Volume 1, Issue 1 (April 2016)

Original research papers

Neutron and
Heavy Ion Radiations


Slavica M. Perovich, Martin P. Calasan

Pages: 1-6

DOI: 10.21175/RadJ.2016.01.01

Received: 17 MAR 2015, Received revised: 11 MAY 2015, Accepted: 15 MAY 2015, Published Online: 28 APR 2016

The problem of finding an exact analytical closed form solution to the degree of the nuclear fuel burn-up simple transcendental equation is studied in some detail, by using the Special trans functions theory (STFT). Structure of the STFT solutions, derivations, numerical results and graphical simulations confirm the validity and base principle of the STFT
  1. V.V. Frolov, Ядерно-физические методы контроля делящихся веществ (Nuclear-Physical Methods of Fissile Materials Control), Moskow, Russia: Энергоатомиздат, 1989.
  2. S.M. Perovic and S. Jovanovic, “A Contribution to the Theory of the Slowing Down in the Carbide of Silicium,” Proc. in Int. Conf. Signal & Systems, vol. 2, Geneva, Switzerland, June 17-19, 1992, pp. 173-180.
  3. R. Gregg, A. Worrall, “Effect of Highly Enriched/ Highly Burnt UO2 Fuels on Fuel Cycle Costs, Radiotoxicity and Nuclear Design Parameters,” Nuclear Technology, Vol. 151, no. 2, pp.126-132, Aug., 2005.
  4. J. Secker et al., “Optimum Discharge Burn-up and Cycle Length for PWRs”, Nuclear Technology, vol. 151, no.2, pp. 109-111, Aug., 2005.
  5. “Experimental Investigation of Burn-up Credit for Safe Transport, Storage, and Disposal of Spent Nuclear Fuel,” NERI 2001 Annual Report, NERI 99-200, US Department of Energy, Washington DC, USA, DOE/NE-0122, pp. 211-212.
  6. S.M. Perovich, “Transcendental Method in the Theory of Neutron Slowing Down,” J Phys A: Math.Gen., vol. 25, no.10, pp. 2969-2689, 1992.
    DOI: 10.1088/0305-4470/25/10/024
  7. S.M. Perovich, “Reply to the Comment on the Transcendental Method,” J Phys A: Math.Gen., vol. 28, no. 14, pp. 4191-4200, 1995.
    DOI: 10.1088/0305-4470/28/14/035
  8. S.M. Perovich, D.V. Tosic, “Transcendental Method in the Nonlinear Circuits Theory,” Electron. Lett, vol. 32, no. 16, pp. 1433-1437, 1996.
    DOI: 10.1049/el:19961000
  9. S.M. Perovich, “Concerning the Analytical Solution of the Disperse Equation in the Linear Transport Theory,” Transport Theory and Statistical Physics, vol. 6, iss. 6, pp. 705-725, 1997.
    DOI: 10.1080/00411459708229331
  10. S.M. Perovich et al., “Some Comments Concerning the Discrete Eigen value,” Nucl. Sci. Eng., vol. 131, no. 3, p. 439, 1999.
  11. S.M. Perovich, S.I. Bauk, “The Analytical Analysis of Hopfield Neuron Parameters by the Application of the Special Trans Function Theory,” in Adaptive and Natural Computing Algorithms, B. Ribeiro, R.F. Al- brecht, A. Dobnikar, D.W. Pearson, N.C. Steele, Eds., New York (NY), USA: Springer, pp. 29–32, 2005.
    DOI: 10.1007/3-211-27389-1_9
  12. S.M. Perovich et al. “On the Analytical Solution of Some Families of Transcendental Equation,” Appl. Math. Lett., vol. 20, iss. 5, p. 493, 2007.
    DOI: 10.1016/j.aml.2006.06.008
  13. N.S. Singh, et al, “Determination of the Solar Cell Junction Ideality Factor Using Special Trans Function Theory (STFT),” Sol. Energy Mater Sol. Cells, vol. 93, iss. 8, pp. 1423-1426, 2009.
    DOI: 10.1016/j.solmat.2009.03.013
  14. S.M. Perovich, S.I. Bauk, “Determination of the Pluto- nium Temperature Using the Special Trans Functions Theory,” Nucl. Tech. & Rad. Protect., vol. 25, iss. 3, pp. 164-170, 2010.
    DOI: 10.2298/NTRP1003164P
  15. S.M. Perovich, S.I. Bauk, “An Inverse Problem of Tempe- rature Estimation for the Combination of the Linear and Non-Linear Resistances,” AIP Advances in Physics, vol. 022110, pp. 1-14, 2011.
    DOI: 10.1063/1.3589909
  16. S.M. Perovich, “The Special Trans Functions Theory,” Research Monograph, Podgorica, Monte Negro: Univ. of Montenegro, 2004.
  17. S.M. Perovich et al., “On the Exact Analytical Solution of Certain Lambert Transcendental Equation,” Math. Probl. Eng., vol. 2011, pp. 1-21, 2011.
    DOI: 10.1155/2011/685485
  18. N.S. Singh et al., “A New Method to Determine the Optimum Load of a Real Solar Cell Using Special Trans Function Theory (STFT),” Int. Jour. Renew. En. Res., vol. 3, no. 2, pp. 378-382, 2013.
  19. S.M. Perovich, M. Orlandic, M. Calasan, “Concerning Exact Analytical STFT Solution to Some Families of Inverse Problems in Engineering Material Theory,” Appl. Math. Modell., vol. 37, iss. 7, pp. 5474-5497, Apr., 2013.
    DOI: 10.1016/j.apm.2012.10.052
  20. S. Marguet, La physique des reacteurs nucleaires (The Physics of Nuclear Reactors), 1st and 2nd ed., Paris, France: Lavoisier, p. 471, 2011, and p. 512, 2013.
  21. S.M. Perovich, M. Calasan, R. Toskovic, “On the Exact Analytical Solution of Some Families of Equilibrium Critical Thickness Transcendental Equations,” AIP Advances 4, vol. 117124, 2014.
    DOI: 10.1063/1.4902161
  22. S.M. Perovich et al., “Concerning a Novel Mathematical Approach to the Solar Cell Junction Ideality Factor Estimation,” Appl. Math. Modell., vol. 39, iss. 12, pp. 3248-3264, June 2015.
    DOI: 10.1016/j.apm.2014.11.026
  23. S.M. Perovich et al., “Concerning Current STFT Estima- tions to the RC Diode Circuit,” 3rd Mediter. Conf. Embed. Comp., Budva, Montenegro, 15-19, June, 2014, pp. 193-197.
    DOI: 10.1109/MECO.2014.6862692