The Boyer-Finley equation, or SU(∞)-Toda equation is both a reduction of the self-dual Einstein equations and the dispersionless limit of the 2d-Toda lattice equation. This suggests that there should be a dispersive version of the self-dual Einstein equation which both contains the Toda lattice equation and whose dispersionless limit is the familiar self-dual Einstein equation. Such a system is...

Traffic injuries are predicted to be the fifth leading cause of death and injury by 2030 if no further action is taken. Generation Y, who are growing up with technology and Internet, are among the most vulnerable road users, so it is crucial to provide effective road safety training for them. In the light of the Uses and Gratification Theory (U&G), we propose a conceptual research model to meas...

We consider the scaling behavior of directed percolation and of the pair contact process with a conjugated field. In particular we determine numerically the equation of state and show that both models are characterized by the same universal scaling function. Furthermore we derive the equation of state for the pair contact process within a mean-field approach which again agrees with the mean-fie...

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now propose a variational principle for Evans’ theory and show that it yields two field equations. The second field equation is algebraic in the torsion...

We present a general procedure for determining quasi-exact solvability of the Dirac and the Pauli equation with an underlying sl(2) symmetry. This procedure makes full use of the close connection between quasi-exactly solvable systems and supersymmetry. The Dirac-Pauli equation with spherical electric field is taken as an example to illustrate the procedure. 1. In this talk we present a general...

The quantum correlations of scalar fields are examined as a power series in derivatives. Recursive algebraic equations are derived and determine the amplitudes; all loop integrations are performed. This recursion contains the same information as the usual loop expansion. The approach is pragmatic and generalizable to most quantum field theories.

We study the static Einstein equation coupled with a scalar field with axial symmetry. The zero curvature equation both for the scalar field and a part of the metric in the scalar-Einstein equation enables one to obtain soliton solutions for both the scalar field and the metric. Of the infinite series of solutions for the metric and the scalar field we focus on the solution composed of 4-solito...

Abstract. Mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to +∞, have been recently introduced by J-M. Lasry and P-L. Lions. Under suitable assumptions, they lead to a system of two coupled partial differential equations, a forward Bellman equation and a backward Fokker-Planck equations. Finite difference schemes for the ap...

We consider a D-dimensional cosmological model describing an evolution of (n+1) Einstein factor spaces (n ≥ 2) in the theory with several dilatonic scalar fields and generalized electro-magnetic forms, admitting an interpretation in terms of intersecting p-branes. The equations of motion of the model are reduced to the Euler-Lagrange equations for the so called pseudo-Euclidean Toda-like system...

Carbon nanotube field-effect transistors (CNTFETs) have been studied in recent years as a potential alternative to CMOS devices, because of the capability of ballistic transport. In order to account for the ballistic transport we solved the coupled Poisson and Schrödinger equations for the analysis these devices. Conventionally the coupled Schrödinger-Poisson equation is solved iteratively, by ...