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...

This paper addresses the problems of stability a nabla discrete distributed-order dynamical system (NDDS). Firstly, based on proposed generalized definition integral, some related definitions calculus are given. Then, several useful inequalities in sense fractional-order difference extended to cases. Meanwhile, basis and Lyapunov direct method, sufficient conditions guaranteeing asymptotic orig...

In this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and operational matrix of product based on the Bernstein basis. Then, we get the Bernstein operational matrix for the Jumarie’s modified Riemann-Liouville fractio...

We consistently develop a recently proposed scheme of matrix extension dispersionless integrable systems for the general case multidimensional hierarchies, concentrating on dimension $d\geqslant 4$. present extended Lax pairs, Lax-Sato equations, equations background vector fields and dressing scheme. Reductions, construction solutions connections to geometry are discussed. consider separately ...

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

Preface These notes treat the problem of counting the number of rational points on a curve defined over a finite field. The notes are an extended version of an earlier set of notes Aritmetisk Algebraisk Geometri – Kurver by Johan P. Hansen [Han] on the same subject. In Chapter 1 we summarize the basic notions of algebraic geometry, especially rational points and the Riemann-Roch theorem. For th...

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 ...

The long standing problem of the relations among the scalar invariants of the Rie-mann tensor is computationally solved for all 6·10 23 objects with up to 12 derivatives of the metric. This covers cases ranging from products of up to 6 undifferentiated Riemann tensors to cases with up to 10 covariant derivatives of a single Riemann. We extend our computer algebra system Invar to produce within ...