Mechanism of Action of Newly Developed Vitamin D Analogue

Okamoto, Sumiaki; Ejima, Eri; Kiriyama, T.; Izumi, Masaaki; Komori, Asako; Suzuki, Hidekazu; Katsumata, T; Nagata, Akihiko

doi:10.1159/000420171

Cited by 2 publications

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“…The Painlevé equation looks like a sophisticated non-linear equation of a rather strange form. However, it just a particular example of a set of Toda τ -functions satisfying the usual bilinear Hirota relation [42]…”

Section: Painlevé VI Equation For Fourier Transformed Conformal Blocksmentioning

confidence: 99%

On determinant representation and integrability of Nekrasov functions

Миронов¹,

Морозов²

2017

Physics Letters B

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Conformal blocks and their AGT relations to LMNS integrals and Nekrasov functions are best described by "conformal" (or Dotsenko-Fateev) matrix models, but in non-Gaussian Dijkgraaf-Vafa phases, where different eigenvalues are integrated along different contours. In such matrix models, the determinant representations and integrability are restored only after a peculiar Fourier transform in the numbers of integrations. From the point of view of conformal blocks, this is Fourier transform w.r.t. the intermediate dimensions and this explains why such quantities are expressed through tau-functions in Miwa parametrization, with external dimensions playing the role of multiplicities. In particular, these determinant representations provide solutions to the Painlev\'e VI equation. We also explain how this pattern looks in the pure gauge limit, which is described by the Brezin-Gross-Witten matrix model.Comment: 15 page

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Section: Painlevé VI Equation For Fourier Transformed Conformal Blocksmentioning

confidence: 99%