DOI: https://doi.org/10.31071/kit2015.12.04 Inventory reference ISSN 1812-7231 Klin.inform.telemed. Volume 11, Issue 12, 2015, Pages 26–30 Author(s) V. P. Martsenyuk, A. S. Sverstyuk, O. M. Kuchvara Institution(s) I. Ya. Horbachevsky Ternopil State Medical University, Ukraine Article title Exercise of optimal control of annealing stage оf polymerase chain reaction Abstract (resume) The general methodology of optimal control for obtaining the solution of the exercise of optimal flow on the annealing stage in the polymerase chain reaction is examined. Pontryagin's maximum principle to the exercise of optimal control is applied and the necessary condition of optimality is formulated. The results are useful for the numerical calculation of optimal control under the examined stage and help to minimize the required time of annealing stage implementation Keywords polymerase chain reaction, annealing stage, optimal control, Pontryagin's maximum principle References 1. Putintseva G. Y. Medychna henetyka: pidruchnyk [Medical genetics: a textbook]. K., 2008, 392 p. (In Ukr.). 2. Aach J., Church G. M. Mathematical models of diffusion-constrained polymerase chainreactions: basis of high-throughput nucleic acid assays and simple self-organizing systems. J. of Theoretical Biology, 2004, vol. 228, pp. 31–46. 3. Pfaffl M. W. A new mathematical model for relative quantification in real-time RT–PCR. Oxford Journals Science & Mathematics Nucleic Acids Research, vol. 29, iss. 900, pp. 45–51. 4. Xiangchun X., Sinton D., Dongqing L. Thermal end effects on electroosmotic flow in capillary. Int. J. of Heat and Mass transfer, 2004, vol. 47, iss. 14–16, pp. 3145–3157. 5. Stone E., Goldes J., Garlick M. A multi-stage model for quantitative PCR. Mathematical biosciences and engineering, 2000, vol. 00, iss. 0, pp. 1–17. 6. Lukes D. L. Differential Equations: Classical to Controlled. Academic Press, New York, 1982, vol. 162, 322 p. 7. Piccinini L. C., Stampacchia G., Vidossich G. Ordinary Differential Equations. In Rn. Problems and Methods Ordinary. Springer-Verlag Publ., Berlin-Heidelberg-New York-Tokyo, 1984, vol. XII, 385 p. 8. Macki J., Strauss A. Introduction to Optimal Control Theory. Springer-Verlag Publ., New York, 1982, vol. XIV, 168 p. 9. Fleming W. H., Rishel R. W. Deterministic and Stochastic Optimal Control. Springer Verlag Publ., New York, 1975, vol. XIII, 222 p. 10. Kamien M. I., Schwartz N. L. Dynamic Optimization. North- Holland Publ., Amsterdam, 1991, vol. 3, 272 p. 11. Pontryagin L. S., Boltyanskiy V. G., Gamkrelidze R. V., Mischenko E. F. Matematycheskaya teoryya optymalnyh protsessov [The mathematical theory of optimal processes]. M., 1983, 393 p. (In Russ.) 12. Kelly K., Kostin M. Non-Arrhenius rate constants involving diffusion and reaction. J. of Chemical Physics, 1986, vol. 85, iss. 12, pp.7318–7335. Full-text version http://kit-journal.com.ua/en/viewer_en.html?doc/2015_12/6.pdf |
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