A recent result of S.-Y. Lee and M. Yang states that the planar orthogonal polynomials with respect to a modified Gaussian measure are multiple type II on contour in complex plane. We show same also I contour, provided exponents weight integer. From this orthogonality, we derive several equivalent Riemann-Hilbert problems. The proof is based fundamental identity Yang, which establish using new ...

Reduced nonlocal matrix integrable modified Korteweg–de Vries (mKdV) hierarchies are presented via taking two transpose-type group reductions in the Ablowitz–Kaup–Newell–Segur (AKNS) spectral problems. One reduction is local, which replaces parameter ? with its complex conjugate ??, and other one nonlocal, negative ???. Riemann–Hilbert problems thus inverse scattering transforms formulated from...

We study a Riemann problem for the unsteady transonic small disturbance equations that results in a diverging rarefaction problem. The self-similar reduction leads to a boundary value problem with equations that change type (hyperbolic-elliptic) and a sonic line that is a free boundary. We summarize the principal ideas and present the main features of the problem. The flow in the hyperbolic par...

In this note, we consider the Riemann problem for a twodimensional nonstrictly hyperbolic system of conservation laws. Without the restriction that each jump of the initial data projects one planar elementary wave, six topologically distinct solutions are constructed by applying the generalized characteristic analysis method, in which the delta shock waves and the vacuum states appear. Moreover...

The paper studies a class of conservation law models for traffic flow on a family of roads, near a junction. A Riemann Solver is constructed, where the incoming and outgoing fluxes depend Hölder continuously on the traffic density and on the drivers’ turning preferences. However, various examples show that, if junction conditions are assigned in terms of Riemann Solvers, then the Cauchy problem...

Extended thermodynamics derives dissipative, hyperbolic field equations for monatomic gases. One example is the system of the 13-field-case, which is a dissipative extension of the Euler equations. In this paper the system is investigated by solving a Riemann problem. Additionally some model equations are introduced so as to discuss the main properties in a transparent manner. There arises an i...

We study a Riemann problem for the two-dimensional isentropic gas dynamics equations which models transonic regular reflection. When written in self-similar coordinates, the system changes type from hyperbolic to mixed hyperbolic-elliptic. Using the theory of one-dimensional hyperbolic conservation laws, we formulate a free boundary problem in the subsonic region and we outline the main ideas f...

It is considered the hyperbolic-parabolic approximation

A Riemann surface is called pseudo-real if it admits anticonformal automorphisms but no anticonformal involution. Pseudo-real Riemann surfaces appear in a natural way in the study of the moduli space MKg of Riemann surfaces considered as Klein surfaces. The moduli space Mg of Riemann surfaces of genus g is a two-fold branched covering of MKg , and the preimage of the branched locus consists of ...