Abstract. We find a local (d + 1)× (d + 1) Riemann-Hilbert problem characterizing the skew-orthogonal polynomials associated to the partition function of the Gaussian Orthogonal Ensemble of random matrices with a potential function of degree d. Our Riemann-Hilbert problem is similar to a local d × d RiemannHilbert problem found by Kuijlaars and McLaughlin characterizing the bi-orthogonal polyno...

We study the domain of existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions. The Riemann problem is the expansion of a quadrant of gas of constant state into the other three vacuum quadrants. The global existence of a smooth solution was established in Dai and Zhang [Arch. Rational Mech. Anal., 155(2000), 277-298] up to the free boundary of vac...

The aim of this paper is to present theoretical basis for computing a representation of a compact Riemann surface as an algebraic plane curve and to compute a numerical approximation for its period matrix. We will describe a program Cars ((3]) that can be used to deene Riemann surfaces for computations. Cars allows one also to perform the Fenchel{Nielsen twist and other deformations on Riemann ...

The theory of Riemann boundary value problem for analytic functions of one complex variable and singular integral equations that are equivalent to it has been extensively studied in the literature. For classical books on this topic see [7, 12, 13] and for an actual overview of them the reader is directed to the monograph by Estrada and Kanwal [6], and the references therein. In the more recent ...

We characterize the biorthogonal polynomials that appear in the theory of coupled random matrices via a Riemann-Hilbert problem. Our Riemann-Hilbert problem is different from the ones that were proposed recently by Ercolani and McLaughlin, Kapaev, and Bertola et al. We believe that our formulation may be tractable to asymptotic analysis.

The solution of the Riemann problem was a building block for general Cauchy problems in conservation laws. A Cauchy problem is approximated by a series of Riemann problems in many numerical schemes. But, since the structure of the Riemann solution holds locally in time only, and, furthermore, a Riemann solution is not piecewise constant in general, there are several fundamental issues in this a...