Download A History of Greek Mathematics, Volume 2: From Aristarchus by Thomas Heath PDF

By Thomas Heath

ISBN-10: 0486240746

ISBN-13: 9780486240749

Volume 2 of an authoritative two-volume set that covers the necessities of arithmetic and lines each landmark innovation and every very important determine, including Euclid, Apollonius, and others.

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Extra info for A History of Greek Mathematics, Volume 2: From Aristarchus to Diophantus (Dover Books on Mathematics)

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Hirao, Chem. Phys. Lett. 432, 585 (2006) 12. Y. Shigeta, H. Miyachi, K. Hirao, J. Chem. Phys. 125, 244102 (2006) 13. Y. Shigeta, H. Miyachi, K. Hirao, Chem. Phys. Lett. 443, 414 (2007) 14. Y. Shigeta, AIP Proceedings 963, 1317 (2007) 15. Y. Shigeta, Chem. Phys. Lett. 461, 310 (2008) 16. Y. Shigeta, J. Chem. Phys. 128, 161103 (2008) 17. Y. Shigeta, H. Miyachi, T. Matsui, K. Hirao, Bull. Chem. Soc. Jpn. 81, 1230 (2008) 18. V. Pereverzev, A. Pereverzev, Y. V. Prezhdo, J. Chem. Phys. 129, 164103 (2008) 19.

The first and second schemes were implemented and we carried out QCD simulations on the one-particle Morse potential. We have shown numerically the difference between the truncation, which is equivalent to QHD2, and the analytic schemes in terms of the phase space structure and the trajectories, although both methods preserved the total energy during 10,000-step calculations. The present scheme conserves the energy and is more robust than the truncation scheme that was initially presented by Prezhdo et al.

Be considered to perform reliable simulations. The table shows that for the analysis of fundamental frequencies, the QCD2 has higher accuracy than the classical results, which can be compared with the VPT2 results in all cases. In spite of the high accuracy, the computational cost of the QCD2 remains low even when applied to larger systems. For HCOOH molecule, the QFF is so anharmonic that the classical simulation does not give clear vibrational frequencies due to the chaotic behavior of the power spectrum.

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