Synopsis. In a cartesian closed category with an initial object and a dominance that classiies it, an intensional notion of approximation between maps |the path relation (c.f. link relation)| is deened. It is shown that if such a category admits strict/upper-closed factorisations then it preorder-enriches (as a cartesian closed category) with respect to the path relation. By imposing further ax...

The famous Drinfeld-Kohno theorem for simple Lie algebras states that the monodromy representation of the Knizhnik-Zamolodchikov equations for these Lie algebras expresses explicitly via R-matrices of the corresponding Drinfeld-Jimbo quantum groups. This result was generalized by the second author to simple Lie superalgebras of type A-G. In this paper, we generalize the Drinfeld-Kohno theorem t...

In this article, we define an algebraic version of the Knizhnik–Zamolodchikov (KZ) functor for degenerate double affine Hecke algebras (a.k.a. trigonometric Cherednik algebras). We compare it with KZ monodromy constructed by Varagnolo–Vasserot. prove centraliser property our and give a characterisation its kernel. establish these results family algebras, called quiver which includes as special ...

We outline a definition of accessible and presentable objects in 2-category K endowed with “KZ context”, that is to say pair lax-idempotent monads interacting prescribed way; this perspective suggests unified treatment many “Gabriel-Ulmer like” theorems, asserting how arise as reflections generating ones. the notion (Gabriel-Ulmer) envelope for KZ context, sufficient concoct Gabriel-Ulmer duali...

This paper presents the development of two empirical ozone-forecasting models for predicting hourly ozone concentrations near Cincinnati, Ohio. This study examined the hourly ozone data collected between 1995 and 1999 at an ozone monitoring station in the Cincinnati area. Two different models, the KZ model and the NN model, were developed using data from 1995 to 1998. The KZ model was developed...

We consider an Sp(4,Z) invariant expression involving two factors of the Kawazumi--Zhang (KZ) each which is a modular graph with one link, and four derivatives on moduli space genus Riemann surfaces. Manipulating it, we show that integral over linear combination links square KZ reduces to boundary integral. also three six space, from deduce In both cases, term completely determined by invariant...

We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions. We prove that under some conditions the solution of KZ system is rational too. We give the method of constructing the corresponding rational solution. We deduce the asymptotic formulas for the solution of KZ system when ρ is integer.