This paper generalizes former works of Derksen, Weyman and Zelevinsky about quivers with potentials. We consider semisimple finite-dimensional algebras E over a field F, such that E?FEop is semisimple. assume contains certain type F-basis which generalization multiplicative basis. study potentials belonging to the algebra formal power series, coefficients in tensor E, any E-E-bimodule on F acts...

We prove a general theorem for constructing integral quantum cluster algebras over Z[q±1/2], namely, that under mild conditions the forms of nilpotent always possess algebra structures. These are then shown to be isomorphic corresponding upper algebras, again defined Z[q±1/2]. Previously, this was only known acyclic algebras. The is applied that, every symmetrizable Kac–Moody g and Weyl group e...

This is the second paper in a series which we develop machine learning (ML) moment closure models for radiative transfer equation (RTE). In our previous work \cite{huang2021gradient}, proposed an approach to directly learn gradient of unclosed high order moment, performs much better than itself and conventional $P_N$ closure. However, ML model \cite{huang2021gradient} not able guarantee hyperbo...

Abstract We consider the approximation of Navier-Stokes equations for a Newtonian fluid by Euler type systems with relaxation both in compressible and incompressible cases. This requires to decompose second-order derivative terms velocity into first-order ones. Usual decompositions lead approximate tensor variables. construct vector variables using Hurwitz-Radon matrices. These are written form...

The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and consider...

We described in [M1] a monoid b G, the face monoid, acting on the integrable highest weight modules of a symmetrizable Kac-Moody algebra. It has similar structural properties as a reductive algebraic monoid whose unit group is a Kac-Moody group G. We found in [M5] two natural extensions of the action of the Kac-Moody group G on its building Ω to actions of the face monoid b G on the building Ω....

We consider a generalization of the quiver varieties of Lusztig and Nakajima to the case of all symmetrizable Kac-Moody Lie algebras. To deal with the non-simply laced case one considers admissible automorphisms of a quiver and the irreducible components of the quiver varieties fixed by this automorphism. We define a crystal structure on these irreducible components and show that the crystals o...