We investigate the dynamical behaviours of n-vortex problem with circulation vector $$\varvec{\Gamma }$$ on a Riemann sphere $${\mathbb {S}}^2$$ , equipped an arbitrary metric g. By mixing perspectives from Riemannian geometry and symplectic geometry, we prove that for any given Hamiltonian is Morse function $${\mathcal {C}}^2$$ generic If some constraints are put then such g possesses finitely...

Angelesco systems of measures with Jacobi type weights are considered. For such systems, strong asymptotics for the related multiple orthogonal polynomials are found as well as the Szegő-type functions. In the procedure, an approach from Riemann-Hilbert problem plays a fundamental role.

The purpose of this paper is to give a proof to the equivalence of the derived category of holonomic systems and that of constructible sheaves. Let X be a paracompact complex manifold and let ® x and 0 x be the sheaf of differential operators and holomorphic functions, respectively. We denote by Mod(^z) the abelian category of left ^^-Modules and by D(^) its derived category. Let ~D^(^x) denote...