. M. R. Williams, The Slowing Down and Thermalization of Neutrons, North-Holland Publ. Company, Amsterdam 1966. (1966) 
  27. R. Zelazny, 10.1063/1.1703738, J. Math. Phys. 2 (1961), 538-542. (1961) Zbl0102.43102MR0129922DOI10.1063/1.1703738

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.