We generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto’s factorization results for biregular bipartite graphs apply, leading to exact factorizations. For (d, r)-regular hypergraphs, we show that a modified Riemann hypothesis is true if and only if the hypergraph is Ramanujan in the sense of Winnie Li and Patrick Solé. Finally, we give an example to show how the...

We consider the Lighthill-Witham-Richards traffic flow model on a junction composed by one mainline, an onramp and an offramp, which are connected by a node. The onramp dynamics is modeled using an ordinary differential equation describing the evolution of the queue length. The definition of the solution of the Riemann problem at the junction is based on an optimization problem and the use of a...

A two-dimensional Riemann solver is proposed for the solution of hyperbolic systems of conservation laws in two dimensions of space. The solver approximates the solution of a so-called angular two-dimensional Riemann problem as the weighted sum of the solutions of one-dimensional Riemann problems. The weights are proportional to the aperture of the regions of constant state. The two-dimensional...

In this paper, we present a general iterative method for the solution of the Riemann problem for hyperbolic systems of PDEs. The method is based on the multiple shooting method for free boundary value problems. We demonstrate the method by solving one-dimensional Riemann problems for hyperelastic solid mechanics. Even for conditions representative of routine laboratory conditions and military b...

We develop the inverse scattering transform method for the Novikov equation ut − utxx + 4uux = 3uuxuxx + uuxxx considered on the line x ∈ (−∞,∞) in the case of non-zero constant background. The approach is based on the analysis of an associated Riemann–Hilbert (RH) problem, which in this case is a 3×3 matrix problem. The structure of this RH problem shares many common features with the case of ...

Coupled modified nonlinear Schrödinger(CMNLS) equations describe the pulse propagation in the picosecond or femtosecond regime of the birefringent optical fibers. In this paper, we use the Fokas method to analyze the initialboundary value problem for the CMNLS equations on the half-line. Assume that the solution u(x, t) and v(x, t) of CMNLS equations are exists, and we show that it can be expre...

The Møller tetrad gravitational energy-momentum expression was recently evaluated for a small vacuum region using orthonormal frames adapted to Riemann normal coordinates. However the result was not proportional to the Bel-Robinson tensor Bαβμν . Treating a modified quasilocal expressions in a similar way, we found one unique combination that gives a multiple of Bαβμν which provides a non-negat...

Abstract The fractional wave equation is presented as a generalization of the wave equation when arbitrary fractional order derivatives are involved. We have considered variable dielectric environments for the wave propagation phenomena. The Jumarie’s modified Riemann-Liouville derivative has been introduced and the solutions of the fractional Riccati differential equation have been applied to ...

It is shown that Schroedinger equation is not consistent with information theory. From the modified form of information which ensures that the most probable density function it yields tallies with a general form of continuous Riemann integrable density function that has real or imaginary zeros or singularities at end points of [a,b]∈R, a new variational formulation for quantum mechanics is prop...

The Riemann-Hilbert problem associated with the integrable PDE is used as a nonlinear transformation of the nearly integrable PDE to the spectral space. The temporal evolution of the spectral data is derived with account for arbitrary perturbations and is given in the form of exact equations, which generate the sequence of approximate ODEs in successive orders with respect to the perturbation. ...