Read e-book online Algebraic Analysis of Differential Equations: from PDF

By T. Aoki, H. Majima, Y. Takei, N. Tose

ISBN-10: 443173239X

ISBN-13: 9784431732396

This quantity includes 23 articles on algebraic research of differential equations and similar issues, so much of which have been awarded as papers on the overseas convention ''Algebraic research of Differential Equations – from Microlocal research to Exponential Asymptotics'' at Kyoto college in 2005. Microlocal research and exponential asymptotics are in detail attached and supply robust instruments which have been utilized to linear and non-linear differential equations in addition to many similar fields resembling genuine and intricate research, indispensable transforms, spectral thought, inverse difficulties, integrable structures, and mathematical physics. The articles contained right here current many new effects and concepts, delivering researchers and scholars with priceless feedback and instructive counsel for his or her paintings. This quantity is devoted to Professor Takahiro Kawai, who's one of many creators of microlocal research and who brought the means of microlocal research into exponential asymptotics. This commitment is made at the get together of Professor Kawai's sixtieth birthday as a token of deep appreciation of the $64000 contributions he has made to the sector. Introductory notes at the clinical works of Professor Kawai also are included.

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Kawai, S. Sasaki, A. Shudo and Y. Takei: Virtual turning points and bifurcation of Stokes curves, J. Phys. A: Math. , 38 (2005), 3317-3336. Takei: New turning points in the exact WKB analysis for higher-order ordinary differential equations, Analyse Alg´ebrique des Perturbations Singuli`eres. I, Hermann, 1994, pp. 69-84. : On the exact WKB analysis for the third order ordinary differential equations with a large parameter, Asian J. , 2 (1998), 625-640. : On the exact steepest descent method: A new method for the description of Stokes curves, J.

II, Academic Press, 1988, pp. 699–726. [V] A. Voros: The return of the quartic oscillator. The complex WKB method, Ann. Inst. Henri Poincar´e, 39(1983), 211–338. [Z] J. Zinn-Justin: Instantons in quantum mechanics: Numerical evidence for a conjecture, J. Math. , 25(1984), 549–555. , Asagaya-kita 2-13-2, Suginami-ku, Tokyo 166-0001, Japan Mitsubishi UFJ Securities Co. , Marunouchi 2-4-1, Chiyoda-ku, Tokyo 100-6317, Japan Department of Physics, Graduate School of Science, Tokyo Metropolitan University, Hachioji 192-0397, Japan Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan Summary.

For any k = 0, . . , l, the element ak is not a zero divisor on R/(a0 , . . , ak−1 ). 2. (a0 , . . , al ) = R. Note that the notion of regular sequences depends on the ordering of a0 , a1 , . . , al . Definition 4. The sequence a0 , a1 , . . , al is called a tame regular sequence if for any k = 0, . . , l and for any (k + 1) choice al0 , al1 , . . , alk of elements in {a0 , a1 , . . , al }, the element alk is not a zero divisor on R/(al0 , . . , alk−1 ). Note that the notion of tame regular sequences is independent of the ordering of aj ’s and that the second condition in Definition 3 is not assumed.

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Algebraic Analysis of Differential Equations: from Microlocal Analysis to Exponential Asymptotics by T. Aoki, H. Majima, Y. Takei, N. Tose


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