English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

[Note: important Corrigendum now available at arXiv:1601.04790] Theisomonodromic tau function defined by Jimbo-Miwa-Ueno vanishes on theMalgrange's divisor of generalized monodromy data for which a vector bundle isnontrivial, or, which is the same, a certain Riemann-Hilbert problem has nosolution. In their original work, Jimbo, Miwa, Ueno did not derive thedependence on the (generalized) monodromy data (i.e. monodromy representationand Stokes' parameters). We fill the gap by providing a (simpler and moregeneral) description in which all the parameters of the problem(monodromy-changing and monodromy-preserving) are dealt with at the same level.We thus provide variational formulae for the isomonodromic tau function withrespect to the (generalized) monodromy data. The construction applies moregenerally: given any (sufficiently well-behaved) family of Riemann-Hilbertproblems (RHP) where the jump matrices depend arbitrarily on deformationparameters, we can construct a one-form Omega (not necessarily closed) on thedeformation space (Malgrange's differential), defined off Malgrange's divisor.We then introduce the notion of discrete Schlesinger transformation: it meansthat we allow the solution of the RHP to have poles (or zeros) at prescribedpoint(s). Even if Omega is not closed, its difference evaluated along theoriginal solution and the transformed one, is shown to be the logarithmicdifferential (on the deformation space) of a function. As a function of theposition of the points of the Schlesinger transformation, yields a naturalgeneralization of Sato formula for the Baker-Akhiezer vector even in theabsence of a tau function, and it realizes the solution of the RHP as such BAvector. Some exemples (Painleve' II and finite Toplitz/Hankel determinants) areprovided.

The dependence on the monodromy data of the isomonodromic tau function