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 comparable subject matters, so much of that have been awarded as papers on the foreign convention "Algebraic research of Differential Equations – from Microlocal research to Exponential Asymptotics" at Kyoto collage in 2005. Microlocal research and exponential asymptotics are in detail hooked up and supply strong instruments which were utilized to linear and non-linear differential equations in addition to many similar fields resembling actual and complicated research, quintessential transforms, spectral concept, inverse difficulties, integrable platforms, and mathematical physics. The articles contained right here current many new effects and concepts, delivering researchers and scholars with necessary 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 celebration of Professor Kawai's sixtieth birthday as a token of deep appreciation of the real contributions he has made to the sector. Introductory notes at the medical works of Professor Kawai also are included.

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45-61. : Exact WKB analysis of non-adiabatic transition probabilities for three levels, J. Phys. A: Math. , 35 (2002), 2401-2430. C. M. Bender and T. T. Wu: Anharmonic oscillator, Phys. , 184 (1969), 1231-1260. H. L. Berk, W. M. Nevins and K. V. Roberts: New Stokes’ line in WKB theory, J. Math. , 23 (1982), 988-1002. R. Courant and D. Hilbert: Methods of Mathematical Physics, II, Interscience, 1962. E. Delabaere, H. Dillinger and F. Pham: Exact semi-classical expansions for one dimensional quantum oscillators, J.

Fl }, the element flk is not a zero divisor on Ox0 /(fl0 , . . , flk−1 ). Note that we do not assume x0 to be a common zero of f0 , f1 , . . , fl . As in the case of regular sequences, we have Theorem 2. Let f0 , f1 , . . , fl be elements in Ox0 . Then the following two conditions are equivalent: 1. The sequence f0 , f1 , . . , fl is a tame regular sequence at x0 . 2. For any k = 0, . . , l and for any (k + 1) choice fl0 , fl1 , . . , flk of elements in {f0 , f1 , . . , fl }, the dimension of V (x0 , fl0 , .

The wording “a new turning point” has been superseded by “a virtual turning point” in recent literature, and here, and in what follows, we use this new wording. As the eﬀect of a virtual turning point is inert in its immediate vicinity, we discuss in Section 2 its relevance to the bifurcation of a Stokes curve so that its eﬀect may become impressively visible. In Section 3 we discuss how this relevance gives a neat interpretation of the strange and intriguing phenomenon that one of us (S. Sasaki; [Sa1], [Sa2]) has found in analyzing the Noumi-Yamada system ([NY]) with the help of a computer.

### Algebraic analysis of differential equations: from microlocal analysis to exponential asymptotics; Festschrift in honor Prof. Takahiro Kawai [on the occasion of his sixtieth birthday] by T. Aoki, H. Majima, Y. Takei, N. Tose

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